The dearth of high-mass hydrogen-atmosphere metal-polluted white dwarfs within 40 pc

We present a population synthesis model which addresses the different mass distributions of the metal-polluted and non-metal-polluted hydrogen-atmosphere white dwarfs identified in volume-limited samples. Specifically, metal-pollution has been observed to be rare in white dwarfs more massive than $\approx$0.7 $M_{\odot}$. Our population synthesis model invokes episodic accretion of planetary debris onto a synthetic population of white dwarfs. We find that the observed difference can be explained in the regime where most debris disks last for $10^4$$-$$10^6$ years. This is broadly consistent with observational estimates that disk lifetimes are on the order 10$^5$$-$10$^7$ years. We also invoke an alternate model which explores an upper limit on planetary system formation and survival around the intermediate-mass progenitors of the more massive white dwarfs. In this scenario, we find an upper limit on the polluted white dwarf mass of $M_{\rm wd}<0.72^{+0.07}_{-0.03}$ M$_{\odot}$. This implies an empirical maximum progenitor mass of $M_{\rm ZAMS}^{\rm max}=2.9^{+0.7}_{-0.3}$ M$_{\odot}$. This value is consistent with the maximum reliable host star mass of currently known exoplanet systems. We conclude by imposing these two results on the sample of He-atmosphere white dwarfs within 40\,pc. We find that both scenarios are capable of providing a consistent solution to the full sample of H- and He-atmosphere white dwarfs.