The Effect of White Dwarf Mass on the Efficiency of a Three-Body Mean Motion Resonance Chain in Polluting the Stellar Atmosphere

White dwarf stars are the burned out cores of former low to intermediate mass main-sequence stars that shine only due to residual heat as nuclear reactions have ceased. The atmospheres of white dwarf stars should be composed of hydrogen and helium. However, a significant fraction of white dwarf stars have atmospheres polluted with elements heavier than helium. One likely source of this pollution is asteroids whose orbits were previously perturbed by planets so that the asteroids were sent inward to their stellar Roche limit where they were torn apart by stellar tidal forces and eventually polluted the atmosphere of the star. This project measured the effect of white dwarf mass on the efficiency of the 6:3:2 and 4:2:1 mean motion resonance chains in delivering asteroids to their stellar Roche limit for the case of planets in initially circular orbits with outer planet mass 0.6 Jupiter mass, inner planet mass 4 Jupiter masses, and asteroid in the innermost orbit with an initially eccentricity of 0.05, and the inner planet with an initial semi-major axis of 10 au. For the 6:3:2 and 4:2:1 resonance chains, an asteroid had from a 0.47 % to 2.37 % and 0.69 % to 2.27 % chance, respectively, of being delivered to the stellar Roche limit over a white dwarf mass range of 0.2M⊙-0.9M⊙. The efficiency had a general trend of exponentially decreasing with increasing white dwarf mass. The average dynamical lifetime of an asteroid generally increased linearly with white dwarf mass, and all average dynamical lifetimes were below 0.1 Myr.