118316787
An exact integral relation between the Ni56 mass and the bolometric light curve of a type Ia supernova
An exact relation between the Ni56 mass and the bolometric light curve of a type Ia supernova can be derived as follows, using the following excellent approximations: 1. the emission is powered solely by Ni56-> Co56 ->Fe56; 2. each mass element propagates at a non-relativistic velocity which is constant in time (free coasting); and 3. the internal energy is dominated by radiation. Under these approximations, the energy E(t) carried by radiation in the ejecta satisfies: dE/dt=-E(t)/t-L(t)+Q(t), where Q(t) is the deposition of energy by the decay which is precisely known and L(t) is the bolometric luminosity. By multiplying this equation by time and integrating over time we find: E(t)*t=\int_0^t Q(t')t'dt' -\int_0^t L(t')t'dt'. At late time, t>> t_peak, the energy inside the ejecta decreases rapidly due to its escape, and thus we have \int_0^t Q(t')t'dt'=\int_0^t L(t')t'dt'. This relation is correct regardless of the opacities, density distribution or Ni56 deposition distribution in the ejecta and is very different from "Arnett's rule", L_peak ~ Q(t_peak). By comparing \int_0^t Q(t')t'dt' with \int_0^t L(t')t'dt' at t~40 day after the explosion, the mass of Ni56 can be found directly from UV, optical and infrared observations with modest corrections due to the unobserved gamma-rays and due to the small residual energy in the ejecta, E(t)*t>0.
18317896
Long-term cycling of Kozai-Lidov cycles: extreme eccentricities and inclinations excited by a distant eccentric perturber.
The very long-term evolution of the hierarchical restricted three-body problem is calculated analytically for high inclinations. The Kozai-Lidov Cycles (KLCs) slowly evolve due to the octupole term in the perturber's potential and exhibit striking features, including extremely high eccentricities and the generation of retrograde orbits with respect to the perturber. These features were found in recent numerical experiments of the nonrestricted three-body problem and were attributed inaccurately to the comparable and low masses of the two orbiting companions. Our calculation is done by averaging for the first time the double averaged secular equations of motion over the KLCs and finding a new constant of the motion. These very long-term effects are likely to be important in various astrophysical systems thought to involve KLCs, such as hot Jupiters, irregular moons of planets, and many others.
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
20954769
MOA-2009-BLG-387Lb: A massive planet orbiting an M dwarf
Aims. We report the discovery of a planet with a high planet-to-star mass ratio in the microlensing event MOA-2009-BLG-387, which exhibited pronounced deviations over a 12-day interval, one of the longest for any planetary event. The host is an M dwarf, with a mass in the range 0.07 M_⊙ < M_(host) < 0.49 M_⊙ at 90% confidence. The planet-star mass ratio q = 0.0132 ± 0.003 has been measured extremely well, so at the best-estimated host mass, the planet mass is m_p = 2.6 Jupiter masses for the median host mass, M = 0.19 M_⊙. Methods. The host mass is determined from two “higher order” microlensing parameters. One of these, the angular Einstein radius θ_E = 0.31 ± 0.03 mas has been accurately measured, but the other (the microlens parallax πE, which is due to the Earth’s orbital motion) is highly degenerate with the orbital motion of the planet. We statistically resolve the degeneracy between Earth and planet orbital effects by imposing priors from a Galactic model that specifies the positions and velocities of lenses and sources and a Kepler model of orbits. Results. The 90% confidence intervals for the distance, semi-major axis, and period of the planet are 3.5 kpc < D_L < 7.9 kpc, 1.1 AU < a < 2.7 AU, and 3.8 yr < P < 7.6 yr, respectively.
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."
119257545
Head-on Collisions of White Dwarfs in Triple Systems Could Explain Type Ia Supernovae
Type Ia supernovae (SNe Ia), thermonuclear explosions of carbon-oxygen white dwarfs (CO-WDs), are currently the best cosmological "standard candles," but the triggering mechanism of the explosion is unknown. It was recently shown that the rate of head-on collisions of typical field CO-WDs in triple systems may be comparable to the SNe Ia rate. Here we provide evidence supporting a scenario in which the majority of SNe Ia are the result of such head-on collisions of CO-WDs. In this case, the nuclear detonation is due to a well understood shock ignition, devoid of commonly introduced free parameters such as the deflagration velocity or transition to detonation criteria. By using two-dimensional hydrodynamical simulations with a fully resolved ignition process, we show that zero-impact-parameter collisions of typical CO-WDs with masses 0.5-1 M ☉ result in explosions that synthesize 56Ni masses in the range of ~0.1-1 M ☉, spanning the wide distribution of yields observed for the majority of SNe Ia. All collision models yield the same late-time ( 60 days since explosion) bolometric light curve when normalized by 56Ni masses (to better than 30%), in agreement with observations. The calculated widths of the 56Ni-mass-weighted line-of-sight velocity distributions are correlated with the calculated 56Ni yield, agreeing with the observed correlation. The strong correlation, shown here for the first time, between 56Ni yield and total mass of the colliding CO-WDs (insensitive to their mass ratio), is suggestive as the source for the continuous distribution of observed SN Ia features, possibly including the Philips relation.
117170107
A New Approach to the Relativistic Schrödinger Equation with Central Potential: Ansatz Method
Applying an ansatz to the eigenfunction, we obtain the exact closed-form solutions of the relativistic Schrödinger equation with the potential V(r) = −a/r + b/r1/2 both in three dimensions and in two dimensions. The restrictions on the parameters of the given potential and the angular momentum quantum number are also presented.
15491159
Exact Solutions of the Two-Dimensional Schrödinger Equation with Certain Central Potentials
By applying an ansatz to the eigenfunction, an exact closed-form solution of theSchrödinger equation in two dimension is obtained with the potentials V(r) =ar2 + br4 + cr6,V(r) = ar + br2 + cr−1,and V(r) = ar2 + br−2+ cr−4 + dr−6,respectively. The restrictions on the parameters of the given potential andthe angular momentum m are obtained.
119387624
The Dirac equation with a Coulomb potential in D dimensions
The Dirac equation is generalized to D + 1 spacetime case. The radial equations of this quantum system are obtained and solved exactly by the Tricomi equation approach. The energy levels E(n, l, D) are analytically presented. The dependences of the energy E(n, l, D) on the dimension D are also analysed. It is shown that the energy E(n, l, D)(l ? 0) is almost independent of the quantum number l, while E(n, 0, D) first decreases and then increases as the dimension D increases. Unexpectedly, there is an absence of bound states for this quantum system with the special case D = 1, which is explained in some detail from the fact that the eigenvalues and eigenfunctions do not exist for D = 1.
122297543
Pseudospin symmetry in the relativistic Manning―Rosen potential including a Pekeris-type approximation to the pseudo-centrifugal term
Abstract Based on the Sturm–Liouville theorem and shape invariance formalism, we study by applying a Pekeris-type approximation to the pseudo-centrifugal term the pseudospin symmetry of a Dirac nucleon subjected to scalar and vector Manning–Rosen potentials including the spin–orbit coupling term. A quartic energy equation and spinor wave functions with arbitrary spin–orbit coupling quantum number k are presented. The bound states are calculated numerically. The relativistic Manning–Rosen potential could not trap a Dirac nucleon in the limit case β → ∞ .
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.