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Metal pollution of the solar white dwarf by solar system small bodies

White dwarfs (WDs) often show metal lines in their spectra, indicating accretion of asteroidal material. Our Sun is to become a WD in several Gyr. Here, we examine how the solar WD accretes from the three major small body populations: the main belt asteroids (MBAs), Jovian trojan asteroids (JTAs), and trans-Neptunian objects (TNOs). Owing to the solar mass loss during the giant branch, 40\% of the JTAs are lost but the vast majority of MBAs and TNOs survive. During the WD phase, objects from all three populations are sporadically scattered onto the WD, implying ongoing accretion. For young cooling ages $\lesssim 100$ Myr, accretion of MBAs predominates; our predicted accretion rate $\sim10^6$ g/s falls short of observations by two orders of magnitude. On Gyr timescales, thanks to the consumption of the TNOs that kicks in $\gtrsim 100$ Myr, the rate oscillates around $10^6-10^7$ g/s until several Gyr and drops to $\sim10^5$ g/s at 10 Gyr. Our solar WD accretion rate from 1 Gyr and beyond agrees well with those of the extrasolar WDs. We show that for the solar WD, the accretion source region evolves in an inside-out pattern. Moreover, in a realistic small body population with individual sizes covering a wide range as WD pollutants, the accretion is dictated by the largest objects. As a consequence, the accretion rate is lower by an order of magnitude than that from a population of bodies of a uniform size and the same total mass and shows greater scatter.