# New chondritic bodies identified in eight oxygen-bearing white dwarfs

Alexandra E. Doyle Earth, Planetary, and Space Sciences, University of
California, Los Angeles, Los Angeles, CA 90095, USA  Beth L. Klein Department
of Physics and Astronomy, University of California, Los Angeles, CA
90095-1562, USA  Patrick Dufour Institut de Recherche sur les Exoplanètes
(iREx), Université de Montréal, Montréal, QC H3C 3J7, Canada  Département de
Physique, Université de Montréal, Montréal, QC H3C 3J7, Canada  Carl Melis
Center for Astrophysics and Space Sciences, University of California, San
Diego, CA 92093-0424, USA  B. Zuckerman Department of Physics and Astronomy,
University of California, Los Angeles, CA 90095-1562, USA  Siyi Xu Gemini
Observatory/NSF’s NOIR Lab, Hilo, HI, 96720, USA  Alycia J. Weinberger Earth
and Planets Laboratory, Carnegie Institution for Science, 5241 Broad Branch Rd
NW, Washington, DC 20015, USA  Isabella L. Trierweiler Earth, Planetary, and
Space Sciences, University of California, Los Angeles, Los Angeles, CA 90095,
USA  Department of Physics and Astronomy, University of California, Los
Angeles, CA 90095-1562, USA  Nathaniel N. Monson  Earth, Planetary, and Space
Sciences, University of California, Los Angeles, Los Angeles, CA 90095, USA
Michael A. Jura∗ Department of Physics and Astronomy, University of
California, Los Angeles, CA 90095-1562, USA  Edward D. Young Earth, Planetary,
and Space Sciences, University of California, Los Angeles, Los Angeles, CA
90095, USA

###### Abstract

We present observations and analyses of eight white dwarf stars that have
accreted rocky material from their surrounding planetary systems. The spectra
of these helium-atmosphere white dwarfs contain detectable optical lines of
all four major rock-forming elements (O, Mg, Si, Fe). This work increases the
sample of oxygen-bearing white dwarfs with parent body composition analyses by
roughly thirty-three percent. To first order, the parent bodies that have been
accreted by the eight white dwarfs are similar to those of chondritic
meteorites in relative elemental abundances and oxidation states. Seventy-five
percent of the white dwarfs in this study have observed oxygen excesses
implying volatiles in the parent bodies with abundances similar to those of
chondritic meteorites. Three white dwarfs have oxidation states that imply
more reduced material than found in CI chondrites, indicating the possible
detection of Mercury-like parent bodies, but are less constrained. These
results contribute to the recurring conclusion that extrasolar rocky bodies
closely resemble those in our solar system, and do not, as a whole, yield
unusual or unique compositions.

00footnotetext: Deceased

##  1 Introduction

Categorization of the compositions of rocky exoplanets, and evaluation of
their similarities to or differences from rocky bodies in our solar system, is
a challenging and flourishing area of study. To this end, many studies have
characterized exoplanet compositions using stellar spectroscopy of FGK, or
Sun-like, stars (e.g., Unterborn & Panero, 2019; Adibekyan et al., 2021;
Kolecki & Wang, 2022) in combination with planetary mass-radius relations. An
alternative approach is to use white dwarf stars (WDs) – stars in the last
stage of stellar evolution – that have been “externally-polluted” by accretion
of rocky bodies from their surrounding planetary systems. Owing to their
strong gravitational acceleration, the atmospheres of WDs are typically devoid
of elements heavier than helium. The heavy elements sink out of the observable
atmosphere on timescales of days to millions of years (Koester, 2009),
depending on the atmospheric temperature and dominant constituent (H or He).
Because of the relatively short settling timescales of heavy elements,
externally-polluted WDs must have acquired their heavy elements relatively
recently compared to their lifetimes. Radiative levitation as a mechanism to
maintain heavy elements in a white dwarf atmosphere (e.g., Chayer et al.,
1995) is not effective for the white dwarfs presented herein (helium
atmosphere WDs with effective temperatures cooler than 20,000K).

WDs for which hydrogen presents the strongest spectral line are referred to as
‘DAs’ and neutral helium as ‘DBs.’ If a spectrum displays both H I and He I
lines, the spectral type can be either DAB or DBA depending on whether H or
He, respectively, has the strongest optical absorption line. White dwarfs are
deemed polluted if any element heavier than He is detected in their
atmosphere; following Sion et al. (1983) and Wesemael et al. (1993), we denote
external-pollution with a ‘Z’ in the spectral classifications.

We now understand that these polluted WDs, constituting 25-50% of all WDs,
accrete material from the planets, asteroids, and comets that orbited the host
star and were subsequently scattered toward the star by the post-main sequence
evolution (Debes & Sigurdsson, 2002; Jura, 2003; Zuckerman et al., 2003, 2010;
Koester et al., 2014; Veras, 2016). Observations of transiting debris from
planetary material that has been tidally disrupted by the WD (Vanderburg et
al., 2015; Xu et al., 2016; Vanderbosch et al., 2020; Guidry et al., 2021;
Vanderbosch et al., 2021) suggest the presence of a body in the process of
being pulverized and accreted by the WD, thus substantiating our understanding
of the source of pollution. Analyses of polluted WDs to evaluate the
compositions of extrasolar rocky bodies have proliferated in the last decade
(e.g., Zuckerman et al., 2007; Klein et al., 2010; Vennes et al., 2010; Melis
et al., 2011; Farihi et al., 2011; Zuckerman et al., 2011; Jura et al., 2012;
Dufour et al., 2012; Gänsicke et al., 2012; Jura & Young, 2014; Xu et al.,
2017; Harrison et al., 2018; Hollands et al., 2018; Doyle et al., 2019; Swan
et al., 2019; Bonsor et al., 2020; Buchan et al., 2022).

To date, the parent bodies being accreted by polluted WDs mostly resemble dry,
rocky bodies similar in size and general composition to asteroids in the solar
system. However, a few water-rich bodies (Farihi et al., 2011, 2013; Raddi et
al., 2015; Hoskin et al., 2020; Klein et al., 2021), including a Kuiper Belt
analog (Xu et al., 2017), have been discovered. Additionally, parent bodies
that resemble giant planets (Gänsicke et al., 2019) and icy moons (Doyle et
al., 2021) have been argued. While just a few dozen WDs are ‘heavily’
polluted, with more than a few rock-forming elements detected, taken together,
23 distinct elements have been detected in polluted WDs (see Table 1 of Klein
et al., 2021). Compositional variations due to igneous differentiation– with
compositions that range from crust-like to core-like – have been identified
(e.g. Zuckerman et al., 2011; Melis et al., 2011; Gänsicke et al., 2012; Jura
& Young, 2014; Melis & Dufour, 2017; Putirka & Xu, 2021; Hollands et al.,
2021; Johnson et al., 2022).

In this work we present new observations of eight heavily polluted DB WDs and
examine the compositions of the accreting rocky parent bodies. We focus on
evaluating these bodies through bulk composition and oxidation state. In
addition to Ca and the four major rock-forming elements (O, Mg, Si, and Fe),
instances of additional elements (e.g., Al, Cr, and Ti) have been detected in
some of the WDs. These new data increase the sample of oxygen-bearing WDs with
parent body composition analyses by $\thicksim$ 33%. This paper is organized
as follows: in Section 2 we list our target selection and observations for the
WDs described. Our atmosphere models are described in Section 3 along with
spectra of the detected major rock-forming elements. Section 4 provides an
analysis of the parent body compositions and in Section 5 we summarize our
findings.

Figure 1: $T_{\rm eff}$ as a function of GALEX colors. Here we show the Gaia
WD candidates from Gentile Fusillo et al. (2019) that have both far-UV (FUV)
and near-UV (NUV) GALEX data, which reveals a distinct dichotomy between DA
and DB WDs. The subset of polluted helium-dominated atmospheres from this work
is represented as red circles. The red curve is our constructed “cut
function,” which we use to assign likely dominant elements based on the
location of the WD parameters on this figure (see also Equation 1).

##  2 Observations

###  2.1 Target Selection

In this paper we focus on eight DB WDs (Table 1). In each of these WDs, all
four major rock-forming elements (O, Mg, Si, Fe) are detected.

Three out of eight WDs in this work have been observed over the years by
members of our team. In particular we obtained HIRES spectra of WD1244$+$498
and SDSSJ1248$+$1005 because they were previously identified as DBZs in SDSS
spectra (Kleinman et al., 2013; Koester & Kepler, 2015), and WD1415$+$234 was
followed up at high resolution due to the possible appearance of a Ca II K
line in Limoges & Bergeron (2010).

The other five WDs were identified in a search for heavily polluted WDs (Melis
et al., 2018). We compiled our list of targets by utilizing the sample of
probable WDs from Gentile Fusillo et al. (2019), which calculates stellar
parameters and the probability of an object being a WD based on fits to Gaia
DR2 data.

Table 1: WD Observation Data

Name | UT Date | Instrument | Coverage (Å) | Int. Time (sec) | SNRa
---|---|---|---|---|---
GaiaJ0218$+$3625 | 2021/08/31 | HIRES (blue) | 3115$-$5950 | 3600 | 43
| 2020/10/08 | HIRES (blue) | 4000$-$5950 | 2000$\times$2 | 7bc
| 2019/07/16 | HIRES (red) | 4715$-$8995 | 3300 | 33
| 2018/12/30 | Kast | 3420$-$5485, 5590$-$7840 | 3300 | 62
WD1244$+$498 | 2018/05/18 | HIRES (blue) | 3115$-$5950 | 2000 | 24
| 2015/04/09 | HIRES (red) | 4715$-$8995 | 1800$\times$2 | 39b
| 2010/03/28 | HIRES (blue) | 3115$-$5950 | 3000 | 25
SDSSJ1248$+$1005 | 2015/04/09 | HIRES (red) | 4715$-$8995 | 3000$\times$2 | 24b
| 2014/05/22 | HIRES (blue) | 3115$-$5950 | 3000$\times$3 | 32b
WD1415$+$234 | 2019/07/16 | HIRES (red) | 4715$-$8995 | 3300 | 43
| 2016/04/01 | HIRES (blue) | 3115$-$5950 | 2400$\times$2 | 40b
| 2015/04/25 | ESI | 3900$-$10900 | 1180$\times$2 | 25b
SDSSJ1734$+$6052 | 2019/09/07 | HIRES (red) | 4715$-$8995 | 3600 | 29
| 2019/07/16 | HIRES (red) | 4715$-$8995 | 3300 | 34
| 2019/07/07 | HIRES (blue) | 3115$-$5950 | 3300 | 27
| 2019/05/29 | Kast | 3415$-$5480, 6420$-$8790 | 3900 | 28
GaiaJ1922$+$4709 | 2020/10/07 | HIRES (red) | 4715$-$8995 | 3600 | 37
| 2020/06/14 | HIRES (blue) | 3115$-$5950 | 3000 | 28
| 2019/12/09 | HIRES (red) | 4715$-$8995 | 3600 | 26
| 2019/10/12 | Kast | 3420$-$5485, 6400$-$8800 | 3000 | 42
EC22211$-$2525 | 2021/08/31 | HIRES (blue) | 3115-5950 | 3300 | 40
| 2020/10/07 | HIRES (red) | 4715$-$8995 | 3600 | 46
| 2019/07/07 | HIRES (blue) | 3115$-$5950 | 3300 | 38
| 2019/07/03 | MagE | 3065$-$9470 | 1200$\times$2 | 78b
| 2018/12/12 | Kast | 3450$-$5475, 5590$-$7840 | 2700 | 17
SDSSJ2248$+$2632 | 2019/09/07 | HIRES (red) | 4715$-$8995 | 3300 | 38
| 2019/07/16 | HIRES (red) | 4715$-$8995 | 3300 | 43
| 2019/07/07 | HIRES (blue) | 3115$-$5950 | 3000 | 36
| 2017/12/11 | Kast | 3430$-$5500, 5625$-$7820 | 3600 | 62

a Signal-to-noise-ratio (SNR) measured at 3445Å for HIRES (blue), 5195Å for
HIRES (red), 5160Å for MagE, 5100Å for Kast, and 6000Å for ESI
b SNR for combined exposures
c Only CCDs 2 and 3 were used in our analysis

To focus on finding DB WDs, we compared GALEX colors (Bianchi et al., 2017) to
effective temperature ($T_{\rm eff}$) (Figure 1). Differences in opacity of DA
and DB WDs have a salient effect on emergent fluxes, particularly at UV
wavelengths as observed with GALEX. These colors reveal a distinct dichotomy
between DA and DB WDs (e.g. Bergeron et al., 2019). We constrained Gaia WD
candidates from Gentile Fusillo et al. (2019) to include only those where Gmag
$<$ 17.0, distance $<$ 300 pc, and far-UV (FUV) and near-UV (NUV) GALEX data
exist, (see Figure 1). Known characterizations of each WD are labeled as
either green squares (DAs) or blue triangles (DBs), and unconfirmed WD
candidates are labeled as gray circles. The polluted DBs analyzed in this
paper are represented as red circles.

To process these data for our purposes, we constructed a “cut function” (red
curve in Figure 1) with the equation

$T_{\rm eff,cut}=28000\exp\left({-\left(\frac{{\rm FUV-
NUV}+0.24}{2}\right)^{1/3}}\right),$ (1)

that applies for $12000<T_{\rm eff}<24000$. We used equation 1 to flag points
as “likely DBs” where $T_{\rm eff}>T_{\rm eff,cut}$ (above the red curve in
Figure 1) and those where $T_{\rm eff}<T_{\rm eff,cut}$ as “likely DAs” (below
the red curve, Figure 1). This allowed us to specifically target WDs that fell
within the range of known DBs. This particular selection method for observing
WDs led to the discovery of many of the polluted DB WDs in this study, as well
as others to be published in future studies.

###  2.2 Instrument Setup

Table 1 lists our target WDs along with their observation dates, instruments,
and resulting data properties. We describe each instrument and observational
setup in more detail below.

####  2.2.1 KAST

Our large-scale survey to search for heavily polluted WDs from Gaia DR2 WD
candidates (described in Section 2.1 and Melis et al. 2018) utilized the KAST
Spectrograph on the 3m Shane telescope at Lick Observatory. Our standard setup
implemented the d57 dichroic, which split blue light through the 600/4310
grism and red light through the 830/8460 grating. This setup provides a
resolving power (R = $\lambda$/$\Delta\lambda$) for a 2″ slit in blue and red
of R = 950 and 1,500, respectively, and wavelength coverage from 3450-7800 Å.
Where indicated in Table 1, we implemented another version of our setup which
tilted the 830/8460 grating to cover redder wavelengths and specifically the
Ca infrared triplet ($\lambda$ 8498/8542/8662 Å) resulting in red arm
wavelength coverage from 6440$-$8750 Å. For both setups, we used slit widths
of 1, 1.5, or 2″ and integration times from 45$-$60 minutes depending on
observing conditions and target brightness. The data were reduced using
standard IRAF routines, including bias subtraction, flat-fielding, wavelength
calibration using arc lamps, and instrumental response calibration using
observations of standard stars (Tody, 1986). Signal-to-noise-ratios (SNRs) for
the resulting spectra are measured at 5100Å and reported in Table 1.

####  2.2.2 MagE

Moderate resolution optical spectra of EC22211$-$2525 were acquired with the
Magellan Echellette (MagE) spectrograph on the Magellan 1 (Baade) telescope at
Las Campanas Observatory on 2019 July 03. EC22211$-$2525 was observed through
the 0.5″ slit providing a resolving power of R $\simeq$ 7,500. Data reduction
was performed with the Carnegie Python pipeline (Kelson et al., 2000; Kelson,
2003) and SNR measurements were made at 5160 Å.

####  2.2.3 ESI

We used the Echellette Spectrograph and Imager (ESI) on the Keck II Telescope
at Maunakea Observatory (Sheinis et al., 2002) to obtain a spectrum for
WD1415$+$234\. ESI data were taken with a 0.3″slit providing a resolving power
of R $\simeq$ 13,000. Data were reduced using MAKEE and IRAF, similar to the
HIRES reduction process described in Klein et al. (2010). SNR for the
resulting combined spectrum was $\thicksim$ 25, measured at 6000Å.

####  2.2.4 HIRES

We used HIRES on the Keck I Telescope at Maunakea Observatory (Vogt et al.,
1994) to obtain higher resolution spectra for each of the eight WDs in this
sample. HIRES data were taken with the C5 decker (slit width 1.148″) for a
resolving power of R $\simeq$ 37,000 and resulting in wavelength coverage of
3115-5950 Å with the blue collimator and 4715-8995 Å with the red collimator.
Exposure times ranged from 30$-$60 minutes and depended on observing
conditions and target brightness. Data were reduced using either the MAKEE
software package with IRAF continuum normalization or IRAF reduction routines
(see Klein et al. 2010 for more details on the methods and routines used). The
SNR for the resulting spectra were measured at 3445Å for HIRES blue and 5195Å
for HIRES red, and are displayed in Table 1.

Table 2: WD Parameters  WD | RA | Dec | G | D | Teff |  logg |  H$\alpha$ |  H$\alpha$ |  H$\alpha$ | CaK | CaK | CaK | Spectral
---|---|---|---|---|---|---|---|---|---|---|---|---|---
Name | (J2000) | (J2000) | (mag) | (pc) | (K) | (cgs) | EW | depth | depth | EW | depth | depth | Type
|  |  |  |  |  |  | (mA) | HIRES | lowres | (mA) | HIRES | lowres |
GaiaJ0218+3625 | 02 18 16.64 | +36 25 07.6 | 16.4 | 116 | 14700 | 7.86 | 475 | 0.10 | 0.06 | 595 | 0.65 | 0.13 | DBZA
WD1244+498 | 12 47 03.28 | +49 34 23.5 | 16.6 | 120 | 15150 | 7.97 | 1600 | 0.26 | 0.16 | 664 | 0.67 | 0.20 | DBAZ
SDSSJ1248+1005 | 12 48 10.23 | +10 05 41.2 | 17.4 | 164 | 15180 | 8.11 | 1750 | 0.28 | 0.17 | 1245 | 0.66 | 0.39 | DBAZ
WD1415+234 | 14 17 55.37 | +23 11 36.7 | 16.6 | 127 | 17300 | 8.17 | 1150 | 0.23 | 0.15 | 274 | 0.63 | 0.07 | DBAZ
SDSSJ1734+6052 | 17 34 35.75 | +60 52 03.2 | 16.9 | 150 | 16340 | 8.04 | 2000 | 0.25 | 0.21 | 256 | 0.67 | 0.08 | DBAZ
GaiaJ1922+4709 | 19 22 23.41 | +47 09 45.4 | 16.6 | 127 | 15500 | 7.95 | 510 | 0.16 | 0.08 | 528 | 0.57 | 0.18 | DBZA
EC22211$-$2525 | 22 23 58.39 |  $-$25 10 43.6 | 16.3 | 109 | 14740 | 7.89 | 1500 | 0.24 | 0.22 | 710 | 0.68 | 0.17 | DBAZ
SDSSJ2248+2632 | 22 48 40.93 | +26 32 51.6 | 16.4 | 123 | 17370 | 8.02 | 750 | 0.18 | 0.15 | 169 | 0.55 | 0.07 | DBAZ

##  3 Data Analysis

###  3.1 Spectral Typing

WD spectral types are established according to the appearance of their optical
spectra and do not always reflect the dominant atmospheric composition (e.g.
GD 16 and GD 362, Koester et al., 2005; Zuckerman et al., 2007). A colleague
prudently pointed out, “Annie Jump Cannon was prophetical when she made it
clear that stellar spectral types should never have physical interpretations,
because she realized models would change but spectral morphology would be
static for a given type” (J. Farihi 2022, private communication).

Three stars in our sample (WD1244+498, SDSSJ1248+1005, WD1415+234) were
previously known WDs; the other five are newly identified in this work. In all
cases, as of the date of this publication, the spectral types in SIMBAD are
either absent or need updating.

In trying to determine the appropriate spectral types for this set of WDs, we
ran into a matter that requires some clarification. In all these spectra, the
He I lines are clearly the dominant optical features: He I $\lambda$5876 Å
equivalent widths (EWs) range from 5-14 Å, and line depths (as defined in
Table 2 note) range from 0.34-0.48, with little depth difference between low
and high resolution spectra. Thus the primary spectral type begins with ‘DB’
in each case (Table 2). However, since each WD also displays H$\alpha$ and
high-Z lines, the question is how to distinguish whether the secondary type
should be DBZA or DBAZ? The paradigm established in Sion et al. (1983) and
Wesemael et al. (1993) states that the spectral type is defined in order of
the “strongest” optical spectral features, but no further definition is given
as to what exactly that means. It is ambiguous whether “strongest” refers to
the equivalent width or the line depth. These comparisons can be substantially
different depending on the instrument spectral resolution, especially for Ca
II $\lambda$3933.663 Å (CaK), which is typically the high-Z line with the
largest EW in our temperature range (Teff $<$ 18,000 K). To illustrate this
point, we list the CaK and H$\alpha$ line depths measured at both higher
resolution (R $\sim$ 37,000) and lower resolution (R $\sim$ 1000), as well as
their EWs in Table 2.

If all we had were low resolution spectra, and if we chose to assign secondary
spectral types by line depth, then four of the WDs would be DBZA and four
DBAZ. But then when those same WDs are observed at high resolution, according
to line depth, the four previous DBAZs would all change to DBZAs. Instead, we
decided to assign the spectral type according to EW: DBAZ if EW(H$\alpha$) $>$
EW(CaK), and DBZA if EW(CaK) $>$ EW(H$\alpha$). As long as spectra have
sufficient signal-to-noise to detect a given line, EW measurements are
essentially independent of the instrument resolution, and thus our choice of
spectral type should be enduring.

###  3.2 Stellar Parameters

The effects of additional opacity from the presence of hydrogen and heavier
elements in the atmospheres of He-dominated WDs with effective temperatures
($T_{\rm eff}$) $<$ 20,000 K have been well described (Dufour et al., 2007,
2010; Coutu et al., 2019).

We follow an iterative procedure to obtain atmospheric parameters for each
target. First, we get a rough estimate for $T_{\rm eff}$ and gravity ( log
$g$) by fitting photometry (typically Sloan Digital Sky Survey (SDSS), but
PanSTARRS was used for EC22211$-$2525). We then fit the Ca II K (CaK) region
and H$\alpha$ from low resolution spectra concurrently with SDSS ugriz
photometry (Alam et al., 2015) or PanSTARRS grizy photometry (Flewelling et
al., 2020) and Gaia parallax (Gaia Collaboration et al., 2016, 2021). Where
available (Table 1) we use KAST spectra, otherwise we use SDSS spectra.
Atmospheric structure calculations are then informed by the hydrogen abundance
by number, n, (log $n$(H)/$n$(He)) and heavy element presence when scaling
elements to the number abundance of Ca in a CI chondrite (Lodders, 2019).

We compared our fits to Gaia and GALEX photometry to confirm good agreement
(see Figure A1); standard de-reddening corrections were applied as described
in Coutu et al. (2019). Our best-fit parameters are given in Table 2. We use
these parameters to calculate the model atmospheres from which we produce
synthetic spectra for each WD.

Figure 2: Selected lines for each of the WDs in this study, displaying the
detected O triplet and example lines for Mg, Si, Ca and Fe. Wavelengths are in
air and shifted to the laboratory frame of rest. The red line is our best-fit
model. Figure 2 (cont.): Selected lines for each of the WDs in this study,
displaying the detected O triplet and example lines for Mg, Si, Ca and Fe.
Wavelengths are in air and shifted to the laboratory frame of rest. The red
line is our best-fit model. Table 3: Observed Atmospheric Elemental Abundances

Name | log($n$(H)/$n$(He)) | log($n$(Be)/$n$(He)) | log($n$(O)/$n$(He)) | log($n$(Na)/$n$(He)) | log($n$(Mg)/$n$(He))
---|---|---|---|---|---
GaiaJ0218+3625 | $-6.03\pm 0.15$ | $<-11.0$ | $-5.53\pm 0.15$ | $-7.11\pm 0.15$ | $-6.64\pm 0.15$
WD1244+498 | $-5.12\pm 0.15$ | $<-11.0$ | $-5.77\pm 0.15$ |  | $-6.79\pm 0.15$
SDSSJ1248+1005 | $-5.18\pm 0.15$ | $<-11.0$ | $-5.44\pm 0.15$ |  | $-6.40\pm 0.15$
WD1415+234 | $-4.92\pm 0.15$ | $<-11.0$ | $-5.59\pm 0.15$ |  | $-5.82\pm 0.17$
SDSSJ1734+6052 | $-4.76\pm 0.15$ | $<-10.3$ | $-5.93\pm 0.15$ |  | $-6.62\pm 0.15$
GaiaJ1922+4709 | $-5.66\pm 0.15$ | $<-10.4$ | $-5.51\pm 0.15$ |  | $-6.14\pm 0.15$
EC22211$-$2525 | $-5.56\pm 0.15$ | $<-11.0$ | $-5.76\pm 0.15$ |  | $-6.52\pm 0.15$
SDSSJ2248+2632 | $-5.12\pm 0.15$ | $<-10.5$ | $-5.94\pm 0.15$ |  | $-6.52\pm 0.15$
Name | log($n$(Al)/$n$(He)) | log($n$(Si)/$n$(He)) | log($n$(Ca)/$n$(He)) | log($n$(Ti)/$n$(He)) | log($n$(Cr)/$n$(He))
GaiaJ0218+3625 | $-7.3\pm 0.2$ | $-6.50\pm 0.15$ | $-7.81\pm 0.21$ | $-9.43\pm 0.15$ | $-8.68\pm 0.15$
WD1244+498 |  | $-6.92\pm 0.15$ | $-7.79\pm 0.17$ | $-9.34\pm 0.15$ | $-8.78\pm 0.16$
SDSSJ1248+1005 |  | $-6.65\pm 0.15$ | $-7.22\pm 0.17$ | $-8.80\pm 0.15$ | $-8.41\pm 0.15$
WD1415+234 |  | $-6.25\pm 0.18$ | $-7.40\pm 0.15$ |  | $-7.81\pm 0.15$
SDSSJ1734+6052 |  | $-6.93\pm 0.15$ | $-7.83\pm 0.17$ |  |
GaiaJ1922+4709 | $-6.9\pm 0.2$ | $-6.02\pm 0.15$ | $-7.53\pm 0.15$ | $-9.05\pm 0.15$ | $-8.30\pm 0.15$
EC22211$-$2525 | $-7.7\pm 0.3$ | $-6.67\pm 0.15$ | $-7.85\pm 0.20$ | $-9.60\pm 0.15$ | $-8.79\pm 0.15$
SDSSJ2248+2632 |  | $-6.83\pm 0.15$ | $-7.45\pm 0.23$ |  |
Name | log($n$(Mn)/$n$(He)) | log($n$(Fe)/$n$(He)) |  |  |
GaiaJ0218+3625 | $-8.84\pm 0.15$ | $-6.85\pm 0.15$ |  |  |
WD1244+498 |  | $-6.58\pm 0.15$ |  |  |
SDSSJ1248+1005 |  | $-6.63\pm 0.15$ |  |  |
WD1415+234 |  | $-5.89\pm 0.15$ |  |  |
SDSSJ1734+6052 |  | $-6.85\pm 0.15$ |  |  |
GaiaJ1922+4709 |  | $-5.88\pm 0.15$ |  |  |
EC22211$-$2525 |  | $-6.84\pm 0.15$ |  |  |
SDSSJ2248+2632 |  | $-7.10\pm 0.27$ |  |  |

Note. — $\rm{G}_{mag}$ and distances (calculated from parallaxes) are from
Gaia EDR3 (Gaia Collaboration et al., 2016, 2021). $\it{T}_{\rm eff}$ and logg
are fit as described in Section 3.2. Typical uncertainties for $\it{T}_{\rm
eff}$ and logg are $\pm$500K and $\pm$0.05, respectively. “lowres” refers to
either SDSS or Kast spectra. Line “depth” is the position of the line center
between the continuum and zero, measured as the fractional distance below the
continuum. Spectral Type assignments are based on equivalent widths (EWs) of
Ca II K (CaK) and H$\alpha$ as described in Section 3.1.

Note. — Abundances by number, n, relative to He and uncertainties for each of
the WDs in this work. Where statistical uncertainties are small ($<$0.15 dex),
we conservatively set them to 0.15 dex. We have included upper limits on Be
abundances, which demonstrate that Be is not detected at the greatly elevated
levels seen in two WDs in Klein et al. (2021). We list observed lines used for
these abundance determinations in Table A2.

###  3.3 Abundance Measurements

Over a series of multiple iterations, we fit these synthetic spectra to the
HIRES data until we find a best-fit abundance solution for each element
detected (Table 3). We show a sample of WD spectral lines for detections of O,
Mg, Si, Fe, and Ca (Figure 2). In each panel our spectra are shown in black,
and our best-fit model is overlain in red, and the numerical average abundance
is given at the bottom of each panel. Our sample of eight WDs have clear
detections of O (7772 Å, multiplet), Mg (4481Å, multiplet), Si (6347Å), Fe
(5169Å), and Ca (3933Å and 8542Å), as well as other detected lines. Measured
radial velocities (RVs) and a full listing of all detected lines with their
EWs are given in the Appendix Tables A1 and A2, respectively. We also discuss
some detections of non-photospheric lines in the Appendix and Table A1.

Abundances are reported by number, n, relative to He along with uncertainties
for each of the WDs in Table 3. Where elements are detected through multiple
lines, we take the average abundance. Uncertainties are measured as the
standard deviation where there are multiple lines of the same element.
Systematic uncertainties, such as from uncertain atomic data (Vennes et al.,
2011; Gänsicke et al., 2012), or other missing physics in atmosphere models
(e.g. Klein et al., 2020; Cukanovaite et al., 2021) are difficult to quantify.
Therefore, where only one line of an element is observed or where
uncertainties are smaller than 0.15 dex, we conservatively set them to 0.15
dex.

##  4 Discussion

###  4.1 Accretion and Diffusion

Three phases of accretion and diffusion of planetary debris onto a WD are
commonly recognized in the literature: the buildup phase, sometimes referred
to as an “increasing” phase, the steady-state phase, and the settling, or
“decreasing” phase (e.g., Dupuis et al., 1992; Koester, 2009). Though the
specific nomenclature varies, the idea remains the same: as a single parent
body accretes onto a WD, the observed pollution will first increase as
material accumulates in the WD atmosphere. Then, as material begins to sink
through the atmosphere, a steady state is eventually reached between accretion
and diffusive settling. Steady state is achieved on a timescale comparable to
a few e-folding times for settling. Once the parent body source is depleted,
material ceases to accrete, and the observed pollution decreases commensurate
with the settling times of the individual elements.

The correction for this effect during steady-state accretion is straight
forward $-$ element ratios are multiplied by the inverse ratio of settling
timescales; see Equation 7 in Koester (2009) and settling timescales in Table
A3.

While it is not clear which accretion state WDs exist in, ongoing accretion
can be assumed for WDs with observed infrared excess, which emerge where
circumstellar debris disks thermally reprocess the light from the star (Jura,
2003). EC22211-2525 is the only WD in the sample with detected infrared excess
(Lai et al., 2021), as can be seen in Figure A1.

Figure 3: Element/magnesium atomic ratios, $z$/Mg, for the parent body
accreted by WD1244$+$498, assuming an increasing phase, relative to $z$/Mg in
various rocks found in our solar system. We compare the calculated parent body
elemental abundances accreted by WD1244$+$498 to CI chondrite (orange,
Lodders, 2019), bulk silicate Earth (BSE) (red, McDonough, 2003), and the
Earth’s continental crust (blue, Rudnick & Gao, 2014). The best match
compositionally for the parent body accreting onto WD1244$+$498 is CI
chondrite. Figure 4: One-to-one comparison of major and minor rock forming
elements (nz), ratioed to Mg (nMg) and CI chondrite (Lodders, 2019) for eight
WDs. Abundances are from Table 3, representative of an increasing phase.
Errors for WDs are propagated from model abundances and uncertainties using a
Monte Carlo approach with a bootstrap of n=1. We report the goodness of fit
using a reduced chi-square statistic, $\chi^{2}_{\nu}$, using the elements Si,
Fe, Ca, Al, Cr, and Ti, where available for each WD (see text), displayed in
the bottom right corner of each plot. Generally, the elemental abundances from
WD data show good agreement with CI chondrites ($\chi^{2}_{\nu,{\rm crit.}}<$
3.5-5.0, depending on which elements are used in the analysis, see text). For
comparison, we calculate $\chi^{2}_{\nu}$ statistics for known compositions of
Earth rocks (bulk Earth (McDonough, 2003), bulk silicate Earth (BSE,
McDonough, 2003), Mid-Ocean Ridge Basalt (MORB, Gale et al., 2013), and the
Earth’s continental crust (Rudnick & Gao, 2014)) compared to CI chondrite.
Bulk Earth and bulk silicate Earth are in good agreement with CI chondrite,
revealing that WD-sized errors in the elements used (Ti, Cr, Ca, Al, Fe, and
Si) are unable to distinguish between the two compositions in the data. Figure
5: As in Figure 4, but assuming steady-state phase (SS) compositions for the
eight WDs presented.

###  4.2 Abundance Pattern

For each of the WDs in this study we compared the observed abundances of rock-
forming elements (Mg, Al, Si, Ca, Ti, Cr, and Fe) to those of typical rocky
compositions in the solar system (CI chondrite, bulk silicate Earth, and
continental crust). In general, the best fit is to CI chondrite. In Figure 3
we illustrate this result using the composition of the parent body polluting
WD1244$+$498 as an example. The parent body is comparable to CI chondrite, as
indicated by the close agreement of chondritic abundances (orange symbols) to
the 1:1 line in Figure 3. Indeed, each element agrees with chondritic
compositions within a factor of 2.

Motivated by Figure 3, we statistically evaluate the hypothesis that the
parent bodies being accreted by these eight WDs were approximately chondritic
in composition. Similar to Xu et al. (2013), Swan et al. (2019), and Doyle et
al. (2021), we compare the goodness-of-fit for rock-forming elemental
abundances observed in each WD to the known composition of CI chondrites using
the reduced chi-square statistic, $\chi^{2}_{\nu}$ (Figure 4). We calculate
$\chi^{2}_{\nu}$ using the elements Al, Si, Ca, Ti, Cr, and Fe, where
available for each WD. Oxygen is excluded due to its correlation with the
other rock-forming elements (see Section 4.4). Additionally, because we ratio
elements to Mg, Mg is not an independent observation for this calculation and
is therefore excluded. The data points and their uncertainties shown in Figure
4 represent propagated uncertainties using a Monte Carlo approach with a
bootstrap of n=1.

The parameter $\alpha$ represents a probability of obtaining $\chi^{2}_{\nu}$
values greater than the observed value by chance. Convention suggests that the
threshold to reject the hypothesis that the data are consistent with a CI
composition is 5% or better, or $\alpha<0.05$ ($\alpha\sim 0.4$ for
$\chi^{2}_{\nu}=1$). Due to the relatively small number of data points per
star, and their uncertainties, the value of $\chi^{2}_{\nu}$ is also
uncertain, which can be accounted for using the approach of Andrae et al.
(2010) in which the uncertainty in $\chi^{2}_{\nu}$ is $\sigma\sim\sqrt{2/N}$
for $N$ data points. Based on a threshold for $\alpha=0.05$ and a 2$\sigma$
error for $\chi^{2}_{\nu}$, we define a critical value, $\chi^{2}_{\nu,{\rm
crit}}$, as the reduced chi-square value corresponding to
$\alpha=0.05+2\sigma$. Based on these critical values, ranging from $3.5$ to
$5.0$, depending on the number of elements involved, the relative elemental
abundances for the polluted WDs examined here are in good agreement with CI
chondrites, with 5 of the 8 WDs having values for $\chi^{2}_{\nu}$ less than
the associated critical values. The remaining WDs have values for
$\chi^{2}_{\nu}$ of $5.08$, $7.3$, and $4.9$, making their fits to CI
tentative. For context, we also calculate $\chi^{2}_{\nu}$ for the bulk Earth,
bulk silicate Earth, and terrestrial crustal rocks compared to CI chondrite,
where we assume errors equal to the average WD error for each element ratioed
to Mg, $n_{z}/n_{\rm M_{g}}$. Note that bulk Earth and bulk silicate Earth
(BSE) are indistinguishable from CI chondrite in this analysis using
uncertainties associated with the WD observations of Mg, Al, Si, Ca, Ti, Cr,
and Fe. The compositions of continental and oceanic crust, the latter
represented by Mid-Ocean Ridge Basalt (MORB), are readily distinguished from
CI chondrite in major elements using WD uncertainties (Figure 4). We see no
evidence for crust-like compositions among the eight polluted WDs considered
here.

In the examples presented above, we used the observed elemental ratios with no
corrections for settling times. This tacitly assumes that the parent body
accretion is in the buildup phase. We calculate the same $\chi^{2}_{\nu}$
statistic to assess the goodness-of-fit for these WDs relative to the CI
elemental ratios assuming the WDs are accreting material in a steady-state
phase (Figure 5). Steady state is often assumed for WDs in which heavy element
settling times are relatively short. Under this assumption, we find that for 3
of the 8 WDs, the $\chi^{2}_{\nu}$ values relative to CI chondrite indicate
better agreement with CI chondrite than for the buildup-phase assumption.
However, with the steady-state assumption, still 5 of the 8 WDs are
indistinguishable from CI chondrites ($\chi^{2}_{\nu}<\chi^{2}_{\nu,crit.}$).
Therefore, regardless of whether these polluted WDs are assumed to be in the
buildup phase or in steady state, they appear to be accreting bodies that are
chondritic, or approximately chondritic, in composition. We note that for
GaiaJ0218$+$3625 (irrespective of accretion phase) the abundance of Na/Mg is
$\simeq$6$\times$ the chondritic ratio. There is likely more work to be done
in future analysis of GaiaJ0218$+$3625, but this particular enhanced relative
abundance is not sufficient alone to reject the assessment that overall, the
accreted bodies of this sample are broadly chondritic.

###  4.3 Parent Body Size

In order to estimate parent body sizes, we calculate the minimum masses of the
parent bodies accreting onto these eight WDs as the sum of the masses of all
heavy elements in the convection zone (CVZ). We convert number abundance
ratios from Table 3 to mass ratios and multiply by the mass of the convection
zone, computed from evolution models from the Montreal White Dwarf Database
(MWDD; Dufour et al.,
2007)111http://dev.montrealwhitedwarfdatabase.org/evolution.html. We find
minimum masses that range from 2.8 $\times$ 10${}^{21}-$ 9.0 $\times$ 1022 g.
These masses are consistent with some of the most massive asteroids in the
solar system ($\thicksim$8 Flora $-$ 10 Hygiea) and some of the mid-sized
moons in the solar system ($\thicksim$ Neptune’s Larissa $-$ Saturn’s
Enceladus). The immensity of these minima for parent body masses supports the
conclusion that only the most massive of polluting objects will be observable
in WDs (Trierweiler et al., 2022). Mass fluxes onto the WD atmosphere can be
obtained by assuming steady state between accretion and settling. For this we
use the CVZ pollution masses and settling times from Table A3. The derived
fluxes range from 1.4 $\times$ 10${}^{8}-$ 8.5 $\times$ 109 g s-1, typical for
polluted WDs under similar assumptions (e.g. Rafikov, 2011; Farihi et al.,
2012; Wyatt et al., 2014; Xu et al., 2019) and would result in parent body
masses that range from 2.1$\times$ 10${}^{21}-$ 1.4 $\times$ 1023 g, assuming
accretion from a disk is sustained for roughly 5$\times$105 yr (Girven et al.,
2012).

###  4.4 Oxygen and Oxidation State

We evaluate the oxidation state of the parent bodies accreting onto each WD by
following the prescription introduced by Doyle et al. (2019) and improved in
Doyle et al. (2020). We use the ratio of $\rm O_{rem}$/Fe, where $\rm O_{rem}$
is the O remaining after assigning O to Mg, Si, Ca, and Al to form the oxides
MgO, SiO2, CaO, and Al2O3, as an indicator for whether a WD will yield a
recoverable oxygen fugacity ($\Delta$IW , see discussion below for complete
definition for this parameter) value and error bounds. We calculate $\rm
O_{rem}$ relative to Fe as:

$\frac{\rm{O}_{rem}}{\rm Fe}=\frac{\rm O}{\rm Fe}-\frac{\rm Mg}{\rm
Fe}-2\frac{\rm Si}{\rm Fe}-\frac{3}{2}\frac{\rm Al}{\rm Fe}-\frac{\rm Ca}{\rm
Fe}.$ (2)

For an ideal rock, in which Fe exists as ferrous iron (effective charge of
2+), the value of $\rm O_{rem}$/Fe should be unity. Where $\rm O_{rem}/Fe>1$,
an oxygen excess exists, suggesting an additional source for oxygen, often due
to accretion of oxygen-bearing volatiles such as H2O from the parent body (we
exclude the effect of Fe3+ here, present as the oxide Fe2O3, under the
assumption that the ferric iron will be relatively minor, $<10\%$ of all Fe,
as it is in most solar-system rocks). Six of the eight WDs in this study have
observed oxygen excesses implying water-rich bodies ($\rm O_{rem}/Fe>1$; Table
4). Of the six WDs with oxygen excesses, five have an observed amount of H
that can account for the excess oxygen assuming a buildup phase. Large
abundances of H in helium-dominated WDs are either from primordial H (prior to
the DA-to-DB evolution, Rolland et al. 2020) or due to the accumulation of H
throughout accretion events, as H floats on the atmospheric surface (Gentile
Fusillo et al., 2017; Izquierdo et al., 2021). Notably, a steady-state
approximation decreases, but does not entirely remove, the oxygen excesses
(Table 4).

The level of oxidation in a geochemical system is described as the non-ideal
partial pressure of O2, or oxygen fugacity ($f_{\rm O_{2}}$), and has
implications for the geochemistry and geophysics of rocky bodies. In the
planet formation regime, oxygen fugacities are often compared with that
defined by the equilibrium reaction between metallic iron (Fe) and FeO, which
in mineral form is w$\ddot{\text{u}}$stite (FeO):

$\text{Fe}+\frac{1}{2}\text{O}_{2}\rightleftharpoons\text{FeO}.$ (3)

Table 4: Oxidation States Determined from WD Data in this Study  Name |  $\Delta$IW | $\rm{O}_{\rm{rem}}/\rm{Fe}$ |  $\rm{O}_{\rm{rem}}/\rm{Fe}$ (steady)
---|---|---|---
GaiaJ0218+3625 | $-1.29^{+0.27}_{-0.37}$ | $14.16^{+11.02}_{-7.52}$ | $9.28^{+8.68}_{-6.68}$
WD1244+498 | $-0.54^{+0.17}_{-0.26}$ | $4.69^{+3.53}_{-2.34}$ | $3.01^{+2.65}_{-2.03}$
SDSSJ1248+1005 | $-1.09^{+0.24}_{-0.34}$ | $11.23^{+8.58}_{-5.68}$ | $7.11^{+6.40}_{-4.90}$
WD1415+234 | $<-0.87$ | $-0.18^{+0.91}_{-0.94}$ | $-0.30^{+0.71}_{-0.79}$
SDSSJ1734+6052 | $-1.04^{+0.26}_{-0.43}$ | $4.62^{+4.13}_{-2.97}$ | $2.72^{+3.24}_{-2.64}$
GaiaJ1922+4709 | $-1.78^{+1.17}$ | $0.17^{+1.01}_{-0.97}$ | $0.03^{+0.89}_{-0.88}$
EC22211$-$2525 | $-1.25^{+0.28}_{-0.44}$ | $6.73^{+6.07}_{-4.36}$ | $4.27^{+4.82}_{-3.89}$
SDSSJ2248+2632 | $-1.74^{+0.49}$ | $5.01^{+8.83}_{-5.48}$ | $2.44^{+5.77}_{-4.73}$

This iron-w$\ddot{\text{u}}$stite (IW) reference reaction assumes pure Fe
metal and FeO oxide. By reporting $f_{\rm O_{2}}$ of a rock to a reference
reaction such as Equation 3, the thermodynamics simplifies to a ratio of
activities, or mole fractions (see Appendix in Doyle et al. (2019) for a full
derivation). The intrinsic oxygen fugacity of a rock or rocky body can thus be
described relative to that for the IW reference, such that

$\Delta\text{IW}\equiv\text{log}\left(f_{\rm O_{2}}\right)_{\rm
rock}-\text{log}\left(f_{\rm O_{2}}\right)_{\rm
IW}=2\text{log}\left(\frac{{x_{\rm FeO}^{\rm rock}}}{{x_{\rm Fe}^{\rm
metal}}}\right).$ (4)

This simplification results in an equation for $\Delta$IW that depends solely
on the mole fraction of FeO in the rock ($x_{\rm FeO}^{\rm rock}$) and the
mole fraction of Fe in the metal ($x_{\rm Fe}^{\rm metal}$).

Where $\rm O_{rem}/Fe<1$, a dearth of oxygen exists, suggesting iron is
present in the form of Fe metal. Of the eight WDs reported in Table 4, three
have lower bounds with values for $\rm O_{rem}/Fe<1$ (WD1415$+$234,
GaiaJ1922$+$4709, and SDSSJ2248$+$2632). In such cases, lower bounds on the
level of oxidation, measured as oxygen fugacity, cannot be obtained.

Figure 6: $\Delta$IW vs $\rm O_{rem}$/Fe. The value of $\rm O_{rem}$/Fe should
be unity for ideal rocks, represented as the dotted silicate line. Where $\rm
O_{rem}/Fe>1$, an oxygen excess exists, and where $\rm O_{rem}/Fe<1$, a dearth
of oxygen exists. Where errors allow $\rm O_{rem}/Fe<1$, lower bounds in
$\Delta$IW cannot be obtained. Such is the case for three WDs in this study
(GaiaJ1922$+$4709, SDSSJ2248$+$2632, and WD1415$+$234). These three WDs are
those in the Figure where lower error bounds in $\rm O_{rem}/Fe$ plot below
the ideal value for silicates.

Of these three, WD1415+234 is represented with an open circle, because the
median is also unrecoverable.

As in Doyle et al. (2019) and Doyle et al. (2020), we use the oxides SiO2,
MgO, FeO, CaO and Al2O3 to characterize the chemical composition of the
accreting rocks. Where Al is not observed, we assume a chondritic Al/Ca ratio
and set uncertainties equal to 0.3 dex. Using oxides ensures charge balance
and provides a means of tracking oxygen that was in the form of rock. We first
assign oxygen to Mg, Si, and Ca to form these oxides, and then we assign the
remaining oxygen, Orem, to Fe to form FeO. In this way, we can assess what
portion of Fe can be paired with O and is presumed to have existed as FeO in
the rock ($x_{\rm FeO}^{\rm rock}$) versus what portion of Fe existed as Fe
metal (i.e. where there is a deficit of O). For application of Equation 4 we
set $x_{\rm Fe}^{\rm metal}=$ 0.85, consistent with estimates for Fe metal in
the core of differentiated bodies from our solar system. We propagate
measurement uncertainties for the polluted WDs using a Monte Carlo approach
with a bootstrap of n=1. We report our calculated $\Delta$IW values in Table
4.

In our solar system, most rocky bodies are oxidized relative to a hydrogen-
rich solar gas ($\Delta$IW $=-6$), with $\Delta$IW values greater than $-3$,
corresponding to $x_{\rm FeO}^{\rm rock}>0.025$. Only Mercury and enstatite
chondrites are “reduced” ($\Delta$IW $<-3$; $x_{\rm FeO}^{\rm rock}<0.025$).
In general, the WDs in this study have $\Delta$IW values similar to
chondrites, consistent with their chondritic bulk chemistry (Figures 4 and 5).
However, there are two WDs in this study for which lower bounds on $\Delta$IW
cannot be obtained (GaiaJ1922$+$4709 and SDSSJ2248$+$2632), and one for which
neither a median nor a lower bound can be obtained (WD1415$+$234). Situations
like these arise where negative $x_{\rm FeO}^{\rm rock}$ values are a
significant fraction of the Monte Carlo draws for error propagation. This in
turn comes about where there is either a relative scarcity of oxygen relative
to the propagated errors or abundance uncertainties are large (refer to
Section 2.3 and Figure 3 in Doyle et al. (2020) for a more detailed
discussion).

Therefore, the calculation of $\rm O_{rem}$/Fe is a good indicator for whether
a WD will yield a recoverable $\Delta$IW value and error bounds. Indeed, the
same three WDs that have lower bounds with negative values for $\rm
O_{rem}$/Fe have unrecoverable lower error bounds for $\Delta$IW (Figure 6).
It is worth noting that one of these WDs, GaiaJ1922$+$4709, is that with the
least good fit to CI chondrite, based on $\chi^{2}_{\nu}$ statistics presented
in Figure 4. It is also worth noting that one of these WDs, SDSSJ2248$+$2632,
has a median value for $\rm O_{rem}$/Fe that indicates excess oxygen, but
large uncertainties for Fe (Table 3). Indeed, it is possible that the parent
bodies accreting onto these WDs had less FeO in the rocky portion of the body
and were more reduced than CI chondrite. While these WDs have oxidation states
that are less constrained, the median values for $\Delta$IW calculated for
this subset of polluted WDs generally adds to the increasing quantity of
chondrite-like parent bodies accreting onto WDs in both bulk composition and
degree of oxidation.

##  5 Conclusions

In this work we present observations for eight heavily polluted DB white
dwarfs and relative elemental abundances for the rocky parent bodies that
accreted onto them. All of the WDs in this data set required new designations
or updates of spectral types. In a step towards some needed clarification to
the spectral classification system, we measured and ordered the “strongest”
spectral features according to equivalent widths (not line depths). That
determined our assignment of spectral types as DBAZ or DBZA.

We assembled our dataset by comparing GALEX colors to $T_{\rm eff}$ for white
dwarf candidates presented in Gentile Fusillo et al. (2019), as well as from
known polluted DB white dwarfs. This comparison reveals a distinct dichotomy
between DA and DB white dwarfs, which we used to target DB white dwarfs to
search for those that are heavily polluted. The white dwarfs presented here
were chosen due to their detections of all four major rock-forming elements
(O, Mg, Si, Fe). Through this work, we have increased the sample of known
oxygen-bearing white dwarfs polluted by rocky parent bodies by $\thicksim$ 33%
222see also note added in proof.

We assessed the bulk compositions and oxidation states of the accreting
bodies, and find that they are indistinguishable from chondritic in
composition. This adds to the growing body of evidence suggesting that
extrasolar rocky bodies closely resemble those in our solar system, and do
not, as a whole, yield unusual or unique compositions. This result is not
dependent on assumptions of an increasing phase versus a steady-state phase of
accretion.

Six of the eight white dwarfs in this study have observed oxygen excesses
implying volatiles, in various abundances, in the parent bodies (a trait
shared by CI chondrites). Generally, the oxidation states of these parent
bodies also corroborate the conclusion that the accreting bodies are
chondritic. Three exceptions exist in which oxidation states are less
constrained and could be more reduced than chondritic (lower oxygen fugacity
values), and one of these white dwarfs (GaiaJ1922$+$4709) is the same WD that
obtains the least good fit to CI chondrite. This result is in accordance with
the assessment that perhaps 1/4 of polluted white dwarfs may be consistent
with more reduced parent bodies that cannot be identified by use of this
method (Doyle et al., 2020). Overall, our results are consistent with the
emerging view that extrasolar rocks across the solar neighborhood are broadly
similar to rocky bodies in our solar system.

This work was supported by NASA 2XRP grant No. 80NSSC20K0270 to EDY. C.M. and
B.Z. acknowledge support from NSF grants SPG-1826583 and SPG-1826550. S. Xu is
supported by the international Gemini Observatory, a program of NSF’s NOIRLab,
which is managed by the Association of Universities for Research in Astronomy
(AURA) under a cooperative agreement with the National Science Foundation, on
behalf of the Gemini partnership of Argentina, Brazil, Canada, Chile, the
Republic of Korea, and the United States of America. The authors thank Simon
Blouin (University of Victoria) for helpful discussions about abundance
modeling, and Jay Farihi (University College London) for helpful discussions
regarding WD spectral type classifications. We also thank the anonymous
reviewer for their comments, which improved the manuscript. Much of the data
presented herein were obtained at the W. M. Keck Observatory, which is
operated as a scientific partnership among the California Institute of
Technology, the University of California and the National Aeronautics and
Space Administration. The Observatory was made possible by the generous
financial support of the W. M. Keck Foundation. The authors wish to recognize
and acknowledge the very significant cultural role and reverence that the
summit of Maunakea has always had within the indigenous Hawaiian community. We
are most fortunate to have the opportunity to conduct observations from this
mountain. Similarly, we acknowledge that Lick Observatory resides on land
traditionally inhabited by the Muwekma Ohlone Tribe of Native Americans.
Research at Lick Observatory is partially supported by a generous gift from
Google. This paper includes data gathered with the 6.5 meter Magellan
Telescopes located at Las Campanas Observatory, Chile. This work has made use
of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.
esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium
(DPAC). Funding for the DPAC has been provided by national institutions, in
particular the institutions participating in the Gaia Multilateral Agreement.
This research has made use of NASA’s Astrophysics Data System, the SIMBAD
database, and the VizieR service. This research has made use of IRAF. IRAF is
distributed by the National Optical Astronomy Observatory, which is operated
by the Association of Universities for Research in Astronomy (AURA) under a
cooperative agreement with the National Science Foundation. The following
atomic spectral line databases were consulted: Vienna Atomic Line Database
(VALD), Kurucz (1995, R. L. Kurucz and B. Bell, CD-ROM No. 23, Cambridge, MA:
Smithsonian Astrophysical Observatory), NIST Standard Reference Database 78,
and van Hoof (2018). Facilities: Shane (Kast), Keck I (HIRES), Keck II (ESI),
Magellan (MagE) Note added in proof. Contemporaneous with this paper,
Izquierdo et al. (2023) reported oxygen detections in ten polluted WDs, though
parent body composition analyses have not yet been carried out. This appendix
presents details of spectral line measurements, broadband spectral energy
distributions (SEDs), diffusion timescales and accretion rates. Radial
velocites (RVs) are given in Table A1, equivalent widths (EWs) are given in
Table A2, SEDs are displayed in Figure A1, and accretion-diffusion data are
reported in Table A3. Equivalent widths were measured by profile fitting using
IRAF’s splot task, and RVs were calculated as Doppler shifts of the measured
line centers relative to laboratory wavelengths (see Klein et al., 2021). Half
of the stars in this sample (WD1415$+$234, SDSSJ1734$+$6052, GaiaJ1922$+$4709,
SDSSJ2248$+$2632) display absorption lines of the Na I resonance doublet
$\lambda$5889.951/5895.924 Å (NaD) with RVs which are significantly blue-
shifted from the photospheric averages based on many photospheric lines (see
Table A1). In some stars non-photospheric Ca II $\lambda$3933.663 Å (CaK)
features are also observed. Based on results from Redfield & Linsky (2008,
http://lism.wesleyan.edu/LISMdynamics.html) and Welsh et al. (2010), it is
probably the case that WD1415+234, SDSSJ1734+6052, and GaiaJ1922+4709 host
interstellar medium (ISM) features. On the other hand, if the non-photospheric
RV is blue-shifted from the photospheric RV by an amount equal to or somewhat
less than the gravitational redshift of the WD, then it could be that the non-
photospheric absorption is occurring in CS gas (co-moving with the WD, but not
fully in its photospheric gravitational well). Referring to Table A1, and
considering an uncertainty range of 3 km s-1 in gravitational redshift plus 2
km s-1 in photospheric RV, a CS origin is reasonable for only two WDs:
SDSSJ1734+6052 and SDSSJ2248+2632. However, we can not rule out the
possibility that absorption may be due to ISM material (especially at
distances $>$ 80 pc; e.g., see Figure 7 of Welsh et al. 2010) or could even
possibly have some association with accretion-related outflows. Unlike the
four aforementioned WDs, the NaD RV in GaiaJ0218+3625 agrees exactly with the
average photospheric RV. There may be a slight chance that an ISM cloud has
the unusually high RV of 39 km s-1 (e.g., Redfield & Linsky 2008 and Welsh et
al. 2010) and is coincidentally the same as the WD RV. We think this unlikely,
and deem the Na line in GaiaJ0218+3625 to originate in the WD photosphere and
be associated with the polluting parent body.

Table A1: Radial Velocities  |  | photospheric lines | sys- | additional lines | vel diff | grav | origin
---|---|---|---|---|---|---|---
WD Name | D | # of | avg | std | temic | NaD2 | NaD2 | CaK | CaK | from | red- | of
|  | lines | RV | dev | RV | EW | RV | EW | RV | phot | shift | extra
| (pc) |  | (km s-1) | (km s-1) | (km s-1) | (mÅ) | (km s-1) | (mÅ) | (km s-1) | (km s-1) | (km s-1) | lines
GaiaJ0218+3625 | 116 | 83 | 39.5 | 1.6 | 16.1 | 45 | 39.2 |  |  | 0.2 | 23.4 | phot
WD1244+498 | 120 | 46 | 39.1 | 2.5 | 11.1 |  |  |  |  |  | 28.0 |
SDSSJ1248+1005 | 164 | 62 | 41.0 | 1.9 | 5.6 |  |  |  |  |  | 35.4 |
WD1415+234 | 127 | 57 | 34.1 | 1.5 | -4.7 | 36 | -15.8 |  |  | 49.9 | 38.8 | ISM
SDSSJ1734+6052 | 150 | 25 | 17.7 | 1.9 | -13.9 | 69 | -31.3 | 9 | -28.1 | 47.8 | 31.6 | ISM
|  |  |  |  |  | 60 | -21.1 | 7 | -18.7 | 38.2 | 31.6 | ISM or CS?
GaiaJ1922+4709 | 127 | 104 | 44.8 | 1.4 | 17.7 | 33 | -22.6 |  |  | 67.8 | 27.1 | ISM
|  |  |  |  |  |  |  | 37 | -16.1 | 60.9 | 27.1 | ISM
EC22211-2525 | 109 | 88 | 47.1 | 1.6 | 22.6 |  |  |  |  |  | 24.5 |
SDSSJ2248+2632 | 123 | 16 | 21.2 | 1.6 | -9.4 | 54 | -9.1 |  |  | 29.9 | 30.6 | ISM or CS?

Table A2: Photospheric Absorption Line Measurements

WD |  | 0218+3625 | 22211$-$2525 | 1244+498 | 1248+1005 | 1922+4709 | 1734+6052 | 1415+234 | 2248+2632
---|---|---|---|---|---|---|---|---|---
Teff |  | 14700 K | 14740 K | 15150 K | 15180 K | 15500 K | 16340 K | 17300 K | 17370 K
Ion |  $\lambda$ (Å) | Equivalent Width (mÅ)
O I | 7771.944 | 200 (27) | 134 (15) | 138 (22) | 266 (59) | 152 (13) | 93 (22) | 80 (11) | 43 (18)
O I | 7774.166 | 129 (30) | 88 (16) | 109 (26) | 106 (28) | 124 (15) | 31 (27) | 35 (9) | 31 (13)
O I | 7775.388 | 100 (19) | 81 (19) | 55 (33) | 71 (21) | 82 (12) | 19 (7) | 29 (10) |
O I | 8446.359 | 149 (57) | 167 (33) | 75 (22) | 395 (141) | 134 (26) |  | 63 (34) |
Na I | 5889.951 | 45 (10) |  |  |  |  |  |  |
Mg I | 3829.355 |  | 11 (3) |  |  |  |  |  |
Mg I | 3832.304 | 31 (5) | 42 (3) | 15 (5) | 43 (8) | 39 (6) |  | 11 (3) |
Mg I | 3838.292 | 58 (4) | 74 (3) | 65 (8) | 76 (16) | 73 (7) |  | 47 (7) |
Mg I | 5172.684 |  | 9 (2) |  |  | 15 (4) |  |  |
Mg I | 5183.604 | 17 (3) | 31 (4) |  |  | 32 (10) |  |  |
Mg II | 4481$\dagger$$\dagger$footnotemark:  | 321 (11) | 400 (8) | 216 (11) | 368 (42) | 374 (25) | 160 (15) | 276 (8) | 97 (13)
Mg II | 7877.054 |  | 208 (64) |  | 179 (68) | 366 (49) |  | 91 (41) |
Mg II | 7896.366 | 309 (72) | 337 (51) |  | 230 (82) | 473 (40) |  | 195 (41) | 104 (36)
Al II | 3587$\dagger$$\dagger$footnotemark:  | 163 (25) | 39 (14) |  |  | 241 (45) |  |  |
Si II | 3853.665 | 19 (4) | 14 (3) |  |  | 35 (6) | 8 (4) | 11 (4) |
Si II | 3856.018 | 105 (3) | 83 (5) | 54 (6) | 72 (5) | 186 (6) | 33 (5) | 82 (3) | 30 (6)
Si II | 3862.595 | 70 (2) | 48 (4) | 19 (4) | 46 (5) | 128 (8) | 21 (4) | 58 (3) | 20 (3)
Si II | 4128.054 | 59 (3) | 36 (5) | 13 (5) | 25 (7) | 133 (13) | 13 (4) | 39 (5) |
Si II | 4130.894 | 92 (3) | 56 (4) | 35 (5) | 80 (13) | 192 (12) | 21 (4) | 58 (5) |
Si II | 5041.024 | 41 (8) | 28 (9) |  |  | 152 (13) |  | 36 (7) |
Si II | 5055.984 | 85 (6) | 58 (12) | 30 (8) | 114 (17) | 203 (27) | 27 (8) | 54 (8) |
Si II | 5957.559 |  |  |  |  | 27 (7) |  |  |
Si II | 5978.930 |  |  |  |  | 81 (13) |  |  |
Si II | 6347.109 | 232 (14) | 200 (16) | 104 (10) | 217 (37) | 413 (13) | 126 (37) | 186 (12) | 97 (7)
Si II | 6371.371 | 153 (12) | 103 (12) | 46 (7) | 158 (29) | 255 (10) | 63 (7) | 89 (11) | 50 (6)
Ca II | 3158.869 | 158 (7) | 136 (8) | 128 (8) | 255 (12) | 187 (11) | 54 (7) | 77 (7) | 26 (5)
Ca II | 3179.331 | 175 (15) | 181 (10) | 154 (13) | 379 (15) | 246 (22) | 82 (15) | 93 (8) | 47 (6)
Ca II | 3181.275 | 52 (6) | 43 (9) |  | 41 (7) | 52 (13) | 6 (3) |  |
Ca II | 3706.024 | 39 (12) | 31 (4) |  | 87 (8) | 66 (8) |  | 9 (2) |
Ca II | 3736.902 | 86 (3) | 86 (3) | 93 (6) | 160 (6) | 137 (10) | 19 (4) | 27 (3) |
Ca II | 3933.663 | 595 (20) | 710 (11) | 664 (33) | 1245 (38) | 528 (23) | 256 (8) | 274 (4) | 169 (7)
Ca II | 3968.469 | 338 (15) | 391 (13) | 430 (59) | 747 (50) | 284 (17) | 149 (3) | 154 (4) | 111 (4)
Ca II | 8498.023 |  |  |  | 173 (53) |  |  |  |
Ca II | 8542.091 | 305 (61) | 305 (40) | 228 (24) | 528 (57) | 255 (18) | 120 (17) | 60 (26) | 88 (31)
Ca II | 8662.141 | 192 (50) | 193 (27) | 175 (24) | 386 (52) | 96 (16) | 53 (16) | 45 (12) |
Ti II | 3168.518 |  |  |  |  |  |  |  |
Ti II | 3234.520 | 20 (2) | 15 (2) |  | 45 (8) |  |  |  |
Ti II | 3236.578 | 16 (3) | 10 (2) |  | 40 (7) |  |  |  |
Ti II | 3239.044 |  | 11 (3) |  | 34 (7) |  |  |  |
Ti II | 3241.994 | 9 (2) | 9 (2) |  | 18 (4) |  |  |  |
Ti II | 3248.598 |  |  |  | 16 (7) |  |  |  |
Ti II | 3322.941 |  |  |  | 35 (7) |  |  |  |
Ti II | 3341.880 | 16 (3) | 8 (3) |  | 36 (4) |  |  |  |
Ti II | 3349.037 | 13 (2) | 8 (2) | 14 (9) | 47 (11) | 26 (5) |  |  |
Ti II | 3349.408 | 36 (3) | 26 (2) | 19 (4) | 56 (6) | 48 (7) |  |  |
Ti II | 3361.218 | 17 (3) | 13 (2) |  | 48 (4) |  |  |  |
Ti II | 3372.800 | 16 (22) | 11 (2) |  | 30 (3) |  |  |  |
Ti II | 3383.768 | 12 (4) | 11 (2) |  | 29 (4) |  |  |  |
Ti II | 3387.846 |  |  |  | 34 (13) |  |  |  |
Ti II | 3685.189 | 17 (6) | 14 (4) |  | 29 (5) |  |  |  |
Ti II | 3759.296 | 11 (2) | 6.3 (1.6) |  | 16 (3) |  |  |  |
Ti II | 3761.323 | 6 (1) | 6.1 (1.3) |  | 13 (3) |  |  |  |
Cr II | 3118.646 | 13 (4) | 18 (4) |  | 31 (8) | 19 (6) |  | 12 (3) |
Cr II | 3120.359 | 28 (5) | 30 (4) |  | 31 (7) | 38 (9) |  | 12 (2) |
Cr II | 3124.973 | 32 (5) | 37 (4) | 27 (6) | 43 (9) | 40 (11) |  | 27 (6) |
Cr II | 3132.053 | 40 (5) | 44 (4) | 28 (5) | 53 (7) | 65 (9) |  | 32 (3) |
Cr II | 3147.220 |  | 9 (3) |  | 14 (4) |  |  |  |
Cr II | 3180.693 | 18 (4) | 16 (4) |  |  |  |  |  |
Cr II | 3197.075 | 8 (3) | 8 (3) |  |  |  |  |  |
Cr II | 3368.041 | 19 (2) | 15 (2) |  | 22 (3) | 28 (7) |  | 12 (3) |
Cr II | 3408.757 | 15 (3) | 13 (2) |  |  |  |  | 9 (2) |
Cr II | 3422.732 | 13 (2) |  |  |  |  |  |  |
Cr II | 3433.295 | 9 (2) |  |  |  |  |  |  |
Mn II | 3441.988 | 17 (2) |  |  |  |  |  |  |
Mn II | 3460.316 | 15 (3) |  |  |  |  |  |  |
Fe I | 3570.097 |  |  |  |  | 25 (7) |  |  |
Fe I | 3581.195 | 7 (2) |  |  |  | 34 (5) |  |  |
Fe I | 3734.864 | 5 (2) |  |  |  | 25 (5) |  |  |
Fe I | 3749.485 |  |  |  |  | 17 (5) |  |  |
Fe II | 3135.360 |  | 25 (4) |  |  | 54 (9) |  | 16 (3) |
Fe II | 3144.752 |  | 10 (3) |  |  | 23 (8) |  |  |
Fe II | 3154.202 | 44 (4) | 61 (5) | 67 (17) | 62 (10) | 79 (10) | 9 (4) | 40 (3) |
Fe II | 3162.798 |  | 11 (3) |  |  | 40 (6) |  |  |
Fe II | 3167.857 | 36 (7) | 23 (2) | 37 (14) | 20 (4) | 77 (9) |  | 32 (4) |
Fe II | 3170.337 |  |  |  |  | 24 (6) |  |  |
Fe II | 3177.532 | 22 (6) | 17 (3) | 17 (4) |  | 56 (8) |  | 34 (6) |
Fe II | 3180.149 |  |  |  |  | 27 (6) |  |  |
Fe II | 3183.111 | 15 (4) | 16 (5) |  |  | 38 (7) |  | 10 (3) |
Fe II | 3186.737 | 16 (4) | 21 (5) | 23 (5) |  | 44 (9) |  | 14 (4) |
Fe II | 3192.909 | 19 (4) | 15 (3) | 12 (3) |  | 45 (9) |  | 12 (2) |
Fe II | 3193.799 | 42 (6) | 32 (4) | 35 (5) | 44 (8) | 79 (7) |  | 34 (4) |
Fe II | 3196.070 | 18 (3) | 24 (3) | 17 (3) | 27 (6) | 62 (15) |  | 14 (3) |
Fe II | 3210.444 | 28 (4) | 39 (4) | 29 (5) | 38 (6) | 78 (9) |  | 27 (3) |
Fe II | 3212.017 |  | 8 (3) |  |  | 41 (8) |  |  |
Fe II | 3213.309 | 55 (4) | 68 (3) | 52 (4) | 41 (4) | 104 (15) | 17 (4) | 39 (3) | 9 (3)
Fe II | 3227.742 | 69 (6) | 84 (4) | 97 (5) | 95 (9) | 151 (7) | 26 (5) | 60 (7) | 16 (5)
Fe II | 3231.706 |  |  |  |  | 24 (5) |  |  |
Fe II | 3232.785 | 8 (2) | 8 (2) | 17 (4) |  | 20 (6) |  | 10 (3) |
Fe II | 3237.399 |  |  |  |  | 30 (9) |  |  |
Fe II | 3237.820 | 10 (3) | 7 (2) |  | 16 (6) | 32 (7) |  | 7 (2) |
Fe II | 3243.723 | 11 (5) | 12 (2) | 16 (4) |  | 35 (6) |  | 9 (3) |
Fe II | 3247.175 | 27 (4) | 15 (3) | 28 (6) | 17 (4) | 75 (8) |  | 18 (2) |
Fe II | 3255.887 | 10 (2) | 11 (2) |  |  | 37 (6) |  | 13 (2) |
Fe II | 3258.771 | 12 (2) | 20 (2) | 10 (3) | 18 (5) | 45 (6) |  | 21 (4) |
Fe II | 3259.051 | 24 (3) | 19 (2) | 20 (4) | 22 (5) | 68 (8) |  | 24 (5) |
Fe II | 3276.604 |  |  |  |  | 20 (5) |  |  |
Fe II | 3277.348 | 13 (2) | 13 (2) |  |  | 30 (5) |  | 9 (2) |
Fe II | 3281.292 |  |  |  |  | 19 (5) |  |  |
Fe II | 3289.354 |  |  |  |  | 28 (5) |  |  |
Fe II | 3323.063 |  | 9 (3) |  |  | 36 (8) |  |  |
Fe II | 3468.678 |  |  |  |  | 30 (4) |  |  |
Fe II | 3493.470 | 11 (3) | 12 (2) |  |  | 37 (6) |  | 14 (2) |
Fe II | 3748.483 |  |  |  |  | 24 (6) |  |  |
Fe II | 4233.170 | 12 (2) | 11 (3) |  |  | 42 (5) |  | 10 (3) |
Fe II | 4351.769 |  |  |  |  | 23 (6) |  |  |
Fe II | 4522.634 |  |  |  |  | 19 (5) |  |  |
Fe II | 4549.474 |  |  |  |  | 54 (11) |  |  |
Fe II | 4583.837 | 13 (2) |  |  |  | 50 (7) |  |  |
Fe II | 4923.927 | 23 (10) | 47 (16) | 29 (13) | 32 (11) | 40 (11) | 9 (3) | 13 (3) |
Fe II | 5001.959 |  |  |  |  | 32 (10) |  |  |
Fe II | 5018.440 | 27 (5) | 31 (11) | 34 (7) | 37 (8) | 68 (10) | 11 (4) | 31 (6) |
Fe II | 5035.708 |  |  |  |  | 16 (5) |  |  |
Fe II | 5100.727 |  |  |  |  | 40 (6) |  |  |
Fe II | 5169.033 | 45 (3) | 56 (6) | 53 (7) | 47 (7) | 143 (12) | 13 (4) | 47 (5) | 8 (2)
Fe II | 5197.577 |  |  |  |  | 19 (4) |  |  |
Fe II | 5216.863 |  |  |  |  | 21 (7) |  |  |
Fe II | 5227.481 |  |  |  |  | 78 (10) |  |  |
Fe II | 5234.625 |  |  |  |  | 24 (3) |  |  |
Fe II | 5247.952 |  |  |  |  | 19 (6) |  |  |
Fe II | 5251.233 |  |  |  |  | 21 (7) |  |  |
Fe II | 5260.259 |  |  |  |  | 86 (10) |  |  |
Fe II | 5276.002 |  |  |  |  | 23 (4) |  |  |
Fe II | 5291.666 |  |  |  |  | 21 (5) |  |  |
Fe II | 5316.615 | 15 (3) |  | 18 (7) |  | 51 (6) |  |  |
Fe II | 5339.585 |  |  |  |  | 47 (16) |  |  |
Fe II | 5362.869 |  |  |  |  | 17 (3) |  |  |
Fe II | 5506.195 |  |  |  |  | 45 (11) |  |  |

††footnotetext: blended multiplet $-$ the EW is the total for the blended
feature.

Note. — Calculated $\Delta$IW and remaining O relative to Fe, along with error
bounds for the WDs in this study. $\rm{O}_{\rm{rem}}/\rm{Fe}$ for an ideal
rock should be unity, and variations from this value are due to oxygen either
in excess or shortage of that required to form MgO, SiO2, CaO, and FeO.
Measurement uncertainties are propagated using a Monte Carlo approach with a
bootstrap of n=1; see Section 4.4 for discussion about absent lower error
bounds for $\Delta$IW . Generally, a steady-state assumption reduces the
remaining oxygen, but does not entirely remove the excess, implying that the 6
WDs with oxygen excesses in the steady-state calculation have some amount of
oxygen-bearing volatiles, such as H2O ice, in the parent body.

Note. — Radial velocities are in the heliocentric frame of rest. “avg” RV is
the average of the set of observed high-Z line RVs (includes gravitational
redshift); “std dev” is the standard deviation of that set, which can be taken
to be a measure of the uncertainty on the average; “systemic” RV is the
kinematic portion of the RV (gravitational redshift subtracted); “vel diff
from phot” = avg RV $-$ NaD and/or CaK RV; “phot” = photosphere. CaK
measurements in this table are of secondary features associated with the CaK
wavelength (3933.663Å in air) that are velocity shifted from the photospheric
CaK lines (reported in Table A2). NaD2 = $\lambda$5889.951Å, the stronger line
of the Na I resonance doublet. SDSSJ1734+6052 has two distinct absorption
lines at each of the two NaD doublet transitions, as well as at CaK.
Gravitational redshifts are from the Montreal White Dwarf Database (Dufour et
al., 2017, https://www.montrealwhitedwarfdatabase.org/evolution.html)
calculated with atmospheric parameters from Table 2. Typical EW uncertainties
are $\sim$ 10-20%. The typical uncertainty for gravitational redshift is 3 km
s-1 as realized by propagating from upper and lower bounds of the Teff/log$g$
uncertainties from Table 2. Systemic RV uncertainties can be calculated as an
additive combination (in quadrature) of the 3 km s-1 from gravitational
redshift with the standard deviation of photospheric lines.

Note. — Wavelengths are in air. EW measurements and uncertainty estimates were
made using IRAF’s task splot as described in Klein et al. (2021).

Figure A1: SEDs for the eight DB WDs in this study. Table A3: Diffusion timescales and accretion rates for WDs in this study  Name |  | $\tau_{\rm Al}$ | $\tau_{\rm Ca}$ | $\tau_{\rm Mg}$ | $\tau_{\rm Si}$ | $\tau_{\rm Fe}$ | $\tau_{\rm O}$ | $\tau_{\rm Na}$ | $\tau_{\rm Ti}$ | $\tau_{\rm Cr}$ | $\tau_{\rm Mn}$
---|---|---|---|---|---|---|---|---|---|---|---
|  | Myr |  |  |  |  |  |  |  |  |
GaiaJ0218$+$3625 |  | 1.71 | 1.19 | 1.77 | 1.73 | 1.16 | 1.77 | 1.70 | 1.09 | 1.12 | 1.12
WD1244$+$498 |  | 0.86 | 0.60 | 0.90 | 0.87 | 0.59 | 0.90 |  | 0.55 | 0.57 |
SDSSJ1248$+$1005 |  | 0.47 | 0.32 | 0.49 | 0.47 | 0.31 | 0.48 |  | 0.29 | 0.30 | 0.30
WD1415$+$234 |  | 0.11 | 0.09 | 0.13 | 0.11 | 0.08 | 0.13 |  |  | 0.08 |
SDSSJ1734$+$6052 |  | 0.35 | 0.25 | 0.37 | 0.33 | 0.24 | 0.38 |  |  |  |
GaiaJ1922$+$4709 |  | 0.77 | 0.53 | 0.81 | 0.76 | 0.53 | 0.81 |  | 0.50 | 0.51 | 0.51
EC22211$-$2525 |  | 1.42 | 0.98 | 1.47 | 1.43 | 0.96 | 1.47 |  |  |  |
SDSSJ2248$+$2632 |  | 0.19 | 0.15 | 0.21 | 0.18 | 0.14 | 0.23 |  |  |  |
Name | ${M}_{\rm CV}$ | $\dot{M}_{\rm Al}$ | $\dot{M}_{\rm Ca}$ | $\dot{M}_{\rm Mg}$ | $\dot{M}_{\rm Si}$ | $\dot{M}_{\rm Fe}$ | $\dot{M}_{\rm O}$ | $\dot{M}_{\rm Na}$ | $\dot{M}_{\rm Ti}$ | $\dot{M}_{\rm Cr}$ | $\dot{M}_{\rm Mn}$
| g | g s-1 |  |  |  |  |  |  |  |  |
GaiaJ0218$+$3625 | 4.4$\times$1027 | 2.77$\times$107 | 1.83$\times$107 | 1.10$\times$108 | 1.79$\times$108 | 2.40$\times$108 | 9.34$\times$108 | 3.72$\times$107 | 5.77$\times$105 | 3.39$\times$106 | 2.50$\times$106
WD1244$+$498 | 2.3$\times$1027 | 5.86$\times$10${}^{7^{a}}$ | 8.15$\times$107 | 3.42$\times$108 | 3.42$\times$108 | 1.98$\times$109 | 2.22$\times$109 |  | 2.89$\times$106 | 1.12$\times$107 |
SDSSJ1248$+$1005 | 1.4$\times$1027 | 2.21$\times$10${}^{8^{a}}$ | 3.14$\times$108 | 8.46$\times$108 | 6.60$\times$108 | 1.79$\times$109 | 4.89$\times$109 |  | 1.03$\times$107 | 2.71$\times$107 | 2.56$\times$106
WD1415$+$234 | 2.6$\times$1026 | 1.68$\times$10${}^{7^{a}}$ | 2.35$\times$107 | 3.83$\times$108 | 1.93$\times$108 | 1.15$\times$109 | 3.97$\times$108 |  |  | 1.24$\times$107 |
SDSSJ1734$+$6052 | 3.7$\times$1026 | 2.23$\times$10${}^{6^{a}}$ | 2.89$\times$106 | 1.90$\times$107 | 1.12$\times$107 | 3.89$\times$107 | 6.07$\times$107 |  |  |  |
GaiaJ1922$+$4709 | 1.9$\times$1027 | 7.01$\times$107 | 3.31$\times$107 | 3.29$\times$108 | 5.29$\times$108 | 2.13$\times$109 | 9.14$\times$108 |  | 1.29$\times$106 | 7.65$\times$106 | 3.98$\times$106
EC22211$-$2525 | 3.8$\times$1027 | 1.25$\times$107 | 1.73$\times$107 | 1.51$\times$108 | 1.27$\times$108 | 2.53$\times$108 | 5.74$\times$108 |  | 4.07$\times$105 | 2.73$\times$106 | 1.21$\times$106
SDSSJ2248$+$2632 | 3.8$\times$1026 | 9.05$\times$10${}^{6^{a}}$ | 1.34$\times$107 | 4.50$\times$107 | 2.66$\times$107 | 4.22$\times$107 | 1.14$\times$108 |  |  |  |
Diffusion timescales are from the Montreal White Dwarf Database (MWDD; Dufour
et al., 2017). Mass fluxes are calculated as described
in Section 4.3 for the steady-state accretion phase. ${M}_{\rm CV}$ is the
convection zone mass.
a Al abundance approximated from a chondritic Al/Ca ratio.

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