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.
121351229
The relativistic bound and scattering states of the Manning-Rosen potential with an improved new approximate scheme to the centrifugal term
The approximately analytical bound and scattering state solutions of the arbitrary l-wave Klein-Gordon equation for the mixed Manning-Rosen potentials are carried out by an improved new approximation to the centrifugal term. The normalized analytical radial wave functions of the l-wave Klein-Gordon equation with the mixed Manning-Rosen potentials are presented and the corresponding energy equations for bound states and phase shifts for scattering states are derived. It is shown that the energy levels of the continuum states, reduce to the bound states of those at the poles of the scattering amplitude. Some useful figures are plotted to show the improved accuracy of our results and the special case for wave is studied briefly.
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.
118387861
Q in Other Solar Systems
A significant fraction of the hot Jupiters with final circularized orbital periods of less than 5 days are thought to form through the channel of high-eccentricity migration. Tidal dissipation at successive periastron passages removes orbital energy of the planet, which has the potential for changes in semi-major axis of a factor of ten to a thousand. In the equilibrium tide approximation we show that, in order for high-eccentricity migration to take place, the relative level of tidal dissipation in Jupiter analogues must be at least 10 times higher than the upper-limit attributed to the Jupiter-Io interaction. While this is not a severe problem for high-e migration, it contradicts the results of several previous calculations. We show that these calculations of high-e migration inadvertently over-estimated the strength of tidal dissipation by three to four orders of magnitude. These discrepancies were obscured by the use of various parameters, such as lag time \tau, tidal quality factor Q and viscous time t_V. We provide the values of these parameters required for the Jupiter-Io interaction, tidal circularization and high-e migration. Implications for tidal theory as well as models of the inflated radii of hot Jupiters are discussed. Though the tidal Q is not, in general, well-defined, we derive a formula for it during high-eccentricity migration where Q is approximately constant throughout evolution.
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.
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.
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.