The Importance of Urca-process Cooling in Accreting ONe White Dwarfs

TL;DR

This paper investigates how Urca-process cooling affects the thermal evolution of accreting ONe white dwarfs, using analytic formulas and MESA simulations to reveal its impact on convective stability and ignition conditions.

Contribution

It provides the first analytic expression for Urca-process cooling rates and demonstrates their significant influence on the thermal and convective evolution of accreting ONe white dwarfs.

Findings

Urca-process cooling substantially modifies WD thermal evolution.

Lower temperature models develop convective regions even with Ledoux criterion.

Oxygen ignites at similar densities with or without Urca cooling.

Abstract

We study the evolution of accreting oxygen-neon (ONe) white dwarfs (WDs), with a particular emphasis on the effects of the presence of the carbon-burning products $\mathrm{^{23}Na}$ and $\mathrm{^{25}Mg}$. These isotopes lead to substantial cooling of the WD via the $\mathrm{^{25}Mg}$-$\mathrm{^{25}Na}$, $\mathrm{^{23}Na}$-$\mathrm{^{23}Ne}$, and $\mathrm{^{25}Na}$-$\mathrm{^{25}Ne}$ Urca pairs. We derive an analytic formula for the peak Urca-process cooling rate and use it to obtain a simple expression for the temperature to which the Urca process cools the WD. Our estimates are equally applicable to accreting carbon-oxygen WDs. We use the Modules for Experiments in Stellar Astrophysics (MESA) stellar evolution code to evolve a suite of models that confirm these analytic results and demonstrate that Urca-process cooling substantially modifies the thermal evolution of accreting ONe WDs. Most importantly, we show that MESA models with lower temperatures at the onset of the $\mathrm{^{24}Mg}$ and $\mathrm{^{24}Na}$ electron captures develop convectively unstable regions, even when using the Ledoux criterion. We discuss the difficulties that we encounter in modeling these convective regions and outline the potential effects of this convection on the subsequent WD evolution. For models in which we do not allow convection to operate, we find that oxygen ignites around a density of $\log(\rho_{\rm c}/\rm g\,cm^{-3}) \approx 9.95$, very similar to the value without Urca cooling. Nonetheless, the inclusion of the effects of Urca-process cooling is an important step in producing progenitor models with more realistic temperature and composition profiles which are needed for the evolution of the subsequent oxygen deflagration and hence for studies of the signature of accretion-induced collapse.