Numerical Solution of the Two-Phase Obstacle Problem by Finite Difference Method

In this paper we consider the numerical approximation of the two-phase membrane (obstacle) problem by finite difference method. First, we introduce the notion of viscosity solution for the problem and construct certain discrete nonlinear approximation system. The existence and uniqueness of the solution of the discrete nonlinear system is proved. Based on that scheme, we propose projected Gauss-Seidel algorithm and prove its convergence. At the end of the paper we present some numerical simulations.Comment: Free Boundary Problem, Two-Phase Membrane Problem, Two-Phase Obstacle Problem, Finite Difference Metho

Constraining Type Ia supernovae through their heights in edge-on galaxies

In this Letter, using classified 197 supernovae (SNe) Ia, we perform an analyses of their height distributions from the disc in edge-on spirals and investigate their light-curve (LC) decline rates $(\Delta m_{15})$. We demonstrate, for the first time, that 91T- and 91bg-like subclasses of SNe Ia are distributed differently toward the plane of their host disc. The average height from the disc and its comparison with scales of thin/thick disc components gives a possibility to roughly estimate the SNe Ia progenitor ages: 91T-like events, being at the smallest heights, originate from relatively younger progenitors with ages of about several 100 Myr, 91bg-like SNe, having the highest distribution, arise from progenitors with significantly older ages $\sim 10$ Gyr, and normal SNe Ia, which distributed between those of the two others, are from progenitors of about one up to $\sim 10$ Gyr. We find a correlation between LC decline rates and SN Ia heights, which is explained by the vertical age gradient of stellar population in discs and a sub-Chandrasekhar mass white dwarf explosion models, where the $\Delta m_{15}$ parameter is a progenitor age indicator.Comment: 7 pages, 2 figures, 8 tables, online data, accepted for publication in MNRAS Letter

The impact of bars on the radial distribution of supernovae in disc galaxies

We present an analysis of the impact of bars on the radial distributions of the different types of supernovae (SNe) in the stellar discs of host galaxies with various morphologies. We find that in Sa-Sbc galaxies, the radial distribution of core-collapse (CC) SNe in barred hosts is inconsistent with that in unbarred ones, while the distributions of SNe Ia are not significantly different. At the same time, the radial distributions of both types of SNe in Sc-Sm galaxies are not affected by bars. We propose that the additional mechanism shaping the distributions of Type Ia and CC SNe can be explained within the framework of substantial suppression of massive star formation in the radial range swept by strong bars, particularly in early-type spirals. The radial distribution of CC SNe in unbarred Sa-Sbc galaxies is more centrally peaked and inconsistent with that in unbarred Sc-Sm hosts, while the distribution of SNe Ia in unbarred galaxies is not affected by host morphology. These results can be explained by the distinct distributions of massive stars in the discs of early-and late-type spirals.Comment: 3 pages, 1 figure. This is a brief summary of arXiv:1511.08896, written for a short contribution in the EWASS-2016 Symposium 16 "Frontiers of massive-star evolution and core-collapse supernovae

Supernovae and their host galaxies - V. The vertical distribution of supernovae in disc galaxies

We present an analysis of the height distributions of the different types of supernovae (SNe) from the plane of their host galaxies. We use a well-defined sample of 102 nearby SNe appeared inside high-inclined (i > 85 deg), morphologically non-disturbed S0-Sd host galaxies from the Sloan Digital Sky Survey. For the first time, we show that in all the subsamples of spirals, the vertical distribution of core-collapse (CC) SNe is about twice closer to the plane of host disc than the distribution of SNe Ia. In Sb-Sc hosts, the exponential scale height of CC SNe is consistent with those of the younger stellar population in the Milky Way (MW) thin disc, while the scale height of SNe Ia is consistent with those of the old population in the MW thick disc. We show that the ratio of scale lengths to scale heights of the distribution of CC SNe is consistent with those of the resolved young stars with ages from ~ 10 Myr up to ~ 100 Myr in nearby edge-on galaxies and the unresolved stellar population of extragalactic thin discs. The corresponding ratio for SNe Ia is consistent with the same ratios of the two populations of resolved stars with ages from a few 100 Myr up to a few Gyr and from a few Gyr up to ~ 10 Gyr, as well as with the unresolved population of the thick disc. These results can be explained considering the age-scale height relation of the distribution of stellar population and the mean age difference between Type Ia and CC SNe progenitors.Comment: 11 pages, 6 figures, 6 tables, accepted for publication in MNRA

The impact of spiral density waves on the star formation distribution: a view from core-collapse supernovae

We present an analysis of the impact of spiral density waves (DWs) on the radial and surface density distributions of core-collapse (CC) supernovae (SNe) in host galaxies with different arm classes. For the first time, we show that the corotation radius normalized surface density distribution of CC SNe (tracers of massive star formation) indicates a dip at corotation in long-armed grand-design (LGD) galaxies. The high SNe surface density just inside and outside corotation may be the sign of triggered massive star formation by the DWs. Our results may support the large-scale shock scenario induced by spiral DWs in LGD galaxies, which predicts a higher star formation efficiency around the shock fronts, avoiding the corotation region.Comment: 6 pages, 4 figures; in press: proceedings of the conference "Instability Phenomena and Evolution of the Universe", Communications of Byurakan Astrophys. Obs., Vol. 65, Is. 2, Dec. 201

Supernovae and their host galaxies -- VII. The diversity of Type Ia supernova progenitors

We present an analysis of the light curve (LC) decline rates $(\Delta m_{15})$ of 407 normal and peculiar supernovae (SNe) Ia and global parameters of their host galaxies. As previously known, there is a significant correlation between the $\Delta m_{15}$ of normal SNe Ia and global ages (morphologies, colours, masses) of their hosts. On average, those normal SNe Ia that are in galaxies from the Red Sequence (early-type, massive, old hosts) have faster declining LCs in comparison with those from the Blue Cloud (late-type, less massive, younger hosts) of the colour-mass diagram. The observed correlations between the $\Delta m_{15}$ of normal SNe Ia and hosts' parameters appear to be due to the superposition of at least two distinct populations of faster and slower declining normal SNe Ia from older and younger stellar components. We show, for the first time, that the $\Delta m_{15}$ of 91bg- and 91T-like SNe is independent of host morphology and colour. The distribution of hosts on the colour-mass diagram confirms the known tendency for 91bg-like SNe to occur in globally red/old galaxies while 91T-like events prefer blue/younger hosts. On average, the youngest global ages of 02cx-like SNe hosts and their positions in the colour-mass diagram hint that these events likely originate from young population, but they differ from 91T-like events in the LC decline rate. Finally, we discuss the possible explosion channels and present our favoured SN Ia models that have the potential to explain the observed SN-host relations.Comment: 17 pages, 9 figures, 13 tables, online data, accepted for publication in MNRA

VizieR Online Data Catalog: Properties of 500 SNe and their 419 hosts (Hakobyan+, 2016)

The full database of 500 individual SNe (SN designation, type, and offset from host galaxy nucleus) and their 419 host galaxies (galaxy SDSS designation, distance, morphological type, bar, corrected g-band D25, a/b, PA, and inclination)