arXiv subjects

A. H. Harutyunyan

Publications and source records attributed to A. H. Harutyunyan.

4 recordsLinked to original sources

arXiv2018

A new exactly integrable hypergeometric potential for the Schrödinger equation

We introduce a new exactly integrable potential for the Schrödinger equation for which the solution of the problem may be expressed in terms of the Gauss hypergeometric functions. This is a potential step with variable height and steepness. We present the general solution of the problem, discuss the transmission of a quantum particle above the barrier, and derive explicit expressions for the reflection and transmission coefficients.

quant-ph↗

arXiv2018

Confluent hypergeometric expansions of the solutions of the double-confluent Heun equation

Several expansions of the solutions of the double-confluent Heun equation in terms of the Kummer confluent hypergeometric functions are presented. Three different sets of these functions are examined. Discussing the expansions without a pre-factor, it is shown that two of these functions provide expansions the coefficients of which obey three-term recurrence relations, while for the third confluent hypergeometric function the corresponding recurrence relation generally involves five-terms. The latter relation is reduced to a three-term one only in the case when the double-confluent Heun equation degenerates to the confluent hypergeometric equation. The conditions for obtaining finite sum solutions via termination of the expansions are discussed. The possibility of constructing expansions of different structure using certain equations related to the double-confluent Heun equation is discussed. An example of such expansion derived using the equation obeyed by a function involving the derivative of a solution of the double-confluent Heun equation is presented. In this way, expansions governed by three- or more term recurrence relations for expansion coefficients can be constructed. An expansion with coefficients obeying a seven-term recurrence relation is presented. This relation is reduced to a five-term one if the additional singularity of the equation obeyed by the considered auxiliary function coincides with a singularity of the double-confluent Heun equation.

math.CA↗

arXiv2010

Two Type Ic supernovae in low-metallicity, dwarf galaxies: diversity of explosions

We present BVRI photometry and optical spectroscopy of two Type Ic supernovae SN 2007bg and SN 2007bi discovered in wide-field, non-targeted surveys and associated with sub-luminous blue dwarf galaxies. Neither SNe 2007bg nor 2007bi were found in association with an observed GRB, but are found to inhabit similar low-metallicity environments as GRB associated supernovae. The radio-bright SN 2007bg is hosted by an extremely sub-luminous galaxy of magnitude MB = -12.4+/-0.6 mag with an estimated oxygen abundance of 12+log(O/H) = 8.18+/-0.17. The lightcurve of SN 2007bg displays one of the fastest post-maximum decline rates of all broad-lined Type Ic supernovae known to date and, when combined with its high expansion velocities, a high kinetic energy to ejected mass ratio (E_K/Mej ~ 2.7). We show that SN 2007bi is possibly the most luminous Type Ic known, reaching a peak magnitude of MR ~ 21.3 mag and displays a remarkably slow decline, following the radioactive decay rate of 56Co to 56Fe throughout the course of its observed lifetime. From a simple model of the bolometric light curve of SN 2007bi we estimate a total ejected 56Ni mass of M_Ni = 3.5 - 4.5 solar masses, the largest 56Ni mass measured in the ejecta of a supernova to date. There are two models that could explain the high luminosity and large ejected 56Ni mass. One is a pair-instability supernova (PISN) which has been predicted to occur for massive stars at low metallicities. We measure the host galaxy metallicity of SN 2007bi to be 12 + log(O/H) = 8.15+/-0.15 which is somewhat high to be consistent with the PISN model. An alternative is the core-collapse of a C+O star of 20 - 40 solar masses which is the core of a star of originally 50 - 100 solar masses. (Abridged)

astro-ph.CO↗

arXiv2008

ESC Supernova spectroscopy of non-ESC targets

We present the spectra of 36 Supernovae (SNe) of various types, obtained by the European Supernova Collaboration. Because of the spectral classification and the phase determination at their discovery the SNe did not warrant further study, and the spectra we present are the only available for the respective objects. In this paper we present and discuss this material using a new software for the automated classification of SNe spectra. As a validation of the software, we verify the classification and phase estimate reported for these objects in their discovery / classification circulars. For the comparison, the software uses the library of template spectra of Padova-Asiago Supernova Archive (ASA). For each spectrum of our sample we present a brief, individual discussion, highlighting the main characteristics and possible peculiarities. The comparison with ASA spectra confirms the previous classification of all objects and refines the age estimates. For our software we determine numerical limits of "safe" spectral classification and the uncertainties of the phase determination.

astro-ph↗