The ultracompact binary systems RX J1914.4+2456 ( catalog V407 Vul ) ( RX J1914.4+2456 ) and RX J0806.3+1527 ( catalog HM Cnc ) ( RX J0806.3+1527 ) – a two-member subclass of the AM CVn stars – continue to pique interest because they defy unambiguous classification .
Three proposed models remain viable at this time , but none of the three is significantly more compelling than the remaining two , and all three can satisfy the observational constraints if parameters in the models are tuned .
One of the three proposed models is the direct impact model of Marsh & Steeghs ( 31 ) , in which the accretion stream impacts the surface of a rapidly-rotating primary white dwarf directly but at a near-glancing angle .
One requirement of this model is that the accretion stream have a high enough density to advect its specific kinetic energy below the photosphere for progressively more-thermalized emission downstream , a constraint that requires an accretion spot size \sim 1.2 \times 10 ^ { 5 } km ^ { 2 } or smaller .
Having at hand a smoothed particle hydrodynamics code optimized for cataclysmic variable accretion disk simulations , it was relatively straightforward for us to adapt it to calculate the footprint of the accretion stream at the nominal radius of the primary white dwarf , and thus to test this constraint of the direct impact model .
We find that the mass flux at the impact spot can be approximated by a bivariate Gaussian with standard deviation \sigma _ { \phi } = 164 km in the orbital plane and \sigma _ { \theta } = 23 km in the perpendicular direction .
The area of the the 2 \sigma ellipse into which \sim 86 % of the mass flux occurs is roughly 47,400 km ^ { 2 } , or roughly half the size estimated by Marsh & Steeghs ( 31 ) .
We discuss the necessary parameters of a simple model of the luminosity distribution in the post-impact emission region .