14062967
Probing ~100 AU Intergalactic Mg II Absorbing “Cloudlets” with Quasar Microlensing
Intergalactic Mg II absorbers are known to have structures down to scales ~102.5 pc, and there are now indications that they may be fragmented on scales 10-2.5 pc according to Hao and coworkers. When a lensed quasar is microlensed, the microimages of the quasar experience creation, destruction, distortion, and drastic astrometric changes during caustic crossings. I show that quasar microlensing can effectively probe Mg II and other absorption "cloudlets" with sizes ~10-4.0 to 10-2.0 pc by inducing significant spectral variability on timescales of months to years. With numerical simulations, I demonstrate the feasibility of applying this method to Q2237+0305, and I show that high-resolution spectra of this quasar in the near future would provide a clear test of the existence of such metal-line absorbing "cloudlets."
118383144
SUPER-ECCENTRIC MIGRATING JUPITERS
An important class of formation theories for hot Jupiters involves the excitation of extreme orbital eccentricity (e = 0.99 or even larger) followed by tidal dissipation at periastron passage that eventually circularizes the planetary orbit at a period less than 10 days. In a steady state, this mechanism requires the existence of a significant population of super-eccentric (e > 0.9) migrating Jupiters with long orbital periods and periastron distances of only a few stellar radii. For these super-eccentric planets, the periastron is fixed due to conservation of orbital angular momentum and the energy dissipated per orbit is constant, implying that the rate of change in semi-major axis a is a-dot {proportional_to}a{sup 1/2} and consequently the number distribution satisfies dN/d log a{proportional_to}a{sup 1/2}. If this formation process produces most hot Jupiters, Kepler should detect several super-eccentric migrating progenitors of hot Jupiters, allowing for a test of high-eccentricity migration scenarios.
54818607
GRB 091029: at the limit of the fireball scenario
Aims. Using high-quality, broad-band afterglow data for GRB 091029, we test the validity of the forward-shock model for gamma-ray burst afterglows. Methods. We used multi-wavelength (NIR to X-ray) follow-up observations obtained with the GROND, BOOTES-3/YA and Stardome optical ground-based telescopes, and the UVOT and the XRT onboard the Swift satellite. The resulting data of excellent accuracy allow us to construct a multi-wavelength light curve with relative photometric errors as low as 1%, as well as the well-sampled spectral energy distribution covering 5 decades in energy. Results. The optical/NIR and the X-ray light curves of the afterglow of GRB 091029 are almost totally decoupled. The X-ray light curve shows a shallow rise with a peak at ∼7 ks and a decay slope of α ∼ 1.2 afterwards, while the optical/NIR light curve shows a much steeper early rise with a peak around 400 s, followed by a shallow decay with temporal index of α ∼ 0.6, a bump and a steepening of the decay afterwards. The optical/NIR spectral index decreases gradually by over 0.3 before this bump, and then slowly increases again, while the X-ray spectral index remains constant throughout the observations. Conclusions. To explain the decoupled light curves in the X-ray and optical/NIR domains, a two-component outflow is proposed. Several models are tested, including continuous energy injection, components with different electron energy indices and components in two different stages of spectral evolution. Only the last model can explain both the decoupled light curves with asynchronous peaks and the peculiar SED evolution. However, this model has so many unknown free parameters that we are unable to reliably confirm or disprove its validity, making the afterglow of GRB 091029 difficult to explain in the framework of the simplest fireball model. This conclusion provides evidence that a scenario beyond the simplistic assumptions is needed to be able to model the growing number of well-sampled afterglow light curves.
119233296
THE STATISTICS OF MULTI-PLANET SYSTEMS
We describe statistical methods for measuring the exoplanet multiplicity function (the fraction of host stars containing a given number of planets) and inclination distribution from transit and radial-velocity (RV) surveys. The analysis is based on the approximation of separability-that the distribution of planetary parameters in an n-planet system is the product of identical 1-planet distributions. We review the evidence that separability is a valid approximation for exoplanets and conclude that it captures many, but not all, of the known characteristics of multi-planet systems. We show how to relate the observable multiplicity function in surveys with similar host-star populations but different sensitivities. We also show how to correct for geometrical selection effects to derive the multiplicity function from transit surveys if the distribution of relative inclinations is known. Applying these tools to the Kepler transit survey and to RV surveys, we find that (1) the Kepler data alone do not constrain the mean inclination of multi-planet systems; even spherical distributions are allowed by the data but only if a small fraction of host stars contain large planet populations ({approx}> 30); (2) comparing the Kepler and RV surveys shows that the mean inclination of multi-planet systems is less than 5 Degree-Sign ;more » and (3) the multiplicity function of the Kepler planets is not well determined by the present data.« less
7872671
The Demographics of Extrasolar Planets Beyond the Snow Line with Ground-based Microlensing Surveys
In the currently-favored paradigm of planet formation, the location of the snow line in the protoplanetary disk plays a crucial role. Determining the demographics of planets beyond the snow line of stars of various masses is thus essential for testing this model. Microlensing is sensitive to planets that are generally inaccessible to other methods, and in particular is most sensitive to cool planets at or beyond the snow line, including very low-mass (i.e. terrestrial) planets. Hence, microlensing is uniquely suited and so essential for a comprehensive study of this region. Microlensing is also sensitive to planets orbiting low-mass stars, free-floating planets, planets in the Galactic bulge and disk, and even planets in external galaxies. These planets can also provide critical constraints on models of planet formation. Although microlensing searches have so far detected only a handful of planets, these have already changed our understanding of planet formation beyond the snow line. Next generation microlensing surveys, which would be sensitive to tens of "cold Earths" in this region, are well advanced in design conception and are starting initial practical implementation.
118452553
The Effect of Differential Limb Magnification on Abundance Analysis of Microlensed Dwarf Stars
Finite source effects can be important in observations of gravitational microlensing of stars. Near caustic crossings, for example, some parts of the source star will be more highly magnified than other parts. The spectrum of the star is then no longer the same as when it is unmagnified, and measurements of the atmospheric parameters and abundances will be affected. The accuracy of abundances measured from spectra taken during microlensing events has become important recently because of the use of highly magnified dwarf stars to probe abundance ratios and the abundance distribution in the Galactic bulge. In this paper, we investigate the importance of finite source effects on spectra by using magnification profiles motivated by two events to synthesize spectra for dwarfs between 5000 K and 6200 K at solar metallicity. We adopt the usual techniques for analyzing the microlensed dwarfs, namely, spectroscopic determination of temperature, gravity, and microturbulent velocity, relying on equivalent widths. We find that ignoring the finite source effects for the more extreme case results in errors in T eff <45 K, in log g of <0.1 dex, and in ξ of <0.1 km s–1. In total, changes in equivalent widths lead to small changes in atmospheric parameters and changes in abundances of <0.06 dex, with changes in [Fe I/H] of <0.03 dex. For the case with a larger source-lens separation, the error in [Fe I/H] is <0.01 dex. This latter case represents the maximum effect seen in events whose light curves are consistent with a point-source lens, which includes the majority of microlensed bulge dwarfs published so far.
121535344
EXACT QUANTIZATION RULE AND ITS APPLICATIONS TO PHYSICAL POTENTIALS
By using the exact quantization rule, we present analytical solutions of the Schrodinger equation for the deformed harmonic oscillator in one dimension, the Kratzer potential and pseudoharmonic oscillator in three dimensions. The energy levels of all the bound states are easily calculated from this quantization rule. The normalized wavefunctions are also obtained. It is found that the present approach can simplify the calculations.
120777661
ANALYTICAL APPROXIMATIONS TO THE SCHRÖDINGER EQUATION FOR A SECOND PÖSCHL–TELLER-LIKE POTENTIAL WITH CENTRIFUGAL TERM
The bound state solutions of the Schrodinger equation for a second Poschl–Teller-like potential with the centrifugal term are obtained approximately. It is found that the solutions can be expressed in terms of the hypergeometric functions 2F1(a, b; c; z). To show the accuracy of our results, we calculate the eigenvalues numerically for arbitrary quantum numbers n and l. It is found that the results are in good agreement with those obtained by other method for short-range potential. Two special cases for l = 0 and V1 = V2 are also studied briefly.
119675826
ALGEBRAIC APPROACH TO THE POSITION-DEPENDENT MASS SCHRÖDINGER EQUATION FOR A SINGULAR OSCILLATOR
We construct a singular oscillator Hamiltonian with a position-dependent effective mass. We find that an su(1, 1) algebra is the hidden symmetry of this quantum system and the isospectral potentials V(x) depend on the different choices of the m(x). The complete solutions are also presented by using this Lie algebra.
122777413
NEW TYPE SHIFT OPERATORS FOR THREE-DIMENSIONAL INFINITE WELL POTENTIAL
New type shift operators for three-dimensional infinite well potential are identified to connect those quantum systems with different radials R but with the same energy spectrum. It should be pointed out that these shift operators depend on all variables contained in wave functions. Thus they establish a novel relation between wave functions ψlm(r) and ψ(l±1)(m±1)(r).
121783508
Quantum states of a sextic potential: hidden symmetry and quantum monodromy
A known terminating polynomial ansatz for a finite sub-set of states of the sextic central potential V(a,b,c;r) = ar2 + br4 + cr6, c>0, subject to integer related parameter constraints, is confirmed to apply in two as well as three dimensions. A hidden symmetry relating the eigenstates of V(a,b,c;r) to those of V(a,-b,c;r) is used to establish the boundary between the ansatz sub-set and the infinite set of higher states. Connections between the radial wavefunctions Rn(a,b,c;r) and Rn'(a,-b,c;r) also provide semiclassical insight into the origin of the parameter constraint. Finally the ansatz eigenvalue dispositions are related to the phenomenon of quantum monodromy.