# The Heavy Metal Survey: Star Formation Constraints and Dynamical Masses of
21 Massive Quiescent Galaxies at $z\approx 1.4-2.2$

Mariska Kriek Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The Netherlands  Aliza G. Beverage Astronomy Department, University of California, Berkeley, CA 94720, USA  Sedona H. Price Department of Physics & Astronomy and PITT PACC, University of Pittsburgh, Pittsburgh, PA 15260, USA  Katherine A. Suess Kavli Institute for Particle Astrophysics and Cosmology and Department of Physics, Stanford University, Stanford, CA 94305, USA  Guillermo Barro University of the Pacific, Stockton, CA 90340 USA  Rachel S. Bezanson Department of Physics & Astronomy and PITT PACC, University of Pittsburgh, Pittsburgh, PA 15260, USA  Charlie Conroy Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA, 02138, USA  Sam E. Cutler Department of Astronomy, University of Massachusetts, Amherst, MA 01003, USA  Marijn Franx Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The Netherlands  Jamie Lin  Department of Physics and Astronomy, Tufts University, 574 Boston Avenue, Medford, MA 02155, USA  Brian Lorenz Astronomy Department, University of California, Berkeley, CA 94720, USA  Yilun Ma Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA  Ivelina G. Momcheva Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117, Heidelberg, Germany  Lamiya A. Mowla Astronomy Department, Whitin Observatory, Wellesley College, 106 Central Street, Wellesley, MA 02481, USA  Imad Pasha Department of Astronomy, Yale University, New Haven, CT 06511, USA  Pieter van Dokkum Department of Astronomy, Yale University, New Haven, CT 06511, USA  Katherine E. Whitaker Department of Astronomy, University of Massachusetts, Amherst, MA 01003, USA  Cosmic Dawn Center (DAWN), Niels Bohr Institute, University of Copenhagen, Jagtvej 128, København N, DK-2200, Denmark

###### Abstract

In this paper, we present the Heavy Metal Survey, which obtained ultra-deep
medium-resolution spectra of 21 massive quiescent galaxies at $1.4\lesssim
z\lesssim 2.2$ with Keck/LRIS and MOSFIRE. With integration times of up to 16
hrs per band per galaxy, we observe numerous Balmer and metal absorption lines
in atmospheric windows. We successfully derive spectroscopic redshifts for all
21 galaxies and for 19 we also measure stellar velocity dispersions
($\sigma_{v}$), ages, and elemental abundances, as detailed in an accompanying
paper. Except for one emission-line AGN, all galaxies are confirmed as
quiescent through their faint or absent H$\alpha$ emission and evolved stellar
spectra. For most galaxies exhibiting faint H$\alpha$, elevated [N
ii]/H$\alpha$ suggests a non-star-forming origin. We calculate dynamical
masses ($M_{\rm dyn}$) by combining $\sigma_{v}$ with structural parameters
obtained from HST/COSMOS(-DASH), and compare them with stellar masses
($M_{*}$) derived using spectrophotometric modeling, considering various
assumptions. For a fixed initial mass function (IMF), we observe a strong
correlation between $M_{\rm dyn}$/$M_{*}$ and $\sigma_{v}$. This correlation
may suggest that a varying IMF, with high-$\sigma_{v}$ galaxies being more
bottom-heavy, was already in place at $z\sim 2$. When implementing the
$\sigma_{v}$-dependent IMF found in the cores of nearby early-type galaxies
and correcting for biases in our stellar mass and size measurements, we find a
low scatter in $M_{\rm dyn}$/$M_{*}$ of 0.14 dex. However, these assumptions
result in unphysical stellar masses, which exceed the dynamical masses by 34%.
This tension suggests that distant quiescent galaxies do not simply grow
inside-out into today’s massive early-type galaxies and the evolution is more
complicated.

Galaxies: evolution — Galaxies: formation

††software: fast (Kriek et al., 2009), fsps(Conroy et al., 2009; Conroy &
Gunn, 2010),Galfit(Cappellari & Emsellem, 2004)

##  1 INTRODUCTION

The majority of stars in today’s universe live in early-type galaxies with
quiescent stellar populations (e.g., Muzzin et al., 2013a). These galaxies are
massive, large, exhibit little to no rotation, and are thought to have formed
the majority of their stars at high redshifts (e.g., Thomas et al., 2005;
McDermid et al., 2015). Nonetheless, despite the wealth of information from
low-redshift studies, the formation histories of massive early-type galaxies
are still poorly understood.

To quantify the growth of massive galaxies and understand the physical
processes driving this evolution, it is imperative to directly observe them
during their early stages. Such studies find that massive galaxies with
quiescent stellar populations already exist when the universe was only a
fraction of its current age. These distant quiescent galaxies were first
identified almost two decades ago (e.g., Franx et al., 2003; Cimatti et al.,
2004; Glazebrook et al., 2004) and have been found to dominate the massive end
of the galaxy distribution out to $z\sim 2.5$ (e.g., Muzzin et al., 2013a;
Tomczak et al., 2014; McLeod et al., 2021). Galaxy formation models originally
failed to predict this quiescent galaxy population and – almost two decades
later – are still struggling to explain their presence.

Our poor understanding of this galaxy population is primarily due to the
difficulty of obtaining high-quality spectra. Quiescent galaxies typically do
not have bright emission lines and thus, we rely on faint stellar absorption
features to measure redshifts and learn about their stellar, chemical, and
kinematic properties. Obtaining such spectra is even more challenging at
$z\gtrsim 1$, as the bulk of the stellar spectrum is shifted to near-IR
wavelengths.

A few years after their initial discovery, the first spectra for $z\sim 2$
quiescent galaxies were obtained, showing broad continuum features (e.g.,
Daddi et al., 2005; Kriek et al., 2006). The first direct detection of Balmer
and metal absorption lines took nearly 30 hours with GNIRS (Gemini-South) on
one galaxy and the lines were still only marginally detected (e.g., Kriek et
al., 2009; van Dokkum et al., 2009). With the advent of more efficient near-IR
spectrographs like X-Shooter (VLT; Vernet et al., 2011), KMOS (VLT; Sharples
et al., 2013) and MOSFIRE (Keck Observatory; McLean et al., 2012),
spectroscopic redshifts, robust velocity dispersion measurements, and
dynamical mass estimates became available for substantial samples or stacks of
distant quiescent galaxies (e.g., van de Sande et al., 2011, 2013; Bezanson et
al., 2013; Belli et al., 2014, 2017a; Lonoce et al., 2015; Onodera et al.,
2015; Mendel et al., 2015; Saracco et al., 2019; Carnall et al., 2022; Zhuang
et al., 2023; Park et al., 2023).

In recent years, spectroscopic studies have pushed to even higher redshifts
($z>3$; e.g., Glazebrook et al., 2017; Schreiber et al., 2018; Tanaka et al.,
2019; Forrest et al., 2020; Esdaile et al., 2021; Carnall et al., 2023; Antwi-
Danso et al., 2023). At the same time, deeper observations have enabled the
first measurements of chemical abundances and resolved stellar kinematics at
$z>2$. These initial studies show intriguing results and demonstrate the power
of using such measurement to gain insights into the formation mechanisms of
distant quiescent galaxies. First, they have old ages and extreme chemical
abundance patterns (Kriek et al., 2016; Jafariyazani et al., 2020), indicating
that they formed their stars in early vigorous bursts, followed by an
efficient quenching process. Second, they appear to be rotationally supported
(Newman et al., 2015, 2018a; Toft et al., 2017).

However, these studies are based on few very massive and/or lensed galaxies
and many questions remain. We do not know how these galaxies became so massive
at such early epochs, when and how fast they formed and assembled their mass,
whether they are supported by rotation or random motions, which physical
processes are responsible for halting their star formation, and how they
evolved into the massive early-type galaxies in the today’s universe.
Addressing these questions requires statistical samples of distant quiescent
galaxies with ultra-deep spectra covering several Balmer and metal absorption
lines, which enable stellar, chemical, and kinematic measurements.

In order to obtain such a spectroscopic galaxy sample, we have conducted the
Heavy Metal Survey with MOSFIRE (McLean et al., 2012) and LRIS (Oke et al.,
1995) on the Keck I Telescope. The Heavy Metal sample observes 21 “bright”
quiescent galaxies over two redshift intervals, $1.3<z<1.5$ and $1.92<z<2.28$,
as well as many more star-forming and fainter quiescent galaxies at similar
redshifts. With integration times of up to 16 hours per filter per mask, we
observe numerous Balmer and metal absorption lines. While this distant
quiescent galaxy sample is not as large as the sample by Belli et al. (2017a,
2019, $\sim$30 galaxies at $z>1.35$), it is unique for its wavelength
coverage, and the only survey so far that obtains ultra-deep spectra at rest-
frame $\sim 4800-5400$ Å for a sample of distant quiescent galaxies. This
wavelength range targets the strongest $\alpha$-element absorption line (i.e.,
Mgb) in the rest-frame optical, as well as several prominent Fe lines.

In this paper we present our survey design and observational strategy, data
reduction and overview (Section 2), methods to derive spectral properties
(Section 3), characteristic of the galaxy sample (Section 4), and discuss the
implications of our finding for galaxy evolution studies (Section 5). The
primary science applications of this data-set, the chemical abundance
measurements, will be presented in an accompanying paper (A. Beverage et al.
in prep). The spectra and chemical abundances for the primary galaxies in
first Heavy Metal mask were also presented in Kriek et al. (2019). Several
other science applications including molecular gas properties and AGN outflows
will be presented in future papers (K. Suess et al. in prep; Y. Ma et al in
prep).

Throughout this work we assume a $\Lambda$CDM cosmology with $\Omega_{\rm
m}=0.3$, $\Omega_{\Lambda}=0.7$, and $H_{0}=70\rm\,kms^{-1}\,Mpc^{-1}$. All
magnitudes are given in the AB-magnitude system (Oke & Gunn, 1983). The
wavelengths of all emission and absorption lines are given in vacuum.

Figure 1: LRIS and MOSFIRE visibility of various rest-frame optical absorption
features as a function of redshift. Each row represents a different spectral
feature, as indicated on the left. The color of the feature reflects the
primary origin of the chemical element, as indicated in the bottom-right box.
The gray bars indicate whether a feature is visible in a certain filter, with
the different shades of gray corresponding to the different filters. The Heavy
Metal low ($1.3<z<1.5$) and high ($1.92<z<2.28$) redshift intervals are
indicated by the dashed and dotted vertical lines, respectively.

##  2 Observations and Data

###  2.1 Survey Design

The Heavy Metal Survey aims to study the formation histories of massive
quiescent galaxies using stellar, chemical, and kinematic measurements.
Achieving this goal requires (i) a statistically significant sample of $\sim
20$ distant quiescent galaxies with (ii) ultradeep rest-frame optical
spectroscopy covering several hydrogen, iron and $\alpha$-element absorption
features, and (iii) ancillary datasets including ultradeep multi-wavelength
photometry and high-resolution imaging.

Table 1: Overview Observations and Data

Mask | Instrument | R.A. | Decl. | P.A. | $N_{\rm gal}$ | Filter | Semesters | $t$ | FWHM
---|---|---|---|---|---|---|---|---|---
|  | (hh:mm:ss) | (dd:mm:ss) | (deg) |  |  |  | (hr) | seeing
HeavyMetal1 | LRIS | 10:00:42.61 | 02:34:43.97 | 93.0 | 19(5) | red | 2016B | 4.4 | 0$\farcs$9
(HM1, $z\sim 1.4$) | MOSFIRE | 10:00:42.01 | 02:34:54.30 | 86.7 | 29(5) | J | 2017A | 11.76 | 0$\farcs$63
|  |  |  |  |  | H | 2017A | 0.86 | 0$\farcs$75
HeavyMetal2 | LRIS | 10:00:44.88 | 01:45:14.24 | -75.0 | 18(6) | red | 2021AB | 6.25/6.5a | 0$\farcs$9
(HM2, $z\sim 1.4$) | MOSFIRE | 10:00:42.59 | 01:45:17.24 | 127.3 | 22(6) | J | 2018B | 11.5 | 0$\farcs$66
|  |  |  |  |  | H | 2018B | 0.92 | 0$\farcs$76
HeavyMetal3 | MOSFIRE | 10:00:44.70 | 02:01:35.48 | -23.1 | 20(5) | J | 2018B, 2019A, 2020B | 14.4 | 0$\farcs$83
(HM3, $z\sim 2.1$) |  |  |  |  |  | H | 2018B, 2019A | 16.7 | $0\farcs 66$
|  |  |  |  |  | K | 2018B, 2019A | 2.2 | 0$\farcs$77
HeavyMetal4 | MOSFIRE | 09:59:13.80 | 01:48:58.90 | 77.6 | 22(5) | J | 2019AB, 2021A | 12.4 | 0$\farcs$73
(HM4, $z\sim 2.1$) |  |  |  |  |  | H | 2019AB, 2020B | 15.5 | 0$\farcs$59
|  |  |  |  |  | K | 2019B, 2021A | 2.6 | 0$\farcs$89

aIn 2021A one of the red detectors was not working. To observe all galaxies,
we used two masks, which differed by 180 degrees, and only used one of the
detectors. The masks were observed for 3.5 and 3.75 hours. In 2021B a new
detector had been installed, and we re-observed the original mask for 2.75
hours. Hence, the integration times varied per galaxy, depending on the
location in the mask.

To that end, we executed the Heavy Metal survey in the overlapping area of the
UltraVISTA (McCracken et al., 2012), COSMOS (Scoville et al., 2007), and
COSMOS-DASH (Momcheva et al., 2017; Mowla et al., 2018) surveys, using the
LRIS and MOSFIRE spectrometers on the Keck I Telescope. The UltraVISTA survey
provides deep multi-wavelength photometry, while the F814W and F160W imaging
from COSMOS and COSMOS-DASH reveals the rest-frame optical structures of
distant galaxies. For our selection we used the COSMOS UltraVISTA v4.1 catalog
by Muzzin et al. (2013b). Quiescent galaxies were identified by their rest-
frame $U-V$ and $V-J$ colors (e.g., Wuyts et al., 2007; Williams et al.,
2009). In this work, we use the $UVJ$ criteria by Muzzin et al. (2013a).

We select the targets to be at $1.3<z<1.5$ or $1.92<z<2.28$. These specific
redshift intervals are chosen such that we observe MgI at 5178 Å and several
FeI and Balmer absorption lines in atmospheric windows, as illustrated in
Figure 1. Furthermore, by using two redshift intervals, combined with deep
spectroscopic surveys at lower redshifts, such as LEGA-C at $0.5<z<1.0$ (van
der Wel et al., 2016, 2021), we can study evolutionary trends. For the
$1.3<z<1.5$ galaxies we use LRIS-RED and MOSFIRE J-band to observe the 4000 Å
break region and the region around MgI at 5178 Å, respectively. For the
$1.92<z<2.28$ galaxies, we target these same regions with MOSFIRE in the J and
H bands. We also obtained shallower spectra in the H and K band, for the low
and high redshift masks, respectively, to obtain additional constraints on
several emission lines (i.e., H$\alpha$, [NII]).

Both LRIS and MOSFIRE are among the most efficient spectrographs at their
respective wavelengths. Nonetheless, even with unprecedented integration
times, only the brightest galaxies are within reach. The $z\sim 1.4$ galaxies
are selected to be brighter than $J=21.6$ and the galaxies at $1.92<z<2.28$
are selected to be brighter than $H=21.8$. These magnitudes limits, combined
with the long integration times (see next section), ensure sufficient signal-
to-noise ratios (S/N) to facilitate the anticipated science.

Figure 2: Footprints of the Heavy Metal observations in the larger COSMOS
field. The middle panel shows the weight map of HST/F160W (Momcheva et al.,
2017). The dark blue contiguous area represents the CANDELS survey (Koekemoer
et al., 2011; Grogin et al., 2011). The three larger and lighter stripes
represent the shallower COSMOS-DASH survey, which overlaps with the deep
UltraVISTA stripes. The smaller dark gray rectangulars represents the MOSFIRE
field of view for all four Heavy Metal pointings. For Heavy Metal 1 and 2,
both targeting lower redshifts ($z\sim 1.4$) we also show the LRIS field of
view by the larger, light-gray rectangulars. For each pointing we show the
zoom-in panels to the left or right of the primary panel. In the zoom panels,
we show the COSMOS-DASH/F160W images and indicate the primary (red circles)
and filler (blue circles) targets.

The large survey area enabled us to identify four pointings for which we
observe at least bright five distant quiescent galaxies, simultaneously. Two
pointings target galaxies at $1.3<z<1.5$ and the other two target galaxies at
$1.92<z<2.28$. In total, we have 21 primary targets. The four pointings are
shown in Figure 2, in comparison to the photometric coverage in HST/WFC3-IR
F160W. In Table 1 we list the mask parameters of all LRIS and MOSFIRE masks.
This sample size is an improvement of an order of magnitude compared to the 2
galaxies at $z\sim 2$ for which spectra of comparable depth and wavelength
coverage were previously available (Kriek et al., 2006; Jafariyazani et al.,
2020).

The remaining slits are placed on fainter quiescent and star-forming galaxies.
We prioritize galaxies at similar redshift. For the Heavy Metal 3 and 4 masks,
we also add quiescent galaxies at $z\sim 1.4$, though for these galaxies we
lack of LRIS observations, which target the most prominent absorption lines
for these redshifts.

###  2.2 Observing Strategy

The Heavy Metal survey was executed over 8 semesters, ranging from 2016B to
2021B. In total 26 nights were allocated, though half of the nights were lost
due to bad weather or technical problems. The primary goal of the Heavy Metal
Survey is to measure faint absorption lines, in particular around 5000 Å. This
regions is targeted by MOSFIRE J-band and H-band for the $z\sim 1.4$ and
$z\sim 2.1$ pointings, respectively. We require integration times of $\sim$12
and $\sim$16 hrs, respectively, for $z\sim 1.4$ (J-band) and $z\sim 2.1$
(H-band), and used our best imaging conditions for these observations. Second
priority is the Balmer/4000 Å break region, which has more prominent features,
and thus requires slightly shorter integration times. This region was observed
for $\sim 4$ and $\sim 12$ hours, respectively, with LRIS and MOSFIRE J-band
for the $z\sim 1.4$ and $z\sim 2.1$ pointings. Finally, for all four pointings
we took shorter integrations ($\sim$1-2 hours) of the wavelength regions
around H$\alpha$, to assess whether the galaxies have any nebular line
emission. This wavelength region is observed with MOSFIRE H-band and K-band
for $z\sim 1.4$ and $z\sim 2.1$, respectively. These observations were planned
to be taken under our least favorable seeing conditions. In Table 1, we
summarize the observing settings and integration times for all masks and
filters.

The MOSFIRE slits were configured with a width of $0\farcs 7$, and have a
minimum length of 7$\arcsec$. The LRIS slits were 1$\arcsec$ wide, with a
minimum length of 10$\arcsec$. For all masks we used a minimum of 5 stars for
the alignment. With MOSFIRE the galaxies were observed using an ABA′B′ dither
pattern and with the longer LRIS slits we used an ABC dither pattern. Both
dither patterns are preferred over an ABBA dither pattern as they result in
better background subtraction and higher S/N (see appendix A in Kriek et al.,
2016).

In all masks we observed at least one star in a slit. These “slit star”
observations have three advantages. First, they enable us to monitor the
seeing and possible drifts while observing. Second, the profiles and positions
of the slit stars aided the data reduction, such that we could accurately
register and weigh the individual science frames. Third, the slit star was
used in the flux calibration, as explained in Kriek et al. (2016) and in the
next section.

###  2.3 Data Reduction

The MOSFIRE data are reduced using a custom software package which was
originally developed for the MOSDEF survey (Kriek et al., 2015). This package
is all automated, working with a single parameter file input, indicating the
mask and target name, directories to raw frames and mask files, filter to be
reduced, and path and name of photometric catalog to be used for the flux
calibration. The first step is to read in all headers and identify the science
and calibration frames. Next, a master dome flat frame is made, which is used
to correct all science frames for pixel-to-pixel sensitivity variations and to
trace the edges of all spectra. Next, we do an initial background subtraction
of all science frames, by subtracting the average of the previous and
following frame. For the first and last science exposure, we only use one
adjacent science frame as sky frame.

The next step is to derive the wavelength solution using bright isolated
skylines. For this step we use the edge solutions from the master flat frame.
This procedure is all automatic, as the position of the slit gives us a rough
position of where to expect the skylines. For the $K$-band we also use the arc
lamp frames, allowing for an offset (i.e., flexure) between the skylines and
the arc lines. The final ingredient for the rectification is the position of
the galaxies in the spectra. The exact position is a combination of the
assigned dither position and the observed drift (about 1 pixel per hour, see
Kriek et al., 2015). We use the wavelength and edge solution to derive this
position in all science frames for the slit star. Thus, for each frame we
collapse the slit star spectrum along the wavelength direction and measure the
position, full width at half maximum (FWHM) of the seeing, and throughput.
This position, combined with the wavelength and edge solutions, now gives us a
transformation from the raw to the reduced frame for each science exposure.

Using the transformations derived in the previous step, we now perform an
additional background subtraction on the (non-rectified) science frames. We do
this step before resampling, so we can better model the remaining sky. We run
L.A. Cosmic (van Dokkum, 2001) on the cleaned frames and combine the cosmic
ray map with the available MOSFIRE bad pixel map. The “cleaned” frames are now
resampled to the final frame in a single transformation. We apply this same
transformation to the sky and mask frames for each science exposure. Finally,
we combine all science frames for each galaxy and filter, while weighing the
frames using the throughput and seeing, and excluding all masked pixels. We
also make a final weight map for each object and filter, as well as two noise
frames, one based on the frame-to-frame variations and one on the sky and
read-out noise. For more details on these steps, see Kriek et al. (2015).

All spectra are calibrated for the relative response using telluric standards.
Instead of observing new telluric standards for each science exposure, we make
use of the library collected by the MOSDEF survey. For each mask and filter we
construct a response spectrum from multiple telluric standards observed at
similar airmass, combined with the stellar spectrum of a star of the same
spectral type. The telluric spectra are reduced using a similar procedure as
the science spectra. See Kriek et al. (2015) for more information on the
construction of the response spectra and the motivation for using this
procedure.

Lastly, we generate one-dimensional (1D) science and error spectra for both
primary and filler targets through an optimal weighing technique, as outlined
by Horne (1986), followed by absolute flux calibration. Our employed MOSDEF
software initially conducts absolute flux calibration for each galaxy by
applying a scaling factor which is derived by comparing the 1D spectrum of a
slit star to its integrated photometry. This step effectively performs a slit-
loss correction for point sources. However, for all primary galaxies we detect
the stellar continuum and thus we directly scale the spectra to their
respective broadband photometry (see Sect. 3.1).

For the LRIS reduction we follow a similar procedure as for the MOSFIRE
spectra. The only major difference is the calibration, as we do not have a
library of telluric standards. To correct for atmospheric transmission
features, we use the slit star spectrum combined with a theoretical sky
spectrum. Furthermore, we calibrate each 1D science spectrum individually
using the photometric data in the overlapping wavelength regime. See Kriek et
al. (2019) for more information.

Figure 3: Overview of UltraVISTA photometric SEDs (left), spectra (middle),
and HST-F160W images (right) of distant quiescent galaxies at $z\sim 1.4$. The
LRIS (4-6 hrs) and MOSFIRE J-band spectra (12 hrs) are shown in the middle-
left and middle-right column, respectively. The spectra are binned by 15 and
10 pixels, respectively, such that each bin corresponds to $\sim$5 Å in rest-
frame. Flux densities ($f_{\lambda}$) are in $10^{-18}\rm
erg\,s^{-1}\,cm^{-2}\,\AA^{-1}$. The extent of the LRIS and MOSFIRE-J panels
are indicated by the light and middle gray rectangulars in the left panels
(arrows indicate that full range exceeds panel). The best-fit FSPS models to
the combined photometry and spectra are shown in gray (left panel) and red
(middle panel). Prominent spectral lines are indicated by the dotted vertical
lines. The orientation of the MOSFIRE (blue) and LRIS (orange) slits are
indicated in the right panel.

Figure 4: Overview of UltraVISTA photometric SEDs (left), spectra (middle),
and HST-F160W images (right) of distant quiescent galaxies at $z\sim 2.1$. The
MOSFIRE J-band (12-14 hrs) and H-band spectra (16-17 hrs) are shown in the
middle-left and middle-right column, respectively. The spectra are binned by
13 and 10 pixels, respectively, such that each bin corresponds to $\sim$5 Å in
rest-frame. Flux densities ($f_{\lambda}$) are in $10^{-18}\rm
erg\,s^{-1}\,cm^{-2}\,\AA^{-1}$ and the extent of the MOSFIRE J-band and
H-band panels are indicated by the light and middle gray rectangulars in the
left panels. The best-fit fsps models to the combined photometry and spectra
are shown in gray (left panels) and red (middle panels). Prominent spectral
lines are indicated by the dotted vertical lines.

Figure 5: 2D and 1D spectra in wavelength region around the H$\alpha$ spectral
feature for all primary Heavy Metal galaxies. For each 1D spectrum the
continuum has been removed. The 1D spectra are shown in black, binned to 3
(non-masked) pixels, and in gray we show the corresponding error spectrum. The
yellow fit presents the best-fit emission-line model to H$\alpha$ and the two
[N ii] lines, with the 68% uncertainty shown by the shaded yellow region. The
vertical red dotted lines indicate the location of the three emission lines.
Galaxy 55878 is the only one with strong H$\alpha$ in emission, and will be
discussed in Ma et al (in prep). We have 8 additional galaxies with marginal
($>\,\sigma$) H$\alpha$ detections (see Table 2) and 11 galaxies for which we
derive upper limits on the H$\alpha$ flux. One galaxy (59375) has a
significantly deeper spectrum; due to a incorrect photometric redshift; the
line was observed in a different filter ($H$) than expected ($K$).

###  2.4 Data Overview

In Figures 3 and 4 we present an overview of the UltraVISTA photometric SEDs
(Muzzin et al., 2013b) (left column), 1D spectra (middle two columns), and the
F160W image from COSMOS-DASH (Mowla et al., 2018; Momcheva et al., 2017) for
all primary targets. The position of the LRIS (yellow) and MOSFIRE (blue)
slits are shown in the images as well.

Figure 3 shows the galaxies in Heavy Metal 1 and 2, targeting $z\sim 1.4$. For
these two masks, we show the LRIS and MOSFIRE J-band spectra, all shifted (in
wavelength only) to rest frame. We observe multiple Balmer absorption lines
(yellow dotted lines) and the two CaII lines (green) around 4000 Å for all 11
galaxies. Most galaxies also show clear MgI and several FeI lines (red) in
their MOSFIRE spectra. None of the targets show Balmer emission lines in their
LRIS and MOSFIRE-J spectra. Nonetheless, three galaxies have either [O ii] or
[O iii] in emission. We will further discuss these emission lines in Section
4.

Figure 4 shows the primary quiescent galaxies at $z\sim 2.1$ targeted by the
Heavy Metal 3 and 4 masks. Instead of LRIS and MOSFIRE J-band, we now show
MOSFIRE J-band and H-band in the middle two columns. Two of the primary
targets (59375 and 60736) scatter out the intended redshift regime
($1.92<z<2.28$), and thus their spectra do not cover all targeted absorption
lines. Nonetheless, we detect additional absorption lines, such as Na for
these galaxies.

Considering the remaining eight targets, six of them show several Balmer
absorption and metal lines in their spectra. Two galaxies, 55878 and 59449, do
not show any clear absorption lines, but their emission lines do reveal their
redshifts. Galaxy 55878 has strong asymmetric emission lines, most likely
originating from an AGN, and no absorption lines are detected. This galaxy
will be discussed in detail in Ma et al. (in prep). Galaxy 59449 shows two [O
iii] emission lines in its spectrum, but no absorption lines are detected. We
would have expected to detect some continuum features and thus, the line and
continuum emission may not originate from the same galaxy. However, we could
not identify a redshift solution just from the continuum emission.

In Figure 5, we present spectra in the H$\alpha$ region for all primary
targets. To illustrate whether H$\alpha$ is detected, we zoom in on a small
wavelength region and show the continuum subtracted 1D spectra (see Sect.
3.2). This spectral range does not encompass critical absorption features;
these observations were taken to assess whether the galaxies have any
H$\alpha$ emission. Hence, the spectra acquired in this band are shallower
compared to the deeper spectra shown in Figures 3 and 4 (refer to Table 1 for
details). It is worth noting that the spectrum of 59375 is significantly
deeper, as H$\alpha$ falls within the H-band, where ultra-deep observations
were conducted, rather than the K-band. Galaxy 60736’s spectrum is not
included, as there is no coverage of H$\alpha$.

Except for 55878 (AGN), none of the galaxies exhibits strong H$\alpha$
emission in their 2D or 1D spectra. Nonetheless, several galaxies show very
faint H$\alpha$ and [N ii] emission lines, in particular after the continuum
removal, as this step corrects for the underlying Balmer absorption feature.
In Section 3.2 we describe our methodology to measure all H$\alpha$ lines in
order to derive constraints on the star formation rates (SFRs).

Table 2: Overview of primary quiescent galaxy sample ID | Coordinates | Observed | $z_{\rm spec}$ | Rest-frame | SPS fitting parameters
---|---|---|---|---|---
| R.A. | Decl. | magnitude |  | colors | log $M_{*}$111Typical uncertainty on stellar mass is 0.1 dex. | log SFRcont222Typical uncertainty on SFR is 0.2 dex. |  $A_{V}$333Typical uncertainty on $A_{V}$ is 0.1 mag.
| (hh:mm:ss) | (dd:mm:ss) | $J$ | $H$ |  | $U-V$ | $V-J$ | $M_{\odot}$ | M⊙/yr |
HM1-213931 | 10:00:48.02 | 02:33:42.95 | 19.2 |  | 1.399 | 1.78 | 0.97 | 11.63 | -1.17 | 0.0
HM1-213947 | 10:00:50.68 | 02:33:55.37 | 20.8 |  | 1.397 | 1.42 | 0.55 | 10.87 | -0.31 | 0.0
HM1-214340 | 10:00:37.09 | 02:34:10.28 | 21.2 |  | 1.418 | 1.48 | 0.78 | 10.80 | -0.47 | 0.0
HM1-214695 | 10:00:32.28 | 02:34:25.12 | 21.1 |  | 1.397 | 1.87 | 0.95 | 11.06 | -0.48 | 0.0
HM1-217249 | 10:00:45.62 | 02:36:19.30 | 21.4 |  | 1.377 | 1.40 | 0.47 | 10.61 | -0.24 | 0.0
HM2-23351 | 10:00:48.44 | 01:43:24.74 | 20.7 |  | 1.421 | 1.59 | 0.72 | 10.99 | -0.66 | 0.0
HM2-23482 | 10:00:46.19 | 01:43:31.31 | 21.1 |  | 1.419 | 1.73 | 1.16 | 11.15 | -0.07 | 0.0
HM2-23621 | 10:00:49.95 | 01:43:38.67 | 21.5 |  | 1.359 | 1.87 | 1.34 | 11.05 | -0.17 | 0.2
HM2-25407 | 10:00:39.85 | 01:45:12.98 | 21.5 |  | 1.358 | 1.62 | 0.92 | 10.70 | -0.34 | 0.0
HM2-25702 | 10:00:49.20 | 01:45:27.47 | 21.1 |  | 1.419 | 1.48 | 0.65 | 10.85 | -0.42 | 0.0
HM2-26888 | 10:00:31.30 | 01:46:27.80 | 21.6 |  | 1.358 | 1.97 | 1.03 | 10.93 | -1.09 | 0.0
HM3-103236 | 10:00:47.18 | 01:59:19.56 |  | 21.7 | 2.243 | 2.05 | 1.25 | 11.13 | -1.06 | 0.2
HM3-104779 | 10:00:41.29 | 02:00:30.36 |  | 21.4 | 2.123 | 1.48 | 0.81 | 11.01 | -0.64 | 0.0
HM3-106812 | 10:00:49.42 | 02:02:07.23 |  | 21.6 | 2.230 | 1.65 | 0.79 | 11.07 | -1.13 | 0.0
HM3-107590 | 10:00:35.45 | 02:02:41.24 |  | 21.3 | 2.234 | 1.28 | 0.54 | 11.07 | -0.11 | 0.0
HM3-108899 | 10:00:42.38 | 02:03:39.19 |  | 20.7 | 2.231 | 1.51 | 0.77 | 11.28 | 0.10 | 0.0
HM4-55878 | 09:59:16.40 | 01:47:23.18 |  | 21.0 | 2.159 | 1.29 | 0.45 | 11.16 | 1.75 | 1.0
HM4-56163 | 09:59:08.14 | 01:47:35.96 |  | 21.4 | 2.158 | 1.63 | 1.00 | 11.08 | -0.19 | 0.0
HM4-59375 | 09:59:11.82 | 01:50:04.61 |  | 20.9 | 1.552 | 2.28 | 1.27 | 11.18 | -6.12 | 0.0
HM4-59449 | 09:59:01.28 | 01:50:04.84 |  | 21.4 | 2.159 | 1.39 | 0.89 | 11.10 | -0.56 | 0.0
HM4-60736 | 09:59:23.74 | 01:59:58.44 |  | 21.2 | 1.862 | 1.53 | 0.80 | 10.88 | -0.30 | 0.0

##  3 Methodology

In this section, we outline the methods we employed to determine the spectral,
photometric, and structural properties of the Heavy Metal galaxies. We begin
by deriving the spectroscopic redshifts, emission-line fluxes, stellar
population characteristics, and rest-frame $UVJ$ colors for both the primary
and filler galaxies (Sect. 3.1). In Section 3.2, we detail our approach to
measuring the H$\alpha$ emission line fluxes and subsequently calculating the
star formation rates (SFRs) for our primary, quiescent targets. Lastly, in
Section 3.3, we present the methodology used to derive the galaxy structures
and estimate dynamical masses for the primary Heavy Metal galaxies.

###  3.1 Redshifts and stellar population properties

For all primary quiescent galaxies, we derive a spectroscopic redshift and
stellar population properties by simultaneously fitting the spectra and the
UltraVISTA photometry with the Flexible Stellar Population Synthesis models
(FSPS; Conroy et al., 2009; Conroy & Gunn, 2010). We assume an exponentially
delayed star formation history, the average Kriek & Conroy (2013) dust
attenuation law, and the Chabrier (2003) initial mass function (IMF). We use a
custom version of the fast fitting code (Kriek et al., 2009), in which the
automatic scaling of the spectra to the photometry has been improved444In the
original fast release, the spectra were scaled to the photometry by convolving
the spectra (in $f_{\nu}$) by the transmission curve of the overlapping
filters. However, the MOSFIRE spectra only partially overlap with the filter
curves, and thus this method does not work for most galaxies. Instead, the
spectra, similar to the photometry, were scaled to the models using least-
square scaling.. To facilitate comparison with the full galaxy distribution
from which the galaxies are selected, we assume solar metallicity. fast does
not fit for the absorption line broadening, and thus we fit binned spectra.

For galaxy HM4-55878 the emission lines are very strong and affecting the
broadband spectral shape. Thus, for this galaxy we first correct the
photometry for the emission line fluxes (see Sect. 5). Furthermore, we mask
the wavelength regions affected by emission lines while fitting. The strong
lines also affect the absolute calibration of our spectra, and our default
method does not work (see Sect. 2.3). Instead, for this galaxy we use the
filter curves and integrated broadband magnitudes, corrected for the partial
overlap between the spectra and filter curve.

The resulting best-fit redshifts, stellar masses, star-formation rates (SFRs),
and magnitudes of dust attenuation ($A_{V}$) are listed in Table 1. The
typical uncertainties on the stellar mass, SFR, and $A_{V}$ are 0.1 dex, 0.2
dex, and 0.1 mag, respectively. These uncertainties include the flux
uncertainties as well as variations in the various assumptions (except for the
IMF) and the stellar population synthesis model (fsps; Bruzual & Charlot,
2003; Maraston, 2005). The best-fit models are shown in Figures 3 and 4. For
displaying purposes, we show the original models convolved to the velocity
dispersion of the spectra, as derived by A. Beverage et al. (in prep.).

While most stellar continuum fits look reasonable, there are a few exceptions.
First, for HM1-213931 the fit is quite poor, probably because it is a blended
spectrum of multiple galaxies, which have a velocity offset. Though we cannot
deblend the spectra of the sources, we find a different spectrum when assuming
different weighing profiles for the extraction (see A. Beverage et al. in prep
for more information on the implications). For HM4-59449 we do not see any
clear absorption lines, and the redshift is based on the faint [O iii]
emission lines.

For the filler galaxies, we derive spectroscopic redshifts by fitting the
emission lines. The majority of the filler targets show multiple emission
lines, resulting in robust spectroscopic redshifts. For the $z\sim 1.4$ masks,
we observed different filler galaxies for the LRIS and MOSFIRE masks. This
strategy results in a larger number of filler galaxies, but lower success rate
of confirming the spectroscopic redshift. For the $z\sim 2.1$ masks, we use
the same filler galaxies in the different settings, and thus had more
wavelength coverage to detect possible spectral features.

Finally, for all galaxies in the observed Heavy Metal masks we determine rest-
frame $U$, $V$, and $J$ colors using the EA$z$Y (Brammer et al., 2008) code.
When available, we assume the spectroscopic redshift, otherwise we adopt the
photometric redshifts provided by (Muzzin et al., 2013b). Each rest-frame
magnitude is determined individually, using a fit to just the surrounding
photometric datapoints. Hence, the colors are not based on the best-fit
stellar population model to the full spectrum.

Table 3: Emission line properties ID | $F_{\rm H\alpha}$ | SFRHα | [N ii]/H$\alpha$
---|---|---|---
|  $10^{-17}$ erg s-1 cm-2 | M⊙/yr |
HM1-213931 | $6.0^{+1.6}_{+1.2}$ | $4.0^{+0.7}_{-1.1}$ | $<0.24$
HM1-213947 | $<1.5$ | $<1.0$ | —
HM1-214340 | $<2.6$ | $<1.8$ | —
HM1-214695 | $<3.5$ | $<2.3$ | —
HM1-217249 | $<1.2$ | $<0.7$ | —
HM2-23351 | $1.4^{+0.3}_{-0.3}$ | $0.9^{+0.3}_{-0.2}$ | $2.05^{+0.72}_{-0.46}$
HM2-23482 | $3.3^{+0.5}_{-0.6}$ | $2.2^{+0.4}_{-0.4}$ | $0.71^{+0.20}_{-0.18}$
HM2-23621 | $2.8^{+0.6}_{-0.5}$ | $2.02^{+0.4}_{-0.3}$ | $0.72^{+0.22}_{-0.20}$
HM2-25407 | $3.1^{+0.3}_{-0.6}$ | $1.9^{+0.2}_{-0.4}$ | $0.74^{+0.19}_{-0.16}$
HM2-25702 | $<1.8$ | $<1.3$ | —
HM2-26888 | $<1.4$ | $<0.9$ | —
HM3-103236 | $<2.1$ | $<5.1$ | —
HM3-104779 | $<2.9$ | $<5.3$ | —
HM3-106812 | $<3.0$ | $<6.3$ | —
HM3-107590 | $<2.5$ | $<5.3$ | —
HM3-108899 | $3.2^{+0.6}_{-0.7}$ | $6.6^{+1.3}_{-1.4}$ | $1.25^{+0.33}_{-0.30}$
HM4-55878 | $60.0^{+0.7}_{-0.7}$ | $465^{+5}_{-6}$ | $0.48^{+0.01}_{-0.02}$
HM4-56163 | $3.2^{+0.5}_{-0.4}$ | $5.4^{+0.7}_{-0.5}$ | $0.40^{+0.11}_{-0.10}$
HM4-59375 | $1.2^{+0.1}_{-0.1}$ | $1.0^{+0.1}_{-0.1}$ | $1.24^{+0.18}_{-0.13}$
HM4-59449 | $<3.2$ | $<6.1$ | —
HM4-60736 | — | — | —
Table 4: Structural and kinematic properties ID | F814W structural properties |  F160W Structural properties555Adopted from Cutler et al. (2022). | $R_{\rm e,major}$ | log $M_{\rm*,c}$666Stellar masses corrected for the total magnitude difference between the photometric catalog and Galfit. |  $\sigma_{v}$777Adopted from A. Beverage et al. (in prep.) | log $M_{\rm dyn}$
---|---|---|---|---|---|---
| $R_{\rm e,major}$ | $n$ | $q$ | $R_{\rm e,major}$ | $n$ | $q$ | @ 5000 Å | $M_{\odot}$ | km s-1 | $M_{\odot}$
| kpc |  |  | kpc |  |  | kpc |  |  |
HM1-213931 | 3.72$\pm$0.17 | 5.7 | 0.75 | 3.79$\pm$0.17 | 4.3 | 0.88 | 3.76$\pm$0.22 | 11.35 | $371^{+13}_{-13}$ | $11.81^{+0.04}_{-0.04}$
HM1-213947 | 0.81$\pm$0.01 | 2.1 | 0.75 | 0.57888Bad Galfit fit | 6.0 | 0.95 | 0.69$\pm$0.04 | 10.73 | $216^{+16}_{-13}$ | $10.71^{+0.07}_{-0.07}$
HM1-214340 | 3.16$\pm$0.17 | 3.7 | 0.76 | 2.13$\pm$0.11 | 2.4 | 0.78 | 2.46$\pm$0.16 | 10.81 | $149^{+19}_{-23}$ | $10.91^{+0.10}_{-0.16}$
HM1-214695 | 1.99$\pm$0.11 | 2.3 | 0.83 | 1.94$\pm$0.14 | 2.5 | 0.98 | 1.96$\pm$0.16 | 11.02 | $210^{+24}_{-25}$ | $11.16^{+0.10}_{-0.11}$
HM1-217249 | 0.59$\pm$0.01 | 2.4 | 0.57 | 0.60$\pm$0.02 | 1.3 | 0.56 | 0.59$\pm$0.03 | 10.60 | $185^{+21}_{-24}$ | $10.46^{+0.09}_{-0.12}$
HM2-23351 | 1.82$\pm$0.03 | 2.2 | 0.31 | 1.58$\pm$0.05 | 2.3 | 0.34 | 1.66$\pm$0.09 | 10.96 | $257^{+14}_{-13}$ | $11.05^{+0.05}_{-0.06}$
HM2-23482 | 2.16$\pm$0.10 | 2.2 | 0.69 | 3.25$\pm$ 0.33 | 5.5 | 0.71 | 2.80$\pm$0.23 | 11.11 | $289^{+38}_{-35}$ | $11.45^{+0.11}_{-0.10}$
HM2-23621 | 5.62$\pm$0.31 | 1.5 | 0.36 | 3.75$\pm$0.24 | 1.7 | 0.40 | 4.42$\pm$0.29 | 10.98 | $199^{+38}_{-41}$ | $11.31^{+0.14}_{-0.23}$
HM2-25407 | 1.36$\pm$0.14 | 5.3 | 0.95 | 1.42$\pm$0.08 | 1.7 | 0.73 | 1.40$\pm$0.10 | 10.66 | $201^{+27}_{-28}$ | $10.92^{+0.13}_{-0.13}$
HM2-25702 | 1.46$\pm$0.12 | 5.8 | 0.74 | 1.41$\pm$0.08 | 3.9 | 0.79 | 1.43$\pm$0.10 | 10.84 | $243^{+21}_{-20}$ | $11.01^{+0.08}_{-0.08}$
HM2-26888 | 2.34$\pm$0.27 | 2.9 | 0.75 | 2.46$\pm$0.19 | 4.1 | 0.89 | 2.41$\pm$0.20 | 10.94 | $166^{+33}_{-27}$ | $10.97^{+0.16}_{-0.16}$
HM3-103236 | — | — | — | 2.41c | 2.6 | 0.58 | 2.36$\pm$0.59 | 11.08 | $197^{+37}_{-35}$ | $11.08^{+0.17}_{-0.25}$
HM3-104779 | — | — | — | — | — | — | — | — | $186^{+30}_{-31}$ | —
HM3-106812 | — | — | — | 3.64$\pm$0.63 | 5.8 | 0.70 | 3.58$\pm$0.65 | 11.14 | $187^{+41}_{-45}$ | $11.11^{+0.22}_{-0.24}$
HM3-107590 | — | — | — | 1.00$\pm$0.07 | 4.3 | 0.83 | 0.98$\pm$0.09 | 11.05 | $173^{+25}_{-23}$ | $10.59^{+0.12}_{-0.13}$
HM3-108899 | — | — | — | 3.46$\pm$0.17 | 3.6 | 0.51 | 3.40$\pm$0.24 | 11.25 | $306^{+24}_{-23}$ | $11.55^{+0.07}_{-0.08}$
HM4-55878 | — | — | — | 2.36$\pm$0.21 | 3.4 | 0.67 | 2.34$\pm$0.24 | 11.20 | — | —
HM4-56163 | — | — | — | 3.55c | 6.0 | 0.93 | 3.51$\pm$0.88 | 11.05 | $213^{+54}_{-48}$ | $11.26^{+0.24}_{-0.27}$
HM4-59375 | — | — | — | — | — | — | — | — | $333^{+42}_{-43}$ | —
HM4-59449 | — | — | — | — | — | — | — | — | — | —
HM4-60736 | — | — | — | 1.58$\pm$0.05 | 2.0 | 0.44 | 1.62$\pm$0.10 | 10.70 | $270^{+30}_{-27}$ | $11.16^{+0.08}_{-0.10}$

###  3.2 H$\alpha$ star formation rate measurements

For the primary quiescent targets we measure the H$\alpha$ emission line flux.
We use the best-fit stellar population model, convolved to the best-fit
velocity dispersion, as the continuum model. This approach ensures that we
incorporate the underlying Balmer absorption. To derive the fluxes and correct
for emission-line blending, we fit H$\alpha$ and the two [N ii] at 6548 Å and
6584 Å, simultaneously. For our model spectrum, we use three Gaussians with
the same velocity dispersion and a fixed ratio between the two [N ii] lines of
a factor of 3. The redshift is fixed to the best-fit absorption line redshift.
If none of the lines are clearly visible, the velocity dispersion of the
emission lines cannot exceed the stellar velocity dispersion by more than 1
$\sigma$. The minimum allowed velocity dispersion is set by the spectral
resolution.

We derive the uncertainties on the emission-line flux measurements using Monte
Carlo simulations. We make 500 realizations of the spectrum around H$\alpha$,
by perturbing the fluxes following the error spectrum. For each realization we
fit all three lines using the same method as for the actual spectrum. We
derive the 16% and 84% confidence intervals on the emission-line fluxes from
the resulting distribution. In Figure 5 we show these fits and confidence
intervals for all 20 galaxies with coverage of H$\alpha$. For galaxies that do
not have a 3$\sigma$ detection for H$\alpha$, we derive the 3$\sigma$ upper
limit. All values are given in Table 3.

For galaxy 213947 we have to do additional masking to derive the H$\alpha$
flux, as the 2D spectrum partially overlaps with the (negative) spectrum of a
close galaxy. This nearby galaxy only has emission lines and no continuum
emission, and thus only a small wavelength range is affected. Thus, for this
galaxy, we mask the wavelengths that are contaminated by the emission lines of
the nearby galaxy.

We convert the integrated H$\alpha$ flux to the integrated luminosity using
the spectroscopic redshift. In order to correct this line for dust
attenuation, we ideally would use the Balmer decrement (H$\alpha$/H$\beta$).
However, with the exception of 55878, H$\beta$ is too faint to yield a useful
Balmer decrement measurement, and thus we use the stellar attenuation for the
dust correction instead. We do note, however, that nearly all galaxies have a
best-fit $A_{V}=0$. For 55878, we do use the Balmer decrement
(H$\alpha$/H$\beta$=4.43) for the dust correction. Finally, we adopt the
conversion by Kennicutt (1998) for solar metallicity and a Kroupa (2001) IMF
(which is comparable to the Chabrier, 2003, IMF) to derive SFRs for all
galaxies with H$\alpha$ coverage (see Table 3). The majority of the galaxies
do not have detected H$\alpha$ emission and thus we derive a 3 $\sigma$ upper
limit on the SFR.

Two galaxies stand out in Figure 5. First, galaxy 55878 has very strong
emission lines and we will further discuss this galaxy in Sect. 4.2). Second,
HM4-59375 stands out, as despite the low H$\alpha$ flux and resulting SFR, the
galaxy has significantly detected emission lines. For this galaxy the
spectrosopic redshift of $z_{\rm spec}=1.552$ is significantly lower than the
photometric redshift used in the selection. Hence, H$\alpha$ does not fall in
the K-band, as the other galaxies in its targeted redshift regime, but in the
H-band for which the observations are significantly deeper. For galaxy 60736,
the spectroscopic redshift falls outside the selection window, and thus we
have no coverage of the H$\alpha$ wavelength regions (see Fig. 1). Hence, this
galaxy is missing from Figure 5.

###  3.3 Structural Measurements and Dynamical Masses

The Heavy Metal pointings overlap with the COSMOS/ACS-F814W (Scoville et al.,
2007) and the COSMOS-DASH/WFC3-IR-F160W imaging (Momcheva et al., 2017; Mowla
et al., 2018; Cutler et al., 2022), enabling structural measurements. We
derive galaxy sizes from the F814W images by fitting single-component Sérsic
models with Galfit (Peng et al., 2002), following the technique described in
Beverage et al. (2021). For the COSMOS-DASH imaging, we adopt the structural
measurements by Cutler et al. (2022).

For the $z\sim 1.4$ galaxies we use both the F814W and F160W structural
parameters in our analyses, listed in Table 4. We derive the structural
parameters ($R_{\rm e,major}$, $n$, $q$) at rest-frame 5000 Å using
interpolation. For HM1-213947, the F160W image results in a bad Galfit fit,
and thus for this galaxy we only use F814W. We use Equation 1 by van der Wel
et al. (2014) to correct the size to rest-frame 5000 Å. For the $z\sim 2.1$
galaxies we only use the F160W measurements, as these galaxies are not or
barely detected in F814W. We also correct these size measurements,
standardizing them to the rest-frame 5000 Å wavelength (see Table 4),
following van der Wel et al. (2014). These corrections are generally subtle,
fluctuating within the range of -0.01 to 0.009. For three galaxies no F160W
size measurements were available, as either the fit failed or there was no
coverage. For two additional galaxies, the fit was qualified as “bad”. We
nonetheless use these structural measurements in the subsequent analysis,
while flagging these galaxies in the figures. For galaxies without given
uncertainties, we adopted uncertainties of 25%, $\pm$1.0 and $\pm$0.1 for
$R_{\rm e}$, $n$, and $q$, respectively.

We also use the Galfit parameters to refine our stellar mass measurements and
ensure their consistency with other structural measurements. For this
refinement process we derive a mass correction factor by comparing the
integrated magnitude from Galfit with the magnitude from the corresponding
filter band in the photometric catalog. For the F814W and F160W filters, which
are absent from the UltraVISTA catalog by (Muzzin et al., 2013b), we compute
their magnitudes by integrating the best-fit fast model using the respective
filter curves. For the $z\sim 2.1$ galaxies we combine the correction factors
from F160W and F814W following their proximity to rest-frame 5000 Å. The
Galfit magnitudes are typically fainter than the catalog magnitudes by 0.094,
resulting in an average mass correction of -0.038 dex. However, for some
galaxies, in particular blended systems, such as HM1-213931, the mass
corrections can be as large as -0.28 dex. The corrected masses ($M_{*,\rm c}$)
for the galaxies with structural measurements are listed in Table 4.

The Heavy Metal spectra yield velocity dispersion measurements ($\sigma_{v}$)
for all but two galaxies, as described in our accompanying paper by A.
Beverage et al. (in prep). These measurements are derived using the absorption
line fitter (alf) code (Conroy & van Dokkum, 2012; Choi et al., 2016; Conroy
et al., 2018). Beverage et al. (2023) shows that the alf velocity dispersions
are in perfect agreement with those found by ppxf (Cappellari & Emsellem,
2004) for a large sample of $z\sim 0.7$ quiescent sample of galaxies. We
increase the measured velocity dispersion measurements ($\sigma_{v}$) by 4% to
obtain the velocity dispersion within 1 $r_{e}$ ($\sigma_{v,\rm e}$) (see van
de Sande et al., 2013).

The velocity dispersions and structural measurements together enable an
estimate of the dynamical mass. We still have a poor understanding of the
internal stellar dynamics within these galaxies. A few resolved investigations
of three lensed distant quiescent galaxies have hinted at the presence of
rotational support to varying degrees (Newman et al., 2015, 2018a; Toft et
al., 2017). Nonetheless, due to our limited knowledge and to facilitate
comparison with similar works, here we define dynamical mass as

$M_{\rm dyn}=\frac{\beta(n)\sigma_{v,e}^{2}R_{\rm e}}{G}$ (1)

with $\beta(n)=8.87-0.831n+0.0241n^{2}$, the virial constant for a spherical
isotropic model described by profile $R_{e}^{1/n}$ for different values of the
Sérsic index $n$ (Cappellari et al., 2006). For $R_{\rm e}$ we take the
circularized radius ($R_{\rm e}=R_{\rm e,major}\sqrt{q}$) at rest-frame
wavelength of 5000 Å. The resulting dynamical masses are listed in Table 4.

##  4 Results

While quiescent galaxies have been studied extensively throughout cosmic time,
the majority of these investigations have relied on photometric data. The
absence of spectroscopic information may lead to biases in our photometric
redshifts, stellar masses, and stellar population properties. Consequently our
studies of the build up and growth of galaxies over cosmic time may be biased
as well. The Heavy Metal Survey provides redshifts for a significant sample of
distant quiescent galaxies, resulting in more accurate stellar population
properties. Additionally, the presence of absorption lines facilitates
kinematic and chemical composition studies, while emission lines offer an
alternative avenue for examining their star formation characteristics. In
Section 4.1 we examine our galaxy sample and compare it with the parent galaxy
sample from which the spectroscopic sample was drawn. In Section 4.2 we
present the star formation properties of the primary Heavy Metal galaxies and
assess whether they indeed have quiescent stellar populations. Moving to
Section 4.3, we discuss their structural properties, and finally, in Section
4.4 we compare the stellar masses to the dynamical masses.

Figure 6: Photometric vs. spectroscopic redshift for all spectroscopically
confirmed primary (circles) and filler (squares) targets in the Heavy Metal
Survey. We measured a spectroscopic redshift of all primary targets. For the
filler galaxies the success rate was much lower with 65%. The normalized
medium absolute deviations ($\sigma_{\rm nmad}$, Brammer et al., 2008) between
the photometric and spectroscopic redshifts are 0.017 and 0.014 for the filler
and primary galaxies, respectively. The shaded areas present the targeted
redshift intervals, used in the selection. Two of the primary targets
scattered out its targeted redshift interval.

Figure 7: Apparent magnitude vs redshift (top panels) and rest-frame $U-V$ vs
$V-J$ colors (bottom panels) for all galaxies observed in the LRIS and MOSFIRE
masks. The Heavy Metal 1 & 2 masks (left panels) primarily targeted bright
($J<21.6$) quiescent galaxies at $1.3<z<1.5$. The Heavy Metal 3 & 4 masks
(right panels) primarily targeted bright ($H<21.8$) quiescent galaxies at
$1.92<z<2.28$. Quiescent galaxies were selected by their red $U-V$ and blue
$V-J$ colors, as in indicated by the selection box. However, several primary
galaxies scattered out of the boxes when including the spectral information.
The fillers are star-forming and fainter quiescent galaxies at similar or
higher/lower redshifts. The filler galaxies for which a spectroscopic redshift
was measured are indicated by the larger boxes. We also show the parent
UltraVISTA galaxy distribution from which the samples were drawn. The $UVJ$
panels only include the UltraVISTA galaxies in the targeted redshift
intervals.

###  4.1 Galaxy sample and success rate

Our primary galaxy sample is selected to have quiescent stellar populations,
be relatively bright, and fall in two redshift intervals, $1.3<z<1.5$ and
$1.92<z<2.28$. In Figure 6 we show the photometric versus spectrospic
redshifts of the primary (circles) and filler (squares) galaxies, as well as
the distribution of the spectroscopic redshifts. Most primary galaxies fall in
or very close to the selection windows and their photometric and spectrscopic
redshifts agree well with a normalized median absolute deviation in $\Delta
z/(1+z_{\rm spec})$ of $\sigma_{\rm nmad}=0.014$. The only exception is
HM4-59375, which has a significantly lower redshift than predicted by the
photometry. This figure also shows the filler galaxies. These galaxies are
drawn from a larger redshift distribution, though galaxies at similar
redshifts were prioritized. The scatter for the filler galaxies is slightly
larger with a $\sigma_{\rm nmad}=0.017$, which may be explained by their
fainter magnitudes.

The histogram in Figure 6 shows that the spectroscopic redshifts of the
primary and filler targets are clustered, and several potential overdensities
may exist, specifically at $z\sim 1.40$ (HM1), $z\sim 1.42$ (HM2), $z\sim
2.16$ (HM4), and $z\sim 2.23$ (HM3). This finding is not surprising, as we
specifically selected pointings for which we can observe multiple quiescent
galaxies in one field of view. A further investigation into these
overdensities is beyond the scope of this paper. Nevertheless, when
interpreting our results, it is important to keep in mind that the
environments in which our galaxies reside may not be typical for distant
quiescent galaxies.

In Figure 7 we show all primary and filler targets in magnitude-redshift and
rest-frame $U-V$ vs. $V-J$ space. The left panels show the galaxies in Heavy
Metal 1 and 2, while the right panels show galaxies in Heavy Metal 3 and 4.
The boxes in the top panels, enclosed by the dotted lines, indicate the
primary target selection in terms of magnitude and redshift. In contrast to
Figure 6, here we show both the confirmed filler galaxies (large squares) and
the filler galaxies for which we did not measure a spectroscopic redshift
(small squares). The top-left box in the bottom panels, enclosed by the solid
lines, indicates our quiescent galaxy selection (red symbols; Muzzin et al.,
2013a). Galaxies outside the box are generally identified as star-forming
galaxies (blue symbols).

While we measure spectroscopic redshifts of all primary targets, for the
filler targets the success rate is lower with 71% (42/59) and 53% (17/32) for
the $z\sim 1.4$ masks and $z\sim 2.1$ masks, respectively. There are several
reasons for the lower success rate of the fillers. First, for Heavy Metal 1
and 2, most fillers are only targeted by either MOSFIRE or LRIS. Second, many
fillers are faint quiescent targets, for which we do not detect clear
absorption lines. The few faint quiescent fillers that are confirmed, all have
emission lines in their spectra. However, in the Heavy Metal 3 and 4 masks,
there are several quiescent filler targets at $z\sim 1.4$ which are as bright
as the faintest primary targets. Unfortunately, we do not capture the 4000 Å
region crucial for spectroscopic redshift measurements for these galaxies.
Finally, for several star-forming fillers, the emission lines may be outside
the atmospheric windows. For example, we find no confirmed star-forming
galaxies below $z=2$ in the Heavy Metal 3 and 4 masks.

Based on the photometric redshifts, all primary targets were initially
selected to be quiescent. However, when re-deriving the rest-frame colors
using the spectroscopic redshifts, two of the primary targets (HM3-107590 &
HM4-55878) just shift outside the quiescent box. Given their location though,
we expect these galaxies to be post-starburst or young quiescent galaxies
(e.g., Whitaker et al., 2012; Belli et al., 2019; Suess et al., 2021; Park et
al., 2023), and thus still have quiescent populations. We will further assess
their star-formation properties in the next section.

Finally, we compare our primary galaxies to the parent galaxy distributions at
$1.3<z<1.5$ and $1.92<z<2.28$ from which the targets are drawn. At $z\sim 1.4$
the primary targets do sample nearly the full distribution along the quiescent
sequence, though there is a bias toward bluer colors. The quiescent galaxies
at $z\sim 2.1$ span a larger range along the quiescent sequence, but on
average are also biased toward the bluer and younger systems. This bias is
expected, as our bright magnitude limit favors galaxies with lower mass-to-
light ratios ($M/L$), which are generally bluer and younger. Obtaining a more
representative sample would require significantly longer integration times and
larger surveys, and thus necessitates more efficient telescopes and
spectrographs, such as NIRSpec on JWST.

Figure 8: SFR derived from the H$\alpha$ emission lines vs. the best-fit SED
SFR and stellar mass for all primary galaxies with coverage of H$\alpha$.
Orange and red symbols present galaxies at $z\sim 1.4$ (Heavy Metal 1 & 2) and
$z\sim 2.1$ (Heavy metal 3 & 4), respectively. For galaxies without detected
H$\alpha$ we show a 3$\sigma$ upper limit. For all but two galaxies with
detected H$\alpha$, the [N ii]/H$\alpha>0.45$ (white plusses), implying that
the H$\alpha$ flux is not dominated by star formation. Thus, for these
galaxies the H$\alpha$ SFR is overestimated, and more comparable to an upper
limit. Consequently, the H$\alpha$ SFRs (and limits) are larger than the SED
SFRs, as illustrated in the left panel. In the right panel, we compare the
H$\alpha$ SFRs with the star-forming main sequence from Leja et al. (2022) at
$z\sim 1.4$ (red shaded area) and $z\sim 2.1$ (orange shaded area). Except for
HM4-55878, which has bright emission lines originating from a luminous AGN,
all other galaxies are significantly below the star-forming main sequence.
When using SED SFRs, they would shift to even lower values. Figure 9: The left
panels shows the effective radius (major axis) at rest-frame 5000 Å vs.
stellar mass for the primary Heavy Metal galaxies. Red and orange symbols
depict galaxies at $z\sim 1.4$ and $z\sim 2.1$, respectively. Stars and
circles represent post-starburst ($V-J<0.7$) and older quiescent galaxies,
respectively. Heavy Metal galaxies at $z\sim 1.4$ exhibit a bias towards
smaller sizes, likely due our selection criteria favoring younger galaxies.
This bias indeed diminishes when excluding post-starburst galaxies (PSBs). The
right panels show how both $M_{\rm stellar}$ and $R_{\rm e,major}$ relate to
the velocity dispersion ($\sigma_{v,\rm e}$). While the post-starburst
galaxies are smaller, their velocity dispersions are comparable to those of
older quiescent galaxies of the same stellar mass.

###  4.2 Star formation constraints

All primary Heavy Metal galaxies are selected to have quiescent stellar
populations, based on their rest-frame $UVJ$ colors. In this section we assess
whether these galaxies indeed have low SFRs using both the stellar continuum
emission and their emission-line properties.

The SFRs derived from fitting the stellar spectra and photometry with SPS
models are listed in Table 2. Except for HM4-55878, all primary galaxies have
best-fit SFRs of $<1\,\rm M_{\odot}\,yr^{-1}$. HM4-55878 has a significantly
higher SFR than expected based on its $UVJ$ colors and the initial photometric
analysis. This disparity is attributed to the influence of strong emission
lines on the broadband SED. In our fitting procedure, we first adjusted the
broadband photometry to account for the impact of these lines, as outlined in
Section 3.1.

When examining the H$\alpha$ SFRs, we find a similar result. With the
exception of HM4-55878, the primary galaxies exhibit either very faint or
undetectable H$\alpha$ emission. Among the 9 galaxies where H$\alpha$ is
detected at $>3\sigma$, 7 display [N ii]/H$\alpha$ ratios exceeding 0.45,
implying that star formation is likely not the primary ionization source
(e.g., Baldwin et al., 1981; Kauffmann et al., 2003; Kewley et al., 2006). Our
study supports previous findings that high [N ii]/H$\alpha$ ratios are common
in distant quiescent galaxies (e.g., Kriek et al., 2007; Newman et al., 2018b;
Belli et al., 2017b). Although such line ratios are commonly associated with
photoionization by active galactic nuclei (AGN; e.g., Kauffmann et al., 2003;
Kewley et al., 2006), in quiescent galaxies, they are thought to originate
from the photoionization by hot evolved stars, including post-asymptotic giant
branch stars (e.g., Yan & Blanton, 2012; Belfiore et al., 2016). For the
majority of the galaxies, we do not have a meaningful measurement of [O
iii]/H$\beta$, and thus we cannot further assess the origin of the line
emission in our sample. Only HM-55878 has a significant detection for all
lines, with its line ratios suggesting an AGN (Ma et al. in prep.). HM1-213931
and HM4-56163 have [N ii]/H$\alpha<0.45$, and thus star formation is likely
the dominant ionization source. These galaxies have low SFRs of 4-5
$M_{\odot}\rm yr^{-1}$, but the uncertainties are significant. For HM1-213931
we also do not see a clear emission line in the 2 D spectrum (see Fig. 5).

In Figure 8 (left panel) we compare the two SFR measurements. For consistency,
both measurements assume solar metallicity and a similar IMF (Kroupa vs.
Chabrier). For galaxies that have no detected H$\alpha$ emission, we show the
3$\sigma$ upper limit (triangles). For galaxies with detected H$\alpha$, we
mark the ones for which star formation is not the primary ionization mechanism
by a plus. For these galaxies the SFRs are overestimated, and the values
should been regarded as upper limits. Additional attenuation toward H ii
regions, however, could potentially have resulted in an underestimation of the
H$\alpha$ SFRs, as indicated by the arrow (right panel).

Figure 8 shows that all SFR upper limits from H$\alpha$ are not inconsistent
with the SED SFRs. The galaxies for which H$\alpha$ does not originate from
star formation are all located above the 1-to-1 line as well. Only for
HM1-213931 and HM4-56163, for which H$\alpha$ is thought to originate from
star formation, the two SFRs are inconsistent. HM1-213931 seems to be a merger
between several galaxies (see Fig. 3), and thus it may not be surprising to
find a low SFR of $4\pm 1\,M_{\odot}$ yr-1. In particular, different physical
regions for the stellar and nebular components may explain the discrepant
values. The low [N II]/H$\alpha$ ratio implies low metallicity, which makes it
more likely that the star formation is either fueled by low-metallicity
infalling gas or associated with a nearby smaller galaxy. Belli et al. (2017b)
find similarly low-levels of (metal-poor) star formation activity in distant
quiescent galaxies, which they attribute to rejuvenation events due minor
mergers or inflowing gas. Higher spatial resolution spectra will be needed to
examine the different components and further assess this galaxy.

In the right panel of Figure 8 we show the H$\alpha$ SFRs vs stellar mass, in
comparison the star-forming main sequence (ridge) from Leja et al. (2022) at
similar redshifts (and for a similar IMF). Except for AGN HM4-55878, all
primary quiescent targets are significantly below the star-forming main
sequence at its redshift. Furthermore, the majority of these data points are
upper limits, either because H$\alpha$ is undetected, or because H$\alpha$ is
not originating from star formation. Hence, except for HM4-55878, all galaxies
have indeed strongly suppressed star formation.

Figure 10: Left: Dynamical vs. stellar mass for all primary Heavy Metal
galaxies for which sizes and stellar velocity dispersion could be measured,
assuming a Chabrier (2003) IMF. We also show the galaxies by Belli et al.
(2017a) with comparable redshifts ($z>1.35$). Right: Difference between the
dynamical and stellar mass vs. the velocity dispersion ($\sigma_{v,e}$), age
of the galaxy, axis ratio $b/a$, and Sérsic index $n$. The ages, adopted from
A. Beverage et al. (in prep), are derived using alf and present the
luminosity-weighted age. In all panels the galaxies are colored coded by their
effective radii at rest-frame 5000 Å (major axis). For the majority of the
galaxies, the dynamical mass exceeds the stellar mass, with a median dark
matter fraction of 28%. Three galaxies have stellar masses that exceed their
dynamical masses. Interestingly, three galaxies with low $M_{\rm dyn}/M_{\rm
stellar}$ are the smallest and youngest galaxies in the sample.

###  4.3 Galaxy structures

Quiescent galaxies follow a size-mass relationship, where galaxies with
greater mass or luminosity exhibit larger effective radii (e.g., Kormendy,
1977; Shen et al., 2003). This relationship evolves over cosmic time, with
galaxies at greater distances appearing more compact (e.g., Trujillo et al.,
2006; van Dokkum et al., 2008; van der Wel et al., 2014; Mowla et al., 2018;
Suess et al., 2019a, b). In Figure 9, we compare the half-light radii at rest-
frame 5000 Å of the Heavy Metal galaxies with the average size-mass relation
at $z=1.25$, $z=1.75$, and $z=2.25$ as reported by Mowla et al. (2018) (using
the same IMF) for a large representative sample of massive quiescent galaxies.
To ensure consistency with prior research, we consider the major axis (non-
circularized) as the half-light radius. In contrast to Figure 8, here we use
the stellar masses that are corrected using the Galfit magnitudes, to make
them consistent with the size measurements (see Sect. 3.3). Mowla et al.
(2018) also applied this correction.

When comparing the galaxies at $z\sim 1.4$ to the relations at $z=1.25$ and
$z=1.75$ (Fig. 9), we find that, on average, the Heavy Metal galaxies are
smaller. This trend can likely be attributed to our selection criteria
favoring quiescent galaxies with lower mass-to-light ratios (M/L), indicative
of younger ages. Several studies have indeed highlighted that younger
quiescent galaxies have smaller half-light radii than their older counterparts
of equivalent mass (e.g., Whitaker et al., 2012; Belli et al., 2015; Yano et
al., 2016; Almaini et al., 2017; Maltby et al., 2018; Wu et al., 2020; Suess
et al., 2020, 2021; Setton et al., 2022). When excluding the youngest galaxies
(stars), as identified by their blue $V-J$ ($<0.7$) colors (e.g., Belli et
al., 2019; Beverage et al., 2021), we find a good agreement between the
relations by Mowla and the Heavy Metal galaxies at $z\sim 1.4$. The sizes of
the $z\sim 2.1$ Heavy Metal galaxies are more challenging to compare, as there
are only five galaxies with robust size measurements, of which two have blue
$V-J$ colors. Our primary quiescent galaxies also have similar sizes to the
spectroscopic galaxy sample by Belli et al. (2017a), when including galaxies
at similar redshifts ($1.35<z<2.45$).

In Figure 9 we also show the stellar masses and sizes in relation to their
velocity dispersions. These panels show that the youngest galaxies, despite
their small sizes, have similar velocity dispersions as older galaxies of the
similar mass. The Heavy Metal galaxies follow a roughly similar distributions
as the sample by Belli et al. (2017a) in both diagrams.

###  4.4 Comparison of dynamical and stellar masses

The combination of deep Keck spectra with high-resolution HST imaging enable
dynamical mass measurements for the majority of the primary Heavy Metal
galaxies, as listed in Table 5. In addition to the stellar content, the
dynamical mass also includes the dark matter and gas components. Thus, in
theory, the dynamical masses should give us insights into these dark
components. In practice, however, this is extremely challenging, as both the
stellar and dynamical mass measurements rely on many assumptions (see Sect.
3.3). Nonetheless, the boundary condition that the stellar mass should not
exceed the dynamical mass provides an independent check on our stellar mass
measurements, and may give us insights into assumptions that went into our
mass estimates.

In Figure 10 we show the dynamical vs. stellar mass for the primary Heavy
Metal galaxies. For the majority of the galaxies, the dynamical mass exceeds
the stellar mass, with a median dark matter fraction of 28%. For two galaxies
the dynamical masses are below their stellar masses, with one galaxy
(HM3-107590) being off by $>3\sigma$. These galaxies are among the smallest
(based on the light-weighted size) and youngest, as shown in the top-right
panel of Figure 10. Interestingly, Runco et al. (2022) found a similar result
for a post-starburst galaxy at redshift $z=1.89$, with the stellar mass also
being significantly larger than the dynamical mass. Cappellari (2023) also
find a trend with age for $z\sim 0.7$ galaxies in the LEGA-C survey, with the
younger galaxies having lower dynamical-to-stellar mass ratios.

In order to assess how the masses compare when adopting different assumptions,
and to understand why some galaxies have $M_{*,c}>M_{\rm dyn}$, we discuss the
different assumptions below. First, when deriving the dynamical mass, we
circularize the effective radius and use a Sérsic dependent virial coefficient
$\beta(n)$. If we would not have circularized the radius, $M_{\rm
dyn}/M_{\rm*,\rm c}$ would increase by 0.023 dex and the scatter would
increase from 0.232 to 0.255 (assumption set 2, Fig.11 and Table 5). Instead
of circularizing, we also explore the axis ratio correction by van der Wel et
al. (2022), which is implemented using an additional virial coefficient
$K(q)$. This combination increases the median $M_{\rm dyn}/M_{\rm*,\rm c}$ by
0.12 dex as well as the scatter (assumption set 3). Assuming a virial constant
of 5 would also increase the scatter in $M_{\rm dyn}/M_{\rm*,\rm c}$, but the
median $M_{\rm dyn}/M_{\rm*,\rm c}$ would decrease by 0.15 dex (assumption set
4).

Figure 11: Left: Median and scatter in $M_{\rm dyn}/M_{\rm*,\rm c}$ for different assumptions when calculating the dynamical and stellar mass (see Table 5). Right: Dynamical vs. stellar mass when adopting the $\sigma_{v}$-dependent IMF by Treu et al. (2010) for the cores of nearby early-type galaxies, sub-solar metallicity, and half-mass radii. For this combination of assumptions, the scatter in $M_{\rm dyn}/M_{\rm*,\rm c}$ is smallest. However, the stellar mass exceeds the dynamical mass by 34%. This tension may imply that distant quiescent galaxies do not simply grow inside-out into massive early-type galaxies today.  Table 5: Dynamical-to-stellar mass ratios for varying assumptions No | $M_{\rm dyn}$ assump. | $M_{*}$ assump. | log $M_{\rm dyn}/M_{\rm*,\rm c}$
---|---|---|---
| $R_{e}$ | VC999Virial coefficient | Z | IMF101010Ch, Sa, and $\sigma_{v}$ refers to the IMFs by Chabrier (2003), Salpeter (1955) and Treu et al. (2010). | med | $\sigma$
1 | circ, light | $\beta(n)$ | 0.0190 | Ch | 0.14 | 0.23
2 | sma, light | $\beta(n)$ | 0.0190 | Ch | 0.23 | 0.25
3 | sma, light | $\beta(n)K(q)$ | 0.0190 | Ch | 0.26 | 0.24
4 | circ, light | 5 | 0.0190 | Ch | -0.01 | 0.24
5 | circ, mass | $\beta(n)$ | 0.0190 | Ch | -0.02 | 0.20
6 | circ, light | $\beta(n)$ | 0.0096 | Ch | 0.09 | 0.20
7 | circ, light | $\beta(n)$ | 0.0190 | Sa | -0.06 | 0.23
8 | circ, mass | $\beta(n)$ | 0.0096 | Sa | -0.24 | 0.19
9 | circ, light | $\beta(n)$ | 0.0190 | $\sigma_{v}$ | 0.01 | 0.17
10 | circ, mass | $\beta(n)$ | 0.0096 | $\sigma_{v}$ | -0.13 | 0.14

Second, in our dynamical mass measurement we assume that the galaxies are
pressure supported. However, if they are (partially) rotationally supported,
our dynamical mass measurement would be off. For example, for HM3-107590 the
low dynamical mass could be explained by a face-on view or by a strong mis-
alignment of the slit and the major axis of the galaxy. For these cases, part
of the velocity field would not be included in our dispersion measurement and
we would underestimate the mass. We check for this possibility by examining
$M_{\rm dyn}/M_{\rm*,\rm c}$ as a function of the Sérsic index and axis ratio
($b/a$) in the right panels of Figure 10. HM3-107590 is nearly round and the
velocity dispersion is indeed lower compared to galaxies of similar mass (Fig.
9). The Sérsic index appears at odds with the galaxy being a disk, though this
measurement is quite uncertain as this galaxy is just barely resolved.

In this context it is interesting to note that Belli et al. (2017a) find
higher $M_{\rm dyn}/M_{\rm*,\rm c}$ for galaxies with low Sérsic indices
($n<2.5$) and low axis ratios, and interpret this finding as evidence for a
significant contribution of rotational motion. We do not see any indications
that galaxies with the highest $M_{\rm dyn}/M_{\rm*,\rm c}$ preferentially
have low $n$ and low $b/a$. However, in contrast to Belli et al. (2017a), we
circularize our effective radii when deriving the dynamical mass, which lowers
$M_{\rm dyn}/M_{\rm*,\rm c}$ for galaxies with low axis ratios, and thus we
partially account for inclination effects. Improving upon our simplified
approach requires a forward modeling method, preferentially combined with
spatially resolved spectroscopy, allowing for dynamical models with different
levels of rotational support and correcting for inclination and aperture
effects (e.g., Price et al., 2016, 2020; van Houdt et al., 2021; de Graaff et
al., 2023).

Third, dynamical masses depend on size measurements, which may have been
biased due to stellar population gradients. Distant quiescent galaxies have
redder centers, with gradient being stronger in galaxies that are more
massive, older, and at lower redshifts (e.g., Mosleh et al., 2017; Suess et
al., 2019a, b, 2020, 2021; Miller et al., 2023). By applying the average size
corrections by Suess et al. (2019a, 2021, $\sim$0.2 dex and $\sim$0.1 dex for
the older quiescent galaxies at $z\sim 1.4$ and $z\sim 2.1$, respectively, and
no corrections for post-starburst galaxies), we find that median $M_{\rm
dyn}/M_{\rm*,\rm c}$ decreases by 0.16 dex (see Fig. 11, assumption set 5).
The color gradient correction also reduces the scatter $M_{\rm
dyn}/M_{\rm*,\rm c}$. The $M_{\rm dyn}$ of the two youngest galaxies remain
unaffected, as post-starburst galaxies tend to display uniform color gradients
(e.g., Setton et al., 2020; Suess et al., 2020, 2021). HM1-217249, the sole
post-starburst galaxy with robust size measurements in both F814W and F160W,
supports this trend. Thus, stellar population gradients do not explain the low
$M_{\rm dyn}/M_{\rm*,\rm c}$ of the few post-starburst galaxies. Instead, they
further lower the median inferred dark matter fraction of our full distant
quiescent galaxy sample. Finally, size underestimation could occur due to the
presence of an AGN, although the full SEDs and spectra provide limited room
for a power-law continuum contribution.

The stellar masses could also be biased. First, as we assume a simple delayed
exponential star-formation history, it is likely that we miss older, and low
$M/L$ stellar populations in our stellar mass. This “outshining” problem has
been discussed in many works (e.g., Papovich et al., 2001; Wuyts et al., 2007;
Leja et al., 2019; Giménez-Arteaga et al., 2023). However, for distant massive
quiescent galaxies this effect is small, and thus the fast and Prospector
masses (Johnson et al., 2021), assuming non-parameterized star formation
histories are very close (Leja et al., 2019). Second, we assume solar
metallicity, while the galaxies, on average, have sub-solar iron abundances
(A. Beverage et al. in prep). Assuming a half-solar metallicity (Z=0.0096)
would increase the median stellar masses by 13% (see Fig. 11) and decreases
the scatter in $M_{\rm dyn}/M_{\rm*,\rm c}$ by 0.035. Third, we assume a
Chabrier (2003) IMF, which, similar to a Kroupa IMF, is relatively bottom
light. Assuming a Salpeter (1955) IMF would increase the stellar masses by 0.2
dex (Fig. 11), such that it exceeds $M_{\rm dyn}$ for the majority of the
galaxies. Combining both stellar mass effects and the color gradient
correction (assumption set 8 in Fig. 11), would lead to stellar masses vastly
exceeding the dynamical masses for nearly all galaxies. Hence, given our
dynamical masses we infer that a Chabrier IMF is more likely than a Salpeter
IMF for distant quiescent galaxies. We will further explore the IMF in the
next section.

##  5 Discussion

###  5.1 Implications for Photometric Studies

While the number of distant star-forming galaxies with spectroscopic redshifts
has increased tremendously in the past decade (e.g., Steidel et al., 2014;
Wisnioski et al., 2015; Kriek et al., 2015), the number of distant quiescent
galaxies with spectroscopic redshifts or other spectroscopic information is
still very small. Detecting absorption lines requires significantly longer
integration times than observing nebular emission lines. Thus, the majority of
studies of quiescent galaxies over cosmic time, including the build up of the
stellar mass function, still rely on photometric data.

Our study presents a re-assuring picture. The initial photometric redshifts of
our primary quiescent galaxies agree well with their spectroscopic redshifts
(see Sect. 4.1) and nearly all galaxies have quiescent stellar populations
with their SFRs significantly below the star-forming main sequence (see Sect.
4.2). We do find, however, that photometric redshifts become less accurate
beyond $z=2$. Furthermore, we show that for one galaxy, the contribution from
strong AGN emission lines mimics the shape of a quiescent galaxy. Schreiber et
al. (2018) shows that the success rate of the $UVJ$ selection criteria further
declines to about 80% when going to $3<z<4$. Forrest et al. (2020) presents a
less optimistic picture with a spectroscopic confirmation rate of about 50%
for quiescent galaxy candidates beyond $z=3$. Nonetheless, out to $z\sim 2$,
we do not expect that mass functions of quiescent galaxies will be strongly
biased by incorrect photometric redshifts or quiescent galaxy classifications.

###  5.2 Implications for the evolution of massive quiescent galaxies

One popular explanations for the size evolution of quiescent galaxies over
cosmic time is growth by minor mergers. This scenario is supported by the
finding that the central mass densities of quiescent galaxies remains roughly
constant, while their (blue) outskirts are building up over time (e.g.,
Bezanson et al., 2009; van Dokkum et al., 2010; Barro et al., 2017; Suess et
al., 2021). Furthermore, distant quiescent galaxies have many small companions
(Newman et al., 2012; Suess et al., 2023). Thus, in this scenario, distant
quiescent galaxies are the cores of massive galaxies today. These same cores
are also found to have a bottom-heavy IMF (e.g., Treu et al., 2010; Conroy &
van Dokkum, 2012), with the highest velocity dispersion galaxies having a
larger excess of low-mass stars. Thus, for this inside-growth scenario, the
IMF in the high-dispersion galaxies should already be bottom-heavy at these
early times.

In Figure 10 we indeed find that $M_{\rm dyn}/M_{\rm*,\rm c}$ correlates with
$\sigma_{v,e}$, which could imply that the IMF may be more bottom heavy in
higher-dispersion galaxies. This trend was already visible in the $M_{\rm
dyn}-M_{*}$ diagrams in several distant quiescent galaxy studies (e.g., van de
Sande et al., 2013; Belli et al., 2017a; Forrest et al., 2022), and discussed
in detail in Mendel et al. (2020). Mendel et al. (2020) argue that this trend
is due to a varying IMF, and that the IMF-$\sigma_{v}$ relation was already in
place at these early times.

To further assess this theory, we show $M_{\rm dyn}/M_{\rm*,\rm c}$ assuming a
$\sigma_{v}$-dependent IMF for our distant quiescent galaxies in Figure 11
(assumption set 9). We use the relation by Treu et al. (2010, Equation 4), in
which the IMF is more bottom-heavy than the Salpeter IMF for galaxies with
$\sigma_{v}>250\rm\,km\,s^{-1}$. This IMF results in a median $M_{\rm
dyn}/M_{\rm*,\rm c}$ of 1.033. The scatter in $M_{\rm dyn}/M_{\rm*,\rm c}$ is
strongly reduced, which is expected as we are (partially) removing the trend
with $\sigma_{v,e}$. Interestingly, when also assuming sub-solar metallicity
(Z=0.0096) and correcting for color gradients, this IMF results in stellar
masses that exceed the dynamical masses for all but one galaxy, with a median
$M_{\rm dyn}/M_{\rm*,\rm c}$ of 0.75 (Fig. 11, assumption set 10). Thus, our
dynamical masses may suggest that compact distant quiescent galaxies do not
“passively” evolved into the cores of massive elliptical galaxies today, and
that the evolution is more complicated (e.g., Wellons et al., 2015). Major
mergers (with galaxies with a different IMF) and/or late-time central star
formation could have affected the average IMF in today’s cores.

Interestingly, van Dokkum et al. (2023) came to the opposite conclusions,
based on a perfect lensing system (see also Mercier et al., 2023). They find
that a bottom-heavy IMF must already be in place for a distant quiescent
galaxy at $z\sim 1.9$, because the stellar mass, assuming the Chabrier (2003)
IMF would lead to an unrealistically large dark matter fraction within the
Einstein radius. Obtaining spectroscopic redshifts for both galaxies as well
as a dynamical mass measurement for the quiescent galaxy lens would be needed
to directly compare our results.

In order to further unravel this puzzle, we need progress on several fronts.
First, we need to measure stellar population gradients and half-mass radii for
our spectroscopic samples. This should preferentially be done from
spectroscopic data, as age, metallicity, and dust gradients result in
different $M/L$ gradients (e.g., van de Sande et al., 2015). We would also
have to re-determine the stellar masses, taking into account these stellar
population gradients. Second, we need to resolve the kinematics of distant
quiescent galaxies, such that we can model their stellar dynamics. Third, we
need a direct spectroscopic measurement of the IMF in distant quiescent
galaxies, to obtain more accurate stellar masses and understand whether the
bottom-heavy IMF was already in place at these early times. Finally, we need
larger samples of galaxy spectra. JWST will book advances in all these areas,
and has already collected spectra of a hand full of distant quiescent galaxies
(Nanayakkara et al., 2022; Carnall et al., 2023; Marchesini et al., 2023;
D’Eugenio et al., 2023; Belli et al., 2023).

##  6 Summary

In this paper, we present an overview of the Heavy Metal Survey, an ultradeep
rest-frame optical spectroscopic survey of 21 distant quiescent galaxy
candidates at $1.4\lesssim z\lesssim 2.2$. The Heavy Metal Survey was executed
with MOSFIRE and LRIS on the Keck I Telescope and overlaps with the UltraVISTA
and COSMOS-DASH surveys. Our primary targets were selected across two redshift
intervals, $1.3<z<1.5$ and $1.92<z<2.28$, allowing the observation of multiple
Balmer and metal (Ca, Mg, Fe) absorption lines in atmospheric windows. The
extensive sky coverage enabled galaxy pointings for which we observe 5-6
“bright” quiescent candidates in one pointing, with two pointings per redshift
interval. The remaining slits were placed on fainter quiescent and star-
forming galaxies at similar redshifts. The $z\sim 1.4$ and $z\sim 2.1$ targets
were observed for a total of $\sim 18$ and $\sim 32$ hrs, respectively. The
Heavy Metal Survey is unique for its wavelength coverage, and presents the
first statistical sample of $z\gtrsim 1.4$ quiescent galaxies with ultra-deep
spectra covering rest-frame $\sim$3700–5400 Å.

We measure spectroscopic redshifts for all primary targets, and nearly all
show clear Balmer and metal absorption lines in their spectra. 20 out of the
21 quiescent candidates indeed have quiescent stellar populations; the SFRs
determined from H$\alpha$ and spectrophotometric fitting are both
significantly below the star-forming main sequence. For 11 out of the 20
quiescent galaxies we detect no H$\alpha$ and derive upper limits on the SFR
from H$\alpha$. For nine targets we do detect faint H$\alpha$ emission, but
seven of them have emission-line ratios which indicate that star formation is
not the primary ionization source; instead they may be powered by hot evolved
stars or low-luminosity AGN. Hence, for these galaxies the H$\alpha$ SFRs are
more comparable to upper limits as well. For the remaining two galaxies with
detected H$\alpha$, the SFRs are very low and for one of them [N ii]/H$\alpha$
suggests that the star formation is likely associated with a nearby smaller
galaxy. Finally, one of the quiescent candidates appeared to be an AGN, with
strong (asymmetric) emission lines mimicking the shape of a quiescent
galaxies. This galaxy will be discussed in detail in Y. Ma et al. (in
preparation).

The primary goal of the Heavy Metal Survey is to measure chemical compositions
and ages from the stellar absorption line spectra. These measurements are
discussed in our accompanying paper by A. Beverage et al. (in preparation).
The stellar population fitting, presented in that paper, also yields accurate
stellar velocity dispersion measurements for 19 out of the 21 primary
galaxies. These measurements, combined, with the structural parameters derived
from HST F814W and F160W imaging, enable us to derive dynamical masses for the
majority of the primary Heavy Metal galaxies.

In this paper, we compare our dynamical masses with the stellar masses from
spectrophotometric modeling, considering various assumptions for both masses.
Interestingly, for a fixed IMF, $M_{\rm dyn}$/$M_{*}$ shows a positive
correlation with $\sigma_{v}$. This correlation may suggest that a varying
IMF, that is more bottom-heavy for high-$\sigma_{v}$ galaxies, was already in
place at these early times (see also Mendel et al., 2020). When implementing
the $\sigma_{v}$-dependent IMF found in the cores of nearby massive early-type
galaxies, and also correcting for biases in our stellar mass and size
measurements, we find a low scatter in $M_{\rm dyn}$/$M_{*}$ of only 0.14 dex
and a median $M_{\rm dyn}$/$M_{*}$ of 0.75. Thus, for these assumptions, the
stellar mass measurements exceed the dynamical masses for nearly all quiescent
galaxies. This result may imply that distant quiescent galaxies do not simply
grow inside-out into massive early-type galaxies in today’s universe and late-
time evolution (major mergers and/or late-time star formation) may be needed.

In order to fully characterize the distant quiescent galaxy population, and
solve this possible tension with the studies of the cores in nearby massive
galaxies, we need to make progress on several fronts. First, we need a
statistical sample of distant quiescent galaxies with resolved stellar
kinematics, ages, elemental abundances, and robust stellar mass profiles.
Moreover, we need to directly measure the IMF in distant quiescent galaxies.
JWST will be able to make progress on all these fronts, and thus will be
transformative for our understanding of the formation histories of distant
quiescent galaxies and their evolutionary link to the massive early-type
galaxies in the present-day universe.

We acknowledge support from NSF AAG grants AST-1908748 and 1909942. CC
acknowledges support from NSF grant AST-131547. The authors wish to recognize
and acknowledge the very significant cultural role and reverence that the
summit of Mauna Kea has always had within the indigenous Hawaiian community.
We are most fortunate to have the opportunity to conduct observations from
this mountain.

## References

  * Almaini et al. (2017) Almaini, O., Wild, V., Maltby, D. T., et al. 2017, MNRAS, 472, 1401, doi: 10.1093/mnras/stx1957
  * Antwi-Danso et al. (2023) Antwi-Danso, J., Papovich, C., Esdaile, J., et al. 2023, arXiv e-prints, arXiv:2307.09590, doi: 10.48550/arXiv.2307.09590
  * Baldwin et al. (1981) Baldwin, J. A., Phillips, M. M., & Terlevich, R. 1981, PASP, 93, 5, doi: 10.1086/130766
  * Barro et al. (2017) Barro, G., Faber, S. M., Koo, D. C., et al. 2017, ApJ, 840, 47, doi: 10.3847/1538-4357/aa6b05
  * Belfiore et al. (2016) Belfiore, F., Maiolino, R., Maraston, C., et al. 2016, MNRAS, 461, 3111, doi: 10.1093/mnras/stw1234
  * Belli et al. (2015) Belli, S., Newman, A. B., & Ellis, R. S. 2015, ApJ, 799, 206, doi: 10.1088/0004-637X/799/2/206
  * Belli et al. (2017a) —. 2017a, ApJ, 834, 18, doi: 10.3847/1538-4357/834/1/18
  * Belli et al. (2019) —. 2019, ApJ, 874, 17, doi: 10.3847/1538-4357/ab07af
  * Belli et al. (2014) Belli, S., Newman, A. B., Ellis, R. S., & Konidaris, N. P. 2014, ApJ, 788, L29, doi: 10.1088/2041-8205/788/2/L29
  * Belli et al. (2017b) Belli, S., Genzel, R., Förster Schreiber, N. M., et al. 2017b, ApJ, 841, L6, doi: 10.3847/2041-8213/aa70e5
  * Belli et al. (2023) Belli, S., Park, M., Davies, R. L., et al. 2023, arXiv e-prints, arXiv:2308.05795, doi: 10.48550/arXiv.2308.05795
  * Beverage et al. (2021) Beverage, A. G., Kriek, M., Conroy, C., et al. 2021, ApJ, 917, L1, doi: 10.3847/2041-8213/ac12cd
  * Beverage et al. (2023) —. 2023, ApJ, 948, 140, doi: 10.3847/1538-4357/acc176
  * Bezanson et al. (2013) Bezanson, R., van Dokkum, P., van de Sande, J., Franx, M., & Kriek, M. 2013, ApJ, 764, L8, doi: 10.1088/2041-8205/764/1/L8
  * Bezanson et al. (2009) Bezanson, R., van Dokkum, P. G., Tal, T., et al. 2009, ApJ, 697, 1290, doi: 10.1088/0004-637X/697/2/1290
  * Brammer et al. (2008) Brammer, G. B., van Dokkum, P. G., & Coppi, P. 2008, ApJ, 686, 1503, doi: 10.1086/591786
  * Bruzual & Charlot (2003) Bruzual, G., & Charlot, S. 2003, MNRAS, 344, 1000, doi: 10.1046/j.1365-8711.2003.06897.x
  * Cappellari (2023) Cappellari, M. 2023, MNRAS, 526, 3273, doi: 10.1093/mnras/stad2597
  * Cappellari & Emsellem (2004) Cappellari, M., & Emsellem, E. 2004, PASP, 116, 138, doi: 10.1086/381875
  * Cappellari et al. (2006) Cappellari, M., Bacon, R., Bureau, M., et al. 2006, MNRAS, 366, 1126, doi: 10.1111/j.1365-2966.2005.09981.x
  * Carnall et al. (2022) Carnall, A. C., McLure, R. J., Dunlop, J. S., et al. 2022, ApJ, 929, 131, doi: 10.3847/1538-4357/ac5b62
  * Carnall et al. (2023) —. 2023, Nature, 619, 716, doi: 10.1038/s41586-023-06158-6
  * Chabrier (2003) Chabrier, G. 2003, PASP, 115, 763, doi: 10.1086/376392
  * Choi et al. (2016) Choi, J., Dotter, A., Conroy, C., et al. 2016, ApJ, 823, 102, doi: 10.3847/0004-637X/823/2/102
  * Cimatti et al. (2004) Cimatti, A., Daddi, E., Renzini, A., et al. 2004, Nature, 430, 184, doi: 10.1038/nature02668
  * Conroy & Gunn (2010) Conroy, C., & Gunn, J. E. 2010, ApJ, 712, 833, doi: 10.1088/0004-637X/712/2/833
  * Conroy et al. (2009) Conroy, C., Gunn, J. E., & White, M. 2009, ApJ, 699, 486, doi: 10.1088/0004-637X/699/1/486
  * Conroy & van Dokkum (2012) Conroy, C., & van Dokkum, P. G. 2012, ApJ, 760, 71, doi: 10.1088/0004-637X/760/1/71
  * Conroy et al. (2018) Conroy, C., Villaume, A., van Dokkum, P. G., & Lind, K. 2018, ApJ, 854, 139, doi: 10.3847/1538-4357/aaab49
  * Cutler et al. (2022) Cutler, S. E., Whitaker, K. E., Mowla, L. A., et al. 2022, ApJ, 925, 34, doi: 10.3847/1538-4357/ac341c
  * Daddi et al. (2005) Daddi, E., Renzini, A., Pirzkal, N., et al. 2005, ApJ, 626, 680, doi: 10.1086/430104
  * de Graaff et al. (2023) de Graaff, A., Rix, H.-W., Carniani, S., et al. 2023, arXiv e-prints, arXiv:2308.09742, doi: 10.48550/arXiv.2308.09742
  * D’Eugenio et al. (2023) D’Eugenio, F., Perez-Gonzalez, P., Maiolino, R., et al. 2023, arXiv e-prints, arXiv:2308.06317, doi: 10.48550/arXiv.2308.06317
  * Esdaile et al. (2021) Esdaile, J., Glazebrook, K., Labbé, I., et al. 2021, ApJ, 908, L35, doi: 10.3847/2041-8213/abe11e
  * Forrest et al. (2020) Forrest, B., Annunziatella, M., Wilson, G., et al. 2020, ApJ, 890, L1, doi: 10.3847/2041-8213/ab5b9f
  * Forrest et al. (2022) Forrest, B., Wilson, G., Muzzin, A., et al. 2022, ApJ, 938, 109, doi: 10.3847/1538-4357/ac8747
  * Franx et al. (2003) Franx, M., Labbé, I., Rudnick, G., et al. 2003, ApJ, 587, L79, doi: 10.1086/375155
  * Giménez-Arteaga et al. (2023) Giménez-Arteaga, C., Oesch, P. A., Brammer, G. B., et al. 2023, ApJ, 948, 126, doi: 10.3847/1538-4357/acc5ea
  * Glazebrook et al. (2004) Glazebrook, K., Abraham, R. G., McCarthy, P. J., et al. 2004, Nature, 430, 181, doi: 10.1038/nature02667
  * Glazebrook et al. (2017) Glazebrook, K., Schreiber, C., Labbé, I., et al. 2017, Nature, 544, 71, doi: 10.1038/nature21680
  * Grogin et al. (2011) Grogin, N. A., Kocevski, D. D., Faber, S. M., et al. 2011, ApJS, 197, 35, doi: 10.1088/0067-0049/197/2/35
  * Horne (1986) Horne, K. 1986, PASP, 98, 609, doi: 10.1086/131801
  * Jafariyazani et al. (2020) Jafariyazani, M., Newman, A. B., Mobasher, B., et al. 2020, ApJ, 897, L42, doi: 10.3847/2041-8213/aba11c
  * Johnson et al. (2021) Johnson, B. D., Leja, J., Conroy, C., & Speagle, J. S. 2021, ApJS, 254, 22, doi: 10.3847/1538-4365/abef67
  * Kauffmann et al. (2003) Kauffmann, G., Heckman, T. M., Tremonti, C., et al. 2003, MNRAS, 346, 1055, doi: 10.1111/j.1365-2966.2003.07154.x
  * Kennicutt (1998) Kennicutt, Jr., R. C. 1998, ARA&A, 36, 189, doi: 10.1146/annurev.astro.36.1.189
  * Kewley et al. (2006) Kewley, L. J., Groves, B., Kauffmann, G., & Heckman, T. 2006, MNRAS, 372, 961, doi: 10.1111/j.1365-2966.2006.10859.x
  * Koekemoer et al. (2011) Koekemoer, A. M., Faber, S. M., Ferguson, H. C., et al. 2011, ApJS, 197, 36, doi: 10.1088/0067-0049/197/2/36
  * Kormendy (1977) Kormendy, J. 1977, ApJ, 218, 333, doi: 10.1086/155687
  * Kriek & Conroy (2013) Kriek, M., & Conroy, C. 2013, ApJ, 775, L16, doi: 10.1088/2041-8205/775/1/L16
  * Kriek et al. (2009) Kriek, M., van Dokkum, P. G., Labbé, I., et al. 2009, ApJ, 700, 221, doi: 10.1088/0004-637X/700/1/221
  * Kriek et al. (2006) Kriek, M., van Dokkum, P. G., Franx, M., et al. 2006, ApJ, 649, L71, doi: 10.1086/508371
  * Kriek et al. (2007) —. 2007, ApJ, 669, 776, doi: 10.1086/520789
  * Kriek et al. (2015) Kriek, M., Shapley, A. E., Reddy, N. A., et al. 2015, ApJS, 218, 15, doi: 10.1088/0067-0049/218/2/15
  * Kriek et al. (2016) Kriek, M., Conroy, C., van Dokkum, P. G., et al. 2016, Nature, 540, 248, doi: 10.1038/nature20570
  * Kriek et al. (2019) Kriek, M., Price, S. H., Conroy, C., et al. 2019, ApJ, 880, L31, doi: 10.3847/2041-8213/ab2e75
  * Kroupa (2001) Kroupa, P. 2001, MNRAS, 322, 231, doi: 10.1046/j.1365-8711.2001.04022.x
  * Leja et al. (2019) Leja, J., Johnson, B. D., Conroy, C., et al. 2019, ApJ, 877, 140, doi: 10.3847/1538-4357/ab1d5a
  * Leja et al. (2022) Leja, J., Speagle, J. S., Ting, Y.-S., et al. 2022, ApJ, 936, 165, doi: 10.3847/1538-4357/ac887d
  * Lonoce et al. (2015) Lonoce, I., Longhetti, M., Maraston, C., et al. 2015, MNRAS, 454, 3912, doi: 10.1093/mnras/stv2150
  * Maltby et al. (2018) Maltby, D. T., Almaini, O., Wild, V., et al. 2018, MNRAS, 480, 381, doi: 10.1093/mnras/sty1794
  * Maraston (2005) Maraston, C. 2005, MNRAS, 362, 799, doi: 10.1111/j.1365-2966.2005.09270.x
  * Marchesini et al. (2023) Marchesini, D., Brammer, G., Morishita, T., et al. 2023, ApJ, 942, L25, doi: 10.3847/2041-8213/acaaac
  * McCracken et al. (2012) McCracken, H. J., Milvang-Jensen, B., Dunlop, J., et al. 2012, A&A, 544, A156, doi: 10.1051/0004-6361/201219507
  * McDermid et al. (2015) McDermid, R. M., Alatalo, K., Blitz, L., et al. 2015, MNRAS, 448, 3484, doi: 10.1093/mnras/stv105
  * McLean et al. (2012) McLean, I. S., Steidel, C. C., Epps, H. W., et al. 2012, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 8446, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, doi: 10.1117/12.924794
  * McLeod et al. (2021) McLeod, D. J., McLure, R. J., Dunlop, J. S., et al. 2021, MNRAS, 503, 4413, doi: 10.1093/mnras/stab731
  * Mendel et al. (2015) Mendel, J. T., Saglia, R. P., Bender, R., et al. 2015, ApJ, 804, L4, doi: 10.1088/2041-8205/804/1/L4
  * Mendel et al. (2020) Mendel, J. T., Beifiori, A., Saglia, R. P., et al. 2020, ApJ, 899, 87, doi: 10.3847/1538-4357/ab9ffc
  * Mercier et al. (2023) Mercier, W., Shuntov, M., Gavazzi, R., et al. 2023, arXiv e-prints, arXiv:2309.15986, doi: 10.48550/arXiv.2309.15986
  * Miller et al. (2023) Miller, T. B., van Dokkum, P., & Mowla, L. 2023, ApJ, 945, 155, doi: 10.3847/1538-4357/acbc74
  * Momcheva et al. (2017) Momcheva, I. G., van Dokkum, P. G., van der Wel, A., et al. 2017, PASP, 129, 015004, doi: 10.1088/1538-3873/129/971/015004
  * Mosleh et al. (2017) Mosleh, M., Tacchella, S., Renzini, A., et al. 2017, ApJ, 837, 2, doi: 10.3847/1538-4357/aa5f14
  * Mowla et al. (2018) Mowla, L., van Dokkum, P., Brammer, G., et al. 2018, ArXiv e-prints.  https://arxiv.org/abs/1808.04379
  * Muzzin et al. (2013a) Muzzin, A., Marchesini, D., Stefanon, M., et al. 2013a, ApJ, 777, 18, doi: 10.1088/0004-637X/777/1/18
  * Muzzin et al. (2013b) —. 2013b, ApJS, 206, 8, doi: 10.1088/0067-0049/206/1/8
  * Nanayakkara et al. (2022) Nanayakkara, T., Glazebrook, K., Jacobs, C., et al. 2022, arXiv e-prints, arXiv:2212.11638, doi: 10.48550/arXiv.2212.11638
  * Newman et al. (2015) Newman, A. B., Belli, S., & Ellis, R. S. 2015, ApJ, 813, L7, doi: 10.1088/2041-8205/813/1/L7
  * Newman et al. (2018a) Newman, A. B., Belli, S., Ellis, R. S., & Patel, S. G. 2018a, ApJ, 862, 126, doi: 10.3847/1538-4357/aacd4f
  * Newman et al. (2018b) —. 2018b, ApJ, 862, 125, doi: 10.3847/1538-4357/aacd4d
  * Newman et al. (2012) Newman, A. B., Ellis, R. S., Bundy, K., & Treu, T. 2012, ApJ, 746, 162, doi: 10.1088/0004-637X/746/2/162
  * Oke & Gunn (1983) Oke, J. B., & Gunn, J. E. 1983, ApJ, 266, 713, doi: 10.1086/160817
  * Oke et al. (1995) Oke, J. B., Cohen, J. G., Carr, M., et al. 1995, PASP, 107, 375, doi: 10.1086/133562
  * Onodera et al. (2015) Onodera, M., Carollo, C. M., Renzini, A., et al. 2015, ApJ, 808, 161, doi: 10.1088/0004-637X/808/2/161
  * Papovich et al. (2001) Papovich, C., Dickinson, M., & Ferguson, H. C. 2001, ApJ, 559, 620, doi: 10.1086/322412
  * Park et al. (2023) Park, M., Belli, S., Conroy, C., et al. 2023, ApJ, 953, 119, doi: 10.3847/1538-4357/acd54a
  * Peng et al. (2002) Peng, C. Y., Ho, L. C., Impey, C. D., & Rix, H.-W. 2002, AJ, 124, 266, doi: 10.1086/340952
  * Price et al. (2016) Price, S. H., Kriek, M., Shapley, A. E., et al. 2016, ApJ, 819, 80, doi: 10.3847/0004-637X/819/1/80
  * Price et al. (2020) Price, S. H., Kriek, M., Barro, G., et al. 2020, ApJ, 894, 91, doi: 10.3847/1538-4357/ab7990
  * Runco et al. (2022) Runco, J. N., Shapley, A. E., Kriek, M., et al. 2022, MNRAS, 517, 4405, doi: 10.1093/mnras/stac2863
  * Salpeter (1955) Salpeter, E. E. 1955, ApJ, 121, 161, doi: 10.1086/145971
  * Saracco et al. (2019) Saracco, P., La Barbera, F., Gargiulo, A., et al. 2019, MNRAS, 484, 2281, doi: 10.1093/mnras/sty3509
  * Schreiber et al. (2018) Schreiber, C., Glazebrook, K., Nanayakkara, T., et al. 2018, A&A, 618, A85, doi: 10.1051/0004-6361/201833070
  * Scoville et al. (2007) Scoville, N., Aussel, H., Brusa, M., et al. 2007, ApJS, 172, 1, doi: 10.1086/516585
  * Setton et al. (2020) Setton, D. J., Bezanson, R., Suess, K. A., et al. 2020, ApJ, 905, 79, doi: 10.3847/1538-4357/abc265
  * Setton et al. (2022) Setton, D. J., Verrico, M., Bezanson, R., et al. 2022, ApJ, 931, 51, doi: 10.3847/1538-4357/ac6096
  * Sharples et al. (2013) Sharples, R., Bender, R., Agudo Berbel, A., et al. 2013, The Messenger, 151, 21
  * Shen et al. (2003) Shen, S., Mo, H. J., White, S. D. M., et al. 2003, MNRAS, 343, 978, doi: 10.1046/j.1365-8711.2003.06740.x
  * Steidel et al. (2014) Steidel, C. C., Rudie, G. C., Strom, A. L., et al. 2014, ApJ, 795, 165, doi: 10.1088/0004-637X/795/2/165
  * Suess et al. (2019a) Suess, K. A., Kriek, M., Price, S. H., & Barro, G. 2019a, ApJ, 877, 103, doi: 10.3847/1538-4357/ab1bda
  * Suess et al. (2019b) —. 2019b, ApJ, 885, L22, doi: 10.3847/2041-8213/ab4db3
  * Suess et al. (2020) —. 2020, ApJ, 899, L26, doi: 10.3847/2041-8213/abacc9
  * Suess et al. (2021) —. 2021, ApJ, 915, 87, doi: 10.3847/1538-4357/abf1e4
  * Suess et al. (2023) Suess, K. A., Williams, C. C., Robertson, B., et al. 2023, ApJ, 956, L42, doi: 10.3847/2041-8213/acf5e6
  * Tanaka et al. (2019) Tanaka, M., Valentino, F., Toft, S., et al. 2019, ApJ, 885, L34, doi: 10.3847/2041-8213/ab4ff3
  * Thomas et al. (2005) Thomas, D., Maraston, C., Bender, R., & Mendes de Oliveira, C. 2005, ApJ, 621, 673, doi: 10.1086/426932
  * Toft et al. (2017) Toft, S., Zabl, J., Richard, J., et al. 2017, Nature, 546, 510, doi: 10.1038/nature22388
  * Tomczak et al. (2014) Tomczak, A. R., Quadri, R. F., Tran, K.-V. H., et al. 2014, ApJ, 783, 85, doi: 10.1088/0004-637X/783/2/85
  * Treu et al. (2010) Treu, T., Auger, M. W., Koopmans, L. V. E., et al. 2010, ApJ, 709, 1195, doi: 10.1088/0004-637X/709/2/1195
  * Trujillo et al. (2006) Trujillo, I., Förster Schreiber, N. M., Rudnick, G., et al. 2006, ApJ, 650, 18, doi: 10.1086/506464
  * van de Sande et al. (2015) van de Sande, J., Kriek, M., Franx, M., Bezanson, R., & van Dokkum, P. G. 2015, ApJ, 799, 125, doi: 10.1088/0004-637X/799/2/125
  * van de Sande et al. (2011) van de Sande, J., Kriek, M., Franx, M., et al. 2011, ApJ, 736, L9, doi: 10.1088/2041-8205/736/1/L9
  * van de Sande et al. (2013) —. 2013, ApJ, 771, 85, doi: 10.1088/0004-637X/771/2/85
  * van der Wel et al. (2014) van der Wel, A., Franx, M., van Dokkum, P. G., et al. 2014, ApJ, 788, 28, doi: 10.1088/0004-637X/788/1/28
  * van der Wel et al. (2016) van der Wel, A., Noeske, K., Bezanson, R., et al. 2016, ApJS, 223, 29, doi: 10.3847/0067-0049/223/2/29
  * van der Wel et al. (2021) van der Wel, A., Bezanson, R., D’Eugenio, F., et al. 2021, ApJS, 256, 44, doi: 10.3847/1538-4365/ac1356
  * van der Wel et al. (2022) van der Wel, A., van Houdt, J., Bezanson, R., et al. 2022, ApJ, 936, 9, doi: 10.3847/1538-4357/ac83c5
  * van Dokkum et al. (2023) van Dokkum, P., Brammer, G., Wang, B., Leja, J., & Conroy, C. 2023, arXiv e-prints, arXiv:2309.07969, doi: 10.48550/arXiv.2309.07969
  * van Dokkum (2001) van Dokkum, P. G. 2001, PASP, 113, 1420, doi: 10.1086/323894
  * van Dokkum et al. (2009) van Dokkum, P. G., Kriek, M., & Franx, M. 2009, Nature, 460, 717, doi: 10.1038/nature08220
  * van Dokkum et al. (2008) van Dokkum, P. G., Franx, M., Kriek, M., et al. 2008, ApJ, 677, L5, doi: 10.1086/587874
  * van Dokkum et al. (2010) van Dokkum, P. G., Whitaker, K. E., Brammer, G., et al. 2010, ApJ, 709, 1018, doi: 10.1088/0004-637X/709/2/1018
  * van Houdt et al. (2021) van Houdt, J., van der Wel, A., Bezanson, R., et al. 2021, ApJ, 923, 11, doi: 10.3847/1538-4357/ac1f29
  * Vernet et al. (2011) Vernet, J., Dekker, H., D’Odorico, S., et al. 2011, A&A, 536, A105, doi: 10.1051/0004-6361/201117752
  * Wellons et al. (2015) Wellons, S., Torrey, P., Ma, C.-P., et al. 2015, MNRAS, 449, 361, doi: 10.1093/mnras/stv303
  * Whitaker et al. (2012) Whitaker, K. E., Kriek, M., van Dokkum, P. G., et al. 2012, ApJ, 745, 179, doi: 10.1088/0004-637X/745/2/179
  * Williams et al. (2009) Williams, R. J., Quadri, R. F., Franx, M., van Dokkum, P., & Labbé, I. 2009, ApJ, 691, 1879, doi: 10.1088/0004-637X/691/2/1879
  * Wisnioski et al. (2015) Wisnioski, E., Förster Schreiber, N. M., Wuyts, S., et al. 2015, ApJ, 799, 209, doi: 10.1088/0004-637X/799/2/209
  * Wu et al. (2020) Wu, P.-F., van der Wel, A., Bezanson, R., et al. 2020, ApJ, 888, 77, doi: 10.3847/1538-4357/ab5fd9
  * Wuyts et al. (2007) Wuyts, S., Labbé, I., Franx, M., et al. 2007, ApJ, 655, 51, doi: 10.1086/509708
  * Yan & Blanton (2012) Yan, R., & Blanton, M. R. 2012, ApJ, 747, 61, doi: 10.1088/0004-637X/747/1/61
  * Yano et al. (2016) Yano, M., Kriek, M., van der Wel, A., & Whitaker, K. E. 2016, ApJ, 817, L21, doi: 10.3847/2041-8205/817/2/L21
  * Zhuang et al. (2023) Zhuang, Z., Leethochawalit, N., Kirby, E. N., et al. 2023, ApJ, 948, 132, doi: 10.3847/1538-4357/acc79b