The Initial-Final Mass Relation among White Dwarfs in Wide Binaries

We present the initial-final mass relation derived from 10 white dwarfs in wide binaries that consist of a main sequence star and a white dwarf. The temperature and gravity of each white dwarf was measured by fitting theoretical model atmospheres to the observed spectrum using a $\chi^{2}$ fitting algorithm. The cooling time and mass was obtained using theoretical cooling tracks. The total age of each binary was estimated from the chromospheric activity of its main sequence component to an uncertainty of about 0.17 dex in log \textit{t} The difference between the total age and white dwarf cooling time is taken as the main sequence lifetime of each white dwarf. The initial mass of each white dwarf was then determined using stellar evolution tracks with a corresponding metallicity derived from spectra of their main sequence companions, thus yielding the initial-final mass relation. Most of the initial masses of the white dwarf components are between 1 - 2 M$_{\odot}$. Our results suggest a correlation between the metallicity of a white dwarf's progenitor and the amount of post-main-sequence mass loss it experiences - at least among progenitors with masses in the range of 1 - 2 M$_{\odot}$. A comparison of our observations to theoretical models suggests that low mass stars preferentially lose mass on the red giant branch.Comment: 28 pages, 8 figures, accepted for publication in Ap

Thermal fracture as a framework for quasi-static crack propagation

We address analytically and numerically the problem of crack path prediction in the model system of a crack propagating under thermal loading. We show that one can explain the instability from a straight to a wavy crack propagation by using only the principle of local symmetry and the Griffith criterion. We then argue that the calculations of the stress intensity factors can be combined with the standard crack propagation criteria to obtain the evolution equation for the crack tip within any loading configuration. The theoretical results of the thermal crack problem agree with the numerical simulations we performed using a phase field model. Moreover, it turns out that the phase-field model allows to clarify the nature of the transition between straight and oscillatory cracks which is shown to be supercritical.Comment: 19 pages, 8 figure