Resolution Study of Thermonuclear Initiation in White Dwarf Tidal Disruption Events

We study the initiation of thermonuclear detonations in tidally disrupted white dwarf stars by intermediate-mass ($10^3 M_\odot$) black holes. The length scales required to resolve the initiation mechanism are not easily reached in three-dimensions, so instead we have devised two-dimensional proxy models which, together with a logarithmic gridding strategy, can adequately capture detonation wave fronts as material undergoes simultaneous compression and stretching from tidal forces. We consider 0.15 and 0.6 solar mass white dwarf stars parameterized by tidal strengths in the range $\beta=4~\text{to}~23$. High spatial resolution elucidates the manner and conditions leading to thermonuclear detonation, linking the initiation sequence to stellar composition and tidal strength. All of our models suffer sustained detonations triggered by a combination of adiabatic compression, mild thermonuclear preconditioning, and collisional heating, in degrees depending primarily on tidal strength. We find many diagnostics, such as temperature, total released energy, and iron group products, are fairly well-converged (better than 10%) at resolutions below 10 km along the scale height of the orbital plane. The exceptions are intermediate mass transients like calcium, which remain uncertain up to factors of two even at 1 km resolution.