211171488
The Solar Wind Prevents Reaccretion of Debris after Mercury’s Giant Impact
The planet Mercury possesses an anomalously large iron core, and a correspondingly high bulk density. Numerous hypotheses have been proposed in order to explain such a large iron content. A long-standing idea holds that Mercury once possessed a larger silicate mantle which was removed by a giant impact early in the the Solar system's history. A central problem with this idea has been that material ejected from Mercury is typically re-accreted onto the planet after a short (~Myr) timescale. Here, we show that the primordial Solar wind would have provided sufficient drag upon ejected debris to remove them from Mercury-crossing trajectories before re-impacting the planet's surface. Specifically, the young Sun likely possessed a stronger wind, fast rotation and strong magnetic field. Depending upon the time of the giant impact, the ram pressure associated with this wind would push particles outward into the Solar system, or inward toward the Sun, on sub-Myr timescales, depending upon the size of ejected debris. Accordingly, the giant impact hypothesis remains a viable pathway toward the removal of planetary mantles, both on Mercury and extrasolar planets, particularly those close to young stars with strong winds.
119432686
The Elusive Origin of Mercury
The MESSENGER mission sought to discover what physical processes determined Mercury's high metal to silicate ratio. Instead, the mission has discovered multiple anomalous characteristics about our innermost planet. The lack of FeO and the reduced oxidation state of Mercury's crust and mantle are more extreme than nearly all other known materials in the solar system. In contrast, moderately volatile elements are present in abundances comparable to the other terrestrial planets. No single process during Mercury's formation is able to explain all of these observations. Here, we review the current ideas for the origin of Mercury's unique features. Gaps in understanding the innermost regions of the solar nebula limit testing different hypotheses. Even so, all proposed models are incomplete and need further development in order to unravel Mercury's remaining secrets.
30705666
The System of Planetary Masses
Space exploration has quickened interest in the determination of planetary masses. Why should anyone be interested? The reasons are manyfold. In combination with the radius, the mass yields the average density-perhaps the most fundamental planetary characteristic because of its many implications for the formation, chemical composition, and evolution of the planetary system. Mass values are also crucial for precise tests of gravitational theories that involve solar system dynamics. As an example on a more practical level, the mass of a planet can be essential in planning certain spacecraft missions: to play celestial billiards successfully by the use of a gravitational assist from one planet to reach another requires precise mass data for the usual fuellimited situation. Present plans call for use of this technique on "grand tour" missions to the major planets later in this decade and on the 1973 VenusMercury flyby mission. The latter may even be enhanced by the use of Mercury's gravity field to insure a reencounter with Mercury a half year later (1). For some purposes, of course, extreme precision in mass determination is not required. Yet for the outermost planet, Pluto, even the first significant figure is in doubt. The situation for
130714297
Mercury: the enigmatic innermost planet
Abstract The planet Mercury, a difficult object for study by astronomical observation and spacecraft exploration alike, poses multiple challenges to our general understanding of the inner planets. Mercury’s anomalously high uncompressed density implies a metal fraction of 60% or more by mass, an extreme outcome of planetary formational processes common to the inner solar system. Whether that outcome was the result of chemical gradients in the early solar nebula or removal by impact or vaporization of most of the silicate shell from a differentiated protoplanet can potentially be distinguished on the basis of the chemical composition of the present crust. Our understanding of the geological evolution of Mercury and how it fits within the known histories of the other terrestrial planets is restricted by the limited coverage and resolution of imaging by the only spacecraft to have visited the planet. The role of volcanism in Mercury’s geological history remains uncertain, and the dominant tectonic structures are lobate scarps interpreted as recording an extended episode of planetary contraction, issues that require global imaging to be fully examined. That Mercury has retained a global magnetic field when larger terrestrial planets have not stretches the limits of standard hydromagnetic dynamo theory and has led to proposals for a fossil field or for exotic dynamo scenarios. Hypotheses for field generation can be distinguished on the basis of the geometry of Mercury’s internal field, and the existence and size of a fluid outer core on Mercury can be ascertained from measurements of the planet’s spin axis orientation and gravity field and the amplitude of Mercury’s forced librations. The nature of Mercury’s polar deposits, suggested to consist of volatile material cold-trapped on the permanently shadowed floors of high-latitude impact craters, can be tested by remote sensing of the composition of Mercury’s surface and polar atmosphere. The extremely dynamic exosphere, which includes a number of species derived from Mercury’s surface, offers a novel laboratory for exploring the nature of the complex and changing interactions among the solar wind, a small magnetosphere, and a solid planet. Recent ground-based astronomical measurements and several new theoretical developments set the stage for the in-depth exploration of Mercury by two spacecraft missions within the coming decade.
129398253
The origin and development of the earth and other terrestrial planets
The moon's surface was formed by the collision of planetesimals up to approximately 100 km in radius. The time required for the addition of the last few kilometers was about 105 years. The earth's surface was formed at temperatures below the melting point of lavas. Iron-nickel objects a few kilometers in radius were embedded in the largest planetesimals that fell on the moon. It is shown that the earth may have accumulated much more rapidly than the moon and yet have not been molten. 
 
The densities of the planets calculated at zero pressure are not the same, and the chemical composition of Mars is nearly uniform throughout though it contains about 30% of iron-nickel alloy. 
 
The elements oxygen in water, nitrogen as ammonium salts or nitrides, and sulfur as iron sulfide were accumulated in condensed form at low temperatures, while carbon was retained at high temperatures as graphite or iron carbide. A two-stage process of accumulation into planetesimals is postulated, the first at low temperatures and the second at high temperatures, both followed by a period during which planetesimals accumulated to form the terrestrial planets. During the high temperature stage a chemical process for the volatilization of silicate while iron remains liquid is possible and it is proposed that these processes account for the varying densities of the planets. The primitive atmosphere of the earth contained water, ammonia, and methane as well as large quantities of hydrogen which escaped. 
 
The newly formed moon was much as it is now. The earth had nearly uniform chemical composition. At present the earth has an iron-nickel core and it is postulated that the mantle below the 20° discontinuity has about 25% by weight of iron-nickel alloy. 
 
The heat balance of the moon indicates that the interior was formed at low temperatures, < 300°C, if the equatorial bulge of Jeffreys is real. The heat balance of the earth is attempted but the results are not decisive. The gravitational energy due to the formation of the core during geological time makes it difficult but not impossible to account for a solid earth, if it is added to the radioactive energy. The constants for calculation are uncertain. 
 
A changing moment of inertia for the earth due to the continuous formation of the core explains discrepancies between the observed secular accelerations and those required by tidal theory. The mass of the inner core relative to the outer core suggests that solid nickel accumulates at the inner core. Such an accumulation could supply sufficient energy for the maintenance of the earth's magnetic field. 
 
Convection currents have been postulated by others as the mechanism for the formation of mountains. It is proposed that an important and probably decisive contribution to the energy arises from the gravitational energy liberated as the core is formed. The moon has no folded mountains and no core has formed. Mars appears to have no mountains, in the opinion of some students at least, and it apparently has no high density core.
121667712
The partial volatilization of Mercury
During recent years my research on the primitive solar nebular has followed two main themes: (1) Very early in the development of the nebula conditions probably favored the occurence of major gaseous instabilities leading to the formation of giant gaseous protoplanets, but the rapid rise of the external temperature soon evaporated the envelopes of these protoplanets, possibly leaving behind precipitated solids which formed the cores and mantles of the terrestrial planets. (2) Models of the nebula indicate a later stage when conditions in the inner Solar System became very hot; at the position of Mercury the temperature was probably in the range 2500–3500°K. This leads to the hypothesis that the original protomercury was a body substantially more massive than the present planet and of normal composition, but that when it was immersed in the high-temperature field of the dissipating solar nebula, most of the rocky mantle was vaporized and mixed into the solar nebula gases and carried away by them. This hypothesis is investigated in the present paper. For simplicity the vaporization of a mantle composed of enstatite, MgSiO3, was computed for a planet with 2.25 the mass of Mercury at a temperature of 3000°K. It is argued that the mantle could probably be largely removed in the available time of 3 × 104 years. Subsequent accretion would restore some magnesium silicates to the mantle of the planet.
55900935
Dynamics of Protoplanetary Disks
Protoplanetary disks are quasi-steady structures whose evolution and dispersal determine the environment for planet formation. I review the theory of protoplanetary disk evolution and its connection to observations. Substantial progress has been made in elucidating the physics of potential angular momentum transport processes—including self-gravity, magnetorotational instability, baroclinic instabilities, and magnetic braking—and in developing testable models for disk dispersal via photoevaporation. The relative importance of these processes depends upon the initial mass, size, and magnetization of the disk, and subsequently on its opacity, ionization state, and external irradiation. Disk dynamics is therefore coupled to star formation, pre-main-sequence stellar evolution, and dust coagulation during the early stages of planet formation and may vary dramatically from star to star. The importance of validating theoretical models is emphasized, with the key observations being those that probe disk structure...
124757510
Accretion onto Pre-Main-Sequence Stars
Accretion through circumstellar disks plays an important role in star formation and in establishing the properties of the regions in which planets form and migrate. The mechanisms by which protostellar and protoplanetary disks accrete onto low-mass stars are not clear; angular momentum transport by magnetic fields is thought to be involved, but the low-ionization conditions in major regions of protoplanetary disks lead to a variety of complex nonideal magnetohydrodynamic effects whose implications are not fully understood. Accretion in pre-main-sequence stars of masses ≲1M⊙ (and in at least some 2–3-M⊙ systems) is generally funneled by the stellar magnetic field, which disrupts the disk at scales typically of order a few stellar radii. Matter moving at near free-fall velocities shocks at the stellar surface; the resulting accretion luminosities from the dissipation of kinetic energy indicate that mass addition during the T Tauri phase over the typical disk lifetime ∼3 Myr is modest in terms of stellar evo...
31109219
KEPLER Mission: development and overview.
The Kepler Mission is a space observatory launched in 2009 by NASA to monitor 170,000 stars over a period of four years to determine the frequency of Earth-size and larger planets in and near the habitable zone of Sun-like stars, the size and orbital distributions of these planets, and the types of stars they orbit. Kepler is the tenth in the series of NASA Discovery Program missions that are competitively-selected, PI-directed, medium-cost missions. The Mission concept and various instrument prototypes were developed at the Ames Research Center over a period of 18 years starting in 1983. The development of techniques to do the 10 ppm photometry required for Mission success took years of experimentation, several workshops, and the exploration of many 'blind alleys' before the construction of the flight instrument. Beginning in 1992 at the start of the NASA Discovery Program, the Kepler Mission concept was proposed five times before its acceptance for mission development in 2001. During that period, the concept evolved from a photometer in an L2 orbit that monitored 6000 stars in a 50 sq deg field-of-view (FOV) to one that was in a heliocentric orbit that simultaneously monitored 170,000 stars with a 105 sq deg FOV. Analysis of the data to date has detected over 4600 planetary candidates which include several hundred Earth-size planetary candidates, over a thousand confirmed planets, and Earth-size planets in the habitable zone (HZ). These discoveries provide the information required for estimates of the frequency of planets in our galaxy. The Mission results show that most stars have planets, many of these planets are similar in size to the Earth, and that systems with several planets are common. Although planets in the HZ are common, many are substantially larger than Earth.
55189162
PHOTOPHORETIC SEPARATION OF METALS AND SILICATES: THE FORMATION OF MERCURY-LIKE PLANETS AND METAL DEPLETION IN CHONDRITES
Mercury's high uncompressed mass density suggests that the planet is largely composed of iron, either bound within metal (mainly Fe-Ni) or iron sulfide. Recent results from the MESSENGER mission to Mercury imply a low temperature history of the planet which questions the standard formation models of impact mantle stripping or evaporation to explain the high metal content. Like Mercury, the two smallest extrasolar rocky planets with mass and size determination, CoRoT-7b and Kepler-10b, were found to be of high density. As they orbit close to their host stars, this indicates that iron-rich inner planets might not be a nuisance of the solar system but be part of a general scheme of planet formation. From undifferentiated chondrites, it is also known that the metal to silicate ratio is highly variable, which must be ascribed to preplanetary fractionation processes. Due to this fractionation, most chondritic parent bodies—most of them originated in the asteroid belt—are depleted in iron relative to average solar system abundances. The astrophysical processes leading to metal silicate fractionation in the solar nebula are essentially unknown. Here, we consider photophoretic forces. As these forces particularly act on irradiated solids, they might play a significant role in the composition of planetesimals forming at the inner edge of protoplanetary disks. Photophoresis can separate high thermal conductivity materials (iron) from lower thermal conductivity solids (silicate). We suggest that the silicates are preferentially pushed into the optically thick disk. Subsequent planetesimal formation at the edge moving outward leads to metal-rich planetesimals close to the star and metal depleted planetesimals farther out in the nebula.
121270283
Iron Silicate Fractionation and the Origin of Mercury
Abstract Compared with the other terrestrial planets, Mercury has anomalously low mass and high iron content. Equilibrium condensation and inhomogeneous accretional models are not compatible with these properties, unless the solar nebula's thermal structure and history meet stringent conditions. Also, such models predict a composition which does not allow a presently molten core. It appears that most of the solid matter which originally condensed in Mercury's zone has been removed. The planet's composition may be explained if the removal process was only slightly more effective for silicates than for iron. It is proposed that planetesimal orbits in the inner solar nebula decayed because of gas drag. This process is a natural consequence of the non-Keplerian rotation of a centrally condensed nebula. A simple quantitative model shows good agreement with the observed mass distribution of the terrestrial planets. The rate of orbital decay is slower for larger and/or denser bodies, because of their smaller area-to-mass ratios. With plausible assumptions as to planetesimal sizes and compositions, this process can produce fractionation of the sense required to produce an iron-rich planet. Cosmogonical implications are discussed.
38340293
Occurrence of Giant Impacts During the Growth of the Terrestrial Planets
Three-dimensional Monte Carlo simulations of the accumulation of the terrestrial planets in the absence of gas drag produced results that are in general agreement with the number and distribution of the present planets. The accumulation process appears to be characterized by impact of bodies as large as three times the mass of Mars at velocities of about 9 kilometers per second. These giant impacts on Earth may have supplied the material and angular momentum that formed the moon, should have heated Earth to the melting point, and may have been responsible for the differences in the content of inert gases of the atmospheres of Earth and Venus.
41450203
Mercury: introduction to an end-member planet.
This Chapter introduces the major themes of this book. In many ways, Mercury is an extreme planet, and thus it provides a unique benchmark for testing our theories about the origin and evolution of other (particularly terrestrial) planets. Emphasis is given to synthesizing and critiqueing the book's chapters on the planet's origin, its metal-rich composition, its thermal and geophysical evolution, and its cratering history; these topics are complex and controversial, and this book contains a variety of new perspectives on them. Mercury's geology, atmosphere and magnetosphere are discussed more briefiy. We also place the study of Mercury in its historical context and in the context of the spacecraft exploration program, both past and future. This Introduction is not intended to be a comprehensive summary of the contents of the book; readers wanting an overview of Mercurian science should supplement this chapter by reading the abstracts of the book's chapters.
121131200
Collisional stripping of Mercury's mantle
Abstract We investigated the conditions under which a giant collision between a hypothetical proto-Mercury and a planet one-sixth its mass would result in the loss of most of the silicate mantle of the planet, leaving behind an iron-rich planet and thus explaining the anomalously high density of Mercury. We carried out a series of numerical simulations using our three-dimensional smoothed particle hydrocode, varying the impact parameter and the relative velocity between the planet and impactor. We demonstrate that the details of the equation of state do not play an important role. We show that a head-on collision at 20 km/sec and an off-axis (impact parameter equal to half the radius of proto-Mercury) collision at 35 km/sec are about equivalent as far as damage to proto-Mercury is concerned. Both collisions leave behind a remnant that has the required characteristics of the present Mercury. Whether this scenario is actually successful depends on the size of the condensates in the ejected cloud of debris. Preliminary estimates show that most of the ejected mass is probably removed from Mercury-crossing orbits. If this turns out to be true, a giant collision is a plausible explanation for the strange density of Mercury.
122714048
The Origin of Mercury
Abstract
Mercury’s unusually high mean density has always been attributed to special circumstances that occurred during the formation of the planet or shortly thereafter, and due to the planet’s close proximity to the Sun. The nature of these special circumstances is still being debated and several scenarios, all proposed more than 20 years ago, have been suggested. In all scenarios, the high mean density is the result of severe fractionation occurring between silicates and iron. It is the origin of this fractionation that is at the centre of the debate: is it due to differences in condensation temperature and/or in material characteristics (e.g. density, strength)? Is it because of mantle evaporation due to the close proximity to the Sun? Or is it due to the blasting off of the mantle during a giant impact?

In this paper we investigate, in some detail, the fractionation induced by a giant impact on a proto-Mercury having roughly chondritic elemental abundances. We have extended the previous work on this hypothesis in two significant directions. First, we have considerably increased the resolution of the simulation of the collision itself. Second, we have addressed the fate of the ejecta following the impact by computing the expected reaccretion timescale and comparing it to the removal timescale from gravitational interactions with other planets (essentially Venus) and the Poynting–Robertson effect. To compute the latter, we have determined the expected size distribution of the condensates formed during the cooling of the expanding vapor cloud generated by the impact.

We find that, even though some ejected material will be reaccreted, the removal of the mantle of proto-Mercury following a giant impact can indeed lead to the required long-term fractionation between silicates and iron and therefore account for the anomalously high mean density of the planet. Detailed coupled dynamical–chemical modeling of this formation mechanism should be carried out in such a way as to allow explicit testing of the giant impact hypothesis by forthcoming space missions (e.g. MESSENGER and BepiColombo).

9990348
Making other earths: dynamical simulations of terrestrial planet formation and water delivery
We present results from 44 simulations of late stage planetary accretion, focusing on the delivery of volatiles (primarily water) to the terrestrial planets. Our simulations include both planetary “embryos” (defined as Moon to Mars sized protoplanets) and planetesimals, assuming that the embryos formed via oligarchic growth. We investigate volatile delivery as a function of Jupiter’s mass, position and eccentricity, the position of the snow line, and the density (in solids) of the solar nebula. In all simulations, we form 1–4 terrestrial planets inside 2 AU, which vary in mass and volatile content. In 44 simulations we have formed 43 planets between 0.8 and 1.5 AU, including 11 “habitable” planets between 0.9 and 1.1 AU. These planets range from dry worlds to “water worlds” with 100 + oceans of water (1 ocean = 1.5 × 10 24 g), and vary in mass between 0.23M⊕ and 3.85M⊕. There is a good deal of stochastic noise in these simulations, but the most important parameter is the planetesimal mass we choose, which reflects the surface density in solids past the snow line. A high density in this region results in the formation of a smaller number of terrestrial planets with larger masses and higher water content, as compared with planets which form in systems with lower densities. We find that an eccentric Jupiter produces drier terrestrial planets with higher eccentricities than a circular one. In cases with Jupiter at 7 AU, we form what we call “super embryos,” 1–2M⊕ protoplanets which can serve as the accretion seeds for 2 + M⊕ planets with large water contents.
119255166
Solar System Formation in the Context of Extra-Solar Planets
Exoplanet surveys have confirmed one of humanity's (and all teenagers') worst fears: we are weird. If our Solar System were observed with present-day Earth technology -- to put our system and exoplanets on the same footing -- Jupiter is the only planet that would be detectable. The statistics of exo-Jupiters indicate that the Solar System is unusual at the ~1% level among Sun-like stars (or ~0.1% among all stars). But why are we different? Successful formation models for both the Solar System and exoplanet systems rely on two key processes: orbital migration and dynamical instability. Systems of close-in super-Earths or sub-Neptunes require substantial radial inward motion of solids either as drifting mm- to cm-sized pebbles or migrating Earth-mass or larger planetary embryos. We argue that, regardless of their formation mode, the late evolution of super-Earth systems involves migration into chains of mean motion resonances, generally followed by instability when the disk dissipates. This pattern is likely also ubiquitous in giant planet systems. We present three models for inner Solar System formation -- the low-mass asteroid belt, Grand Tack, and Early Instability models -- each invoking a combination of migration and instability. We identify bifurcation points in planetary system formation. We present a series of events to explain why our Solar System is so weird. Jupiter's core must have formed fast enough to quench the growth of Earth's building blocks by blocking the flux of inward-drifting pebbles. The large Jupiter/Saturn mass ratio is rare among giant exoplanets but may be required to maintain Jupiter's wide orbit. The giant planets' instability must have been gentle, with no close encounters between Jupiter and Saturn, also unusual in the larger (exoplanet) context. Our Solar System system is thus the outcome of multiple unusual, but not unheard of, events.
123229997
Satellite-Sized Planetesimals and Lunar Origin
Abstract Exploratory calculations using accretionary theory are made to demonstrate plausible sizes of second-largest, third-largest, etc., bodies at the close of planet formation in heliocentric orbits near the planets, assuming asteroid-like size distributions at the start of the calculation. Many satellite-sized bodies are found to be available for capture, cratering, or collisional fragmentation. In the case of Earth-sized planets, the models suggest second-largest bodies of 500 to 3000 km radius, and tens of bodies larger than 100 km radius. Many of these interact with the planet before suffering any fragmentation events with each other. Collision of a large body with Earth could eject iron-deficient crust and upper mantle material, forming a cloud of refractory, volatile-poor dust that could form the Moon. Other satellite systems may have been affected by major capture or collision events of chance character.
4413525
Origin of the Moon in a giant impact near the end of the Earth's formation
The Moon is generally believed to have formed from debris ejected by a large off-centre collision with the early Earth. The impact orientation and size are constrained by the angular momentum contained in both the Earth's spin and the Moon's orbit, a quantity that has been nearly conserved over the past 4.5 billion years. Simulations of potential moon-forming impacts now achieve resolutions sufficient to study the production of bound debris. However, identifying impacts capable of yielding the Earth–Moon system has proved difficult. Previous works found that forming the Moon with an appropriate impact angular momentum required the impact to occur when the Earth was only about half formed, a more restrictive and problematic model than that originally envisaged. Here we report a class of impacts that yield an iron-poor Moon, as well as the current masses and angular momentum of the Earth–Moon system. This class of impacts involves a smaller—and thus more likely—object than previously considered viable, and suggests that the Moon formed near the very end of Earth's accumulation.
17089080
Formation of Phobos and Deimos via a giant impact
Abstract Although the two moons of Mars, Phobos and Deimos, have long been thought to be captured asteroids, recent observations of their compositions and orbits suggest that they may have formed from debris generated by one or more giant impacts of bodies with ∼0.01× target mass. Recent studies have both analytically estimated debris produced by giant impacts on Mars and numerically examined the evolution of circum-Mars debris disks. We perform a numerical study (Smoothed Particle Hydrodynamics simulation) of debris retention from giant impacts onto Mars, particularly in relation to a Borealis-scale giant impact ( E ∼ 3 × 10 29  J) capable of producing the Borealis basin. We find that a Borealis-scale impact is capable of producing a disk of mass ∼ 5 × 10 20  kg (∼1–4% of the impactor mass), sufficient debris to form at least one of the martian moons according to recent numerical studies of martian debris disk evolution. While a Borealis-scale impact may generate sufficient debris to form both Phobos and Deimos, further studies of the debris disk evolution are necessary. Our results can serve as inputs for future studies of martian debris disk evolution.
119061548
On the Impact Origin of Phobos and Deimos I: Thermodynamic and Physical Aspects
Phobos and Deimos are the two small moons of Mars. Recent works have shown that they can accrete within an impact-generated disk. However, the detailed structure and initial thermodynamic properties of the disk are poorly understood. In this paper, we perform high-resolution SPH simulations of the Martian moon-forming giant impact that can also form the Borealis basin. This giant impact heats up the disk material (around $\sim 2000$ K in temperature) with an entropy increase of $\sim 1500$ J K$^{-1}$ kg$^{-1}$. Thus, the disk material should be mostly molten, though a tiny fraction of disk material ($< 5\%$) would even experience vaporization. Typically, a piece of molten disk material is estimated to be meter sized due to the fragmentation regulated by their shear velocity and surface tension during the impact process. The disk materials initially have highly eccentric orbits ($e \sim 0.6-0.9$) and successive collisions between meter-sized fragments at high impact velocity ($\sim 3-5$ km s$^{-1}$) can grind them down to $\sim100 \mu$m-sized particles. On the other hand, a tiny amount of vaporized disk material condenses into $\sim 0.1 \mu$m-sized grains. Thus, the building blocks of the Martian moons are expected to be a mixture of these different sized particles from meter-sized down to $\sim 100 \mu$m-sized particles and $\sim 0.1 \mu$m-sized grains. Our simulations also suggest that the building blocks of Phobos and Deimos contain both impactor and Martian materials (at least 35%), most of which come from the Martian mantle (50-150 km in depth; at least 50%). Our results will give useful information for planning a future sample return mission to Martian moons, such as JAXA's MMX (Martian Moons eXploration) mission.
19558835
A Giant Impact Origin of Pluto-Charon
Pluto and its moon, Charon, are the most prominent members of the Kuiper belt, and their existence holds clues to outer solar system formation processes. Here, hydrodynamic simulations are used to demonstrate that the formation of Pluto-Charon by means of a large collision is quite plausible. I show that such an impact probably produced an intact Charon, although it is possible that a disk of material orbited Pluto from which Charon later accumulated. These findings suggest that collisions between 1000-kilometer-class objects occurred in the early inner Kuiper belt.
118786665
Explaining why the uranian satellites have equatorial prograde orbits despite the large planetary obliquity
We show that the existence of prograde equatorial satellites is consistent with a collisional tilting scenario for Uranus. In fact, if the planet was surrounded by a proto-satellite disk at the time of the tilting and a massive ring of material was temporarily placed inside the Roche radius of the planet by the collision, the proto-satellite disk would have started to precess incoherently around the equator of the planet, up to a distance greater than that of Oberon. Collisional damping would then have collapsed it into a thin equatorial disk, from which the satellites eventually formed. The fact that the orbits of the satellites are prograde requires Uranus to have had a non-negligible initial obliquity (comparable to that of Neptune) before it was finally tilted to 98°.
119009531
Forming Mercury by Giant Impacts
The origin of Mercury's high iron-to-rock ratio is still unknown. In this work we investigate Mercury's formation via giant impacts and consider the possibilities of a single giant impact, a hit-and-run, and multiple collisions, in one theoretical framework. We study the standard collision parameters (impact velocity, mass ratio, impact parameter), along with the impactor's composition and the cooling of the target. It is found that the impactor's composition affects the iron distribution within the planet and the final mass of the target by up to 25%, although the resulting mean iron fraction is similar. We suggest that an efficient giant impact has to be head-on at high velocity, while in the hit-and-run case the impact can occur closer to the most probable collision angle (45°). It is also shown that Mercury's current iron-to-rock ratio can be a result of multiple collisions, with their exact number depending on the collision parameters. Mass loss is found to be more significant when the collisions are close together in time.
119216095
Mercurian impact ejecta: Meteorites and mantle
We have examined the fate of impact ejecta liberated from the surface of Mercury due to impacts by comets or asteroids, in order to study 1) meteorite transfer to Earth, and 2) reaccumulation of an expelled mantle in giant-impact scenarios seeking to explain Mercurys large core. In the context of meteorite transfer during the last 30 Myr, we note that Mercurys impact ejecta leave the planets surface much faster (on average) than other planets in the solar system because it is the only planet where impact speeds routinely range from 5 to 20 times the planets escape speed; this causes impact ejecta to leave its surface moving many times faster than needed to escape its gravitational pull. Thus, a large fraction of Mercurian ejecta may reach heliocentric orbit with speeds sufficiently high for Earth-crossing orbits to exist immediately after impact, resulting in larger fractions of the ejecta reaching Earth as meteorites. We calculate the delivery rate to Earth on a time scale of 30 Myr (typical of stony meteorites from the asteroid belt) and show that several percent of the high-speed ejecta reach Earth (a factor of 23 less than typical launches from Mars); this is one to two orders of magnitude more efficient than previous estimates. Similar quantities of material reach Venus. These calculations also yield measurements of the re-accretion time scale of material ejected from Mercury in a putative giant impact (assuming gravity is dominant). For Mercurian ejecta escaping the gravitational reach of the planet with excess speeds equal to Mercurys escape speed, about one third of ejecta reaccretes in as little as 2 Myr. Thus collisional stripping of a silicate proto-Mercurian mantle can only work effectively if the liberated mantle material remains in small enough particles that radiation forces can drag them into the Sun on time scale of a few million years, or Mercury would simply re-accrete the material.
121849703
Radiation forces on small particles in the solar system
Abstract We present a new and more accurate expression for the radiation pressure and Poynting-Robertson drag forces; it is more complete than previous ones, which considered only perfectly absorbing particles or artificial scattering laws. Using a simple heuristic derivation, the equation of motion for a particle of mass m and geometrical cross section A, moving with velocity v through a radiation field of energy flux density S, is found to be (to terms of order v c ) m v = ( SA c )Q pr [(1 − r c ) S − v c ] , where Ŝ is a unit vector in the direction of the incident radiation, r is the particle's radial velocity, and c is the speed of light; the radiation pressure efficiency factor Qpr ≡ Qabs + Qsca(1 − 〈cos α〉), where Qabs and Qsca are the efficiency factors for absorption and scattering, and 〈cos α〉 accounts for the asymmetry of the scattered radiation. This result is confirmed by a new formal derivation applying special relativistic transformations for the incoming and outgoing energy and momentum as seen in the particle and solar frames of reference. Qpr is evaluated from Mie theory for small spherical particles with measured optical properties, irradiated by the actual solar spectrum. Of the eight materials studied, only for iron, magnetite , and graphite grains does the radiation pressure force exceed gravity and then just for sizes around 0.1 μm; very small particles are not easily blown out of the solar system nor are they rapidly dragged into the Sun by the Poynting-Robertson effect. The solar wind counterpart of the Poynting-Robertson drag may be effective, however, for these particles. The orbital consequences of these radiation forces-including ejection from the solar system by relatively small radiation pressures-and of the Poynting-Robertson drag are considered both for heliocentric and planetocentric orbiting particles. We discuss the coupling between the dynamics of particles and their sizes (which diminish due to sputtering and sublimation). A qualitative derivation is given for the differential Doppler effect, which occurs because the light received by an orbiting particle is slightly red-shifted by the solar rotation velocity when coming from the eastern hemisphere of the Sun but blue-shifted when from the western hemisphere; the ratio of this force to the Poynting-Robertson force is ( R ⊙ r ) 2 [( w ⊙ n ) − 1] , where R⊙ and w⊙ are the solar radius and spin rate, and n is the particle's mean motion. The Yarkovsky effect, caused by the asymmetry in the reradiated thermal emission of a rotating body, is also developed relying on new physical arguments. Throughout the paper, representative calculations use the physical and orbital properties of interplanetary dust, as known from various recent measurements.
4406814
Hit-and-run planetary collisions
Terrestrial planet formation is believed to have concluded in our Solar System with about 10 million to 100 million years of giant impacts, where hundreds of Moon- to Mars-sized planetary embryos acquired random velocities through gravitational encounters and resonances with one another and with Jupiter. This led to planet-crossing orbits and collisions that produced the four terrestrial planets, the Moon and asteroids. But here we show that colliding planets do not simply merge, as is commonly assumed. In many cases, the smaller planet escapes from the collision highly deformed, spun up, depressurized from equilibrium, stripped of its outer layers, and sometimes pulled apart into a chain of diverse objects. Remnants of these ‘hit-and-run’ collisions are predicted to be common among remnant planet-forming populations, and thus to be relevant to asteroid formation and meteorite petrogenesis.
140545165
Mercury and other iron-rich planetary bodies as relics of inefficient accretion
Unlike the other terrestrial planets, Mercury has a relatively thin silicate mantle. Numerical and statistical models suggest that Mercury and other metallic planetary bodies could be survivors of accretion that had their mantles stripped in collisions with larger impactors.
122214626
Cratering erosion of planetary embryos
Abstract I have performed 3D numerical hydrodynamic simulations of impacts of stony projectiles on stony planar targets in a range of impact velocities from 1.25 to 60 km/s. The projectile and target masses ejected at speeds greater than some given values have been calculated. This provided a possibility to determine impact erosion of a target which undergoes bombardment with comparatively small bodies. The relative losses of target masses and masses of retained projectile material have been averaged over impact angles and approximated by analytical formulas as functions of impact and escape velocities. The balance between escaped material of a target and retained material of a projectile determines growth or reduction of a target mass. The target cratering erosion predominates over the projectile retention when the impacts have velocities of more than 3–5 times the escape velocity of a target. The results can be applied to collisions of planetary embryos with planetesimals, which have higher velocities than embryo–embryo impacts. Estimates for impact velocities 1–10 km/s show that while large embryos accrete planetesimals smaller embryos erode and can completely vanish or partly lose their silicate shells if they are differentiated. Application of calculated erosion efficiency to Mercury made it possible to test a hypothesis (Vityazev, A.V., Pechernikova, G.V., Safronov, V.S. [1988]. Formation of Mercury and removal of its silicate shell. In: Vilas, F., Chapman, C.R., Matthews, M.S. (Eds.), Mercury. Univ. Arizona Press., Tucson, pp. 667−669) that differentiated massive proto-Mercury has lost its mantle due to collisions with objects of moderate sizes. It turned out that in order for this to happen, relative collision velocities must exceed 25 km/s. As alternatives to the widely-known hypothesis of a giant impact on a massive proto-Mercury, other possibilities are considered, which do not require such high speeds. The first one is formation of a number of small-sized metal-rich embryos which lose their silicate shells due to cratering erosion. The second is that a small proto-Mercury was metallic and gained its mantle at the latest stage of its accumulation when it grew so large that the erosion became ineffective.
118035213
Solar system dynamics
The Solar System is a complex and fascinating dynamical system. This is the first textbook to describe comprehensively the dynamical features of the Solar System and to provide students with all the mathematical tools and physical models they need to understand how it works. It is a benchmark publication in the field of planetary dynamics and destined to become a classic. Clearly written and well illustrated, Solar System Dynamics shows how a basic knowledge of the two- and three-body problems and perturbation theory can be combined to understand features as diverse as the tidal heating of Jupiter's moon Io, the origin of the Kirkwood gaps in the asteroid belt, and the radial structure of Saturn's rings. Problems at the end of each chapter and a free Internet Mathematica® software package are provided. Solar System Dynamics provides an authoritative textbook for courses on planetary dynamics and celestial mechanics. It also equips students with the mathematical tools to tackle broader courses on dynamics, dynamical systems, applications of chaos theory and non-linear dynamics.
16088329
On the Evolutionary Status of Class I Stars and Herbig-Haro Energy Sources in Taurus-Auriga
We present high-resolution (R ~ 34,000) optical (6330-8750 A) spectra obtained with the HIRES spectrograph on the W. M. Keck I telescope of stars in Taurus-Auriga whose circumstellar environment suggests that they are less evolved than optically revealed T Tauri stars. Many of the stars are seen only via scattered light. The sample includes 15 class I stars and all class II stars that power Herbig-Haro flows in this region. For 28 of the 36 stars observed, our measurements are the first high-dispersion optical spectra ever obtained. Photospheric features are observed in all stars with detected continuum, 11 of 15 class I stars (42% of known Taurus class I stars) and 21 of 21 class II stars; strong emission lines (e.g., Hα) are detected in the spectra of all stars. These spectra, in combination with previous measurements, are used to search for differences between stars that power Herbig-Haro flows and stars that do not and to reassess the evolutionary state of so-called protostars (class I stars) relative to optically revealed T Tauri stars (class II stars). The stellar mass distribution of class I stars is similar to that of class II stars and includes three spectroscopically confirmed class I brown dwarfs. Class I stars (and brown dwarfs) in Taurus are slowly rotating (v sin i < 35 km s^(-1)); the angular momentum of a young star appears to dissipate prior to the optically revealed T Tauri phase. The amount of optical veiling and the inferred mass accretion rates of class I stars are surprisingly indistinguishable from class II stars. Class I stars do not have accretion-dominated luminosities; the accretion luminosity accounts for ~25% of the bolometric luminosity. The median mass accretion rate of class I and class II stars of K7-M1 spectral type is 4 × 10^(-8) M_☉ yr^(-1), and the median mass outflow rate is 5% of the mass accretion rate. The large ranges in mass accretion rate (~2 orders of magnitude), mass outflow rate (~3 orders of magnitude), and the ratio of these quantities (~2 orders of magnitude) represent real dispersions in young accreting stars of similar mass. We confirm previous results that find larger forbidden-line emission associated with class I stars than class II stars. We suggest that this is caused by an orientation bias that allows a more direct view of the somewhat extended forbidden emission line regions than of the obscured stellar photospheres, rather than being caused by larger mass outflow rates. Overall, the similar masses, luminosities, rotation rates, mass accretion rates, mass outflow rates, and millimeter flux densities of class I stars and class II stars are best explained by a scenario in which most class I stars are no longer in the main accretion phase and are much older than traditionally assumed. Similarly, although stars that power Herbig-Haro flows appear to have larger mass outflow rates, their stellar and circumstellar properties are generally indistinguishable from those of similar mass stars that do not power these flows.
1927438
Accretion-powered Stellar Winds. II. Numerical Solutions for Stellar Wind Torques
In order to explain the slow rotation observed in a large fraction of accreting pre-main-sequence stars (CTTSs), we explore the role of stellar winds in torquing down the stars. For this mechanism to be effective, the stellar winds need to have relatively high outflow rates, and thus would likely be powered by the accretion process itself. Here, we use numerical magnetohydrodynamical simulations to compute detailed two-dimensional (axisymmetric) stellar wind solutions, in order to determine the spin-down torque on the star. We discuss wind driving mechanisms and then adopt a Parker-like (thermal pressure driven) wind, modified by rotation, magnetic fields, and enhanced mass-loss rate (relative to the Sun). We explore a range of parameters relevant for CTTSs, including variations in the stellar mass, radius, spin rate, surface magnetic field strength, mass-loss rate, and wind acceleration rate. We also consider both dipole and quadrupole magnetic field geometries. Our simulations indicate that the stellar wind torque is of sufficient magnitude to be important for spinning down a "typical" CTTS, for a mass-loss rate of ~10−9 M☉ yr−1. The winds are wide-angle, self-collimated flows, as expected of magnetic rotator winds with moderately fast rotation. The cases with quadrupolar field produce a much weaker torque than for a dipole with the same surface field strength, demonstrating that magnetic geometry plays a fundamental role in determining the torque. Cases with varying wind acceleration rate show much smaller variations in the torque, suggesting that the details of the wind driving are less important. We use our computed results to fit a semianalytic formula for the effective Alfven radius in the wind, as well as the torque. This allows for considerable predictive power, and is an improvement over existing approximations.
51417657
NEW DEBRIS DISKS AROUND YOUNG, LOW-MASS STARS DISCOVERED WITH THE SPITZER SPACE TELESCOPE
We present 24 μm and 70 μm Multiband Imaging Photometer for Spitzer (MIPS) observations of 70 A through M-type dwarfs with estimated ages from 8 Myr to 1.1 Gyr, as part of a Spitzer guaranteed time program, including a re-analysis of some previously published source photometry. Our sample is selected from stars with common youth indicators such as lithium abundance, X-ray activity, chromospheric activity, and rapid rotation. We compare our MIPS observations to empirically derived K_s -[24] colors as a function of the stellar effective temperature to identify 24 μm and 70 μm excesses. We place constraints or upper limits on dust temperatures and fractional infrared luminosities with a simple blackbody dust model. We confirm the previously published 70 μm excesses for HD 92945, HD 112429, and AU Mic, and provide updated flux density measurements for these sources. We present the discovery of 70 μm excesses for five stars: HD 7590, HD 10008, HD 59967, HD 73350, and HD 135599. HD 135599 is also a known Spitzer IRS (InfraRed Spectrograph) excess source, and we confirm the excess at 24 μm. We also present the detection of 24 μm excesses for 10 stars: HD 10008, GJ 3400A, HD 73350, HD 112429, HD 123998, HD 175742, AT Mic, BO Mic, HD 358623 and Gl 907.1. We find that large 70 μm excesses are less common around stars with effective temperatures of less than 5000 K (3.7^(+7.6)_(–1.1)%) than around stars with effective temperatures between 5000 K and 6000 K (21.4^(+9.5)_(–5.7)%), despite the cooler stars having a younger median age in our sample (12 Myr vs. 340 Myr). We find that the previously reported excess for TWA 13A at 70 μm is due to a nearby background galaxy, and the previously reported excess for HD 177724 is due to saturation of the near-infrared photometry used to predict the mid-infrared stellar flux contribution. In the Appendix, we present an updated analysis of dust grain removal timescales due to grain-grain collisions and radiation pressure, Poynting-Robertson (P-R) drag, stellar wind drag, and planet-dust dynamical interaction. We find that drag forces can be important for disk dynamics relative to grain-grain collisions for L_(IR)/L_* < 10^(–4), and that stellar wind drag is more important than P-R drag for K and M dwarfs, and possibly for young (<1 Gyr) G dwarfs as well.
119273950
A GRID OF MHD MODELS FOR STELLAR MASS LOSS AND SPIN-DOWN RATES OF SOLAR ANALOGS
Stellar winds are believed to be the dominant factor in the spin-down of stars over time. However, stellar winds of solar analogs are poorly constrained due to observational challenges. In this paper, we present a grid of magnetohydrodynamic models to study and quantify the values of stellar mass loss and angular momentum loss rates as a function of the stellar rotation period, magnetic dipole component, and coronal base density. We derive simple scaling laws for the loss rates as a function of these parameters, and constrain the possible mass loss rate of stars with thermally driven winds. Despite the success of our scaling law in matching the results of the model, we find a deviation between the 'solar dipole' case and a real case based on solar observations that overestimates the actual solar mass loss rate by a factor of three. This implies that the model for stellar fields might require a further investigation with additional complexity. Mass loss rates in general are largely controlled by the magnetic field strength, with the wind density varying in proportion to the confining magnetic pressure B {sup 2}. We also find that the mass loss rates obtained using our grid models drop muchmore » faster with the increase in rotation period than scaling laws derived using observed stellar activity. For main-sequence solar-like stars, our scaling law for angular momentum loss versus poloidal magnetic field strength retrieves the well-known Skumanich decline of angular velocity with time, Ω{sub *}∝t {sup –1/2}, if the large-scale poloidal magnetic field scales with rotation rate as B{sub p}∝Ω{sub ⋆}{sup 2}.« less
119376640
The solar wind in time: a change in the behaviour of older winds?
In the present paper, we model the wind of solar analogues at different ages to investigate the evolution of the solar wind. Recently, it has been suggested that winds of solar type stars might undergo a change in properties at old ages, whereby stars older than the Sun would be less efficient in carrying away angular momentum than what was traditionally believed. Adding to this, recent observations suggest that old solar-type stars show a break in coronal properties, with a steeper decay in X-ray luminosities and temperatures at older ages. We use these X-ray observations to constrain the thermal acceleration of winds of solar analogues. Our sample is based on the stars from the `Sun in time' project with ages between 120-7000 Myr. The break in X-ray properties leads to a break in wind mass-loss rates ($\dot{M}$) at roughly 2 Gyr, with $\dot{M}$ (t 2 Gyr) $\propto$ $t^{-3.9}$. This steep decay in $\dot{M}$ at older ages could be the reason why older stars are less efficient at carrying away angular momentum, which would explain the anomalously rapid rotation observed in older stars. We also show that none of the stars in our sample would have winds dense enough to produce thermal emission above 1-2 GHz, explaining why their radio emissions have not yet been detected. Combining our models with dynamo evolution models for the magnetic field of the Earth we find that, at early ages ($\approx$100 Myr) our Earth had a magnetosphere that was 3 or more times smaller than its current size.
43200119
Stellar magnetism: empirical trends with age and rotation
We investigate how the observed large-scale surface magnetic fields of low-mass stars (∼0.1– 2M� ), reconstructed through Zeeman–Doppler imaging, vary with age t, rotation and Xray emission. Our sample consists of 104 magnetic maps of 73 stars, from accreting premain sequence to main-sequence objects (1Myr t 10 Gyr). For non-accreting dwarfs we empirically find that the unsigned average large-scale surface field is related to age as t −0.655 ± 0.045 . This relation has a similar dependence to that identified by Skumanich, used as the basis for gyrochronology. Likewise, our relation could be used as an age-dating method (‘magnetochronology’). The trends with rotation we find for the large-scale stellar magnetism are consistent with the trends found from Zeeman broadening measurements (sensitive to large- and small-scale fields). These similarities indicate that the fields recovered from both techniques are coupled to each other, suggesting that small- and large-scale fields could share the same dynamo field generation processes. For the accreting objects, fewer statistically significant relations are found, with one being a correlation between the unsigned magnetic flux and rotation period. We attribute this to a signature of star–disc interaction, rather than being driven by the dynamo.
119382211
The Primordial Solar Wind as a Sculptor of Terrestrial Planet Formation
Our Solar system is almost entirely devoid of material interior to Mercury's orbit, in sharp contrast to the multiple Earth masses of material commonly residing within the analogous region of extrasolar planetary systems. Recent work has suggested that Jupiter's orbital migration early in the Solar system's history fragmented primordial planetary material within the inner Solar System. However, the reason for the absence of subsequent planet formation within 0.4AU remains unsolved. Here, we show that the up debris interior to Mercury's current orbit is susceptible to outward migration driven by the early Solar wind, enhanced by the Sun's primordial rapid rotation and strong magnetic field. The ram pressure arising from azimuthal motion of the Solar wind plasma transported ~100m-sized objects and smaller from 0.1AU out to the terrestrial planet-forming zone within the suspected ~30-50,Myr timespan of the Earth's formation. The mass of material within this size class typically exceeds Mercury, and can rival that of Earth. Consequently, the present-day region of terrestrial planets and the asteroid belt has been supplied by a large mass of material from the innermost, hot Solar system, providing a potential explanation for the evidence of high-temperature alteration within some asteroids and the high iron content of Mercury.
199528503
The evolution of Earth’s magnetosphere during the solar main sequence

 As a star spins-down during the main sequence, its wind properties are affected. In this work, we investigate how Earth’s magnetosphere has responded to the change in the solar wind. Earth’s magnetosphere is simulated using 3D magnetohydrodynamic models that incorporate the evolving local properties of the solar wind. The solar wind, on the other hand, is modelled in 1.5D for a range of rotation rates Ω from 50 to 0.8 times the present-day solar rotation (Ω⊙). Our solar wind model uses empirical values for magnetic field strengths, base temperature, and density, which are derived from observations of solar-like stars. We find that for rotation rates ≃10 Ω⊙, Earth’s magnetosphere was substantially smaller than it is today, exhibiting a strong bow shock. As the Sun spins-down, the magnetopause standoff distance varies with Ω−0.27 for higher rotation rates (early ages, ≥1.4 Ω⊙) and with Ω−2.04 for lower rotation rates (older ages, <1.4 Ω⊙). This break is a result of the empirical properties adopted for the solar wind evolution. We also see a linear relationship between the magnetopause distance and the thickness of the shock on the subsolar line for the majority of the evolution (≤10 Ω⊙). It is possible that a young fast rotating Sun would have had rotation rates as high as 30–50 Ω⊙. In these speculative scenarios, at 30 Ω⊙, a weak shock would have been formed, but for 50 Ω⊙, we find that no bow shock could be present around Earth’s magnetosphere. This implies that with the Sun continuing to spin-down, a strong shock would have developed around our planet and remained for most of the duration of the solar main sequence.
121591840
Dynamical theory of the solar wind
This paper is a review of the basic theoretical dynamical properties of an atmosphere with an extended temperature strongly bound by gravity. The review begins with the historical developments leading up to the realization that the only dynamical equilibrium of an atmosphere with extended temperature is supersonic expansion. It is shown that sufficient conditions for supersonic expansion are T(r) declining asymptotically less rapidly than 1/r, or the density at the base of the corona being less than Nbgiven by (40) if no energy is available except through thermal conductivity, or the temperature falling within the limits given by (18) if T ∝ Nα-1 throughout the corona. Less extended temperatures lead to equilibria which are subsonic or static. The hypothetical case of a corona with no energy supply other than thermal conduction from its base is considered at some length because the equations may be solved by analytical methods and illustrate the transition from subsonic to supersonic equilibrium as the temperature becomes more extended. Comparison with the actual corona shows that the solar corona is actively heated for some distance into space by wave dissipation.The dynamical stability of the expanding atmosphere is demonstrated, and in a later section the radial propagation of acoustic and Alfvén waves through the atmosphere and wind is worked out. The calculations show that the magnetometer will probably detect waves more easily than the plasma instrument, but that both are needed to determine the mode and direction of the wave. An observer in the wind at the orbit of Earth can “listen” to disturbances generated in the corona near the sun and in turbulent regions in interplanetary space.The possibility that the solar corona is composed of small-scale filaments near the sun is considered. It is shown that such filamentary structure would not be seen at the orbit of Earth. It is pointed out that the expansion of a non-filamentary corona seems to lead to too high a calculated wind density at the orbit of Earth to agree with the present observations, unless T(r) is constant or increases with r. A filamentary corona, on the other hand, would give the observed wind density for declining T(r).It is shown that viscosity plays no important role in the expansion of an atmosphere either with or without a weak magnetic field. The termination of the solar wind, presumably between 10–103 AU, is discussed briefly. The interesting development here is the interplanetary Lαrecently observed, which may come from the interstellar neutral hydrogen drifting into the outer regions of the solar wind.Theory is at the present time concerned with the general dynamical principles which pertain to the expansion equilibrium of an atmosphere. It is to be expected that the rapid progress of direct observations of the corona and wind will soon permit more detailed studies to be carried out. It is important that the distinction between detailed empirical models and models intended to illustrate general principles be kept clearly in mind at all times.
26719275
TESTING A PREDICTIVE THEORETICAL MODEL FOR THE MASS LOSS RATES OF COOL STARS
The basic mechanisms responsible for producing winds from cool, late-type stars are still largely unknown. We take inspiration from recent progress in understanding solar wind acceleration to develop a physically motivated model of the time-steady mass loss rates of cool main-sequence stars and evolved giants. This model follows the energy flux of magnetohydrodynamic turbulence from a subsurface convection zone to its eventual dissipation and escape through open magnetic flux tubes. We show how Alfven waves and turbulence can produce winds in either a hot corona or a cool extended chromosphere, and we specify the conditions that determine whether or not coronal heating occurs. These models do not utilize arbitrary normalization factors, but instead predict the mass loss rate directly from a star's fundamental properties. We take account of stellar magnetic activity by extending standard age-activity-rotation indicators to include the evolution of the filling factor of strong photospheric magnetic fields. We compared the predicted mass loss rates with observed values for 47 stars and found significantly better agreement than was obtained from the popular scaling laws of Reimers, Schroder, and Cuntz. The algorithm used to compute cool-star mass loss rates is provided as a self-contained and efficient computer code. We anticipate that the results from this kind of model can be incorporated straightforwardly into stellar evolution calculations and population synthesis techniques.
121175309
Protostellar Mass and Angular Momentum Loss
Recent radio observations have indicated that appreciable, continuing mass loss is occurring from regions of star formation. The conditions under which massive protostellar objects may exhibit strong, rotationally driven winds are investigated. For plausible rotational velocities and magnetic field strengths, ejection of about 10,000 solar masses a year at speeds of 10-100 km/s can be maintained for time scales of about 0.0001 yr; these values are insensitive to the protostellar luminosity. An evolutionary scenario is sketched which suggests that protostellar clouds may be expected to be rapidly rotating and to possess substantial magnetic fields when the clouds have contracted to radii of about 10 to the 14th cm. The centrifugally driven winds proposed present an alternative to fragmentation for providing the angular momentum loss required in the phase of rapid cloud contraction.
122102420
Fundamentals of Plasma Physics
The widespread importance of plasmas in many areas of contemporary physics makes good textbooks in the field that are both introductory and comprehensive invaluable. This new book by Paul Bellen from CalTech by and large meets these goals. It covers the traditional textbook topics such as particle orbits, the derivation of the MHD equations from Vlasov theory, cold and warm plasma waves, Landau damping, as well as in the later chapters less common subjects such as magnetic helicity, nonlinear processes and dusty plasmas. The book is clearly written, neatly presented, and each chapter has a number of exercises or problems at their end. The author has also thankfully steered clear of the pitfall of filling the book with his own research results. The preface notes that the book is designed to provide an introduction to plasma physics for final year undergraduate and post-graduate students. However, it is difficult to see many physics undergraduates now at UK universities getting to grips with much of the content since their mathematics is not of a high enough standard. Students in Applied Mathematics departments would certainly fare better. An additional problem for the beginner is that some of the chapters do not lead the reader gently into a subject, but begin with quite advanced concepts. Being a multi-disciplinary subject, beginners tend to find plasma physics quite hard enough even when done simply. For postgraduate students these criticisms fade away and this book provides an excellent introduction. More senior researchers should also enjoy the book, especially Chapters 11?17 where more advanced topics are discussed. I found myself continually comparing the book with my favourite text for many years, `The Physics of Plasmas' by T J M Boyd and J J Sanderson, reissued by Cambridge University Press in 2003. Researchers would want both books on their shelves, both for the different ways basic plasma physics is covered, and the diversity of more advanced topics. For the undergraduate level, I would find it easier to construct an introductory course from Boyd and Sanderson.
208625853
Alfvénic velocity spikes and rotational flows in the near-Sun solar wind
The prediction of a supersonic solar wind1 was first confirmed by spacecraft near Earth2,3 and later by spacecraft at heliocentric distances as small as 62 solar radii4. These missions showed that plasma accelerates as it emerges from the corona, aided by unidentified processes that transport energy outwards from the Sun before depositing it in the wind. Alfvénic fluctuations are a promising candidate for such a process because they are seen in the corona and solar wind and contain considerable energy5–7. Magnetic tension forces the corona to co-rotate with the Sun, but any residual rotation far from the Sun reported until now has been much smaller than the amplitude of waves and deflections from interacting wind streams8. Here we report observations of solar-wind plasma at heliocentric distances of about 35 solar radii9–11, well within the distance at which stream interactions become important. We find that Alfvén waves organize into structured velocity spikes with duration of up to minutes, which are associated with propagating S-like bends in the magnetic-field lines. We detect an increasing rotational component to the flow velocity of the solar wind around the Sun, peaking at 35 to 50 kilometres per second—considerably above the amplitude of the waves. These flows exceed classical velocity predictions of a few kilometres per second, challenging models of circulation in the corona and calling into question our understanding of how stars lose angular momentum and spin down as they age12–14.Data collected by the Parker Solar Probe in the solar corona are used to determine the organization of Alfvén waves, revealing an increasing flow velocity peaking at 35–50 km s−1.
2067917
An internet server for pre-main sequence tracks of low- and intermediate-mass stars
We present new grids of pre-main sequence (PMS) tracks for stars in the mass range 0.1 to 7.0 M. The computa- tions were performed for four different metallicities (Z=0.01, 0.02, 0.03 and 0.04). A fifth table has been computed for the solar composition (Z=0.02), including a moderate overshooting. We describe the update in the physics of the Grenoble stellar evolu- tion code which concerns mostly changes in the equation of state (EOS) adopting the formalism proposed by Pols et al. (1995) and in the treatment of the boundary condition. Comparisons of our models with other grids demonstrate the validity of this EOS in the domain of very low-mass stars. Finally, we present a new server dedicated to PMS stellar evolution which allows the determination of stellar parameters from observational data, the calculation of isochrones, the retrieval of evolutionary files and the possibility to generate graphic outputs.
123275774
Elementary derivation of the perturbation equations of celestial mechanics
The equations of celestial mechanics that govern the time rates of change of the orbital elements are completely derived using elementary dynamics, starting from only Newton’s equation and its solution. Two orbital equations and the four most meaningful orbital elements—semimajor axis a, eccentricity e, inclination i, and longitude of pericenter Ω—are written in terms of the orbital energy E and angular momentum H per unit mass. The six resulting equations are differentiated with respect to time to see the effect on the orbital elements of small changes in E and H. The usual perturbation equations in terms of disturbing force components are then derived by computing the manner in which perturbing forces change E and H. The results are applied in a qualitative discussion of the orbital evolution of particles in nonspherical gravitational fields, through atmospheres, and under the action of tides.
128820151
The Exchange of Impact Ejecta Between Terrestrial Planets
Orbital histories of ejecta from the terrestrial planets were numerically integrated to study their transfer to Earth. The properties of the lunar and martian meteorites are consistent with a recurrent ejection of small meteoroids as a result of impacts on their parent bodies. Long-range gravitational effects, especially secular resonances, strongly influence the orbits of many meteoroids, increasing their collision rates with other planets and the sun. These effects and collisional destruction in the asteroid belt result in shortened time scales and higher fluxes than previously believed, especially for martian meteorites. A small flux of mercurian ejecta appears possible; recovery of meteorites from the Earth and Venus is less likely.
119128344
REBOUND: An open-source multi-purpose N-body code for collisional dynamics
REBOUND is a new multi-purpose N-body code which is freely available under an open-source license. It was designed for collisional dynamics such as planetary rings but can also solve the classical N-body problem. It is highly modular and can be customized easily to work on a wide variety of different problems in astrophysics and beyond. 
REBOUND comes with three symplectic integrators: leap-frog, the symplectic epicycle integrator (SEI) and a Wisdom-Holman mapping (WH). It supports open, periodic and shearing-sheet boundary conditions. REBOUND can use a Barnes-Hut tree to calculate both self-gravity and collisions. These modules are fully parallelized with MPI as well as OpenMP. The former makes use of a static domain decomposition and a distributed essential tree. Two new collision detection modules based on a plane-sweep algorithm are also implemented. The performance of the plane-sweep algorithm is superior to a tree code for simulations in which one dimension is much longer than the other two and in simulations which are quasi-two dimensional with less than one million particles. 
In this work, we discuss the different algorithms implemented in REBOUND, the philosophy behind the code's structure as well as implementation specific details of the different modules. We present results of accuracy and scaling tests which show that the code can run efficiently on both desktop machines and large computing clusters.
119640488
WHFAST: a fast and unbiased implementation of a symplectic Wisdom-Holman integrator for long-term gravitational simulations
We present WHFast, a fast and accurate implementation of a Wisdom-Holman symplectic integrator for long-term orbit integrations of planetary systems. WHFast is significantly faster and conserves energy better than all other Wisdom-Holman integrators tested. We achieve this by significantly improving the Kepler-solver and ensuring numerical stability of coordinate transformations to and from Jacobi coordinates. These refinements allow us to remove the linear secular trend in the energy error that is present in other implementations. For small enough timesteps we achieve Brouwer's law, i.e. the energy error is dominated by an unbiased random walk due to floating-point round-off errors. We implement symplectic correctors up to order eleven that significantly reduce the energy error. We also implement a symplectic tangent map for the variational equations. This allows us to efficiently calculate two widely used chaos indicators the Lyapunov characteristic number (LCN) and the Mean Exponential Growth factor of Nearby Orbits (MEGNO). WHFast is freely available as a flexible C package, as a shared library, and as an easy-to-use python module.
120891614
Symplectic maps for the N-body problem.
The present study generalizes the mapping method of Wisdom (1982) to encompass all gravitational n-body problems with a dominant central mass. The rationale for the generalized mapping method is discussed as well as details for the mapping for the n-body problem. Some refinements of the method are considered, and the relationship of the mapping method to other symplectic integration methods is shown. The method is used to compute the evolution of the outer planets for a billion years. The resulting evolution is compared to the 845 million year evolution of the outer planets performed on the Digital Orerry using standard numerical integration techniques. This calculation provides independent numerical confirmation of the result of Sussman and Wisdom (1988) that the motion of the planet Pluto is chaotic.
119129294
ias15: a fast, adaptive, high-order integrator for gravitational dynamics, accurate to machine precision over a billion orbits
We present IAS15, a 15th-order integrator to simulate gravitational dynamics. The integrator is based on a Gaus-Radau quadrature and can handle conservative as well as non-conservative forces. We develop a step-size control that can automatically choose an optimal timestep. The algorithm can handle close encounters and high-eccentricity orbits. The systematic errors are kept well below machine precision and long-term orbit integrations over 10 9 orbits show that IAS15 is optimal in the sense that it follows Brouwer’s law, i.e. the energy error behaves like a random walk. Our tests show that IAS15 is superior to a mixed-variable symplectic integrator (MVS) and other high-order integrators in both speed and accuracy. In fact, IAS15 preserves the symplecticity of Hamiltonian systems better than the commonly-used nominally symplectic integrators to which we compared it. We provide an open-source implementation of IAS15. The package comes with several easy-to-extend examples involving resonant planetary systems, Kozai-Lidov cycles, close encounters, radiation pressure, quadrupole moment, and generic damping functions that can, among other things, be used to simulate planet-disc interactions. Other non-conservative forces can be added easily.
199668860
REBOUNDx: a library for adding conservative and dissipative forces to otherwise symplectic N-body integrations

 Symplectic methods, in particular the Wisdom–Holman map, have revolutionized our ability to model the long-term, conservative dynamics of planetary systems. However, many astrophysically important effects are dissipative. The consequences of incorporating such forces into otherwise symplectic schemes are not always clear. We show that moving to a general framework of non-commutative operators (dissipative or not) clarifies many of these questions, and that several important properties of symplectic schemes carry over to the general case. In particular, we show that explicit splitting schemes generically exploit symmetries in the applied external forces, which often strongly suppress integration errors. Furthermore, we demonstrate that so-called ‘symplectic correctors’ (which reduce energy errors by orders of magnitude at fixed computational cost) apply equally well to weakly dissipative systems and can thus be more generally thought of as ‘weak splitting correctors’. Finally, we show that previously advocated approaches of incorporating additional forces into symplectic methods work well for dissipative forces, but give qualitatively wrong answers for conservative but velocity-dependent forces like post-Newtonian corrections. We release REBOUNDx, an open-source C library for incorporating additional effects into REBOUNDN-body integrations, together with a convenient python wrapper. All effects are machine independent and we provide a binary format that interfaces with the SimulationArchive class in REBOUND to enable the sharing and reproducibility of results. Users can add effects from a list of pre-implemented astrophysical forces, or contribute new ones.
120150386
Collision rates and impact velocities in the Main Asteroid Belt
Abstract We have computed, using G.W. Wetherill's (1967, J. Geophys. Res. 72, 2429–2444) algorithm, mutual collision probabilities and impact velocities for a set of 682 asteroids of diameter > 50 km, intended to represent a bias-free sample of asteroid orbits. For every asteroid, we have obtained the intrinsic collision probability, P i , the average collision velocity, V , and the number of projectile orbits which can intersect the target asteroid's orbit, N cross , using the proper orbital elements of A. Milani and Z. Kneževic (1990, Celest. Mech. 49, 247–411). The average values and the corresponding standard deviations for the whole asteroid sample are: 〈 P i 〉 = 2.85 ± 0.66 × 10 −18 km −2 year −1 , 〈 V 〉 = 5.81 ± 1.88 km/sec, 〈 N cross 〉 = 601 (88% of the existing orbit pairs). No significant differences were found in the average values of P i, V , or N cross using osculating elements instead of proper elements, although results for individual asteroids could change by ≈10%. A running box mean of the intrinsic collision probability with semimajor axis shows a peak near 2.7 AU with 〈 P i 〉 = 3.4 × 10 −18 km −2 year −1 followed by a nearly monotonic decrease to 〈 P i 〉 = 1.8 × 10 −18 km −2 year −1 at 3.3 AU. Collision probabilities are nearly independent of eccentricities but show a significant decrease with larger inclinations. As expected, collisional velocities grow rapidly with increasing orbital eccentricities and inclinations, but they show surprisingly little variation across the asteroid belt. Family asteroids undergo collisions with other members of the same family two to three times more frequently than with nonfamily projectiles, but the relative speed of these intrafamily impacts is comparatively low for the Koronis and Themis families.
32647702
Hf-W chronology of the accretion and early evolution of asteroids and terrestrial planets
The 182 Hf– 182 W systematics of meteoritic and planetary samples provide firm constraints on the chronology of the accretion and earliest evolution of asteroids and terrestrial planets and lead to the following succession and duration of events in the earliest solar system. Formation of Ca,Al-rich inclusions (CAIs) at 4568.3 ± 0.7 Ma was followed by the accretion and differentiation of the parent bodies of some magmatic iron meteorites within less than � 1 Myr. Chondrules from H chondrites formed 1.7 ± 0.7 Myr after CAIs, about contemporaneously with chondrules from L and LL chondrites as shown by their 26 Al– 26 Mg ages. Some magmatism on the parent bodies of angrites, eucrites, and mesosiderites started as soon as � 3 Myr after CAI formation and may have continued until � 10 Myr. A similar timescale is obtained for the high-temperature metamorphic evolution of the H chondrite parent body. Thermal modeling combined with these age constraints reveals that the different thermal histories of meteorite parent bodies primarily reflect their initial abundance of 26 Al, which is determined by their accretion age. Impact-related processes were important in the subsequent evolution of asteroids but do not appear to have induced large-scale melting. For instance, Hf–W ages for eucrite metals postdate CAI formation by � 20 Myr and may reflect impact-triggered thermal metamorphism in the crust of the eucrite parent body. Likewise, the Hf–W systematics of some non-magmatic iron meteorites were modified by impact-related processes but the timing of this event(s) remains poorly constrained. The strong fractionation of lithophile Hf from siderophile W during core formation makes the Hf–W system an ideal chronometer for this major differentiation event. However, for larger planets such as the terrestrial planets the calculated Hf–W ages are particularly sensitive to the occurrence of large impacts, the degree to which impactor cores re-equilibrated with the target mantle during large collisions, and changes in the metal-silicate partition coefficients of W due to changing fO2 in differentiating planetary bodies. Calculated core formation ages for Mars range from 0 to 20 Myr after CAI formation and currently cannot distinguish between scenarios where Mars formed by runaway growth and where its formation was more protracted. Tungsten model ages for core formation in Earth range from � 30 Myr to >100 Myr after CAIs and hence do not provide a unique age for the formation of Earth. However, the identical 182 W/ 184 W ratios of the lunar and terrestrial mantles provide powerful evidence that the Moon-forming giant impact and the final stage of Earth’s core formation occurred after extinction of 182 Hf (i.e., more than � 50 Myr after CAIs), unless the Hf/W ratios of the bulk silicate Moon and Earth are
53073168
Effects of core formation on the Hf-W isotopic composition of the Earth and dating of the Moon-forming impact.
Earth's core formation set the initial compositions of the core and mantle. Various aspects of core formation, such as the degree of metal-silicate equilibration, oxygen fugacity, and depth of equilibration, have significant consequences for the resulting compositions, yet are poorly constrained. The Hf-W isotopic system can provide unique constraints on these aspects relative to other geochemical or geophysical methods. Here we model the Hf-W isotopic evolution of the Earth, improving over previous studies by combining a large number of N-body simulations of planetary accretion with a core formation model that includes self-consistent evolution of oxygen fugacity and a partition coefficient of tungsten that evolves with changing pressure, temperature, composition, and oxygen fugacity. The effective average fraction of equilibrating metal is constrained to be k > 0.2 for a range of equilibrating silicate masses (for canonical accretion scenarios), and is likely <0.55 if the Moon formed later than 65 Ma. These values of k typically correspond to an effective equilibration depth of ~0.5-0.7× the evolving core-mantle boundary pressure as the planet grows. The average mass of equilibrating silicate was likely at least 3× the impactor's silicate mass. Equilibration temperature, initial fO2 initial differentiation time, semimajor axis, and planetary mass (above ~0.9 M⊕) have no systematic effect on the 182W anomaly, or on f Hf/W (except for fO2), when applying the constraint that the model must reproduce Earth's mantle W abundance. There are strong tradeoffs between the effects of k, equilibrating silicate mass, depth of equilibration, and timing of core formation, so the terrestrial Hf-W isotopic system should be interpreted with caution when used as a chronometer of Earth's core formation. Because of these strong tradeoffs, the Earth's tungsten anomaly can be reproduced for Moon-forming impact timescales spanning at least 10-175 Ma. Early Moon formation ages require a higher degree of metal-silicate equilibration to produce Earth's 182W anomaly.
4373071
Hf–W–Th evidence for rapid growth of Mars and its status as a planetary embryo
Terrestrial planets are thought to have formed through collisions between large planetary embryos of diameter ∼1,000–5,000 km. For Earth, the last of these collisions involved an impact by a Mars-size embryo that formed the Moon 50–150 million years (Myr) after the birth of the Solar System. Although model simulations of the growth of terrestrial planets can reproduce the mass and dynamical parameters of the Earth and Venus, they fall short of explaining the small size of Mars. One possibility is that Mars was a planetary embryo that escaped collision and merging with other embryos. To assess this idea, it is crucial to know Mars’ accretion timescale, which can be investigated using the 182Hf–182W decay system in shergottite-nakhlite-chassignite meteorites. Nevertheless, this timescale remains poorly constrained owing to a large uncertainty associated with the Hf/W ratio of the Martian mantle and as a result, contradicting timescales have been reported that range between 0 and 15 Myr (refs 6–10). Here we show that Mars accreted very rapidly and reached about half of its present size in only Myr or less, which is consistent with a stranded planetary embryo origin. We have found a well-defined correlation between the Th/Hf and 176Hf/177Hf ratios in chondrites that reflects remobilization of Lu and Th during parent-body processes. Using this relationship, we estimate the Hf/W ratio in Mars’ mantle to be 3.51 ± 0.45. This value is much more precise than previous estimates, which ranged between 2.6 and 5.0 (ref. 6), and lifts the large uncertainty that plagued previous estimates of the age of Mars. Our results also demonstrate that Mars grew before dissipation of the nebular gas when ∼100-km planetesimals, such as the parent bodies of chondrites, were still being formed. Mars’ accretion occurred early enough to allow establishment of a magma ocean powered by decay of 26Al.
6629600
Mercury crater statistics from MESSENGER flybys: Implications for stratigraphy and resurfacing history
Abstract The primary crater population on Mercury has been modified by volcanism and secondary craters. Two phases of volcanism are recognized. One volcanic episode that produced widespread intercrater plains occurred during the period of the Late Heavy Bombardment and markedly altered the surface in many areas. The second episode is typified by the smooth plains interior and exterior to the Caloris basin, both of which have a different crater size-frequency distribution than the intercrater plains, consistent with a cratering record dominated by a younger population of impactors. These two phases may have overlapped as parts of a continuous period of volcanism during which the volcanic flux tended to decrease with time. The youngest age of smooth plains volcanism cannot yet be determined, but at least small expanses of plains are substantially younger than the plains associated with the Caloris basin. The spatial and temporal variations of volcanic resurfacing events can be used to reconstruct Mercury's geologic history from images and compositional and topographic data to be acquired during the orbital phase of the MESSENGER mission.
4431823
A low mass for Mars from Jupiter’s early gas-driven migration
Jupiter and Saturn formed in a few million years (ref. 1) from a gas-dominated protoplanetary disk, and were susceptible to gas-driven migration of their orbits on timescales of only ∼100,000 years (ref. 2). Hydrodynamic simulations show that these giant planets can undergo a two-stage, inward-then-outward, migration. The terrestrial planets finished accreting much later, and their characteristics, including Mars' small mass, are best reproduced by starting from a planetesimal disk with an outer edge at about one astronomical unit from the Sun (1 au is the Earth–Sun distance). Here we report simulations of the early Solar System that show how the inward migration of Jupiter to 1.5 au, and its subsequent outward migration, lead to a planetesimal disk truncated at 1 au; the terrestrial planets then form from this disk over the next 30–50 million years, with an Earth/Mars mass ratio consistent with observations. Scattering by Jupiter initially empties but then repopulates the asteroid belt, with inner-belt bodies originating between 1 and 3 au and outer-belt bodies originating between and beyond the giant planets. This explains the significant compositional differences across the asteroid belt. The key aspect missing from previous models of terrestrial planet formation is the substantial radial migration of the giant planets, which suggests that their behaviour is more similar to that inferred for extrasolar planets than previously thought.
9267977
Jupiter’s decisive role in the inner Solar System’s early evolution
Significance The Solar System is an unusual member of the galactic planetary census in that it lacks planets that reside in close proximity to the Sun. In this work, we propose that the primordial nebula-driven process responsible for retention of Jupiter and Saturn at large orbital radii and sculpting Mars’ low mass is also responsible for clearing out the Solar System’s innermost region. Cumulatively, our results place the Solar System and the mechanisms that shaped its unique orbital architecture into a broader, extrasolar context. The statistics of extrasolar planetary systems indicate that the default mode of planet formation generates planets with orbital periods shorter than 100 days and masses substantially exceeding that of the Earth. When viewed in this context, the Solar System is unusual. Here, we present simulations which show that a popular formation scenario for Jupiter and Saturn, in which Jupiter migrates inward from a > 5 astronomical units (AU) to a ≈ 1.5 AU before reversing direction, can explain the low overall mass of the Solar System’s terrestrial planets, as well as the absence of planets with a < 0.4 AU. Jupiter’s inward migration entrained s ≳ 10−100 km planetesimals into low-order mean motion resonances, shepherding and exciting their orbits. The resulting collisional cascade generated a planetesimal disk that, evolving under gas drag, would have driven any preexisting short-period planets into the Sun. In this scenario, the Solar System’s terrestrial planets formed from gas-starved mass-depleted debris that remained after the primary period of dynamical evolution.
121848403
Local inertial effects in dynamic fragmentation
A general definition of dynamic fragmentation can encompass any impulsive process which partitions a body of material into discrete domains. Two examples are fragmentation due to brittle fracture under impact loading and fragmentation due to shear banding in shock‐compression plastic deformation. In application, prediction of fragment size or shear band spacing is frequently either the objective, or else requisite to understanding the process. An approach is presented whereby surface or interface area created in the fragmentation process is governed by an equilibrium balance of the surface or interface energy and a local inertial or kinetic energy. Fragment size can be approximately related to surface or interface area. Relations provided by the analysis compare well with experimental dynamic fracture and shock‐wave shear‐band results.
16017767
Extraterrestrial Cause for the Cretaceous-Tertiary Extinction
Platinum metals are depleted in the earth's crust relative to their cosmic abundance; concentrations of these elements in deep-sea sediments may thus indicate influxes of extraterrestrial material. Deep-sea limestones exposed in Italy, Denmark, and New Zealand show iridium increases of about 30, 160, and 20 times, respectively, above the background level at precisely the time of the Cretaceous-Tertiary extinctions, 65 million years ago. Reasons are given to indicate that this iridium is of extraterrestrial origin, but did not come from a nearby supernova. A hypothesis is suggested which accounts for the extinctions and the iridium observations. Impact of a large earth-crossing asteroid would inject about 60 times the object's mass into the atmosphere as pulverized rock; a fraction of this dust would stay in the stratosphere for several years and be distributed worldwide. The resulting darkness would suppress photosynthesis, and the expected biological consequences match quite closely the extinctions observed in the paleontological record. One prediction of this hypothesis has been verified: the chemical composition of the boundary clay, which is thought to come from the stratospheric dust, is markedly different from that of clay mixed with the Cretaceous and Tertiary limestones, which are chemically similar to each other. Four different independent estimates of the diameter of the asteroid give values that lie in the range 10 � 4 kilometers.
119100412
The Absence of Cold Dust and the Mineralogy and Origin of the Warm Dust Encircling BD +20 307
Spitzer Space Telescope photometry and spectroscopy of BD +20 307 show that all of the dust around this remarkable Gyr-old spectroscopic binary arises within 1 AU. No additional cold dust is needed to fit the infrared excess. Peaks in the 10 and 20 ?m spectrum are well fit with small silicates that should be removed on a timescale of years from the system. This is the dustiest star known for its age, which is 1 Gyr. The dust cannot arise from a steady-state collisional cascade. A catastrophic collision of two rocky, planetary-scale bodies in the terrestrial zone is the most likely source for this warm dust because it does not require a reservoir of planetesimals in the outer system.
56108044
Abundant Circumstellar Silica Dust and SiO Gas Created by a Giant Hypervelocity Collision in the ~12 Myr HD172555 System
The fine dust detected by IR emission around the nearby Beta Pic analogue star HD172555 is very peculiar. The dust mineralogy is composed primarily of highly refractory, non-equilibrium materials, with approximately three-quarters of the Si atoms in silica (SiO2) species. Tektite and obsidian lab thermal emission spectra (non-equilibrium glassy silicas found in impact and magmatic systems) are required to fit the data. The best-fit model size distribution for the observed fine dust is dn/da = a-3.95 +/- 0.10. This steep a size distribution, with abundant micron-sized particles, argues for a fresh source of material within the last 0.1 Myr. The location of the dust with respect to the star is at 5.8 +/- 0.6 AU (equivalent to 1.9 +/- 0.2 AU from the Sun), within the terrestrial planet formation region but at the outer edge of any possible terrestrial habitability zone. The mass of fine dust is 4 x 10^19 - 2 x 10^20 kg, equivalent to a 150 - 200 km radius asteroid. Significant emission features centered at 4 and 8 um due to fluorescing SiO gas are also found. Roughly 10^22 kg of SiO gas, formed by vaporizing silicate rock, is also present in the system, and a separate population of very large, cool grains, massing 10^21 - 10^22 kg and equivalent to the largest sized asteroid currently found in the Solar System's main asteroid belt, dominates the solid circumstellar material by mass. The makeup of the observed dust and gas, and the noted lack of a dense circumstellar gas disk, strong primary x-ray activity, or an extended disk of Beta-meteroids argues that the source of the observed circumstellar materials is a giant hypervelocity (> 10 km sec^-1) impact between large rocky planetesimals, similar to the ones which formed the Moon and which stripped the surface crustal material off of Mercury's surface.
120154404
A Reevaluation of Impact Melt Production
The production of melt and vapor is an important process in impact cratering events. Because significant melting and vaporization do not occur in impacts at velocities currently achievable in the laboratory, a detailed study of the production of melt and vapor in planetary impact events is carried out with hydrocode simulations. 
 
Sandia's two-dimensional axisymmetric hydrocode CSQ was used to estimate the amount of melt and vapor produced for widely varying initial conditions: 10 to 80 km/sec for impact velocity, 0.2 to 10 km for the projectile radius. Runs with different materials demonstrate the material dependency of the final result. These results should apply to any size projectile (for given impact velocity and material), since the results can be dynamically scaled so long as gravity is unimportant in affecting the early-time flow. 
 
In contrast with the assumptions of previous analytical models, a clear difference in shape, impact-size dependence, and depth of burial has been found between the melt regions and the isobaric core. In particular, the depth of the isobaric core is not a good representation of the depth of the melt regions, which form deeper in the target. While near-surface effects cause the computed melt region shapes to look like “squashed spheres” the spherical shape is still a good analytical analog. 
 
One of the goals of melt production studies is to find proper scaling laws to infer melt production for any impact event of interest. We tested the point source limit scaling law for melt volumes (μ = 0.55–0.6) proposed by M. D. Bjorkman and K. A. Holsapple (1987,Int. J. Impact Eng.5, 155–163). Our results indicate that the point source limit concept does not apply to melt and vapor production. Rather, melt and vapor production follows an energy scaling law (μ = 0.67), in good agreement with previous results of T. J. Ahrens and J. D. O'Keefe [1977, inImpact and Explosion Cratering(D. J. Roddy, R. O. Pepin, and R. B. Merrill, Eds.), pp. 639–656, Pergamon Press, Elmsford, NY]. 
 
Finally we tested the accuracy of our melt production calculation against a terrestrial dataset compiled by R. A. F. Grieve and M. J. Cintala (1992,Meteorities27, 526–538). The hydrocode melt volumes are in good agreement with the estimated volumes of that set of terrestrial craters on crystalline basements. At present there is no good model for melt production from impact craters on sedimentary targets.
16971154
Shock vaporization of silica and the thermodynamics of planetary impact events
[1] The most energetic planetary collisions attain shock pressures that result in abundant melting and vaporization. Accurate predictions of the extent of melting and vaporization require knowledge of vast regions of the phase diagrams of the constituent materials. To reach the liquid-vapor phase boundary of silica, we conducted uniaxial shock-and-release experiments, where quartz was shocked to a state sufficient to initiate vaporization upon isentropic decompression (hundreds of GPa). The apparent temperature of the decompressing fluid was measured with a streaked optical pyrometer, and the bulk density was inferred by stagnation onto a standard window. To interpret the observed post-shock temperatures, we developed a model for the apparent temperature of a material isentropically decompressing through the liquid-vapor coexistence region. Using published thermodynamic data, we revised the liquid-vapor boundary for silica and calculated the entropy on the quartz Hugoniot. The silica post-shock temperature measurements, up to entropies beyond the critical point, are in excellent qualitative agreement with the predictions from the decompressing two-phase mixture model. Shock-and-release experiments provide an accurate measurement of the temperature on the phase boundary for entropies below the critical point, with increasing uncertainties near and above the critical point entropy. Our new criteria for shock-induced vaporization of quartz are much lower than previous estimates, primarily because of the revised entropy on the Hugoniot. As the thermodynamics of other silicates are expected to be similar to quartz, vaporization is a significant process during high-velocity planetary collisions.
205232792
A sub-Mercury-sized exoplanet
Since the discovery of the first exoplanets, it has been known that other planetary systems can look quite unlike our own. Until fairly recently, we have been able to probe only the upper range of the planet size distribution, and, since last year, to detect planets that are the size of Earth or somewhat smaller. Hitherto, no planets have been found that are smaller than those we see in the Solar System. Here we report a planet significantly smaller than Mercury. This tiny planet is the innermost of three that orbit the Sun-like host star, which we have designated Kepler-37. Owing to its extremely small size, similar to that of the Moon, and highly irradiated surface, the planet, Kepler-37b, is probably rocky with no atmosphere or water, similar to Mercury.
346314
Collisional Stripping and Disruption of Super-Earths
The final stage of planet formation is dominated by collisions between planetary embryos. The dynamics of this stage determine the orbital configuration and the mass and composition of planets in the system. In the solar system, late giant impacts have been proposed for Mercury, Earth, Mars, and Pluto. In the case of Mercury, this giant impact may have significantly altered the bulk composition of the planet. Here we present the results of smoothed particle hydrodynamics simulations of high-velocity (up to ~5v esc) collisions between 1 and 10 M ⊕ planets of initially terrestrial composition to investigate the end stages of formation of extrasolar super-Earths. As found in previous simulations of collisions between smaller bodies, when collision energies exceed simple merging, giant impacts are divided into two regimes: (1) disruption and (2) hit-and-run (a grazing inelastic collision and projectile escape). Disruption occurs when the impact parameter is near zero, when the projectile mass is small compared to the target, or at extremely high velocities. In the disruption regime, we derive the criteria for catastrophic disruption (when half the total colliding mass is lost), the transition energy between accretion and erosion, and a scaling law for the change in bulk composition (iron-to-silicate ratio) resulting from collisional stripping of a mantle.
89604609
A giant impact as the likely origin of different twins in the Kepler-107 exoplanet system
Measures of exoplanet bulk densities indicate that small exoplanets with radius less than 3 Earth radii (R⊕) range from low-density sub-Neptunes containing volatile elements1 to higher-density rocky planets with Earth-like2 or iron-rich3 (Mercury-like) compositions. Such astonishing diversity in observed small exoplanet compositions may be the product of different initial conditions of the planet-formation process or different evolutionary paths that altered the planetary properties after formation4. Planet evolution may be especially affected by either photoevaporative mass loss induced by high stellar X-ray and extreme ultraviolet (XUV) flux5 or giant impacts6. Although there is some evidence for the former7,8, there are no unambiguous findings so far about the occurrence of giant impacts in an exoplanet system. Here, we characterize the two innermost planets of the compact and near-resonant system Kepler-107 (ref. 9). We show that they have nearly identical radii (about 1.5–1.6R⊕), but the outer planet Kepler-107 c is more than twice as dense (about 12.6 g cm–3) as the innermost Kepler-107 b (about 5.3 g cm−3). In consequence, Kepler-107 c must have a larger iron core fraction than Kepler-107 b. This imbalance cannot be explained by the stellar XUV irradiation, which would conversely make the more-irradiated and less-massive planet Kepler-107 b denser than Kepler-107 c. Instead, the dissimilar densities are consistent with a giant impact event on Kepler-107 c that would have stripped off part of its silicate mantle. This hypothesis is supported by theoretical predictions from collisional mantle stripping10, which match the mass and radius of Kepler-107 c.Kepler-107 b and c have the same radius but, contrary to expectations, the outermost Kepler-107 c is much denser. This difference cannot be explained by photoevaporation by stellar high-energy particle flux and it suggests that Kepler-107 c experienced a giant impact event.
119239320
Two Terrestrial Planet Families with Different Origins
The potentially important role of stellar irradiation in envelope removal for planets with diameters of $\lessapprox$ 2 R$_{\Earth}$ has been inferred both through theoretical work and the observed bimodal distribution of small planet occurrence as a function of radius. We examined the trends for small planets in the three-dimensional radius-insolation-density space and find that the terrestrial planets divide into two distinct families based on insolation. The lower insolation family merges with terrestrial planets and small bodies in the solar system and is thus Earth-like. The higher insolation terrestrial planet family forms a bulk-density continuum with the sub-Neptunes, and is thus likely to be composed of remnant cores produced by photoevaporation. Based on the density-radius relationships, we suggest that both terrestrial families show evidence of density enhancement through collisions. Our findings highlight the important role that both photoevaporation and collisions have in determining the density of small planets.
118052299
Consolidating and Crushing Exoplanets: Did it happen here?
The Kepler mission results indicate that systems of tightly-packed inner planets (STIPs) are present around of order 5% of FGK field stars (whose median age is ~5 Gyr). We propose that STIPs initially surrounded nearly all such stars and those observed are the final survivors of a process in which long-term metastability eventually ceases and the systems proceed to collisional consolidation or destruction, losing roughly equal fractions of systems every decade in time. In this context, we also propose that our Solar System initially contained additional large planets interior to the current orbit of Venus, which survived in a metastable dynamical configuration for 1-10% of the Solar System's age. Long-term gravitational perturbations caused the system to orbit cross, leading to a cataclysmic event which left Mercury as the sole surviving relic.
204772199
Oxygen fugacities of extrasolar rocks: Evidence for an Earth-like geochemistry of exoplanets
Peering inside extrasolar rocky bodies The oxygen fugacity of a rock, fO2, is a measure of how oxidizing or reducing its surroundings were when the rock formed. Different minerals form at different fO2 and have different physical properties, so the internal structure of an exoplanet depends on this value. Doyle et al. exploited the signature left behind when rocky bodies impact a white dwarf—the remnant of a dead star. By examining the rock-forming elements left on the surface of each white dwarf, they determine fO2 in the impacting body. Six systems all had similar fO2 to bodies in the Solar System, consistent with the idea that rocky exoplanets often have internal properties similar to those of Earth and Mars. Science, this issue p. 356 Observations of rock-forming elements on polluted white dwarfs indicate the oxygen fugacity of extrasolar rocky bodies. Oxygen fugacity is a measure of rock oxidation that influences planetary structure and evolution. Most rocky bodies in the Solar System formed at oxygen fugacities approximately five orders of magnitude higher than a hydrogen-rich gas of solar composition. It is unclear whether this oxidation of rocks in the Solar System is typical among other planetary systems. We exploit the elemental abundances observed in six white dwarfs polluted by the accretion of rocky bodies to determine the fraction of oxidized iron in those extrasolar rocky bodies and therefore their oxygen fugacities. The results are consistent with the oxygen fugacities of Earth, Mars, and typical asteroids in the Solar System, suggesting that at least some rocky exoplanets are geophysically and geochemically similar to Earth.
34832522
The Major-Element Composition of Mercury’s Surface from MESSENGER X-ray Spectrometry
Geochemical data show that the major rock-forming components of Mercury are characterized by high sulfur content. X-ray fluorescence spectra obtained by the MESSENGER spacecraft orbiting Mercury indicate that the planet’s surface differs in composition from those of other terrestrial planets. Relatively high Mg/Si and low Al/Si and Ca/Si ratios rule out a lunarlike feldspar-rich crust. The sulfur abundance is at least 10 times higher than that of the silicate portion of Earth or the Moon, and this observation, together with a low surface Fe abundance, supports the view that Mercury formed from highly reduced precursor materials, perhaps akin to enstatite chondrite meteorites or anhydrous cometary dust particles. Low Fe and Ti abundances do not support the proposal that opaque oxides of these elements contribute substantially to Mercury’s low and variable surface reflectance.
128943663
Is Mercury a volatile‐rich planet?
] Data returned from the gamma-ray spectrometeronboard the Mercury Surface, Space Environment, Geo-chemistry, and Ranging (MESSENGER) spacecraft havebeen interpreted to say that Mercury is a volatile-rich planet(elevated K/Th and K/U), which is important given itsheliocentricdistance.TheMESSENGERX-rayspectrometerprovided chemical information from the surface of Mercurywhich we used to calculate an average surface compositionfortheregionsanalyzed. ThehighSabundanceandlowFeOabundance of the surface indicates that the oxygen fugacityof the Mercurian interior is very reducing ( 6.3 to 2.6 logf
118959814
The structure of terrestrial bodies: Impact heating, corotation limits, and synestias
During accretion, terrestrial bodies attain a wide range of thermal and rotational states, which are accompanied by significant changes in physical structure (size, shape, pressure and temperature profile, etc.). However, variations in structure have been neglected in most studies of rocky planet formation and evolution. Here we present a new code, the Highly Eccentric Rotating Concentric U (potential) Layers Equilibrium Structure (HERCULES) code, that solves for the equilibrium structure of planets as a series of overlapping constant-density spheroids. Using HERCULES and a smoothed particle hydrodynamics code, we show that Earth-like bodies display a dramatic range of morphologies. For any rotating planetary body, there is a thermal limit beyond which the rotational velocity at the equator intersects the Keplerian orbital velocity. Beyond this corotation limit (CoRoL), a hot planetary body forms a structure, which we name a synestia, with a corotating inner region connected to a disk-like outer region. By analyzing calculations of giant impacts and models of planet formation, we show that typical rocky planets are substantially vaporized multiple times during accretion. For the expected angular momentum of growing planets, a large fraction of post-impact bodies will exceed the CoRoL and form synestias. The common occurrence of hot, rotating states during accretion has major implications for planet formation and the properties of the final planets. In particular, the structure of post-impact bodies influences the physical processes that control accretion, core formation, and internal evolution. Synestias also lead to new mechanisms for satellite formation. Finally, the wide variety of possible structures for terrestrial bodies also expands the mass-radius range for rocky exoplanets.
130302717
Turbulent Mixing of Metal and Silicate during Planet Accretion – and interpretation of the Hf-W chronometer
In the current view of planet formation, the final assembly of the Earth involved giant collisions between proto-planets (> 1000 km radius), with the Moon formed as a result of one such impact. At this stage the colliding bodies had likely differentiated into a metallic core surrounded by a silicate mantle. During the Moon-forming impact, nearly all metal sank into the Earth's core. We investigate to what extent large self-gravitating iron cores can mix with surrounding silicate and how this influences the short-lived chronometer, Hf–W, used to infer the age of the Moon. We present fluid dynamical models of turbulent mixing in fully liquid systems, attempting to place constraints on the degree of mixing. Erosion of sinking cores driven by Rayleigh–Taylor instability does lead to intimate mixing and equilibration, but large blobs (> 10 km diameter) do not emulsify entirely. Emulsification is enhanced if most of the accreting metal cores deform into thin structures during descent through the Earth's mantle. Yet, only 1–20% of Earth's core would equilibrate with silicate during Earth's accretion. The initial speed of the impactor is of little importance. We proceed to evaluate the mixing potential for shear instabilities where silicate entrainment across vertical walls causes mixing. The turbulent structure indicates that vortices remain at the largest scale and do not mix to centimeter length scale, where diffusion operates and isotopes can equilibrate. Thus, incomplete emulsification and equilibration of accreting iron cores is likely to occur. 
 
The extent of metal–silicate equilibration provides key information for interpretation of siderophile budgets and the timing of core formation using the Hf–W chronometer. The time scale of core formation derived from the Hf–W chronometer is usually tied to the last major metal–silicate re-equilibration, believed to coincide with time of the Moon-forming impact. However, we show that large cores have limited ability to reset the Hf–W system in the silicate Earth. Excess ^(182)W in bulk silicate Earth is more sensitive to early core formation processes than to radiogenic ingrowth after the last giant impact.
206536549
Radioactive Elements on Mercury’s Surface from MESSENGER: Implications for the Planet’s Formation and Evolution
Gamma-ray emission from the surface of Mercury indicates that the planet accreted from relatively volatile-enriched material. The MESSENGER Gamma-Ray Spectrometer measured the average surface abundances of the radioactive elements potassium (K, 1150 ± 220 parts per million), thorium (Th, 220 ± 60 parts per billion), and uranium (U, 90 ± 20 parts per billion) in Mercury’s northern hemisphere. The abundance of the moderately volatile element K, relative to Th and U, is inconsistent with physical models for the formation of Mercury requiring extreme heating of the planet or its precursor materials, and supports formation from volatile-containing material comparable to chondritic meteorites. Abundances of K, Th, and U indicate that internal heat production has declined substantially since Mercury’s formation, consistent with widespread volcanism shortly after the end of late heavy bombardment 3.8 billion years ago and limited, isolated volcanic activity since.
128516615
LUNAR VOLATILE DEPLETION DUE TO INCOMPLETE ACCRETION WITHIN AN IMPACT-GENERATED DISK.
The Moon may have formed from an Earth-orbiting disk of vapor and melt produced by a giant impact.1 The Moon and Earth's mantles have similar compositions. However, it is unclear why lunar samples are more depleted in volatile elements than terrestrial mantle rocks2-3, given that an evaporative escape mechanism4 appears inconsistent with expected disk conditions.5 Dynamical models6-7 suggest that the Moon initially accreted from the outermost disk, but later acquired up to 60% of its mass from melt originating from the inner disk. Here we combine dynamical, thermal and chemical models to show that volatile depletion in the Moon can be explained by preferential accretion of volatile-rich melt in the inner disk to the Earth, rather than to the growing Moon. Melt in the inner disk is initially hot and volatile-poor, but volatiles condense as the disk cools. In our simulations, the delivery of inner disk melt to the Moon effectively ceases when gravitational interactions cause the Moon's orbit to expand away from the disk, and this termination of lunar accretion occurs prior to condensation of potassium and more volatile elements. Thus, the portion of the Moon derived from the inner disk is expected to be volatile depleted. We suggest that this mechanism may explain part or all of the Moon's volatile depletion, depending on the degree of mixing within the lunar interior.
119184520
The origin of the Moon within a terrestrial synestia
The giant impact hypothesis remains the leading theory for lunar origin. However, current models struggle to explain the Moon's composition and isotopic similarity with Earth. Here we present a new lunar origin model. High-energy, high-angular momentum giant impacts can create a post-impact structure that exceeds the corotation limit (CoRoL), which defines the hottest thermal state and angular momentum possible for a corotating body. In a typical super-CoRoL body, traditional definitions of mantle, atmosphere and disk are not appropriate, and the body forms a new type of planetary structure, named a synestia. Using simulations of cooling synestias combined with dynamic, thermodynamic and geochemical calculations, we show that satellite formation from a synestia can produce the main features of our Moon. We find that cooling drives mixing of the structure, and condensation generates moonlets that orbit within the synestia, surrounded by tens of bars of bulk silicate Earth (BSE) vapor. The moonlets and growing moon are heated by the vapor until the first major element (Si) begins to vaporize and buffer the temperature. Moonlets equilibrate with BSE vapor at the temperature of silicate vaporization and the pressure of the structure, establishing the lunar isotopic composition and pattern of moderately volatile elements. Eventually, the cooling synestia recedes within the lunar orbit, terminating the main stage of lunar accretion. Our model shifts the paradigm for lunar origin from specifying a certain impact scenario to achieving a Moon-forming synestia. Giant impacts that produce potential Moon-forming synestias were common at the end of terrestrial planet formation.
118968681
Inefficient volatile loss from the Moon-forming disk: Reconciling the giant impact hypothesis and a wet Moon
The Earth's Moon is thought to have formed from a circumterrestrial disk generated by a giant impact between the proto-Earth and an impactor approximately 4.5 billion years ago. Since this impact was energetic, the disk would have been hot (4000–6000 K) and partially vaporized (20–100% by mass). This formation process is thought to be responsible for the geochemical observation that the Moon is depleted in volatiles (e.g., K and Na). To explain this volatile depletion, some studies suggest the Moon-forming disk was rich in hydrogen, which was dissociated from water, and it escaped from the disk as a hydrodynamic wind accompanying heavier volatiles (hydrodynamic escape). This model predicts that the Moon should be significantly depleted in water, but this appears to contradict some of the recently measured lunar water abundances and D/H ratios that suggest that the Moon is more water-rich than previously thought. Alternatively, the Moon could have retained its water if the upper parts (low pressure regions) of the disk were dominated by heavier species because hydrogen would have had to diffuse out from the heavy-element rich disk, and therefore the escape rate would have been limited by this slow diffusion process (diffusion-limited escape). To identify which escape the disk would have experienced and to quantify volatiles loss from the disk, we compute the thermal structure of the Moon-forming disk considering various bulk water abundances (100–1000 ppm) and mid-plane disk temperatures (2500–4000 K). Assuming that the disk consists of silicate (SiO_2 or Mg_2SiO_4) and water and that the disk is in the chemical equilibrium, our calculations show that the upper parts of the Moon-forming disk are dominated by heavy atoms or molecules (SiO and O at _(mid) >2500–2800 K and H_2O at _(mid) <2500–2800 K) and hydrogen is a minor species. This indicates that hydrogen escape would have been diffusion-limited, and therefore the amount of lost water and hydrogen would have been small compared to the initial abundance assumed. This result indicates that the giant impact hypothesis can be consistent with the water-rich Moon. Furthermore, since the hydrogen wind would have been weak, the other volatiles would not have escaped either. Thus, the observed volatile depletion of the Moon requires another mechanism.