# Live Fast, Die $\alpha$-Enhanced: The Mass-Metallicity-$\alpha$ Relation of
the Milky Way’s Disrupted Dwarf Galaxies

Rohan P. Naidu Center for Astrophysics $|$ Harvard & Smithsonian, 60 Garden
Street, Cambridge, MA 02138, USA  Charlie Conroy Center for Astrophysics $|$
Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Ana Bonaca
Observatories of the Carnegie Institution for Science, 813 Santa Barbara St.,
Pasadena, CA 91101, USA  Dennis Zaritsky Steward Observatory, University of
Arizona, 933 North Cherry Avenue, Tucson, AZ 85721-0065, USA  Yuan-Sen Ting
(丁源森) Research School of Astronomy & Astrophysics, Australian National
University, Cotter Road, Weston Creek, ACT 2611, Canberra, Australia  Research
School of Computer Science, Australian National University, Acton ACT 2601,
Australia  Nelson Caldwell Center for Astrophysics $|$ Harvard & Smithsonian,
60 Garden Street, Cambridge, MA 02138, USA  Phillip Cargile Center for
Astrophysics $|$ Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138,
USA  Joshua S. Speagle (沈佳士) Banting & Dunlap Fellow  Department of
Statistical Sciences, University of Toronto, Toronto, ON M5S 3G3, Canada
David A. Dunlap Department of Astronomy & Astrophysics, University of Toronto,
Toronto, ON M5S 3H4, Canada  Dunlap Institute for Astronomy & Astrophysics,
University of Toronto, Toronto, ON M5S 3H4, Canada  Vedant Chandra Center for
Astrophysics $|$ Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138,
USA  Benjamin D. Johnson Center for Astrophysics $|$ Harvard & Smithsonian, 60
Garden Street, Cambridge, MA 02138, USA  Turner Woody Center for Astrophysics
$|$ Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA  Jiwon
Jesse Han Center for Astrophysics $|$ Harvard & Smithsonian, 60 Garden Street,
Cambridge, MA 02138, USA

###### Abstract

The Milky Way’s satellite galaxies (“surviving dwarfs”) have been studied for
decades as unique probes of chemical evolution in the low-mass regime. Here we
extend such studies to the “disrupted dwarfs”, whose debris constitutes the
stellar halo. We present abundances ([Fe/H], [$\alpha$/Fe]) and stellar masses
for nine disrupted dwarfs with $M_{\rm{\star}}\approx
10^{6}-10^{9}M_{\rm{\odot}}$ from the H3 Survey (Sagittarius, Gaia-Sausage-
Enceladus, Helmi Streams, Sequoia, Wukong/LMS-1, Cetus, Thamnos, I’itoi,
Orphan/Chenab). The surviving and disrupted dwarfs are chemically distinct: at
fixed mass, the disrupted dwarfs are systematically metal-poor and
$\alpha$-enhanced. The disrupted dwarfs define a mass-metallicity relation
(MZR) with a similar slope as the $z=0$ MZR followed by the surviving dwarfs,
but offset to lower metallicities by $\Delta$[Fe/H]${\approx}0.3{-}0.4$ dex.
Dwarfs with larger offsets from the $z=0$ MZR are more $\alpha$-enhanced with
[$\alpha$/Fe] =
$0.43^{+0.09}_{-0.09}\times\Delta\rm{[Fe/H]}+0.08^{+0.03}_{-0.03}$. In
simulations as well as observations, galaxies with higher $\Delta$[Fe/H]
formed at higher redshifts – exploiting this, we infer the disrupted dwarfs
have typical star-formation truncation redshifts of $z_{\rm{trunc}}{\sim}1-2$.
We compare the chemically inferred $z_{\rm{trunc}}$ with dynamically inferred
accretion redshifts and find almost all dwarfs are quenched only after
accretion. The differences between disrupted and surviving dwarfs are likely
because the disrupted dwarfs assembled their mass rapidly, at higher
redshifts, and within denser dark matter halos that formed closer to the
Galaxy. Our results place novel archaeological constraints on low-mass
galaxies inaccessible to direct high-$z$ studies: (i) the redshift evolution
of the MZR along parallel tracks but offset to lower metallicities extends to
$M_{\rm{\star}}\approx 10^{6}-10^{9}M_{\rm{\odot}}$; (ii) galaxies at
$z\approx 2-3$ are $\alpha$-enhanced with [$\alpha$/Fe]$\approx$0.4.

Galaxy: halo — Galaxy: kinematics and dynamics — Galaxy: evolution — Galaxy:
formation — Galaxy: stellar content

††facilities: MMT (Hectochelle), Gaia††software:  IPython (Pérez & Granger,
2007), matplotlib (Hunter, 2007), numpy (Oliphant, 2006–), scipy (Virtanen et
al., 2020), jupyter (Kluyver et al., 2016), gala (Price-Whelan, 2017; Price-
Whelan et al., 2017), Astropy (Astropy Collaboration et al., 2013, 2018),

##  1 Introduction

In the $\Lambda$CDM paradigm, galaxies like the Milky Way (MW) grow by
assimilating smaller galaxies (e.g., White & Frenk, 1991). While some of these
accreted galaxies orbit the MW largely intact (“surviving dwarfs”), the vast
majority ($\gtrsim 70-80\%$, e.g., Fattahi et al. 2020; Santistevan et al.
2020) are predicted to have been tidally shredded (“disrupted dwarfs”). The
remains of these disrupted dwarfs are expected to comprise the bulk of the
stellar halo (e.g., Bullock & Johnston, 2005; Cooper et al., 2010; Monachesi
et al., 2019; Font et al., 2020).

A puzzle in this context was revealed by chemical abundance surveys of the
surviving dwarfs. These dwarfs were found to be deficient in
$\alpha$-elements, often with sub-solar [$\alpha$/Fe] compared to halo stars
with [$\alpha$/Fe]$\approx 0.2-0.3$ at similar metallicity (e.g., Fulbright,
2002; Shetrone et al., 2003; Tolstoy et al., 2003; Venn et al., 2004; Geisler
et al., 2005). If the halo was built out of dwarf accretion, why is it
chemically distinct from the surviving dwarfs? A proposed solution came from
simulations that predicted that the majority of halo stars arose from a
handful of relatively massive, $\alpha$-enhanced galaxies accreted at
$z\gtrsim 2$ (e.g., Font et al., 2006). For instance, Robertson et al. (2005)
argued that the observed halo abundance pattern was likely driven by a handful
of massive $M_{\rm{\star}}\approx 2.5\times 10^{8}M_{\rm{\odot}}$ dwarfs
disrupted $\approx 10$ Gyrs ago. The predicted $\alpha$-enhancement was due to
their rapid star-formation histories necessitated by their early accretion
times. In short, these solutions posited that the disrupted dwarfs had
distinct stellar populations from the surviving dwarfs.

Tracing every star in the halo back to its parent dwarf galaxy has been a
long-harbored ambition of Galactic astronomy (e.g., Johnston et al., 1996;
Helmi & de Zeeuw, 2000; Brown et al., 2005). Thanks to Gaia and complementary
spectroscopic surveys this ambition is now being fulfilled – the majority of
halo stars have been associated with distinct parent galaxies (e.g., Naidu et
al., 2020a; Yuan et al., 2020; Bonaca et al., 2021; An & Beers, 2021; Horta et
al., 2021; Ji et al., 2021; Malhan et al., 2022). For instance, one of the
massive dwarfs anticipated by Robertson et al. (2005) is now known to be Gaia-
Sausage Enceladus (GSE, Belokurov et al. 2018b; Helmi et al. 2018; Naidu et
al. 2021), which merged with the MW at $z\approx 1-2$ (e.g., Gallart et al.,
2019; Bonaca et al., 2020; Belokurov et al., 2020; Montalbán et al., 2021;
Xiang & Rix, 2022). GSE ([$\alpha$/Fe]$\approx 0.2$) comprises $\approx 50\%$
of the stellar halo, and the vast majority of the [Fe/H]$<-1$ halo in the
solar neighborhood (e.g., Naidu et al., 2020a). This single accreted object
largely explains the higher [$\alpha$/Fe] of the local halo compared to
surviving dwarfs.

With the halo now resolved into a collection of distinct progenitors, we can
directly compare stellar populations of disrupted and surviving dwarfs. A
large body of theoretical work has predicted significant differences – for
instance, the disrupted dwarfs are expected to have been accreted much
earlier, largely at $z\gtrsim 1$, whereas the surviving dwarfs are generally
expected to be more recent arrivals with extended star-formation histories
(e.g., Sales et al., 2007; Tissera et al., 2012; Fattahi et al., 2020). These
differences are expected to manifest in chemical abundance patterns (e.g.,
Robertson et al., 2005; Font et al., 2006). Indeed, several observational
studies have contrasted the chemistry (e.g., $\alpha$-abundances) and make-up
(e.g., relative fractions of RR Lyrae subtypes) of halo stars as a whole vs.
the surviving dwarfs, finding stark differences (e.g., Venn et al., 2004;
Tolstoy et al., 2003, 2009; Zinn et al., 2014; Stetson et al., 2014;
Fiorentino et al., 2015, 2017; Belokurov et al., 2018a). Here we disaggregate
the halo to offer an apples-to-apples comparison of surviving vs. disrupted
dwarfs at fixed stellar mass.

Independent of their relationship to the MW satellites, the disrupted dwarfs
provide convenient access to early-Universe stellar abundances at a spatial
resolution (star-by-star) and mass-range ($M_{\rm{\star}}\lesssim
10^{9}M_{\rm{\odot}}$) currently inaccessible to direct high-$z$ studies.
While the surviving dwarfs provide the clearest view of e.g., the $z=0$
stellar mass-stellar metallicity relation (MZR, e.g., Kirby et al. 2013), the
disrupted dwarfs are expected to have formed and disintegrated at higher
redshifts on average (e.g., Fattahi et al., 2020). The disrupted dwarfs are
already being used in “high-$z$” studies to make timing arguments that exploit
the disruption redshift and infer that both core-collapse supernovae (CCSNe)
and neutron star mergers produce $r$-process elements (e.g., Matsuno et al.,
2021a; Naidu et al., 2022). Here we derive novel archaeological constraints on
the stellar chemistry of low-mass galaxies at $z\approx 1-3$ complementary to
direct high-$z$ studies.

This paper is organized as follows. In §2 we assemble [Fe/H], [$\alpha$/Fe],
and stellar masses for the surviving and disrupted dwarfs. In §3 we describe
the four interlinked figures in this paper, and then interpret them in §4 –
§4.1 and §4.2 explain the differences between the disrupted and surviving
dwarfs, §4.3 compares accretion and quenching redshifts, and §4.4 describes
the archaeological connection to high-$z$ stellar abundances. “Dwarfs” always
denotes dwarf galaxies, and never refers to low luminosity stars. “Z” denotes
metallicity, and “$z$” stands for redshift. We use medians to describe the
central values of distributions, with uncertainties on the median (16th and
84th percentiles) from bootstrap resampling. In converting between redshifts
and lookback times we adopt the Planck Collaboration et al. (2020) cosmology.

Table 1: Properties of disrupted dwarf galaxies from the H3 Survey.

Galaxy | $\log(M_{\star}/M_{\rm{\odot}})$ | [Fe/H] | [$\alpha$/Fe] |  $\Delta$[Fe/H] | $z_{\rm{trunc}}$ | $z_{\rm{acc}}$ | $N_{\rm{\star}}$
---|---|---|---|---|---|---|---
Sagittarius | 8.8 | -0.96${}^{+0.03}_{-0.03}$ | 0.12${}^{+0.00}_{-0.01}$ | 0.01 | $<0.1$ | 0.6 | 675
Gaia-Sausage-Enceladus | 8.7 | -1.18${}^{+0.00}_{-0.01}$ | 0.21${}^{+0.00}_{-0.00}$ | 0.30 | 1.2 | 2.0 | 2684
Helmi Streams | 8.0 | -1.28${}^{+0.02}_{-0.04}$ | 0.15${}^{+0.01}_{-0.01}$ | 0.19 | 0.8 | 1.0 | 91
Sequoia | 7.2 | -1.59${}^{+0.03}_{-0.04}$ | 0.14${}^{+0.03}_{-0.01}$ | 0.25 | 0.7 | – | 72
Wukong/LMS-1 | 7.1 | -1.58${}^{+0.06}_{-0.03}$ | 0.24${}^{+0.03}_{-0.01}$ | 0.23 | 0.9 | 1.1 | 111
Cetus | 7.0 | -1.85${}^{+0.04}_{-0.04}$ | 0.29${}^{+0.01}_{-0.02}$ | 0.45 | 2.3 | 0.5 | 56
Thamnos | 6.7 | -1.90${}^{+0.08}_{-0.06}$ | 0.29${}^{+0.04}_{-0.01}$ | 0.41 | 1.9 | $\gtrsim 2$ | 32
I’itoi | 6.3 | -2.39${}^{+0.07}_{-0.07}$ | 0.38${}^{+0.04}_{-0.01}$ | 0.79 | $>6$ | – | 65
Orphan/Chenab | 6.1 | -1.75${}^{+0.10}_{-0.20}$ | 0.04${}^{+0.10}_{-0.07}$ | 0.10 | $0.3$ | – | 11

Note. — Stellar masses for Sgr, GSE, and Helmi Streams are from tailored
N-body simulations, and for the remaining galaxies from star-counts (see
§2.1). $\Delta$[Fe/H] measures the vertical offset of a galaxy from the $z=0$
MZR in Kirby et al. (2013), with metal-poor (metal-rich) galaxies defined to
have positive (negative) $\Delta$[Fe/H] – see Eqn. 3. $z_{\rm{trunc}}$ is the
SFH truncation redshift, defined as the redshift at which the galaxy lies on
the MZR from the FIRE simulations (Ma et al., 2016), see Eqn. 5. The accretion
redshift ($z_{\rm{acc}}$) is when the disrupted system makes its first
pericentric passage, and is based on N-body simulations listed in §2.1.
$N_{\rm{\star}}$ is the number of stars identified in Naidu et al. (2020a) as
part of each structure, except for Cetus and Orphan/Chenab that are selected
from the current H3 giants sample (see §2.1).

Table 2: Properties of surviving dwarf galaxies.

Galaxy | $\log(M_{\star}/M_{\rm{\odot}})$ | [Fe/H] | [$\alpha$/Fe] |  $\Delta$[Fe/H] | $z_{\rm{trunc}}$ | $z_{\rm{acc}}$ | $N_{\rm{Fe}}$ | $N_{\rm{Mg}}$
---|---|---|---|---|---|---|---|---
Large Magellanic Cloud | 9.4 | -0.71${}^{+0.00}_{-0.01}$ | 0.04${}^{+0.00}_{-0.00}$ | 0.05 | 0.15 | 0.11 | 3908 | 3907
Small Magellanic Cloud | 8.5 | -1.08${}^{+0.00}_{-0.01}$ | 0.0${}^{+0.00}_{-0.00}$ | 0.14 | 0.46 | 0.11 | 1143 | 1142
Fornax | 7.4 | -1.04${}^{+0.01}_{-0.01}$ | -0.13${}^{+0.01}_{-0.01}$ | -0.23 | – | 2.12 | 672 | 372
Leo I | 6.7 | -1.45${}^{+0.01}_{-0.01}$ | 0.16${}^{+0.03}_{-0.04}$ | -0.03 | – | 0.18 | 814 | 170
Sculptor | 6.6 | -1.68${}^{+0.01}_{-0.01}$ | 0.20${}^{+0.02}_{-0.05}$ | 0.17 | 0.57 | 2.05 | 375 | 96
Antlia 2 | 6.2 | -1.90${}^{+0.04}_{-0.04}$ | – | 0.28 | 1.06 | – | 283 | –
Leo II | 6.1 | -1.63${}^{+0.01}_{-0.01}$ | 0.14${}^{+0.03}_{-0.07}$ | -0.04 | – | 0.68 | 256 | 54
Carina | 6.0 | -1.72${}^{+0.01}_{-0.01}$ | 0.18${}^{+0.03}_{-0.03}$ | 0.04 | 0.13 | 1.66 | 437 | 60
Sextans | 5.8 | -1.94${}^{+0.01}_{-0.01}$ | 0.11${}^{+0.06}_{-0.03}$ | 0.2 | 0.72 | – | 123 | 65
Ursa Minor | 5.7 | -2.13${}^{+0.01}_{-0.01}$ | 0.32${}^{+0.07}_{-0.01}$ | 0.36 | 1.53 | 1.81 | 190 | 26
Crater 2 | 5.6 | -2.16${}^{+0.04}_{-0.04}$ | – | 0.34 | 1.39 | – | 141 | –
Draco | 5.5 | -1.98${}^{+0.01}_{-0.01}$ | 0.12${}^{+0.07}_{-0.07}$ | 0.14 | 0.48 | 1.34 | 269 | 14
Canes Venatici I | 5.5 | -1.91${}^{+0.01}_{-0.01}$ | – | 0.06 | 0.2 | 1.09 | 151 | –

Note. — See caption of Table 1 for column definitions. See §2.2 for references
for $\log(M_{\star}/M_{\rm{\odot}})$, [Fe/H], and [Mg/Fe]. $z_{\rm{acc}}$
values are from Fillingham et al. (2019). $N_{\rm{Fe}}$ and $N_{\rm{Mg}}$ are
the number of stars used to estimate [Fe/H] and [$\alpha$/Fe] respectively. A
negative $\Delta$[Fe/H] means the galaxy is more metal-rich than expected from
the $z=0$ MZR – the corresponding $z_{\rm{trunc}}$ from Eqn. 5 is undefined,
consistent with relatively recent star-formation observed in such systems
(e.g., Fornax).

##  2 Data & Methods

###  2.1 Disrupted galaxy sample

This study builds on results from the H3 Survey (Conroy et al., 2019) – an
ongoing high-latitude ($|b|>20^{\circ}$), high-resolution ($R=32,000$)
spectroscopic survey of $\approx 300,000$ stars in the distant
($d_{\rm{helio}}\approx 2-100$ kpc) Galaxy. H3 is measuring radial velocities
precise to $\lesssim$1 km $\rm{s^{-1}}$, [Fe/H] and [$\alpha$/Fe] abundances
precise to $\lesssim$0.1 dex, and spectrophotometric distances precise to
$\lesssim$10$\%$ (Cargile et al., 2020). Combined with Gaia proper motions
(SNR$>$3 for $>$90$\%$ of the sample), H3 provides full 6D phase-space and 2D
chemical-space for detecting and characterizing substructure. Naidu et al.
(2020a) used the H3 sample of giant stars (N=5684, $|b|{>}40^{\circ}$,
$d_{\rm{helio}}=3-50$ kpc) to assign almost the entire distant Galaxy to
individual structures including known accreted dwarfs (e.g., Sagittarius), as
well as hitherto unknown structures (e.g., Wukong).

The sample of disrupted dwarf galaxies analyzed in this work is as defined in
Naidu et al. (2020a), and includes Sagittarius (Ibata et al., 1994; Law &
Majewski, 2010; Johnson et al., 2020), Gaia-Sausage-Enceladus (Belokurov et
al., 2018b; Haywood et al., 2018; Myeong et al., 2018; Helmi et al., 2018;
Feuillet et al., 2021; Buder et al., 2022), the Helmi Streams (Helmi et al.,
1999; Koppelman et al., 2019b; Limberg et al., 2021), Sequoia (Myeong et al.,
2019; Matsuno et al., 2019, 2021b; Monty et al., 2020; Aguado et al., 2021),
Wukong (independently discovered as LMS-1 in Yuan et al. 2020, and studied in
Malhan et al. 2021, 2022; Shank et al. 2022), Thamnos (Koppelman et al.,
2019a; Sofie Lövdal et al., 2022; Ruiz-Lara et al., 2022), and I’itoi.

We note three relevant developments since Naidu et al. (2020a). The Arjuna
structure identified in that work is treated here as the highly retrograde
debris of GSE, and is thus included as a part of GSE (see Naidu et al. 2021
for details). With the acquisition of new southern fields covering the
dynamically cold Cetus stream (e.g., Newberg et al., 2009; Thomas & Battaglia,
2021; Yuan et al., 2021), the current H3 giants sample ($>2.5\times$ larger
than the sample studied in Naidu et al. 2020a) now has $N=56$ confident Cetus
members. Due to its dynamical coherence, Cetus is easily selected as follows:

$\displaystyle(L_{\rm{y}}>0.7)\land(L_{\rm{x}}>2.0)\land(-3.4<L_{\rm{z}}<-1.4)$
$\displaystyle\land\ (-1<E_{\rm{tot}}<-0.6),$ (1)

where total orbital energy ($E_{\rm{tot}}$) is in units of $10^{5}\
\rm{km^{2}\ s^{-2}}$ and angular momenta ($L_{\rm{x}}$, $L_{\rm{y}}$,
$L_{\rm{z}}$) are in units of $10^{3}\ \rm{kpc}\ \rm{km\ s^{-1}}$. Similarly,
we now also have $N=11$ confident members in the Orphan/Chenab galaxy (e.g.,
Grillmair, 2006; Newberg et al., 2010; Shipp et al., 2018; Koposov et al.,
2019; Erkal et al., 2019) that we select as follows:

$\displaystyle(L_{\rm{z}}>-6)\land(L_{\rm{x}}<-3.0)\land(-6.0<L_{\rm{z}}<-3.5)$
$\displaystyle\land\ (-0.7<E_{\rm{tot}}<-0.4).$ (2)

The median [Fe/H] we derive ($-1.75^{+0.10}_{-0.20}$) is in excellent
agreement with the Orphan ($-1.85^{+0.07}_{-0.07}$) and Chenab
($-1.78^{+0.04}_{-0.04}$) samples studied by the S5 Survey using the CaT
feature with $R\approx 10,000$ spectroscopy (Li et al., 2019, 2022).

We adopt the [Fe/H] and [$\alpha$/Fe] abundances reported in Table 1 of Naidu
et al. (2020a) based on $\approx 10$ stars in the least sampled system
(Orphan/Chenab) and $\approx 2700$ stars in the best sampled system (GSE).
Statistical errors on the median [Fe/H] and [$\alpha$/Fe] are generally small
($<0.05$) except in a handful of cases (see Table 1).

For total stellar masses we rely on: (i) tailored N-body simulations for the
more massive galaxies (GSE, Sgr, Helmi Streams), and (ii) star counts for the
other galaxies from Naidu et al. (2020a). Tailored N-body simulations have
been run for GSE (Naidu et al., 2021), Sgr (e.g., Laporte et al., 2018), the
Helmi Streams (Koppelman et al., 2019b), Wukong (Malhan et al., 2021), Thamnos
(Koppelman et al., 2019a), and Cetus (Chang et al., 2020). These simulations
qualitatively reproduce the phase-space distribution of debris, but the
downside is that their dynamics are largely set by the total mass, and they
are thus reliant on stellar mass - halo mass relations (SMHMRs). This is not a
problem for the more massive ($M_{\rm{\star}}>10^{8}M_{\rm{\odot}}$) systems
(GSE, Sgr, Helmi Streams) – the SMHMR is relatively well-determined in this
regime (e.g., Behroozi et al., 2019), and multiple cross checks on the stellar
mass are available (e.g., chemical evolution modeling with hundreds of stars).

For lower mass systems we use relative star counts reported in Naidu et al.
(2020a). Here we translate their relative star counts to stellar masses
assuming GSE has an $M_{\rm{\star}}=5\times 10^{8}M_{\rm{\odot}}$. For
instance, Wukong’s star counts are $\approx 2.5\%$ of those of GSE, and so we
infer its mass is $\approx 1.3\times 10^{7}M_{\rm{\odot}}$. We choose GSE as
the reference object to derive other systems’ masses because its stellar mass
has been estimated via multiple independent methods that agree well with each
other (e.g., Helmi et al., 2018; Kruijssen et al., 2020; Mackereth & Bovy,
2020; Naidu et al., 2021; Callingham et al., 2022), and because it is fairly
well mixed within the H3 Survey footprint (Han et al., 2022). As a sanity
check, based on this method, Sgr would have an inferred stellar mass of
$\approx 3\times 10^{8}M_{\rm{\odot}}$, which is in excellent agreement with
various literature estimates that span $\approx 2-6\times
10^{8}M_{\rm{\odot}}$ (e.g., Niederste-Ostholt et al., 2010; Law & Majewski,
2010; Kruijssen et al., 2020; Vasiliev & Belokurov, 2020), and within a factor
of 2 of our adopted value ($6\times 10^{8}M_{\rm{\odot}}$) from Laporte et al.
2018. This cross-check inspires confidence that even for relatively unmixed
systems our derived stellar masses are reasonable, and gives a sense of the
systematic uncertainty for our reported values.

Note that the relative star counts are corrected for the survey selection
function (see §2.3 of Naidu et al. 2020a for details). We also checked the
“orbit bias” across the various low-mass structures is negligible – i.e.,
whether the integrated orbits of stars from a particular system over the last
10 Gyrs spend significantly longer/shorter periods within our survey footprint
and distance range probed compared to the GSE sample. The exception is the
dynamically cold, unmixed Cetus – our reported stellar mass for Cetus comes
with this caveat, i.e., that it may be underestimated by $\approx 2\times$.
Finally, we correct the relative star-counts for structures selected via sharp
cuts on their MDF in Naidu et al. (2020a) in order to avoid contamination from
the low-eccentricity tail of GSE (e.g., I’itoi). We model these MDFs as having
multiple components – i) the GSE MDF model fit in Naidu et al. (2020a), and
ii) Gaussians centred at the peak metallicity of the dwarfs in question. The
only counts that require meaningful revision are I’itoi’s ($\approx-30\%$) and
Sequoia’s ($\approx+35\%$) which translate to modest 0.1 dex shifts in their
inferred stellar mass. The resulting stellar masses for all systems are listed
in Table 1.

An important caveat to bear in mind is that the sample studied in Naidu et al.
(2020a) spans $r_{\rm{gal}}\approx 6-50$ kpc. That is, we are missing dwarfs
entirely contained in the inner few kpc (e.g., Kraken, Kruijssen et al. 2020)
as well as those exclusively inhabiting the outer reaches of the galaxy.
Broadly, the systems with the entirety of their debris at $>50$ kpc are likely
to be very recent accretion events ($z\lesssim 0.5$), and those buried in the
Galactic center were likely accreted very early ($z\gtrsim 2$) (e.g., Pfeffer
et al., 2020). In other words, there is a diverse spectrum of disrupted
dwarfs, and our findings must be read as applying to a specific portion of
this spectrum corresponding to intermediate accretion redshifts. The mapping
between accretion redshift and the distance at which debris is deposited holds
to first order, but is scrambled by other factors like the dwarf’s orbit,
size, and mass (see Amorisco 2017; Naidu et al. 2021 for parameter studies).

###  2.2 Surviving dwarfs sample

The $M_{\rm{\star}}$ range of interest for comparison with the disrupted dwarf
sample is $\approx 10^{5}-10^{9}M_{\rm{\odot}}$, which includes 13 known Milky
Way satellites. For Fornax, Leo I, Leo II, Sculptor, Draco, Sextans, Ursa
Minor (UMin), and Canes Venatici I we draw stellar masses (estimated via
integrated luminosities) and metallicities from the Kirby et al. (2013)
compilation that are homogeneously derived from Keck/DEIMOS medium-resolution
($R\approx 6500$) spectroscopy. Given that this compilation comprises the
majority of our sample, we also adopt the $z=0$ Kirby et al. (2013) MZR for
comparison. For the remaining five dwarfs of interest not included in Kirby et
al. (2013), metallicities and stellar masses are sourced from van der Marel et
al. (2009); Nidever et al. (2020); Hasselquist et al. (2021) for the
Magellanic Clouds, Ji et al. (2021) for Crater 2 and Antlia 2, and Koch et al.
(2006, 2008); de Boer et al. (2014) for Carina.

We use [Mg/Fe] to approximate [$\alpha$/Fe] since the H3 spectral window (5150
- 5300 Å) is mostly sensitive to the prominent Mgi triplet at 5175 Å(Cargile
et al., 2020). We adopt Mg abundances derived from high-resolution
spectroscopy when available, combining samples from multiple studies when
required to build up numbers. For the Magellanic Clouds we use the sample in
Hasselquist et al. (2021), for Fornax we combine Letarte et al. (2010, 2018);
Hendricks et al. (2014); Hasselquist et al. (2021), for Leo I and Leo II we
use Shetrone et al. (2009) along with the high-SNR subset ($<0.3$ dex errors
on [Mg/Fe]) of Kirby et al. (2011), for Sculptor we draw on Hill et al.
(2019), for Carina we use Norris et al. (2017), for Sextans we combine
Shetrone et al. (2003); Tafelmeyer et al. (2010); Theler et al. (2020);
Mashonkina et al. (2022), for UMin we combine Shetrone et al. (2003); Sadakane
et al. (2004); Cohen & Huang (2010); Ural et al. (2015), and finally for Draco
we combine Shetrone et al. (2003); Cohen & Huang (2009). Antlia 2 and Crater 2
have no [Mg/Fe] reported, and Canes Venatici I has too few stars measured
robustly (N=2 in Kirby et al. 2011 with $<0.3$ dex error on [Mg/Fe]) to make a
meaningful estimate. Almost all the stars we compile here are giant stars,
similar to our disrupted dwarf sample. All values for [Mg/Fe] reported in
Table 2 are medians and associated uncertainties are errors on the median from
bootstrap resampling.

Figure 1: [$\alpha$/Fe] vs. [Fe/H] for disrupted dwarfs from the H3 Survey
(purple stars) and for surviving dwarfs from the literature (gray squares). At
fixed [Fe/H], the disrupted dwarfs are relatively $\alpha$ enhanced compared
to the surviving dwarfs, particularly at [Fe/H]$>-1.5$. Note the difference
between GSE, which dominates the [Fe/H]$<-1$ halo around the Sun in terms of
star counts, and Fornax/SMC that lie at comparable metallicity. This
difference explains the well-known result (e.g., Venn et al., 2004) that the
stellar halo is $\alpha$-enhanced at fixed metallicity compared to stars in
the surviving dwarfs. Figure 2: Left: Stellar metallicity vs. stellar mass for
the surviving (gray) and disrupted (purple) dwarfs. The gray line is the $z=0$
MZR (Kirby et al., 2013), while the purple line is offset by 0.3 dex, which is
the median offset of the disrupted dwarfs. Sgr and I’itoi are notable
outliers, likely due to their low and high disruption redshifts respectively
(see Fig. 3). Right: [$\alpha$/Fe] vs. stellar mass. At fixed mass, the
disrupted dwarfs are systematically $\alpha$-enhanced compared to the
surviving dwarfs, particularly at $M_{\rm{\star}}>10^{7}M_{\rm{\odot}}$. UMin
and Orphan/Chenab are notable exceptions. Like most of the disrupted dwarfs,
UMin had a rapid star-formation history ($\approx 400$ Myrs, Kirby et al.
2011), and was likely accreted very early ($z\approx 2$, Fillingham et al.
2019), while on the other hand, Orphan/Chenab appears to be a relatively
recent arrival based on its high orbital energy (apocenter of $\approx 70$
kpc), which is comparable to Sgr, and typical for $z<0.5-1$ accretion (e.g.,
Pfeffer et al., 2020).

##  3 Results

In Figure 1 we plot [Fe/H] vs. [$\alpha$/Fe] for disrupted dwarfs (purple
stars) and contrast them with the surviving dwarfs (gray squares). Generally,
the disrupted dwarfs are $\alpha$-enhanced compared to the surviving dwarfs.
This is particularly apparent at [Fe/H]$\gtrsim-1.4$ with GSE, the Helmi
Streams and Sagittarius lying $\approx 0.2-0.3$ dex higher than Fornax and the
Magellanic Clouds that have comparable metallicities.

Figure 1 explains the well-known result (e.g., Venn et al., 2004; Tolstoy et
al., 2003, 2009) that at fixed metallicity the local halo is preferentially
$\alpha$-enhanced compared to surviving dwarf stars. This follows from the
finding that the [Fe/H]$<-1$ halo within a few kpc from the Sun is dominated
by GSE (e.g., Di Matteo et al., 2019; Bonaca et al., 2020; An & Beers, 2021).
Further, not just GSE, but almost all the disrupted dwarfs appear
systematically $\alpha$-enhanced compared to their surviving peers. We make a
more controlled comparison at fixed stellar mass that makes this apparent in
the following figures.

In Figure 2 we depict stellar masses and stellar metallicities. As a gray
dashed line we show the $z=0$ MZR estimated from 35 MW and local group dwarfs,
most of which are not shown in Figure 2 (Kirby et al., 2013). The disrupted
dwarfs fall along a fairly tight sequence that runs almost parallel to the
$z=0$ MZR but is offset to lower metallicities. The median offset, computed by
subtracting the expected [Fe/H] as per the $z=0$ MZR from the observed [Fe/H],
is $0.27^{+0.05}_{-0.02}$ dex. Formally, we fit the disrupted dwarf MZR to be:

$\displaystyle\rm{[Fe/H]}=-2.11^{+0.11}_{-0.12}+0.36^{+0.12}_{-0.04}\log{\left(\frac{\textit{M}_{\star}}{10^{6}\textit{M}_{\rm{\odot}}}\right)}.$
(3)

The slope for the disrupted dwarf MZR is almost identical to the $z=0$ Kirby
et al. (2013) MZR for surviving dwarfs ($0.30^{+0.02}_{-0.02}$), and the
normalization is offset to lower metallicities by $\approx 0.4$ dex
($-2.11^{+0.11}_{-0.12}$ vs. $-1.69^{+0.04}_{-0.04}$). Sgr, which straddles
the boundary between surviving and disrupted, as it is still in the process of
being stripped and has been forming stars as recently as 2 Gyrs ago (e.g.,
Alfaro-Cuello et al., 2019) as well as I’itoi, which was likely accreted
significantly earlier than the rest of our sample are clear outliers in Fig. 2
and excluded from this fit. Including them results in a steeper slope of
$0.50^{+0.08}_{-0.08}$ and a similar offset of $-2.30^{+0.15}_{-0.12}$.

In the right panel of Figure 2 we plot [$\alpha$/Fe] vs. stellar mass for the
dwarf samples. At fixed stellar mass, almost all the disrupted dwarfs are
systematically $\alpha$-enhanced, forming a sequence that lies above their
surviving peers. That is, not only is the stellar halo $\alpha$-enhanced
compared to the surviving dwarfs in aggregate, but this trend also holds when
the halo is resolved into distinct galaxies. Not just GSE, but all the
disrupted dwarfs in the inner halo are systematically $\alpha$-enhanced
compared to the surviving dwarfs. UMin and Orphan/Chenab are instructive
exceptions and are discussed in §4.1.

In Figure 3 we plot [$\alpha$/Fe] as a function of $\Delta$[Fe/H], i.e., how
metal-poor a galaxy is compared to the expectation from the $z=0$ Kirby et al.
(2013) MZR for its stellar mass. The motivation for introducing $\Delta$[Fe/H]
comes from high-$z$ observations (e.g., Henry et al., 2021; Topping et al.,
2021; Sanders et al., 2021) and hydrodynamical simulations (e.g., Ma et al.,
2016; Davé et al., 2017; De Rossi et al., 2017; Torrey et al., 2019; Langan et
al., 2020) that show that the MZR evolves along parallel tracks towards lower
metallicities at higher redshifts (discussed further in §4.4). We interpret
$\Delta$[Fe/H] as tracking the redshift at which the galaxy falls on the MZR,
i.e., a higher $\Delta$[Fe/H] implies the galaxy would be a typical galaxy at
a higher redshift. We compute $\Delta$ [Fe/H] as follows:

$\displaystyle\Delta\rm{[Fe/H]}$ $\displaystyle=\rm{[Fe/H]}\ \rm{(MZR\ |\
\it{M}_{\rm{\star}}\ \rm{obs.})}-\rm{[Fe/H]\ (obs.)}$
$\displaystyle=-1.69+0.30\log{\left(\frac{M_{\star}\rm{(obs.)}}{10^{6}M_{\rm{\odot}}}\right)}-\rm{[Fe/H](obs.)},$
(4)

where [Fe/H] (obs.) and $M_{\star}$ (obs.) are the observed metallicity and
stellar mass, as listed in Table 1. To translate $\Delta$[Fe/H] into the
redshift when the dwarf was located on the MZR ($z_{\rm{trunc}}$, i.e., the
redshift of star-formation truncation), we adopt the MZR evolution from the
FIRE simulations (Ma et al., 2016) that is consistent with latest constraints
for $M_{\rm{\star}}\gtrsim 10^{9}M_{\rm{\odot}}$ galaxies (reviewed in
Maiolino & Mannucci 2019):

$\displaystyle z_{\rm{trunc}}=-2\ln\left(1-\Delta\rm{[Fe/H]}/0.67\right).$ (5)

Figure 3: [$\alpha$/Fe] vs. $\Delta$[Fe/H], where the latter measures how
metal-poor a galaxy is compared to the expectation from the $z=0$ MZR (see
Eqn. 3). The dashed line is fit to both surviving and disrupted dwarfs. Fits
to 100 bootstrap samples of the data are shown as transparent orange lines.
The more metal-poor a dwarf is compared to the expectation from the the $z=0$
MZR (i.e., a higher $\Delta$[Fe/H]), the more $\alpha$-enhanced it is likely
to be. In hydrodynamical simulations $\Delta$[Fe/H] correlates with the
redshift of star-formation truncation ($z_{\rm{trunc}}$), and so the above
plot may be interpreted as a trend of higher [$\alpha$/Fe] on average at
higher redshifts. Shown at the top are $z_{\rm{trunc}}$ values corresponding
to $\Delta$[Fe/H] from the FIRE simulations (Eqn. 6, Ma et al. 2016). We
highlight Sgr and I’itoi as extremes among the disrupted dwarfs, and UMin and
Fornax as extremes among the surviving dwarfs. While Fornax and Sgr have
formed stars till very recently ($z\approx 0$), UMin and I’itoi likely
assembled their mass rapidly and very early.

This conversion allows us to associate each dwarf with a redshift when it
likely finished assembling its mass. The key caveat for this conversion is
that across $z\approx 1-3$ a modest amount of intrinsic scatter is observed in
the MZR at $M_{\rm{\star}}>10^{9}M_{\rm{\odot}}$ ($\approx 0.1$ dex, Sanders
et al. 2021), but the magnitude of scatter in lower mass galaxies is currently
unconstrained. As a confidence-inspiring cross-check, for the two disrupted
dwarfs with well-measured star-formation histories (SFHs), GSE and Sgr, we
find $z_{\rm{trunc}}=1.2$ and $z_{\rm{trunc}}<0.1$, in excellent agreement
with their reported SFHs (e.g., Bonaca et al., 2020; Alfaro-Cuello et al.,
2019).

In Figure 3 we see $\Delta$[Fe/H] correlates remarkably well with
[$\alpha$/Fe] for both disrupted and surviving dwarfs. Systems with large
$\Delta$[Fe/H], that likely assembled their stars at higher redshifts are more
$\alpha$-enhanced. The relationship, fit to surviving as well as disrupted
dwarfs is described as follows:

$\displaystyle[\alpha/\rm{Fe}]=0.43^{+0.09}_{-0.09}\times\Delta\rm{[Fe/H]}+0.08^{+0.03}_{-0.03}.$
(6)

In Figure 4 we compare the star-formation truncation redshift inferred via
chemistry ($z_{\rm{trunc}}$, Eqn. 5) and the accretion redshift inferred via
dynamics ($z_{\rm{acc}}$). For the disrupted dwarfs we adopt $z_{\rm{acc}}$
(i.e., when the first pericentric passage occurs) from the simulations listed
in §2, whereas for the surviving dwarfs we rely on Fillingham et al. (2019)
who inferred $z_{\rm{acc}}$ by comparing Gaia satellite dynamics (Fritz et
al., 2018) to the Phat ELVIS simulations of MW-mass galaxies (Kelley et al.,
2019). Sgr is an exception, for which we adopt $z_{\rm{acc}}$ from Lian et al.
2020; Ruiz-Lara et al. 2020 who measured starbursts in the MW disk that are
likely coincident with Sgr’s pericentric passages (Di Cintio et al., 2021).
For Thamnos we interpret the arguments in Koppelman et al. (2019a) as implying
$z_{\rm{acc}}>2$. In particular, for a $\approx 10^{6}M_{\rm{\odot}}$ galaxy
to have sunk as deep as Thmanos in the potential –
$E_{\rm{tot}}\approx-1.35\times 10^{5}$ km2 s-2, the lowest orbital energy of
all the galaxies considered here – strongly implies $z_{\rm{acc}}>2$ (see
e.g., first row of Fig. 3 in Pfeffer et al. 2020).

Given the entirely independent methods that go into deriving $z_{\rm{acc}}$
and $z_{\rm{trunc}}$, it is encouraging that both the disrupted and surviving
dwarfs are not randomly scattered in Figure 4. Further, for the disrupted
dwarfs $z_{\rm{trunc}}\propto z_{\rm{acc}}$, consistent with these systems
being quenched shortly after accretion. Cetus is the exception, with
$z_{\rm{trunc}}>>z_{\rm{acc}}$, which may be linked to uncertainty in its
derived stellar mass (§2.1). There are caveats. Systematic uncertainties are
significant and poorly understood – e.g., the simulations informing
$z_{\rm{acc}}$ do not account for an evolving MW potential with distortions
produced by the Magellanic Clouds (e.g., Garavito-Camargo et al., 2019, 2021;
Cunningham et al., 2020; Conroy et al., 2021) that likely biases the inferred
$z_{\rm{acc}}$ in a non-trivial fashion. On the other axis, $z_{\rm{trunc}}$
is inferred from one suite of hydrodynamical simulations (FIRE, Ma et al.
2016), though we have verified excellent agreement for Sgr and GSE.

Figure 4: Accretion redshift ($z_{\rm{acc}}$) from N-body simulations vs. the
star-formation truncation redshift ($z_{\rm{trunc}}$) for disrupted (purple
stars) and surviving (gray squares) dwarfs. The surviving dwarfs with
$z_{\rm{trunc}}$ consistent with recent/ongoing star-formation (i.e.,
$\Delta$[Fe/H]$>0$) are shown with gray arrows. The correlation between these
quantities for the disrupted dwarfs is heartening given that they are
estimated independently – $z_{\rm{acc}}$ from dynamics and $z_{\rm{trunc}}$
from chemistry. The $1:1$ line is shown in purple. The clustering of purple
points along this line argues for the truncation of SFH in disrupted dwarfs
being due to their interactions with the Milky Way. No sources, except for
Cetus, are consistent with being quenched significantly before accretion.

##  4 Discussion

###  4.1 Star-formation timescales explain why the disrupted dwarfs are metal-
poor and $\alpha$-enhanced

At fixed mass, the disrupted dwarfs are systematically metal-poor compared to
the $z=0$ MZR and $\alpha$-enhanced compared to the surviving dwarfs (Figure
2). This difference may be understood in terms of star-formation timescales –
to grow to a given stellar mass, the disrupted dwarfs, with typical
$z_{\rm{trunc}}\approx 1-2$, formed stars on a shorter timescale (i.e., pre-
disruption) compared to dwarfs of similar mass that survived to $z=0$ (e.g.,
GSE compared to SMC/LMC/Sgr, Sequoia/Wukong compared to Fornax). The
compressed star-formation history leaves less time for [$\alpha$/Fe] elevated
by Type II supernovae to be diluted by Fe from Type I supernovae (e.g.,
Tinsley, 1979; Robertson et al., 2005; Font et al., 2006). Let us consider a
few informative outliers that add to this picture.

UMin is the most metal-poor and $\alpha$-enhanced of the surviving dwarfs, and
lies closer to the disrupted dwarfs in all our figures (e.g., Fig. 3). Of the
surviving dwarfs, it has among the most rapid star-formation timescales,
assembling almost all its mass in $\approx 400$ Myrs (e.g., Kirby et al.,
2011; Weisz et al., 2014; Gallart et al., 2015). UMin was likely accreted at
$z\approx 2$ (Fillingham et al., 2019) and quenched shortly after by e.g., ram
pressure stripping. Its circular orbit ($e\approx 0.4-0.5$, Fritz et al. 2018;
Li et al. 2021; Battaglia et al. 2022) and low mass relative to the other
disrupted dwarfs may have kept it from being disrupted, since these properties
prolong the dynamical friction timescale (e.g., Amorisco, 2017; Naidu et al.,
2021; Vasiliev et al., 2022). We also make note of Crater 2 and Antlia 2,
which lie on the disrupted dwarf MZR and have the highest $\Delta$[Fe/H]
(0.34, 0.28) after UMin (0.36). These extended, low surface brightness dwarfs
do show signs of disruption (e.g., Ji et al., 2021) and may also have been
quenched early – our empirical relation predicts an elevated [$\alpha$/Fe] in
these galaxies.

Conversely, Sgr and Orphan/Chenab have the lowest $\Delta$[Fe/H],
[$\alpha$/Fe], and $z_{\rm{trunc}}$ of all the disrupted dwarfs, in line with
them being relatively recent arrivals to the MW with extended star-formation
histories. This is consistent with Panithanpaisal et al. (2021), who analysed
the FIRE2 simulations (Wetzel et al., 2016; Garrison-Kimmel et al., 2019) to
conclude that dwarf galaxies still observable as cogent stellar streams are
often chemically similar to the surviving dwarfs. Note that Orphan/Chenab has
the highest orbital energy (second only to Sgr) of all systems analyzed in
this work – recently infalling low-$\alpha$ streams like Orphan/Chenab may
comprise a large fraction of the halo beyond 50 kpc that we do not analyze in
this work (in fact, Font et al. 2006 suggest low [$\alpha$/Fe] as a search
strategy for such dwarfs).

These examples highlight that despite the broad differences we find in this
work between the surviving and the disrupted dwarfs, there is overlap in their
stellar populations – particularly when considering the disrupted dwarfs at
$>50$ kpc not in our sample, which likely resemble the surviving dwarfs. While
the star-formation timescale is informative, it may not be the entire story –
e.g., Sculptor/Sextans appear to also have rapidly built up their mass at
comparable redshifts to the disrupted dwarfs (e.g., Kirby et al., 2011; Weisz
et al., 2014; Gallart et al., 2015), but are not as $\alpha$-enhanced as
I’itoi/Thamnos, though the difference is not as stark as at
$>10^{7}M_{\rm{\odot}}$. Further, a deeper question persists – why were
galaxies like GSE/Wukong/Thamnos able to form as much mass as SMC/Fornax/Leo I
in a fraction of the time? We tackle these issues in the following section.

###  4.2 Different formation channels for disrupted and surviving dwarfs?

A generic prediction of $\Lambda$CDM simulations is that disrupted dark matter
subhalos are accreted and destroyed at higher redshifts than surviving
subhalos (e.g., Gao et al., 2004; Zentner et al., 2005; van den Bosch et al.,
2005). This trend is also borne out in zoom-in simulations of MW-like stellar
halos that find disrupted dwarfs have higher accretion redshifts (typical
$z_{\rm{acc}}>1$) compared to their surviving peers (e.g., Fattahi et al.,
2020). Subhalos that assembled their mass at higher redshifts are more
concentrated with a higher characteristic overdensity ($\propto(1+z)^{3}$, Mo
et al. 2010), and are also likely to inhabit clustered, overdense environments
(see Wechsler & Tinker 2018 for a recent review).

In light of this, we offer the following scenario. The disrupted dwarfs were
likely born in concentrated dark matter halos in a dense, gas-rich environment
close to the MW. Their halos resisted the loss of enriched gas to feedback.
They were able to sustain high star-formation efficiencies for large fractions
of their lifetimes, resulting in high [$\alpha$/Fe]. Nonetheless, their
proximity to the MW resulted in prompt accretion within a few Gyrs after
formation, which is reflected in their high $z_{\rm{trunc}}$ and
$z_{\rm{acc}}$ (e.g., GSE, Thamnos, I’itoi). On the other hand, most surviving
dwarfs, as well as disrupted dwarfs accreted recently (e.g., Orphan/Chenab)
began their journey towards our galaxy from farther low-density regions and/or
were born in less-concentrated halos that found it difficult to retain
enriched gas (explaining differences between I’itoi/Thamnos vs.
Sculptor/Sextans). The longer journeys and less concentrated halos directly
translate to extended star-formation histories, low [$\alpha$/Fe], and lower
$z_{\rm{acc}}$. We note that Gallart et al. (2015) made an analogous argument
based on star-formation histories and dynamics to explain why “fast”-forming
dwarfs like UMin differed from “slow”-forming dwarfs like Fornax.

###  4.3 Timing accretion, quenching, and disruption

All surviving and disrupted dwarfs (Cetus being the one significant exception)
have $z_{\rm{acc.}}>z_{\rm{trunc.}}$ – that is, these dwarfs were first
accreted onto the Milky Way, and only subsequently quenched with some delay.
Note that $z_{\rm{trunc}}\geq z_{\rm{acc}}$ is also in principle possible due
to e.g., self-quenching via feedback or group preprocessing prior to infall
(e.g., Panithanpaisal et al., 2021; Samuel et al., 2022) – Figure 4 suggests
this must be rare at $M_{\star}\gtrsim 10^{6}M_{\rm{\odot}}$.

The clustering of the disrupted dwarfs close to the $1:1$ line in Fig. 4
implies that whatever the mechanisms for quenching after infall (e.g., ram
pressure stripping by the circumgalactic medium, tidal dissolution), they
allow time for a few pericenters and some additional star-formation. This
additional star-formation is predicted to be only $\approx 10\%$ of the mass,
Fattahi et al. 2020, and perhaps seen empirically for GSE between 8-10 Gyrs in
Bonaca et al. 2020. This chronology is reminiscent of the Wetzel et al. (2013)
“delayed-then-rapid” quenching scenario for satellites falling into galaxy
clusters whose star-formation is abruptly truncated, but only a handful of
pericenters after infall – in our case the MW plays the role of the cluster.
Interestingly, the difference between $z_{\rm{acc}}$ and $z_{\rm{trunc}}$ is
larger, and shows more scatter for the surviving dwarfs – this may reflect a
combination of their orbital and structural parameters that have managed to
keep dynamical friction at bay and delayed quenching.

That $z_{\rm{acc}}>z_{\rm{trunc}}$ for virtually all sources in Figure 4 is an
archaeological way of inferring that $\gtrsim 10^{6}M_{\rm{\odot}}$ field
dwarfs are rarely quenched, and that quenching is intimately linked to
interactions with a massive host. While the fraction of field dwarfs that are
observed to be quenched at $z\approx 0$ is very low (e.g., Geha et al., 2012),
our results suggest that this continues to be the case even at higher
redshifts.

The timing constraints from this work also bracket the epoch when the stellar
halo between $\approx 10-50$ kpc was built up. The disrupted dwarfs in our
sample largely arrived in the Galaxy at $z\gtrsim 1$, with the
$z_{\rm{trunc.}}$ of any individual source typically acting as a lower limit
on the accretion redshift (Fig. 4). This is in excellent agreement with
simulations that predict the majority of the disrupted dwarfs have
$z_{\rm{acc}}>1$ (e.g., Fattahi et al., 2020).

###  4.4 High-$z$ stellar abundances: a Galactic archaeology approach

The current redshift frontier for direct, in-situ studies of stellar and gas-
phase abundances is $z\approx 2-3$111A handful of constraints at higher
redshifts ($z\approx 4-8$) exist on individual objects (e.g., Shapley et al.,
2017; Matthee et al., 2021) or via calibrations where the current systematic
uncertainties are likely on the order of the expected evolution in the
abundance trends (e.g., Faisst et al., 2016; Jones et al., 2020). This is set
to change soon thanks to JWST (Shapley et al., 2021; Strom et al., 2021; Curti
et al., 2021). (e.g., Steidel et al., 2016; Strom et al., 2018; Cullen et al.,
2019; Shapley et al., 2019; Topping et al., 2020; Sanders et al., 2020, 2021;
Cullen et al., 2021; Kashino et al., 2022; Strom et al., 2022). A key trend
reported in these studies is that galaxies at these redshifts are
significantly metal-poor compared to their $z=0$ counterparts. The MZR is
offset to lower metallicities, but runs almost parallel to the $z=0$ MZR.
Further, these studies infer $\alpha$-enhancement at $z\approx 2-3$ on the
order of [$\alpha$/Fe]$\approx 0.4$, i.e., ($\alpha$/Fe)$\approx
2.5\times$($\alpha$/Fe)⊙, based on e.g., comparisons of rest-UV spectra with
stellar population synthesis models.

There are two main limitations to these findings, where MW halo constraints
are uniquely complementary. Due to observational feasibility, the stellar mass
range probed at $z\approx 2-3$ is $\gtrsim 10^{9}M_{\rm{\odot}}$. Whether the
reported trends extend to lower mass systems is a key open question with wide-
ranging implications e.g., for reionization vis-a-vis the expected ionizing
power of low luminosity systems that dominate integrals of UV luminosity
functions (e.g., Finkelstein et al. 2019; Naidu et al. 2020b; Matthee & Naidu
et al. 2022). Further, calibrations of strong-line indicators required to
convert observed nebular emission to abundances are challenging (e.g., Sanders
et al., 2021), and several critical unknowns in stellar models of massive,
metal-poor stars remain (see Eldridge & Stanway 2022 for a recent review) for
which observational constraints are notoriously sparse (only a handful of O
stars at [Fe/H]$\lesssim-1$ have UV spectra, Telford et al. 2021). Given these
systematics, any independent lines of evidence would inspire greater
confidence.

Dynamical constraints (N-body simulations) suggest typical accretion and
disruption redshifts of $z\approx 1-2$ for the disrupted dwarfs in our sample
(Figure 4). From Figure 2 and our fit in Eqn. 3 we see that the disrupted
dwarfs support the trend of an MZR with a similar slope, but an offset to
lower metallicities continuing into the $10^{6}-10^{9}M_{\rm{\odot}}$ range at
these redshifts. The magnitude of the offset ($\approx$0.3-0.4 dex, §3) is
slightly lower than the 0.6 dex reported at $z\approx 3.5$ (Cullen et al.,
2019, 2021) and 0.8 dex reported at $z\approx 2.2$ (Kashino et al., 2022),
which is not surprising given that we are probing slightly lower redshifts.

As for [$\alpha$/Fe], we can use our fit in Figure 3 (Eqn. 6) to predict the
expected $\alpha$-enhancement at $z\approx 2-3$. For an average $\Delta$[Fe/H]
of $0.6-0.8$ (Cullen et al., 2019; Kashino et al., 2022), we predict
[$\alpha$/Fe]$\approx 0.35-0.45$. This value is in remarkable agreement with
the inferred [$\alpha$/Fe] for $\approx 10^{9}-10^{11}M_{\rm{\odot}}$ star-
forming galaxies (e.g., Cullen et al., 2021; Strom et al., 2022; Kashino et
al., 2022), and is an entirely independent line of evidence for elevated
[$\alpha$/Fe] of this magnitude, and in low-mass galaxies, at $z\approx 2-3$.
The similar mapping between $\Delta$[Fe/H] and [$\alpha$/Fe] across such a
wide-range in stellar mass ($\approx 10^{6}-10^{11}\,M_{\rm{\odot}}$) argues
for weak mass-dependence in these abundance trends.

##  5 Summary & Outlook

This paper presented a comparative analysis of the MW’s surviving and
disrupted dwarfs. While the surviving dwarfs are relatively well-
characterized, the majority of the disrupted dwarfs have only recently been
discovered thanks to Gaia and spectroscopic surveys like H3. We derive and
compile stellar masses and abundances for almost all known disrupted and
surviving dwarfs with $M_{\rm{\star}}\approx 10^{6}-10^{9}M_{\rm{\odot}}$ [§2,
Table 1, 2]. We find the following:

  * •

At fixed stellar mass, the disrupted dwarfs are relatively metal-poor and
$\alpha$-enhanced compared to the surviving dwarfs. [Fig. 2]

  * •

The disrupted dwarfs define a mass-metallicity relation that runs parallel to
the $z=0$ MZR, but is offset towards lower metallicities by $\approx 0.3-0.4$
dex. [Fig. 2, Eqn. 3]

  * •

Both surviving and disrupted dwarfs follow a $\Delta$[Fe/H] - [$\alpha$/Fe]
relation – the more metal-poor a galaxy is compared to the $z=0$ MZR, the more
$\alpha$-enhanced it is. [Fig. 3, Eqn. 6].

  * •

Comparison of chemically inferred star-formation truncation redshifts
($z_{\rm{trunc}}$) with dynamically inferred accretion redshifts
($z_{\rm{acc}}$) shows that almost all dwarfs are quenched only after being
accreted ($z_{\rm{acc}}>z_{\rm{trunc}}$). The disrupted dwarfs are quenched
promptly within a few pericenters after accretion ($z_{\rm{acc}}\approx
z_{\rm{trunc}}$), whereas the surviving dwarfs display longer lag times. This
is an archaeological way of inferring that field dwarfs are rarely quenched,
not just at $z\approx 0$ as has been established by direct observations, but
also at higher redshifts. [Fig. 4, §4.3]

  * •

The chemical differences between the surviving and disrupted dwarfs are likely
a consequence of their star-formation efficiencies, with the disrupted dwarfs
having built up their mass relatively rapidly (typical $z_{\rm{trunc}}\approx
1-2$). We propose this is because the dark matter halos hosting the disrupted
dwarfs formed at higher redshifts, were more concentrated, and were embedded
in dense environments proximal to the Milky Way – all conditions conducive to
high star-formation efficiencies. [§4.1, §4.2]

  * •

We place archaeological constraints on high-$z$ stellar chemistry in a mass
regime currently beyond the reach of direct studies. The disrupted dwarfs with
typical accretion and disruption redshifts of $z\approx 1-2$ have
$\Delta$[Fe/H]$\approx 0.3-0.4$, supporting extrapolations of the MZR
evolution at $M_{\rm{\star}}\gtrsim 10^{9}M_{\rm{\odot}}$ to lower masses. Our
$\Delta$[Fe/H]-[$\alpha$/Fe] relation (Eqn. 6) predicts $z\approx 2-3$
galaxies have [$\alpha$/Fe]$\approx 0.4$, in remarkable agreement with
recently inferred values for $M_{\rm{\star}}>10^{9}M_{\rm{\odot}}$ systems.
Our findings suggest these abundance trends are mass-independent across
$M_{\rm{\star}}\approx 10^{6}-10^{11}M_{\rm{\odot}}$. [§4.4]

We emphasize once again that our findings apply to the disrupted dwarfs
catalogued by the H3 Survey in Naidu et al. 2020a ($r_{\rm{gal}}\approx 6-50$
kpc, $|b|>40^{\rm{\circ}}$) – disrupted dwarfs lying entirely at larger
distances were likely accreted recently ($z\lesssim 0.5$) and resemble the
surviving dwarfs, whereas those entirely buried in the inner galaxy were
preferentially accreted early ($z\gtrsim 2$), and are likely even more metal-
poor and $\alpha$-enhanced than than the dwarfs studied here. Some of the
arguments introduced (e.g., translating $\Delta$[Fe/H] to [$\alpha$/Fe], the
archaeological connection to direct high-$z$ studies) are promising, but
nonetheless preliminary, since they are based on a limited sample. However,
this is set to change imminently. For every $\gtrsim 10^{5}M_{\rm{\odot}}$
surviving satellite the Milky Way accreted, there were likely two that were
disrupted (e.g., Fattahi et al., 2020). In other words, there may be $\gtrsim
100$ disrupted dwarfs dissolved across the Galaxy awaiting discovery. While
our current sample is preferentially sampling the most massive of these
sources, we are on the brink of a major expansion. In the coming decade there
is a clear path to much larger halo samples than the H3 Survey has amassed
thanks to the DESI (Allende Prieto et al., 2020), SDSS-V (Kollmeier et al.,
2017), 4MOST (Helmi et al., 2019), and WEAVE (Dalton et al., 2012) surveys,
which promise to complete our census of dwarf galaxies, both surviving and
disrupted, out to the virial radius of the Galaxy.

RPN gratefully acknowledges an Ashford Fellowship granted by Harvard
University. CC and PC acknowledge support from NSF grant NSF AST-2107253. YST
acknowledges financial support from the Australian Research Council through
DECRA Fellowship DE220101520. NC acknowledges support from NSF AST-1812461. We
thank the Hectochelle operators and the CfA and U. Arizona TACs for their
continued support of the H3 Survey. This paper uses data products produced by
the OIR Telescope Data Center, supported by the Smithsonian Astrophysical
Observatory. The computations in this paper were run on the FASRC Cannon
cluster supported by the FAS Division of Science Research Computing Group at
Harvard University. 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,
https://www.cosmos.esa.int/web/gaia/dpac/consortium) (Gaia Collaboration et
al., 2016, 2018). Funding for the DPAC has been provided by national
institutions, in particular the institutions participating in the Gaia
Multilateral Agreement.

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