0 White dwarfs accreting the remnants of evolved planetary systems have recently been confirmed as a new class of X-ray source using Chandra. This is the first direct evidence that these degenerate stars are actively accreting the remains of the planetary systems that orbit them. Metals from accreted planetary remnants have been identified in thousands of white dwarfs but inferring accretion rates and parent body compositions depends on accurate white dwarf atmospheric models. The inferred accretion rate is always averaged over the diffusion timescale which can range from days to millions of years. This hampers any search for variability in the accretion rate. The discovery of X-rays produced from the accretion of planetary debris provides the first independent measurement of the accretion rate of these systems, enabling a measurement of the instantaneous accretion rate. We propose to exploit HST to search for long-term variations in the inferred accretion rate of the only system with a measured X-ray accretion rate detected to date, G29-38. This object is one of the closest metal-polluted white dwarfs, has a diffusion timescale of approximately one year and ongoing X-ray monitoring, which makes it the stand-out target for this study. We propose multi-cycle observations (2 orbits in each of the next 3 cycles) with COS to search for variability in the metal absorption (and emission) lines as a proxy for accretion rate. The COS observations will be obtained using the G130M grating centered at 1300\,\AA, providing a wavelength coverage 1140--1440\,\AA, an identical setup to the existing sets of COS observations, in order to allow the best chance to detect photospheric abundance variations of Si, C, Fe, and O. From the publicly available 2010 and 2021 COS observations, we measured a Si abundance of $\mathrm{[Si/H]}$=$-5.32\pm0.1$ and $-5.50 \pm 0.1$, respectively, and a C abundance of $\mathrm{[C/H]}$=$-6.71\pm0.1$ and $-6.52 \pm 0.1$, respectively. In order to interpret the Chandra observations, contemporaneous COS observations are essential to establish the photospheric abundance baseline. Combined with the two archival epochs, our observations will provide three additional epochs which will be sufficient to probe variations on yearly timescales. The proposed multi-epoch observations will ensure a S/N\,$>$\,30. This will yield a 10\% precision on Si and C abundances, allowing to compare against the independent measurement of accretion rate provided by X-ray (\textit{Chandra}) observations. As the pulsation periods of G29-38 span $\simeq$110--1240\,s, every HST orbit will cover at least two cycles of all the excited pulsation modes. We therefore request two orbits per cycle in order to average over four of the longest pulsation periods. The high S/N of the proposed observations of G29-38 will provide accurate, multi-epoch abundances of C, O, Si, and Fe, and be sensitive to S, P, Al, Cr, Mn, and Ni. An inferred accretion rate at each epoch will be computed by coupling these measured abundances to state-of-the-art WD atmosphere models of metal diffusion \cite{cunningham19,koester2020}. The detailed time-dependent knowledge of the atomic composition of the debris disk at G29-38 will be a critical input for the mineralogical modeling of the JWST NIRSpec+MIRI spectroscopy of the dust that will be obtained in the Cycle 4 program. T. Cunningham, P.-E. Tremblay, O. F. Toloza Castillo and D. Koester have extensive expertise on white dwarf model atmospheres, metal lines, 3D radiation-hydrodynamics, accretion-diffusion of planetesimals, and convective overshoot. Together their model atmospheres have been used by the vast majority of the white dwarf community. T. Cunningham, P. Wheatley and G. King have led analysis of X-ray (Chandra) observations of this system. D. Veras is an expert on evolved planetary systems and the sources of white dwarf pollution. B. Gaensicke, has led various HST COS observing programs of white dwarfs with metal pollution, including determination of average accretion rates. I. Caiazzo has expertise with spectroscopic and photometric observations of white dwarfs. Exoplanets and Exoplanet Formation Stellar Physics and Stellar Types 6 false true false false false false false SUPPORTED STAR DA ZZ CETI STAR NO This object was generated by the targetselector and retrieved from the SIMBAD database. All values re-entered from SIMBAD for the 2016 epoch, and double-checked in the ESA Gaia Archive. J2000 J2000 COS/FUV Spectroscopic No No G130M 1291 1787842086211 The scheduling data was generated by CASM 34.2. 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