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.
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
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."
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.
119219662
The rate of WD-WD head-on collisions may be as high as the SNe Ia rate
We show that a White Dwarf-White Dwarf (WD-WD) binary with semi-major axis a=1-300 AU, which is orbited by a stellar mass outer perturber with a moderate pericenter r_{p, out} \sim 3-10 x a, has a few percent chance of experiencing a head-on collision within ~5 Gyr. Such a perturber is sufficiently distant to allow the triple system to remain intact for millions of orbits while efficiently exchanging angular momentum with the WD-WD binary. In ~ 5% of the initial orientations, the inner orbit efficiently scans the (equal energy) phase space in the region of zero angular momentum. In these systems, the binary experiences increasingly closer, stochastic, pericenter approaches r_p ~ a/2N with the increasing number (N) of orbits elapsed. Within N~10^5(a/30AU) orbits, a collision is likely to occur. This is shown by performing \simten thousand 3-body integrations and is explained by simple analytic arguments. The collisions are conservatively restricted to "clean" collisions in which all passages prior to the collision are greater than 4R_WD=4x10^9cm. In particular, within the last single orbit, the pericenter changes from r_p>4R_WD to a collision value of r_p 3000 km/s and the collision is likely to detonate the WDs leading to a type Ia SNe. If a significant fraction of WDs reside in such triples, the rate of such collisions is as high as the SNe Ia rate, and it is possible that some or all type Ia SNe occur in this way. Such SNe have a unique gravitational wave signature, which will allow a decisive identification in the future.
40006839
Water in HD 209458b's atmosphere from 3.6 - 8 microns IRAC photometric observations in primary transit
The hot Jupiter HD 209458b was observed during primary transit at 3.6, 4.5, 5.8 and 8.0 microns using the Infrared Array Camera (IRAC) on the Spitzer Space Telescope. We detail here the procedures we adopted to correct for the systematic trends present in the IRAC data. The light curves were fitted including limb darkening effects and fitted using Markov Chain Monte Carlo and prayer-bead Monte Carlo techniques, finding almost identical results. The final depth measurements obtained by a combined Markov Chain Monte Carlo fit are at 3.6 microns, 1.469 +- 0.013 % and 1.448 +- 0.013 %; at 4.5 microns, 1.478 +- 0.017 % ; at 5.8 microns, 1.549 +- 0.015 % and at 8.0 microns 1.535 +- 0.011 %. Our results clearly indicate the presence of water in the planetary atmosphere. Our broad band photometric measurements with IRAC prevent us from determining the additional presence of other other molecules such as CO, CO2 and methane for which spectroscopy is needed. While water vapour with a mixing ratio of 10^-4-10^-3 combined with thermal profiles retrieved from the day-side may provide a very good fit to our observations, this data set alone is unable to resolve completely the degeneracy between water abundance and atmospheric thermal profile.
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.
116297185
Quantum Monodromy in the Spectrum of Schrödinger Equation with a Decatic Potential
In this study the spectral problem of the two-dimensional Schrödinger equation with the cylindrically symmetrical decatic potential is carried out. The concept of quantum monodromy is introduced to give insight into the energy levels of system with this potential. It is shown that quantum monodromy occurs at ρ = 0 in the distribution of eigenstates around a critical point on the spectrum at E = 0 with zero angular momentum, such that there can be no smoothly valid assignment of quantum number. Cases with the three-well and four-well potentials are presented to give rise to the double degeneracies with respect to energy except for the angular momentum m = 0.
122105643
Exact solutions of dirac equation for a new spherically asymmetrical singular oscillator
In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of scalar and vector spherically asymmetrical singular oscillators. This is done provided that the vector potential is equal to the scalar potential. The spinor wave functions and bound state energy levels are presented. The case V(r) = -S(r) is also considered.
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).
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.