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The polluted white dwarf (WD) system SDSS J122859.93+104032.9 (SDSS J1228) shows variable emission features interpreted as originating from a solid core fragment held together against tidal forces by its own internal strength, orbiting within its surrounding debris disk. Estimating the size of this orbiting solid body requires modeling the accretion rate of the polluting material that is observed mixing into the WD surface. That material is supplied via sublimation from the surface of the orbiting solid body. The sublimation rate can be estimated as a simple function of the surface area of the solid body and the incident flux from the nearby hot WD. On the other hand, estimating the accretion rate requires detailed modeling of the surface structure and mixing in the accreting WD. In this work, we present MESA WD models for SDSS J1228 that account for the thermohaline instability and mixing in addition to heavy element sedimentation to constrain accurately the sublimation and accretion rate necessary to supply the observed pollution. We derive a total accretion rate of M ̇ acc = 1.8 × 10 11 g s − 1 , several orders of magnitude higher than the M ̇ acc = 5.6 × 10 8 g s − 1 estimate obtained in earlier efforts. The larger mass accretion rate implies that the minimum estimated radius of the orbiting solid body is r min = 72 km, which, although significantly larger than prior estimates, still lies within the upper bounds (a few hundred kilometers) for which the internal strength could no longer withstand the tidal forces from the gravity of the WD. [ABSTRACT FROM AUTHOR]