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This paper reports circular spectropolarimetry and X-ray observations ofseveral polluted white dwarfs including WD 1145+017, with the aim to constrainthe behavior of disk material and instantaneous accretion rates in theseevolved planetary systems. Two stars with previously observed Zeeman splitting,WD 0322-019 and WD 2105-820, are detected above 5 sigma and <Bz> > 1 kG, whileWD 1145+017, WD 1929+011, and WD 2326+049 yield (null) detections below thisminimum level of confidence. For these latter three stars, high-resolutionspectra and atmospheric modeling are used to obtain limits on magnetic fieldstrengths via the absence of Zeeman splitting, finding B* < 20 kG based on datawith resolving power R near 40 000. An analytical framework is presented forbulk Earth composition material falling onto the magnetic polar regions ofwhite dwarfs, where X-rays and cyclotron radiation may contribute to accretionluminosity. This analysis is applied to X-ray data for WD 1145+017, WD1729+371, and WD 2326+049, and the upper bound count rates are modeled withspectra for a range of plasma kT = 1 - 10 keV in both the magnetic andnon-magnetic accretion regimes. The results for all three stars are consistentwith a typical dusty white dwarf in a steady-state at 1e8 - 1e9 g/s. Inparticular, the non-magnetic limits for WD 1145+017 are found to be well belowprevious estimates of up to 1e12 g/s, and likely below 1e10 g/s, thussuggesting the star-disk system may be average in its evolutionary state, andonly special in viewing geometry.

Magnetism, X-rays, and Accretion Rates in WD 1145+017 and other Polluted White Dwarf Systems