#  The Large Early Galaxy Astrophysics Census (LEGA-C) Data Release 3: 3000
High-Quality Spectra of $K_{s}$-selected galaxies at $z>0.6$

Arjen van der Wel  Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan
281 S9, 9000 Gent, Belgium  Max-Planck Institut für Astronomie Königstuhl,
D-69117, Heidelberg, Germany  Rachel Bezanson  University of Pittsburgh,
Department of Physics and Astronomy, 100 Allen Hall, 3941 O’Hara St,
Pittsburgh PA 15260, USA  Francesco D’Eugenio  Sterrenkundig Observatorium,
Universiteit Gent, Krijgslaan 281 S9, 9000 Gent, Belgium  Caroline Straatman
Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281 S9, 9000 Gent,
Belgium  Marijn Franx  Leiden Observatory, Leiden University, P.O.Box 9513,
NL-2300 AA Leiden, The Netherlands  Josha van Houdt  Max-Planck Institut für
Astronomie Königstuhl, D-69117, Heidelberg, Germany  Michael V. Maseda  Leiden
Observatory, Leiden University, P.O.Box 9513, NL-2300 AA Leiden, The
Netherlands  Anna Gallazzi  INAF-Osservatorio Astrofisico di Arcetri, Largo
Enrico Fermi 5, I-50125 Firenze, Italy  Po-Feng Wu (吳柏鋒)  National
Astronomical Observatory of Japan, Osawa 2-21-1, Mitaka, Tokyo 181-8588, Japan
Camilla Pacifici  Space Telescope Science Institute, 3700 San Martin Drive,
Baltimore, MD 21218, USA  Ivana Barisic  Max-Planck Institut für Astronomie
Königstuhl, D-69117, Heidelberg, Germany  Gabriel B. Brammer  Cosmic Dawn
Center (DAWN)  Niels Bohr Institute, University of Copenhagen, Jagtvej 128,
København N, DK-2200, Denmark  Juan Carlos Munoz-Mateos  European Southern
Observatory, Karl-Schwarzchild Straße 2, D-85748 Garching bei Munchen, Germany
Sarah Vervalcke  Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan
281 S9, 9000 Gent, Belgium  Stefano Zibetti  INAF-Osservatorio Astrofisico di
Arcetri, Largo Enrico Fermi 5, I-50125 Firenze, Italy  David Sobral
Department of Physics, Lancaster University, Lancaster LA1 4YB, UK  Anna de
Graaff  Leiden Observatory, Leiden University, P.O.Box 9513, NL-2300 AA
Leiden, The Netherlands  Joao Calhau  Instituto de Astrofísica de Canarias,
E-38200 La Laguna, Tenerife, Spain  Departamento de Astrofísica, Universidad
de La Laguna, E-38206 La Laguna, Spain  Yasha Kaushal  University of
Pittsburgh, Department of Physics and Astronomy, 100 Allen Hall, 3941 O’Hara
St, Pittsburgh PA 15260, USA  Adam Muzzin  Department of Physics and
Astronomy, York University, 4700 Keele St., Toronto, Ontario, M3J 1P3, Canada
Eric F. Bell  Department of Astronomy, University of Michigan, 1085 South
University Ave., Ann Arbor, MI 48109, USA  Pieter G. van Dokkum  Astronomy
Department, Yale University, 52 Hillhouse Ave, New Haven, CT 06511, USA

###### Abstract

We present the third and final data release of the Large Early Galaxy
Astrophysics Census (LEGA-C), an ESO/VLT public spectroscopic survey targeting
$0.6<z<1.0$, Ks-selected galaxies. The data release contains 3528 spectra with
measured stellar velocity dispersions and stellar population properties, a
25-fold increase in sample size compared to previous work. This
$K_{s}$-selected sample probes the galaxy population down to $\sim 0.3L^{*}$,
for all colors and morphological types. Along with the spectra we publish a
value-added catalog with stellar and ionized gas velocity dispersions, stellar
absorption line indices, emission line fluxes and equivalent widths,
complemented with structural parameters measured from HST/ACS imaging. With
its combination of high precision and large sample size, LEGA-C provides a new
benchmark for galaxy evolution studies.

galaxies: high-redshift – galaxies: kinematics and dynamics – galaxies:
structure

††software: Astropy (Astropy Collaboration et al., 2013), Matplotlib (Hunter,
2007), galfit (Peng et al., 2010), XCSAO, (Kurtz et al., 1992)

##  1 Introduction

The successful tenure of ESO’s VLT/VIMOS spectrograph (Le Fèvre et al., 2003)
was completed by the implementation of the two most recent Public
Spectroscopic Surveys: LEGA-C (van der Wel et al., 2016; Straatman et al.,
2018) and VANDELS (McLure et al., 2018; Pentericci et al., 2018). Both
surveys, carried out from 2015 to 2018, are characterized by a focus on depth
and data quality, representing a clear departure from VIMOS’ previous use as
the ‘redshift machine’ for which it was designed. The detector upgrade and
instrument refurbishment in 2010 made this possible.

The practical goal of the LEGA-C survey is to collect high signal-to-noise,
high resolution spectra for thousands of galaxies in the redshift range
$0.6\lesssim z\lesssim 1$. This allows, for the first time for the general
galaxy population, to probe stellar populations (ages and metallicities) and
stellar kinematics (velocity dispersions) of thousands of galaxies at a look-
back time of $\sim 7$ Gyr.

The primary science goals span all key open questions in the field of galaxy
formation and evolution. First, what are the star-formation histories of
galaxies? The spectra constrain the bulk formation age of the stellar
population, the metal enrichment history and how bursty the star formation
history is. Crucially, at large look-back time it is easier to resolve the
main formation phase; in the present-day Universe most stars formed many Gyr
ago, and old stellar populations are difficult to dissect due to their slow
spectral evolution. Second, how does star formation quench in massive
galaxies? Does this occur rapidly due to strong outflows, possibly associated
with a preceding increase in star formation, or relatively slowly due to a
lack of cooling to supplement fuel? The role of environment, Active Galactic
Nuclei and mergers can be examined thanks to the large sample size. Third, how
do galaxies evolve after the cessation of star formation? They can evolve
merely passively, or continue growth and structural evolution through merging.
The kinematic properties and chemical composition constrain this process.

These topics are interconnected and also connect to quantifying the
fundamental properties of the galaxy population as a whole. Given the
dynamical mass measurements and spectroscopy-based estimates with
unprecedented quality of the stellar mass, we will be able to assess the
contribution of dark matter (and/or a bottom-heavy stellar initial mass
function) across galaxy types, and how this changes with cosmic time. The
abundances of heavy elements can be constrained and compared with those of the
(ionized) interstellar medium to indirectly constrain the importance of in-
and outflows of galaxies.

Initial results based on the 1st and 2nd data releases (Straatman et al.,
2018, hereafter, DR2) illustrate the broad range of applications of LEGA-C
data. Bezanson et al. (2018a) showed that $z\sim 1$ quiescent galaxies show
more rotation in their stellar body than equally massive counterparts at
$z\sim 0$, providing strong evidence for a reduction in net angular momentum
through merging after galaxies become quiescent, with modest environmental
dependence (Cole et al., 2020). At the same time, the question whether
galaxies change their structure upon ‘quenching’ – the transition from an
actively star-forming state to a quiescent state – remains open. Wu et al.
(2020) and D’Eugenio et al. (2020) show that post-starburst galaxies rapidly
formed a large number of stars in the central regions of galaxies, producing
compact galaxies. But, at the same time, larger galaxies are generally younger
(Wu et al., 2018a), reflecting a complexity in galaxy evolution that can only
be revealed by high-quality spectroscopic data. The specific implication here
is that there are multiple evolutionary pathways to reach a quiescent state.
This is just one example of how constraints on stellar populations (Wu et al.,
2018b) increase our physical insight into the evolutionary process, and our
first attempts to quantify this information demonstrated that the ‘downsizing’
trend – that galaxies with higher stellar masses are older – was already
evident at $z\sim 1$ (Chauke et al., 2018). The quality of the LEGA-C
spectroscopy is also such that, for the first time, we could detect and
quantify bursts of star formation at $z\sim 1$ that occurred after an initial
period of quiescence at $z\sim 2$ (Chauke et al., 2019), as well as a novel
approach to quantifying dust attenuation in star-forming galaxies; Barišić et
al. (2020) shows steep attenuation curves, especially for face-on galaxies,
and frequently detect the 2175Åbump in individual galaxies for the first time.

The ultimate goal to jointly analyse the evolution of stellar populations and
the kinematic state of the stellar body is now within reach, which starts with
examining the evolution and detailed properties of scaling relations such as
the Fundamental Plane (de Graaff et al., 2020, 2021). Detailed comparisons
with the latest cosmological simulations of galaxy formation will then improve
the fidelity of the physical models used in those simulations. Finally, the
large sample size also allows to probe rare classes of objects such as radio-
loud Actice Galactic Nuclei and explore their kinematic and stellar population
properties of the first time (Barišić et al., 2017).

With the full LEGA-C sample, where we increase the sample of spectra with
measured redshifts and stellar velocity dispersions from 1447 to 3528 compared
with DR2, we enable the community to pursue this line of research. In this
paper we will first present the updated sample and the improvements in the
data reduction pipeline compared to DR2, as well as an analysis of the Hubble
Space Telescope/Advanced Camera for Surveys (HST/ACS) data that are available
for nearly all objects in our sample (Section 2). We then describe the basic
measurements that we are publishing with this paper: stellar and ionized gas
velocity dispersions, spectral indices, and emission line fluxes, as well as
inferred quantities such as dynamical mass estimates (Section 3). Our
published measurements are independent of cosmological parameters, with the
exception of dynamical mass, which has one element (galaxy size) that requires
a conversion from observed to physical units. There we adopt a flat
$\Lambda$CDM cosmology with $\Omega_{m}=0.3$ and $H_{0}=70$ km s-1.

##  2 Data

Table 1:  Sample selection and success rate Sample | Redshift |  $K$-band limit | # in UltraVISTA1 | # in LEGA-C | with $z$ | with $\sigma^{\prime}_{\star,\rm{int}}$
---|---|---|---|---|---|---
Parent | Any |  $<23.4$ (90% compl.) | 157,667 | 4,081 | 3,937 | 3,528
Primary | $0.6<z<1.0$ | $<20.7-7.5\log((1+z)/1.8)$ | 8,655 | 3,029 | 3,018 | 2,932
Filler I | $z>1$ | $<20.36$ | 3,511 | 260 | 184 | 163
Filler II | $0.6<z<1.0$ | $>20.7-7.5\log((1+z)/1.8)$ | 32,261 | 590 | 553 | 380
Filler III | Other | Other | 113,240 | 202 | 182 | 53

###  2.1 The LEGA-C Survey: Observations

Figure 1: $K_{s}$ band distribution of the Ultra-VISTA catalog for galaxies
with (spectroscopic or photometric) redshifts in the range $0.6<z<1$ compared
to the $K_{s}$-band selected parent sample of candidates for the LEGA-C
survey. The gradual decrease with $K$ magnitude for the parent sample is the
result of the redshift-dependent $K_{s}$ limit. The darkest histogram gives
the $K_{s}$-band distribution for targets with LEGA-C observations. Masks were
designed by including objects sorted by $K_{s}$ flux (brightest first). As a
result, down to $K_{s}\sim 19.5$ LEGA-C observed 50% or more of the
population, while for $K_{s}=20-20.5$ it is around 30%.  Figure 2: Survey
footprint and source distribution in the COSMOS field. Symbol size reflects
the stellar velocity dispersion (Section 3.2) in order to emphasize the more
massive galaxies.  Figure 3: Example comparison of DR2 (red) and DR3 (black)
versions of the same spectrum, illustrating the improvements and changes to
the data processing techniques. The overall normalization is affected (on the
level of a few percent) by the zero point changes in the photometry used for
the flux calibration (Appendix B). The shape of the continuum is affected by
the changes in the photometric SED fit (2.2.3). The improved telluric
absorption correction (2.2.2) is most clearly seen in the wavelength range
$7600-7700$ Å, where the systematic residual in the form of high-frequency
‘beating’ is reduced in the DR3 version of the spectrum.

The survey goals and design were extensively discussed by van der Wel et al.
(2016) and Straatman et al. (2018). The key characteristic of the survey is
that it is $K_{s}$-band selected. As we will see, the long integration times
of $\sim$20 hours lead to a very high success rate in measurement redshifts,
stellar kinematics, and stellar population properties, even for the faintest,
reddest targets. From the UltraVISTA catalog (Muzzin et al., 2013b) we first
create a parent sample of galaxies with (spectroscopic or photometric)
redshifts in the range $0.6<z<1$ and with $K_{s}$ magnitudes brighter than a
redshift-dependent limit $K_{s,\rm{LIM}}=20.7-7.5\log((1+z)/1.8)$ (Fig. 1).
When designing the slit masks we included targets ordered by $K_{s}$ magnitude
(brightest first). As the mask fills up, slit collisions prevent the inclusion
of fainter galaxies, leading to higher (and precisely quantifiable)
completeness for brighter targets. Any remaining mask space is used to include
fillers: $K_{s}$-bright objects at $z>1$, fainter targets in the LEGA-C
redshift range, and a mixed bag objects at lower redshifts and faint, higher-
redshift objects. We refer to Table 1 and, for comparison, to the equivalent
Table 1 in the survey paper (van der Wel et al., 2016) for an overview of the
LEGA-C sample. The success rate of the redshift and stellar velocity
dispersions (discussed in Section 3) is also given.

The final survey footprint is created by 30 slightly overlapping pointings,
together covering 1.4255 square degrees (Figure 2), giving a total survey co-
moving volume of $3.664\times 10^{6}$ Mpc3 between $z=0.6$ and $z=1.0$,
equivalent to the local volume out to $\sim$100 Mpc ($z\sim 0.023$).

Two additional pointings, contained within the main footprint, were chosen for
specific purposes. One of these has the same selection approach as the 30 main
pointings but the slits are oriented in the East-West direction where all
other masks and slits in the North-South direction. The goal here is to obtain
kinematic information along two perpendicular axes. The other extra mask has a
different selection function and is optimized to include red, low-mass
galaxies that are otherwise rarely included in the survey. This increases the
dynamic range in scaling relations.

The 32 masks produced 4081 galaxy spectra, with 3741 unique objects (340 are
observed more than once). We have 3029 spectra of primary targets (compare
their $K$ magnitude distribution with the $K$ magnitude distribution of the
parent sample in Figure 1), and 1052 of fillers. The success rate (in terms of
making key measurements) is very high; the fraction of primary spectra with
successful redshift and stellar velocity dispersion measurements is close to
100% as described in detail below (Section 3). The completeness of the LEGA-C
sample in relation to both the parent sample and the full galaxy population is
discussed in detail in Appendix A.

Observations were carried out between December 2014 and March 2018. In total,
211 (mostly partial) nights were spent observing in Visitor Mode, for a total
on-source integration time of 695 hours out of the allocated 1107 hours. The
resulting efficiency of 63% includes not only the usual overheads, but also
weather and technical losses. The anticipated efficiency in the survey
management plan was also precisely 63% (including weather losses); from a
scheduling and execution perspective LEGA-C can then be considered a success.
The motivation for executing the survey in Visitor Mode is obvious: even
without weather and technical losses Service Mode observations would have at
most 50% efficiency given standard calibration requirements and scheduling
constraints. The increased efficiency is mainly due to an efficient
calibration plan and flexibility in designing the observations, circumventing
the need for hourly re-acquisition and alignment. On a general note, given
that VIMOS was not originally designed for long exposures and tracking objects
for many hours, the performance of instrument and telescope has been very
good.

###  2.2 Custom LEGA-C pipeline

As described in the DR2 paper we designed a custom pipeline built on top of
ESO-provided data handling infrastructure. Here, for DR3, we make three
improvements in the data analysis related to 1) sky subtraction/object
extraction, 2) telluric absorption correction, and 3) flux calibration.

####  2.2.1 Sky Subtraction / Object Extraction

For DR2 we created sky$+$object models in the spatial direction where the
object was represented by a Gaussian. We knew that a Gaussian imperfectly
describes seeing-convolved galaxy light profiles, and we had already addressed
this by refitting the object in the co-added, 2-dimensional spectra with a
Moffat profile. For most galaxies this worked fine, but for the many bright
galaxies that illuminate more than half of the slit this approach was
insufficient. For DR3 we make use of the fact that most galaxies have been
imaged by HST, for which we derived Sérsic light profiles (see Section 2.3).
Based on the observed light profile in the LEGA-C spectra, collapsed in the
wavelength direction, we construct a galaxy$+$seeing profile by convolving the
Sérsic profile with a Moffat profile, and propagating the resulting profile
through a rectangular slit with width 1 arcsec. The two Moffat parameters are
optimized in this fit, producing a spectral extraction kernel that encompasses
both the galaxy and the seeing. As before (see DR2) this kernel is used at
each wavelength bin to fit for the sky and the object flux.

After co-addition of the sky-subtracted 2-dimensional spectra we check for
systematic effects in the sky subtraction. For some galaxies located near the
edge of their slit, or where multiple objects lie in the same slit, the sky
subtraction was imperfect. In those cases, as for DR2, a new sky subtraction
was performed by fitting a new Moffat profile, producing a new sky and a new
object extraction.

####  2.2.2 Telluric Absorption

For DR2 we created a telluric absorption spectrum for each of the 32 masks
based on the spectrum of a blue star included in those masks. This left two
unaddressed problems. First, for some blue stars the wavelength coverage was
insufficient to probe the strong telluric features around 9000Å. Second, a
fixed telluric spectrum for each of the $>100$ objects in a mask leaves very
significant high-frequency residuals (see Fig. 3) due to 2 effects: errors in
the wavelength calibration at the level of $\sim 0.1-0.2$Å due to small, but
unavoidable variations in object-slit alignments (if the blue star has a
different alignment than a galaxy, then there will be a wavelength shift in
the spectrum and, consequently, a difference in the telluric absorption
spectrum); galaxies are not point sources, such that the line-spread function
is broader for objects with larger angular sizes, leading to a smoother
telluric absorption spectra for galaxies than for stars – this effect varies
from galaxy to galaxy.

To remedy these effects we revised the telluric absorption correction for DR3
compared to DR1 and DR2:

  * •

All telluric absorption features in the $6000-9300$Å wavelength range arise
due to only two species: $H_{2}O$ and $O_{2}$. We choose a well-calibrated
white dwarf spectrum taken with ESO/X-SHOOTER (WD0839-327, Programme ID
098.D-0392(A)) and create $H_{2}O$ and $O_{2}$ telluric absorption template
spectra using the wavelength ranges $6860<\lambda/$Å$\leavevmode\nobreak\
<6925$ and $7580<\lambda/$Å$\leavevmode\nobreak\ <7710$ (the A and B bands)
for $O_{2}$ and the wavelength ranges $6925<\lambda/$Å$\leavevmode\nobreak\
<7580$ and $\lambda/$Å$\leavevmode\nobreak\ >7710$ for $H_{2}O$. Note that the
combination covers the entire wavelength range $\lambda>6860$Å, that is, most
of the LEGA-C spectra.

  * •

We fit the $H_{2}O$ and $O_{2}$ templates to the blue star spectrum, varying
the strength of the $H_{2}O$ and $O_{2}$ features. The key here is all
features arising due to $O_{2}$ vary together (primarily as a function of
airmass) as do the $H_{2}O$ features (mostly as a function of humidity). This
produces a master telluric absorption spectrum for each mask. This approach
remedies incomplete wavelength coverage for the blue stars in some of our
masks.

  * •

For each galaxy the co-added 1D spectrum is divided by the master absorption
spectrum for its mask, but allowing two parameters to vary: a shift in
wavelength (to account for slit misalignments) and a smoothing factor (to
account for the fact that galaxies have a broader line-spread functions than
stars). Note that the strengths of the telluric absorption features are kept
fixed for this step.

The resulting telluric absorption correction spectra are divided into the
galaxy spectra and propagated into the variance spectra.

####  2.2.3 Flux Calibration

The standard procedure for flux calibration, based on spectroscopic
observations of standard stars with the same instrumental setup, is not
feasible for LEGA-C. Slit/galaxy alignment varies from exposure to exposure,
and throughout the field of view, so that it is impossible to construct a
calibration spectrum that can be applied to all galaxy spectra. Instead, we
calibrate our galaxy spectra with the aid of well-calibrated photometric
spectral energy distributions.

The approach used for DR3 is conceptually the same as described in the DR2
paper, but several improvements were made. As demonstrated in Appendix B, the
photometric zero points are improved compared to the original photometry from
Muzzin et al. (2013b), and we only use a subset of photometric bands
($BVrizYJ$) for the SED fit. For consistency with full-spectral fitting
results that will be described in a forthcoming paper, we perform the
photometric SED fits with the bagpipes code (Carnall et al., 2018) instead of
FAST (Kriek et al., 2009), which was used for DR2. We use bagpipes to fit the
new photometric SED with double power-law star-formation histories (instead of
exponentially declining star-formation histories which were used for DR2);
recent work (e.g., Carnall et al., 2019) shows that, especially for star-
forming galaxies, rising-then-declining star-formation rates are a necessary
choice to avoid biases in, e.g., stellar mass estimates. But for our purpose
of flux calibration this change is not particularly relevant, and only made
for consistency. The best-fitting templates from the SED fits are compared
with the uncalibrated LEGA-C spectra by fitting a 5th-order Legendre
polynomial to the ratio of the two. The calibrated spectra (as well as the
variance spectra) are then obtained by multiplying the polynomials with the
uncalibrated spectra. The resulting, calibrated DR3 spectra differ slightly in
overall shape and normalization compared to DR2, as illustrated for a typical
example in Figure 3.

###  2.3 Hubble Space Telescope Imaging

We measure structural parameters as described by (van der Wel et al., 2016)
from the relatively shallow (but wide area) COSMOS HST/ACS imaging (Scoville
et al., 2007). The formal uncertainties on the structural parameters are
assigned on the basis of the total $S/N$ of the object, as described by van
der Wel et al. (2012), but as described below they are adapted based the
comparison with the structural parameters from CANDELS (Grogin et al., 2011;
Koekemoer et al., 2011; van der Wel et al., 2012) as determined with the
MegaMORPH software package (Häußler et al., 2013). The latter are obtained
from deeper data, and with differences in methodology, most notably distortion
correction, PSF construction and background subtraction. It is beyond the
scope of this paper to present an in-depth analysis of the differences, and
here we simply compare the results and interpret these as indicative of the
systematic uncertainties. For the 151 overlapping galaxies in our catalog for
which the Sérsic parameters did not reach a limiting value (such as Sérsic
index $n=6$) in galfit (Peng et al., 2010) we find a median effective radius
difference of $-2\%$ (our estimates are smaller), with a bi-weight scatter of
11%. For the Sérsic index, shape $b/a$, position angle, and total magnitude
these statistics are, respectively: $+3\pm 17\%$, $-1\pm 3\%$, $-1.8\pm
2.8\deg$, and $0.06\pm 0.18$ mag (ours are fainter). We apply these scatter
values (but not the systematic offsets) as minimum uncertainties in our
catalog. Correlations of this scatter with object brightness, size, and Sérsic
index are very weak; the scatter is, apparently, not due to limiting $S/N$ in
the COSMOS imaging but must be mainly due to a series of systematic effects
resulting from differences in methodology. We can therefore interpret the
scatter values as the random uncertainty, and we assign those values to all
objects for which the formal random uncertainties are smaller. This is the
case for more than $90\%$ of the galaxies in our sample.

Figure 4: Compilation of 2707 normalized spectra with measured stellar
velocity dispersions and H$\gamma_{A}$ indices. Top: The color coding is based
on the order of H$\gamma_{A}$ absorption (strongest/youngest: blue;
weakest/oldest: red) . Bottom: Horizontally aligned, vertically sorted by
H$\gamma_{A}$ absorption. For visualization purposes outlying wavelength
elements were replaced by the continuum model described in Section 3.3
(outliers are defined as wavelength elements with fluxes more than 10%
different from the model), and boxcar smoothed by 200 km s-1. In addition, the
additive and multiplicative polynomials used to match the model spectra and
the observed spectra were removed: this way variations in spectral slope that
are not associated with the stellar content (e.g., dust attenuation and errors
in the relative flux calibration) are removed. The color intensity (top panel)
declines at longer wavelengths due to the smaller number of spectra with
wavelength coverage.

Figure 5: Four spectra and HST images of galaxies with typical $S/N$ for their
respective global properties such as luminosity and redshift. From top to
bottom, a blue star-forming galaxy, a red star-forming galaxy, a post-
starburst galaxy / merger remnant, and a massive elliptical galaxy. The
templates indicated with red (blue) lines represent the stellar continuum
excluding (including) nebular emission lines. The stellar templates are the
theoretical Conroy templates used for measuring stellar velocity dispersions.
For the star-forming galaxies the broad Balmer absorption lines are filled
with narrow Balmer line emission. In the bottom panel no emission lines are
present; the green line represents the stellar continuum model using empirical
stellar spectra rather than theoretical stellar spectra (see Sections 3.2 and
3.3 for details).

Figure 6: See caption of Figure 5 for a full description. The top three panels
show spectra of objects that were flagged on the basis of their morphology
(FLAG_MORPH – see text for details). 127622 shows 4 closely separated galaxies
in the HST image, most likely all at the same redshift. The combined light in
the spectrum is unambiguous in its interpretation, but the structural
properties and stellar kinematics are difficult to assess. 187404 is flagged
due to the ambiguous interpretation of the spectrum: this spectrum (as well as
the HST image) shows two galaxies at different redshifts. 225103 shows an
almost perfect Einstein ring of a galaxy at an unknown redshift, lensed by an
elliptical galaxy. The fourth panel (66076) shows an example of the several
dozen $z>1.2$ Mg absorbers in the LEGA-C sample: this merger galaxy shows
outflowing material with velocities up to $\sim 2000$ km s-1.  Figure 7:
Left: H$\delta_{A}$ vs. DN4000, color-coded with FE4383. Right: H$\delta_{A}$
vs. FE4383, color-coded with DN4000.

Figure 8: Effective radius vs. stellar velocity dispersion for galaxies in the
redshift range $0.6\lesssim z\lesssim 1$, color-coded $H\delta_{A}$ absorption
equivalent width. From left to bottom right: literature compilation before
LEGA-C (see text for references); the full LEGA-C sample; quiescent galaxies
in LEGA-C; star-forming galaxies in LEGA-C. A trend between $H\delta_{A}$ and
$\sigma^{\prime}_{\star,\rm{int}}$ is evident; older galaxies have higher
velocity dispersions. A similar trend with size is not as clear.  Figure 9:
HST/ACS F814W images ($\sim$30 physical kpc on the side) as a function of
$H\delta_{A}$ absorption equivalent width and stellar velocity dispersion
$\sigma^{\prime}_{\star,\rm{int}}$. All galaxies with HST images, and measured
$\sigma^{\prime}_{\star,\rm{int}}$, $H\delta_{A}$ and Sérsic $n$ are included
in the figure, with a non-overlapping foreground layer of 257 galaxies. The
inset panel shows the full distribution, now color-coded with Sérsic index.
From top (young) to bottom (old) we see a gradual transition from late- to
early-type visual morphologies. At high $H\delta_{A}>6$ we also often see
irregular morphologies, indicative of interactions. The key observation is
that at fixed $\sigma^{\prime}_{\star,\rm{int}}$ galaxies show a large variety
in visual morphology and Sérsic index, while H$\delta_{A}$ (an age indicator)
predicts these properties rather well. And conversely, morphology and Sérsic
index broadly predict age.

##  3 Spectral Measurements

###  3.1 Redshifts

Given the depth of the spectra a redshift measurement is almost always
possible, especially for the primary targets. The 4081 spectra yield 3937
redshift measurements ($99.6\%$ for primary targets; $87.4\%$ for fillers –
see Table 1), determined by the XCSAO cross-correlation software package
(Kurtz et al., 1992) with the galaxy templates from Hinton et al. (2016)
amended with four high-$S/N$ LEGA-C spectra DR2 for galaxies with different
properties (quiescent, star-forming, dusty and emission-line dominated). The
redshift measurements are further refined below (Section 3.2) when modeling
the stellar and gas kinematics.

###  3.2 Stellar and Ionized Gas Kinematics

We use the recent Python implementation of pPXF (Cappellari, 2017) to estimate
stellar and ionized gas velocity dispersions. The procedure is explained in
detail by Bezanson et al. (2018b) and in the DR2 paper. Briefly, we use a set
of single stellar population models based on high-resolution ($R=10,000$)
theoretical templates from C. Conroy (priv. communication); this high
resolution allows us to take maximum advantage of the high effective
resolution of the LEGA-C spectra (see DR2 paper: $R\sim 3500$; FWHM=$86$km$/$s
or $\sigma=36$km$/$s). In addition to the stellar continuum model we add a set
of emission lines (see Table 2). The pPXF fit consists of optimizing the
combination of the templates, emission lines, a 3rd-order multiplicative
polynomials and an additive polynomial to reproduce the integrated,
1-dimensional spectra. The integrated stellar velocity dispersions
$\sigma^{\prime}_{\star,\rm{int}}$ and$\sigma^{\prime}_{g,\rm{int}}$111The
notation $\sigma$ ‘prime’ and ‘integrated’, introduced by Bezanson et al.
(2018b), refers to the fact that these are line-of-sight dispersions,
integrated over the entire galaxy (modulo slit losses). are estimated by
broadening the templates with Gaussians (no higher-order moments are fit); the
stellar and emission line dispersions are allowed to be different, but
emission lines all have the same velocity dispersion in a given spectrum. This
produces a stellar velocity dispersion for 3528 of the 3937 spectra with
redshift measurements ($96.8\%$ for primary targets; $56.7\%$ for fillers –
see Table 1). The precision of the resulting uncertainties is assessed in
Appendix C. The pPXF fit also refines the initial redshift measurement
described in Section 3.1. If no successful pPXF fit was performed, the initial
redshift is adopted as the final redshift estimate.

###  3.3 Emission Line Fluxes and Equivalent Widths

As a first step we rerun pPXF as described above in Section 3.2 but replacing
the theoretical Conroy templates with the lower-resolution empirical templates
based on the MILES library (Sánchez-Blázquez et al., 2006; Falcón-Barroso et
al., 2011). The reason for this choice is that the empirical templates better
reproduce the stellar continuum than the theoretical templates (see Figure 5,
bottom panel for an illustration), perhaps due to missing species in the
theoretical spectra (C. Conroy, priv. comm.). We prefer the theoretical
templates for the kinematic measurements due to their superior spectral
resolution; $R=10000$ (or FWHM$=30\leavevmode\nobreak\ $km$/$s) vs. $R\sim
1800$ (or FWHM=$167\leavevmode\nobreak\ $km$/$s). We also note that these
theoretical templates are limited to fixed, solar abundance ratios, and do not
use variable abundance ratios as in, e.g., Conroy et al. (2018). Importantly,
there is no systematic difference between the inferred stellar velocity
dispersions and the typical difference is about half of the measurement
uncertainty. This implies that template mismatch does not play a dominant role
in our velocity dispersion measurements.

Since the empirical templates produce a more accurate continuum subtraction
they provide a better representation of the emission line velocity profiles
and strengths. This produces an ionized gas velocity dispersion for 2674 of
the 3937 spectra with redshift measurements ($67.9\%$) – many of the passive
galaxies do not show sufficiently bright emission lines to allow for a
dispersion measurement. To determine emission line fluxes and equivalent
widths we use platefit (Brinchmann et al., 2004) on the stellar continuum
subtracted spectra. All lines are fit simultaneously, allowing for a 300 km
s-1 offset between the Balmer and forbidden lines. The equivalent widths are
then computed with respect to the stellar continuum model. The procedure (and
first scientific application) are described in full detail by Maseda et al.
(in prep.). The reason for not using pPXF to measure the emission-line fluxes
is that it is not advisable to include a large number of (mostly faint)
emission lines, which would interfere with the continuum modeling; only the
Balmer lines and bright Oxygen lines are therefore modeled with pPXF. Platefit
is custom-made to measure a large number of emission lines in a flexible
manner.

The uncertainties are described in full in Appendix C, but here it is
important to emphasize that the irregular spatial distribution of line-
emitting regions within galaxies leads to unpredictable slit losses. Our
duplicate observations regularly show differences in emission line
characteristics – kinematic as well as line strength – that far exceed the
measurement uncertainties. Visual inspection reveals that such cases arise due
to particularly bright, centrally offset emission-line regions, which may fall
inside the slit for one of the duplicates but outside for the other. These
differences arise through variations in slit alignment. This implies a
systematic uncertainty that cannot be quantified on a case by case basis, as
we do not have a good description of the spatial distribution of emission
lines.222For stellar light we rely on the HST image, and variations in slit
losses play a very minor role for the more symmetric stellar light in the
first place. We estimate that this uncertainty on the emission line fluxes and
gas velocity dispersions is of the order of 15%, but we do not propagate this
into the generally much more precise formal measurement uncertainties in the
catalog.

###  3.4 Absorption Line Indices

Absorption lines are often weak and variations among galaxies small.
Controlling for systematic effects in the sky subtraction, the noise model,
and the wavelength calibration is challenging, especially in the red part of
the optical spectrum with large and rapid changes in variance with wavelength.
Absorption line indices are defined to be measured from constant-variance
spectra – which is a good assumption in the blue part of the optical spectrum
– but weighing wavelength elements differently across the index wavelength
interval introduces a bias in the equivalent width. Yet ignoring the variance
spectrum can also introduce a bias, and always increases the random
uncertainty due to the equal weights given to high-noise wavelength elements.
These issues do not have a perfect solution and motivate the full spectral
fitting approach, but since those are strongly model dependent, index
measurements still play an indispensable role in empirically presenting
stellar population properties in a manner that will not change over time as
our knowledge of the spectral evolution of stellar populations further
improves.

We implement a solution for obtaining approximately bias-free index
measurements that do not strongly suffer from high-noise wavelength elements
as follows. We create a model spectrum consisting of a linear combination of
the stellar spectra in the MILES library333We do not use the continuum models
constructed in Secs. 3.2 and 3.3 in order to reduce as much as possible any
stellar population model dependency in our index measurements and a 15th
order, multiplicative Legendre polynomial444The order of the polynomial was
based on a convergence test with increasingly larger orders. Higher orders do
not change the statistical properties of the residuals, while lower orders
leave systematic residuals.. First, we scale the error spectrum such that the
reduced $\chi^{2}$ value is unity, resulting in slightly (typically, 20%)
larger formal measurement uncertainties. Second, we linearly interpolate over
spectral elements that deviate by more than 2$\sigma$ (and with a minimum of
10%) from the model. About 7% of all wavelength elements used in index
measurements are flagged and interpolated over in this manner. If the fraction
of deviating pixels exceeds 30% within the wavelength bandpasses of the index
then the index is considered to be not measured. To reiterate: the model is
only used to identif deviant wavelength elements, not to replace them; the
models do not directly enter into the index measurements. In Appendix C we
assess the formal measurement uncertainties. Note that the indices are
measured without wavelength convolution to a fixed spectra resolution; a
$\sigma_{*}$ dependence therefore exists. This is usually accounted for when
comparing with models (e.g., Gallazzi et al., 2014).

The catalog (Section 4.2) includes all measured indices, but we recommend
using only those for which the galaxy has a measured stellar velocity
dispersion. But given that $>95\%$ of primary targets have a
$\sigma^{\prime}_{\star,\rm{int}}$ measurement the subsample with stellar
population information is highly complete. Naturally, which absorption
features are actually measured depends on the wavelength coverage. For
example, 81% of primary targets with $\sigma^{\prime}_{\star,\rm{int}}$
measurements have a H$\gamma$ absorption measurement, but only 21% have a
Mg$b$ absorption measurement. The wavelength coverage of each spectrum is
provided in the catalog.

To illustrate the bulk stellar population properties and trends for the galaxy
population as a whole we show in Figure 7 the distribution of DN4000,
H$\delta_{A}$, and FE4383. The age and metallicity indicators are strongly
correlated, but unfortunately this does not translate in a straightforward
manner into a correlation between age and metallicity: metal features such as
FE4383 are also primarily sensitive to age, as is shown by the age-metallicity
grid. In forthcoming papers the stellar population properties will be analyzed
in detail to provide age and metallicity estimates, and we will build on our
previous full-spectral fitting efforts (Chauke et al., 2018, 2019; Barišić et
al., 2020) to explore the full star-formation and chemical enrichment
histories.

##  4 Data Release Contents

###  4.1 Spectra

The primary data product consists of the spectra and corresponding weights
(inverse variance spectra)555The spectra and catalog have been released by
ESO: http://archive.eso.org/cms/eso-archive-news/Third-and-final-release-of-
the-Large-Early-Galaxy-Census-LEGA-C-Spectroscopic-Public-Survey-
published.html,666The spectra and catalog are available on this website:
https://users.ugent.be/~avdrwel/research.html#legac. Figure 4 compiles 2707
emission-line subtracted spectra with measured stellar velocity dispersions
and H$\gamma_{A}$ absorption indices, visualizing the rich content of the
dataset. First, we see how the Balmer break seen for young galaxies gradually
transitions into the 4000Å break for old galaxies. Second, although the old
galaxies show stronger metal features, the spectra of individual young
galaxies show the same features, enabling the measurement of their star-
formation histories and metallicities.

For a more detailed look into the characteristics of the data we examine a
small subset of galaxies in Figure 5, which shows four very different types of
galaxies, from blue/late-type to red/early-type. All steps in the analysis
described above are illustrated here. The Doppler broadening of the absorption
and emission line features – decomposed into two components: continuum and
emission lines – produces velocity dispersion measurements (for the two
examples in the top two panels the gas and stellar dispersions agree well).
The bottom panel demonstrates the difficulty of finding a single-size-fits-all
analysis method: the high-spectral resolution theoretical stellar population
models used for stellar velocity dispersion measurements do not fit the
spectra of old galaxies as well as models based on empirical stellar
libraries. This mismatch, which may be the result of missing species in the
theortical templates and/or non-solar abundance ratios, will be explored in
future work.

Figure 6 shows four examples of non-standard objects. We see an early-stage
merger, a projected pair (that would have been classified as a merger without
a spectrum), and a strong gravitational lens – these 3 objects are flagged in
the catalog as described in Section 4.2. Finally, we show an outflow seen in
Mg absorption at $z=1.3$. The LEGA-C sample size guarantees the frequent
occurrence of such cases, and makes for a fascinating treasure trove.

###  4.2 Catalog

In Table 2 we list the contents of the electronic public data release. For the
4081 spectra we provide 61 quantities and, where relevant, their
uncertainties. For each quantity we indicate for how many of the spectra it
has been measured and with what range in values and uncertainties. For
example, we have a median redshift (Z_SPEC) of $z=0.808$ and 3528 measured
stellar velocity dispersions $\sigma^{\prime}_{\star,\rm{int}}$
(SIGMA_STARS_PRIME) with a median value of 161 km s-1 (the 16-84%-ile range is
106 to 222 km s-1) and median uncertainty of 13 km s-1 (the 16-84%-ile range
is 7 to 24 km s-1).

The user should be aware of various meta parameters and peculiarities of the
dataset. ID_LEGAC is a running integer number to identify unique spectra, but
because of the duplicate observations, there are cases with multiple spectra
of the same objects and some ID entries from the Muzzin et al. (2013a) catalog
appear more than once. The PRIMARY flag indicates whether the galaxy was
selected from the $Ks$-band selected parent sample (1) or as a filler (0).

We have created two flags that should be kept in mind when assigning meaning
to the measured quantities. FLAG_SPEC: A subset of spectra show clear evidence
of AGN affecting the continuum shape, compromising the interpretation of the
index measurements. Upon visual inspection we decided to flag all 107 galaxies
with mid-infrared and/or X-ray AGN even if the majority do not show an obvious
issue; the catalog entry FLAG_SPEC$=$1 indicates such AGN. Narrow-line and
radio AGN do not present a problem for our spectral analysis and are not
flagged. However, in 25 cases we found that the photometry-based flux
calibration showed significant imperfections, potentially compromising the
measurement of absorption and emission indices. These are indicated by
FLAG_SPEC$=$2.

FLAG_MORPH: In most cases the light coming through the slit is from a single
galaxy with a regular morphology, but in a significant minority of cases this
is not the case. In order to address this we devise the catalog parameter
FLAG_MORPH with value 0, 1 or 2. Single galaxies with regular morphologies
have a value 0. Spectra for which the light coming through the slit does not
come from single, regular galaxies get a flag value 1; these are often
irregular galaxies such as merger remnants, but also multiple galaxies that
are separated in the HST image, but not in the spectrum. The guiding principle
when assigning flag values of 1 is that the combination of the stellar
velocity dispersion (from the spectrum) and structural parameters (from the
HST image) cannot be included in an analysis of the Fundamental Plane or other
scaling relations. Spectra that have, on top of this, the problem that the
light comes from galaxies at different redshifts receive a flag value 2.
Again, the guiding principle is that the presence of a secondary object at the
different redshift prevents us from using the stellar velocity dispersion and
the structural parameters for a scaling relation analysis. In total, 257 are
flagged, 14 of which have flag value 2. Many more galaxies have low-level
‘contamination’ from secondary sources in the slit, but not to the extent that
the measurements presented here are ambiguous in their interpretation.

Note that the measurements as presented in the catalog are not wrong for
spectra with FLAG_MORPH value 1 or 2 – the flag simply alerts the user to a
possible issue with the interpretation of the measurement, not an issue with
the measurements themselves. For example, we have a spectrum with a correctly
measured velocity dispersion of 623 km s-1, and close inspection of the HST
image reveals a double nucleus. This combination indicates that we are seeing
an early-stage merger where the two components happen to be aligned almost
perfectly or closely separated in real space. Obviously, the high stellar
velocity dispersion does not trace the internal dynamical structure of either
component, but rather the orbital motion of the pair.

The structural parameters (Section 2.3) for 3800 objects are also included in
the catalog. Most missing values are the result of imperfect overlap between
the LEGA-C and COSMOS-ACS footprints. We give a SERSIC_LIMIT flag to indicate
for which objects the parameters reached the galfit limiting value (e.g.,
$n=6$).

Finally, we publish the virial mass (LOG_MVIR) and its uncertainty, derived as
explained in an accompanying paper (van Houdt et al., in prep.). In short, it
is given by

$M_{\rm{vir}}=K(n)\frac{\sigma^{2}_{\star,\rm{vir}}R_{\rm{sma}}}{G},$ (1)

where $n$ is SERSIC_N, $K(n)=8.87-0.831n+0.0241n^{2}$, $R_{\rm{sma}}$ is the
semi-major axis length SERSIC_RE in kpc, $G$ the gravitational constant, and
$\sigma_{\star,\rm{vir}}$ (SIGMA_STARS_VIR) is the inclination- and aperture-
corrected velocity dispersion:

$\sigma_{\star,\rm{vir}}=\sigma^{\prime
2}_{\star,\rm{int}}\left(0.87+0.39\cdot e^{-3.78(1-q)}\right),$ (2)

with $q$ the projected axis ratio (SERSIC_Q). In principle, at least for flat
galaxies, one might expect a difference in $\sigma_{\star,\rm{vir}}$ (and
$\sigma^{\prime}_{\star,\rm{int}}$), depending on the angle between the major
axis of the galaxy and the slit, but we find no significant evidence. This
might be due to the small sample size of just ten duplicate observations for
flat galaxies ($b/a<0.5$) and for which the position angle differs by more
than 45 degrees, and for those we can only constrain the effect on
$\sigma_{\star,\rm{vir}}$ (and $\sigma^{\prime}_{\star,\rm{int}}$) to be less
than 10%. Larger samples are needed to provide a more precise constraint.

Our new definition of the virial mass is different from (and up to 50% higher
than) what has been the norm in the high-redshift community: instead of
circularized radius we use the major-axis length, and we use an inclination-
corrected velocity dispersion relying on the observational result that most
galaxies are oblate rotators (e.g., Weijmans et al., 2014; Foster et al.,
2017). (Most intrinsically round ellipticals have $q\sim 0.8$, and therefore
have an inclination correction near unity.) These masses were calibrated
against dynamical models applied to spatially resolved stellar kinematic
measurements.

##  5 First-Look Results & Outlook

In order to visualize the increase in sample size and parameter space compared
to previous work that LEGA-C represents (not counting previous LEGA-C data
releases), we show the size-$\sigma^{\prime}_{\star,\rm{int}}$ distribution in
Figure 8. Before LEGA-C the combined efforts of observing programs with the
goal to collect spectra with sufficient quality to determine the stellar
velocity dispersions for individual galaxies with HST imaging in the
$0.6\lesssim z\lesssim 1$ redshift range yielded 231 such measurements (van
der Wel et al., 2005; Treu et al., 2005; Gallazzi et al., 2014; Bezanson et
al., 2015), of which the vast majority are quiescent and very massive due to
sample selection. A subset of 119 of these have stellar population
measurements from Gallazzi et al. (2014) and Shetty & Cappellari (2015).777For
the galaxies from Shetty & Cappellari (2015) we crudely estimated
$H\delta_{A}$ from their published ages. While not very precise these
estimates serve the purpose of illustrating the existing samples before
LEGA-C. We note that the SHELS survey Geller et al. (2016) that mostly targets
galaxies at $z\sim 0.3$ has a high-redshift tail of $\sim$60 galaxies at
$z\sim 0.6$. Their $\sigma_{*}$ and stellar population properties have been
used in publications (Zahid et al., 2016) but not published in tabulated form.

LEGA-C expands the sample of galaxies with measured and stellar population
properties and velocity dispersions to over 3000, while also greatly expanding
parameter space of galaxy mass and type. Note that we only counted ‘field’
galaxies in this comparison – dozens of cluster galaxies in this redshift
range also have $\sigma_{*}$ measurements (van Dokkum et al., 1998; Wuyts et
al., 2004; Holden et al., 2010; Jørgensen & Chiboucas, 2013). In addition,
field galaxy measurements at $z>1$ now also number in the dozens (van Dokkum
et al., 2009; Newman et al., 2010; Toft et al., 2012; van de Sande et al.,
2013, 2014; Belli et al., 2014; Longhetti et al., 2014; Newman et al., 2015;
Hill et al., 2016; Belli et al., 2017; Toft et al., 2017; Saracco et al.,
2019).

The near-absence of a correlation between galaxy size and velocity dispersion
– this is an almost face-on projection of the fundamental plane – vividly
reveals the connection between galaxy structure and stellar population
content. High-$\sigma$ galaxies have weaker H$\delta$ absorption (that is,
older ages), a trend that is seen for the population as a whole as well as for
UVJ-selected star-forming galaxies. Within the quiescent population there is a
smattering for compact galaxies with strong H$\delta$ absorption, which we can
readily identify as post-starburst galaxies (Wu et al., 2018a, 2020). It goes
far beyond the scope of this paper, but Figure 8 clearly invites an analysis
as presented for present-day galaxies by Graves et al. (2009) with the added
advantage of being able to measure evolution in the
size-$\sigma^{\prime}_{\star,\rm{int}}$ plane.

Figure 9 makes the explicit connection between galaxy morphology, structure,
kinematics and stellar population age. Morphologically late-type galaxies
generally have young ages and low stellar velocity dispersion, whereas early-
type galaxies have old ages and high $\sigma_{*}$. At fixed $\sigma_{*}$ we
see, from young to old age, a change from late- to early-type morphology, and
an increase in Sérsic index. Galaxy morphology at fixed H$\delta$ shows less
variety or trend than at fixed $\sigma_{*}$, although for late types we do see
an increased Sérsic index at high $\sigma_{*}$, that is, increased bulge
prominence. In short, the visual (morphological) appearance of a galaxy in
this redshift range first and foremost reflects its age, rather than its
dynamical structure. A more in-depth analysis is beyond the scope of this data
release paper, but this Figure shows the potential of LEGA-C to produce a
significant leap forward in our understanding of galaxy formation and
evolution by providing for the first time SDSS-quality spectroscopy for the
general galaxy population 7 Gyr ago. We encourage the community to take
advantage of this unique, publicly available dataset.

Based on observations made with ESO Telescopes at the La Silla Paranal
Observatory under programme IDs 194-A.2005 and 1100.A-0949 (The LEGA-C Public
Spectroscopy Survey). This project has received funding from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and
innovation programme (grant agreement No. 683184). CMSS acknowledges support
from Research Foundation - Flanders (FWO) through Fellowship 12ZC120N. CP is
supported by the Canadian Space Agency under a contract with NRC Herzberg
Astronomy and Astrophysics.

Table 2: Catalog Contents

Catalog Entry | Unit | N objects | Value Range | Uncertainty Range | Comment
---|---|---|---|---|---
|  |  | [min,max] or [16, 50, 84%-ile] | [16, 50, 84%-ile] |
ID_LEGAC | INT | 4081 | [1, 4081] |  |
ID | INT | 4081 | [3945, 262197] |  | Muzzin et al. (2013b)
MASK | INT | 4081 | [1, 102] |  | LEGA-C mask id
RAJ2000A | degrees | 4081 | [149.379760, 150.774770] |  | J2000
DECJ2000 | degrees | 4081 | [1.747992, 2.804280] |  | J2000
PRIMARY | INT | [1053, 3028] | [0, 1] |  | primary (1) / filler (0)
Z |  | 3937 | [0.672, 0.808, 0.964] |  | LEGA-C spec.-$z$
SIGMA_STARS_PRIME | km s-1 | 3528 | [106, 161, 222] | [7, 13, 24] | $\sigma^{\prime}_{\star,\rm{int}}$
SIGMA_GAS_PRIME | km s-1 | 2674 | [68, 128, 201] | [2, 7, 21]2 | $\sigma^{\prime}_{g,\rm{int}}$
LICK_HD_A | Å | 3147 | [0.3, 3.8, 6.3] | [0.3, 0.6, 1.4] | Absorption line
LICK_HD_F |  | 3175 | [1.5, 3.3, 4.9] | [0.2, 0.4, 0.9] | ””
LICK_HG_A | Å | 2899 | [-3.2, 1.4, 4.9] | [0.4, 0.7, 1.5] | ””
LICK_HG_F | Å | 2913 | [-0.1, 2.5, 4.5] | [0.2, 0.4, 0.9] | ””
LICK_HB | Å | 1579 | [2.0, 3.3, 4.9] | [0.4, 0.7, 1.6] | ””
LICK_CN1 | mag | 3029 | [-0.12, -0.06, 0.03] | [0.01, 0.02, 0.04] | ””
LICK_CN2 | mag | 3033 | [-0.07, -0.01, 0.08] | [0.01, 0.02, 0.05] | ””
LICK_CA4227 | Å | 3115 | [0.1, 0.7, 1.1] | [0.2, 0.4, 0.8] | ””
LICK_G4300 | Å | 3032 | [0.2, 2.5, 4.8] | [0.4, 0.7, 1.5] | ””
LICK_FE4383 | Å | 2800 | [0.8, 2.7, 4.3] | [0.5, 1.0, 2.2] | ””
LICK_CA4455 | Å | 2701 | [0.1, 0.9, 1.4] | [0.3, 0.5, 1.1] | ””
LICK_FE4531 | Å | 2470 | [1.2, 2.5, 3.5] | [0.4, 0.8, 1.9] | ””
LICK_C4668 | Å | 2026 | [0.5, 3.6, 6.1] | [0.7, 1.3, 2.9] | ””
LICK_FE5015 | Å | 1120 | [1.6, 3.8, 5.2] | [0.6, 1.2, 2.8] | ””
LICK_MG1 | mag | 438 | [0.00, 0.03, 0.08] | [0.01, 0.01, 0.03] | ””
LICK_MG2 | mag | 432 | [0.046, 0.11, 0.20] | [0.01, 0.02, 0.04] | ””
LICK_MGB | Å | 761 | [1.0, 2.3, 3.7] | [0.3, 0.6, 1.5] | ””
LICK_FE5270 | Å | 525 | [0.8, 2.0, 2.8] | [0.4, 0.7, 1.7] | ””
LICK_FE5335 | Å | 435 | [0.9, 1.9, 2.7] | [0.4, 0.7, 2.0] | ””
LICK_FE5406 | Å | 320 | [0.4, 1.1, 1.8] | [0.3, 0.6, 1.4] | ””
D4000_N |  | 2838 | [1.23, 1.40, 1.76] | [0.02, 0.03, 0.06] |
OII_3727_FLUX |  $10^{-19}$ erg/s/cm${}^{2}/$Å | 2777 | [53, 316, 863] | [12, 21, 41]2 | Emission line
OII_3727_EW | Å | 2765 | [1.51, 8.74, 25.9] | [0.32, 0.6, 1.2]2 | ””
NEIII_3869_FLUX |  $10^{-19}$ erg/s/cm${}^{2}/$Å | 3139 | [-5, 14, 47] | [8, 13, 24]2 | ””
NEIII_3869_EW | Å | 3130 | [-0.11, 0.28, 0.98] | [0.14, 0.28, 0.55]2 | ””
HEI_3890_FLUX |  $10^{-19}$ erg/s/cm${}^{2}/$Å | 3190 | [3, 27, 71] | [8, 14, 25]2 | ””
HEI_3890_EW | Å | 3181 | [0.09, 0.62, 1.55] | [0.18, 0.33, 0.66]2 | ””
Hd_FLUX |  $10^{-19}$ erg/s/cm${}^{2}/$Å | 3392 | [-3, 29, 103] | [8, 13, 25]2 | ””
Hd_EW | Å | 3368 | [-0.04, 0.59, 2.13] | [0.13, 0.25, 0.52]2 | ””
Hg_FLUX |  $10^{-19}$ erg/s/cm${}^{2}/$Å | 3195 | [1, 61, 212] | [8, 16, 28]2 | ””
Hg_EW | Å | 3163 | [0.04, 1.25, 4.29] | [0.13, 0.26, 0.56]2 | ””
OIII_4363_FLUX |  $10^{-19}$ erg/s/cm${}^{2}/$Å | 3167 | [-15, 2, 19] | [8, 14, 26]2 | ””
OIII_4363_EW | Å | 3205 | [-0.21, 0.03, 0.29] | [0.11, 0.20, 0.42]2 | ””
Hb_FLUX |  $10^{-19}$ erg/s/cm${}^{2}/$Å | 1858 | [7, 164, 580] | [11, 19, 34]2 | ””
Hb_EW | Å | 1830 | [0.09, 3.26, 10.8] | [0.13, 0.28, 0.58]2 | ””
OIII_4959_FLUX |  $10^{-19}$ erg/s/cm${}^{2}/$Å | 1501 | [4.2, 44, 149] | [9, 17, 30]2 | ””
OIII_4959_EW | Å | 1529 | [0.03, 0.43, 2.0] | [0.06, 0.11, 0.24]2 | ””
OIII_5007_FLUX |  $10^{-19}$ erg/s/cm${}^{2}/$Å | 1372 | [28, 127, 429] | [12, 22, 42]2 | ””
OIII_5007_EW | Å | 1348 | [0.36, 1.5, 6.7] | [0.13, 0.26, 0.61]2 | ””
SERSIC_RE | arcsec | 3800 | [0.29, 0.61, 1.13] | [0.03, 0.07, 0.13] | Eff. radius (maj.axis)
SERSIC_N |  | 3800 | [0.82, 2.53, 5.32] | [0.14, 0.44, 0.92] | Sérsic index
SERSIC_Q |  | 3800 | [0.38, 0.64, 0.85] | [0.03, 0.03, 0.03] | Axis ratio
SERSIC_PA | degrees | 3800 | [-62, 2, 61] | [2.8, 2.8, 2.8] | From North to East
SERSIC_MAG | F814W AB mag | 3800 | [20.7, 21.5, 22.7] | [0.18, 0.18, 0.18] | Total mag
SERSIC_LIMIT | INT | [3341, 459] | [0, 1] |  | Galfit constraint flag
SIGMA_STARS_VIR | km s-1 | 3100 | [106, 160, 222] | [7, 12, 24] | Virial vel. disp.
LOG_MVIR | $M_{\odot}$ | 3100 | [10.80, 11.22, 11.59] | [0.06, 0.08, 0.14] | Virial mass
SN | Å-1 | 3933 | [5.3, 12, 24.8]1 |  | Avg. $S/N$
SN_RF_4000 | Å-1 | 3764 | [7, 14.8, 26.4]1 |  |  $S/N$ at rest 4000Å
SN_OBS_8030 | Å-1 | 3904 | [6.8, 15.8, 30.9]1 |  |  $S/N$ at obs 8030Å
TCOR |  | 2830 | [1.5, 2.4, 6.3] |  | Completeness corr.
SCOR |  | 2830 | [1.7, 2.6, 4.4] |  | Selection corr.
VCOR |  | 2830 | [1.0, 1.0, 1.5] |  | Volume corr.
FLAG_MORPH | INT | [3824, 243, 14] | [0, 1, 2] |  | Morphology flag
FLAG_SPEC | INT | [3949, 107, 25] | [0, 1, 2] |  | Spectroscopy flag

Note. — Sample selection criteria for the primary sample and the 3 categories
of fillers. Numbers of spectra with successfully measured redshifts and
stellar velocity dispersions (Section 3 are given in the last two columns. 1:
in Muzzin et al. (2013a) catalog and within LEGA-C footprint (Fig. 2).

Note. — Data release catalog. Percentile value ranges are given for those
objects for which the quantity was measured, that is, non-detections and
failed measurements are not included. 1The $S/N$ values are given for the full
sample, not just the primary targets that have higher $S/N$ than non-primary
targets. 2 These are the formal measurement uncertainties. As described in
Section 3.3 there is a systematic uncertainty of 15% due to unknown variations
in slit losses.

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##  Appendix A Completeness

Figure 10: Stellar mass vs. redshift for the primary LEGA-C targets, color-
coded with the $K_{s}$-dependent completeness with respect to the parent
sample of $K_{s}$-selected galaxies; this is the inverse of the completeness
correction factor Scor in the catalog as described in Section 4.2). The black
line indicates the stellar mass completeness limit of the parent sample from
which the LEGA-C primary targets have been selected: above this stellar mass
limit all galaxies have $K_{s}$-band magnitudes brighter than $K_{s,LIM}$,
whereas below the limit (a subset of dusty) galaxies have fainter magnitudes.
The open data points show the few galaxies without velocity dispersion
measurements. The dotted line – the knee of the stellar mass function as
determined by Leja et al. (2020) – is shown for reference. LEGA-C is
representative down to $\sim$0.3$L*$ at $z=0.6$ and $\sim L*$ at $z=1$. The
color coding demonstrates that completeness with respect to the parent sample
increases with mass, as a result of survey design: probability of observation
is determined by $K_{s}$ magnitude as described in Section 2.  Figure 11:
Rest-frame $U-V$ color vs. stellar mass for galaxies in the redshift range
$0.7<z<0.8$. The primary LEGA-C targets is color-coded with the
$K_{s}$-dependent completeness with respect to the parent sample of
$K_{s}$-selected galaxies, as in Figure 10. The blue open circles represent
the (unobserved) parent sample of $K_{s}$-selected galaxies; the red open
circles represent all other galaxies in the UltraVISTA photometric catalog
with $K_{s}$-band magnitudes fainer than the selection limit. The observed
sample is less complete toward lower masses, but in a well-understood manner,
with $Scor$ as the correction factor. The $K_{s}$ magnitude limit is color-
dependent, with a lower stellar mass limit for blue galaxies compared to red
galaxies. The LEGA-C sample is representative at $z=0.7-0.8$ down to a stellar
mass limit of $\sim 3\times 10^{10}\leavevmode\nobreak\ M_{odot}$.

Figure 12: Rest-frame color-color diagrams for two stellar mass-redshift bins
to illustrate the completeness of the $K_{s}$-selected parent sample. Left:
example of a bin where all galaxies are brighter than the $K_{s}$ magnitude
limit of the parent sample (there are no red open circles). The filled, color-
coded circles are the galaxies included in the LEGA-C survey. The completeness
of the observed galaxies (1/Scor in the catalog), with respect to the parent
sample, is $\sim 35\%$ in this bin, but this number depends on galaxy color:
redder galaxies are less likely to be included (due to their fainer $K_{s}$
magnitude) but since the parent sample itself does not suffer from
incompleteness the observed galaxies are representative of the parent sample,
removing any biases by assigning weight factors Scor to each individual
galaxy. Right: example of a bin below the stellar mass limit. A large fraction
of (red, dusty) galaxies has faint $K_{s}$ magnitudes so that they are not
included in the parent sample. The observed galaxies are representative of the
parent sample (the blue data points) but not the full population in this
stellar mass-redshift bin.  Figure 13: Observed-frame color-magnitude diagram
($i_{p}$ \- $Ks$ vs. $Ks$) of the primary sample, indicating those galaxies
without successful redshift or stellar velocity dispersion measurements
(naturally, a measured redshift is a prerequisite for a dispersion
measurement). The success rate is extremely high – even among the tail of
optically faint targets ($i_{p}\sim 22.5-23.0$) a velocity dispersion is
measured in 85% of the cases (see text for details).

The measurements from high-redshift galaxy spectroscopic surveys are often
difficult to connect to the full galaxy population in terms of their
completeness. Three factors play a key role in establishing this connection:

  1. 1.

How does the parent sample from which the spectroscopic targets are chosen
connect to the full galaxy population in terms of its physical parameters?
(For example, for LEGA-C, how does the $K_{s}$ magnitude limit connect to a
stellar mass limit?)

  2. 2.

Given the parent sample, how are targets prioritized for observation? (If
chosen randomly, this is not an issue; for LEGA-C, brighter targets in $K_{s}$
have higher priority.)

  3. 3.

What is the success rate of measuring the desired quantities? (For LEGA-C,
these are stellar velocity dispersions and stellar population properties for
which the success rate is very high: 97%.)

The LEGA-C survey is designed to control all three factors. Factor 1: Our
$K_{s}$-band selection of the parent sample from which the targets are chosen
is fairly close (but clearly not identical) to a stellar mass selection, with
the added advantage that the stellar mass is a model-dependent quantity that
may change over time, while the interpretation of a magnitude is fixed. To
illustrate the effect of our parent sample selection – $K_{s}<K_{s,LIM}$ as
described in Section 2 and Figure 1 – on completeness in terms of stellar mass
we show in Figure 10 the stellar mass-redshift distribution of the primary
targets888Stellar mass estimates do not play a major role in this data release
paper and are used only to illustrate the issue of completeness here. The
stellar masses used here, determined with the Prospector SED fitting code with
the setup used by Leja et al. (2019) and the $BVrizYJ$ photometry described in
Appendix B.. $K_{s,LIM}$ results in a redshift-dependent stellar mass limit
above which _all_ galaxies satisfy $K_{s}<K_{s,LIM}$, and below which this is
not the case.

In Figure 11 we show the color-dependence on the mass completeness limit. This
effect is illustrated in more detail in Figure 12 where we show, for specific
stellar mass and redshift bins, the color-color distribution of the LEGA-C
targets, the galaxies in the parent sample from which the targets are chosen,
and galaxies that are fainter than $K_{s,LIM}$ (if they exist). There we see
that below the mass limit the parent sample is incomplete in terms of the
reddest (dusty) galaxies. This implies that this completeness limit in reality
depends on the science question at hand: if a user is interested in face-on
blue disks the stellar mass completeness limit will be much lower. Figure 10
and Figure 12 merely serve to illustrate the mechanism by which incompleteness
can be assessed, depending on one’s requirements.

Factor 2: Galaxies from the $K_{s}$-selected parent sample are sorted by
$K_{s}$ flux and included in the mask designs in order of decreasing flux. As
a result, a larger fraction of $K_{s}$-bright galaxies from the parent sample
are included in the survey compared to $K_{s}$-faint galaxies. In fact, the
fraction of included galaxies (with respect to the parent sample) is a
strictly monotonously increasing function of $K_{s}$ magnitude, which means
that we know the probability of survey inclusion based on (and only on)
$K_{s}$ magnitude. This probability is the inverse of the sample correction
factor (Scor in the catalog – see Section 4.2). In Figure 12 the filled data
points (included in LEGA-C) are representative of the blue data points (the
parent sample) when taking into account the completeness via Scor.

A second correction – the volume correction factor Vcor – accounts for the
fact that a galaxy at $z=0.7$ that is brighter than $K_{s,LIM}$ might not be
sufficiently bright if it had been at $z=0.9$. The product of Scor and Vcor –
which we call Tcor in the catalog – allows for the calculation of volume-
limited quantities such as the stellar velocity dispersion function. The
extent to which this is useful depends on the amount of evolution in the time
between $z=1$ and $z=0.6$; the correction Tcor implicitly assumes $z=0.6$ and
$z=1$ galaxies are the same.

Factor 3: Crucially, the observed primary sample is highly successful in
measuring redshifts and stellar velocity dispersion measurements (Figure 13).
Only 11 (0.4%) of primary targets do not have a redshift measurement, for a
variety of technical and astrophysical reasons. Two galaxies had previously
measured spectroscopic measurements that turned out to be incorrect; three
have poor spectra for technical reasons (e.g., vignetting), four spectra
suffer from contamination by lower-redshift interlopers, preventing the useful
extraction of spectrum, and two galaxies have good spectra without absorption
or emission features. 97 (3%) do not have a stellar velocity dispersion
measurement; a measured velocity dispersion also serves as an indication that
the stellar population properties (in the form of absorption line index
values) can be measured with reasonable precision. A stellar velocity
dispersion measurement most commonly fails among the faintest, reddest
galaxies. But even among those 148 galaxies with $i$-band magnitudes fainter
than 22.5, 85% have a successful stellar velocity dispersion measurement, and
all have redshift measurements. Other causes that lead to a failed
$\sigma_{*}$ measurement are AGN and (very rarely) flux calibration errors.
These issues are flagged as described below. The implication is that
measurement success plays a negligible role in assessing the survey
completeness.

In summary, connecting the LEGA-C sample to the full galaxy population at
$z=0.6-1$ is possible thanks to the high success rate of relevant measurements
and the well-understood selection function.

One issue has been neglected in the above analysis: we have assumed that the
photometric redshift used for target selection is identical to the actual
redshift (as measured on the basis of LEGA-C spectra). In reality there is a
r.m.s. of 0.02 in $\Delta z=z_{\rm{phot}}-z_{\rm{LEGA-C}}$ for primary
targets. For 97% of the primary sample this scatter does not matter:
$(z_{\rm{phot}}$ and $z_{\rm{LEGA-C}}$ are both in the redshift range
$0.6<z<1.0$.

The other 3% can be divided into two groups. First, the group that arises due
to random scatter near the redshift limits $z=0.6$ and $z=1$. We assign to
this group all galaxies (2%) with $0.56<z_{\rm{LEGA-C}}<0.60$ and
$1.00<z_{\rm{LEGA-C}}<1.04$, that is, within $2\sigma$ of the the redshift
limits. These are still treated as primary targets and included in the above
completeness and volume corrections. This does not artificially increase the
number density, since there is a set of galaxies that is not included in the
survey while they should have been: galaxies with $0.6<z<1.0$ but with
$0.56<z_{\rm{phot}}<0.6$ or $1.00<z_{\rm{phot}}<1.04$. Since the scatter in
$\Delta z$ is symmetric, the sets of galaxies that were accidentally included
and accidentally excluded cancel out in the above volume correction
calculation.

The second group consists of galaxies (1%) with more strongly deviating
redshift measurements: $z_{\rm{LEGA-C}}<0.56$ or $z_{\rm{LEGA-C}}>1.04$. These
‘catastrophic’ outliers are excluded from the primary sample and not taken
into account when calculating the completeness and volume corrections, which
has a negligible effect on the analysis given their small number.

##  Appendix B Photometry and Fitting the Spectral Energy Distribution

We use a subset of the photometry from Muzzin et al. (2013b, hereafter: M13)
with revised zero points. In M13 zero point corrections are applied that
remove systematic differences between the initially calibrated photometry and
template spectral energy distributions. While this greatly aids photometric
redshift estimates, systematic errors in the colors of galaxies can be
propagated into the catalog if the templates themselves – which are based on a
particular flavor of stellar population synthesis models – contain systematic
errors. We will show below that small but significant systematic offsets exist
in the rest-frame UV and near-IR parts of the spectrum. But first we reassess
the relative flux calibrations of the M13 UltraVISTA catalog.

In Figure 14 (left-hand panel) we show that the near-IR photometry of stars in
the original M13 catalog does not coincide with the synthesized photometry of
the Pickles (1998) library of stellar spectra999M stars or AGB stars in the
Pickles library are known to have imperfect model spectra, but only a few such
stars (the reddest in Figure 14) are included here, and these do not affect
our analysis.. An examination of the photometry in all nine filters listed in
Table 3 made clear that the $K_{s}$ photometry is systematically offset from
the other UltraVISTA filters ($Y$, $J$, and $H$) by 0.07 mag. Applying this
shift aligns the observed and synthesized stellar photometry well. We elected
to keep the total $K_{s}$ band magnitude unchanged in order not to change the
absolute calibration of the source detection filter ($K_{s}$). For the optical
filters $V$, $r$, $i$ and $z$ similar – marginally smaller – offsets were
required to align the photometry (Table 3). For the $B$ band a larger shift
was required (see Figure 15). All in all, only the $B$ and $K_{s}$ filters
received a relative zero point correction larger than 0.03 mag. The filters
$V$, $r$, $i$, $z$, $Y$, $J$ and $H$ were already consistent with each other
to within 3%.

Now that we have accurate zero points that are independent of stellar
population synthesis models we are in a position to verify those models for
systematic errors. In Figure 16 (left-hand panel) we show the $J-H$ and
$H-K_{s}$ colors with revised zero points for a sample of 76 quiescent
galaxies (UVJ selected) with stellar velocity dispersions
$\sigma>200\leavevmode\nobreak\ km\leavevmode\nobreak\ s^{-1}$ and in the
redshift range $0.72<z<0.74$, chosen to contain a significant overdensity of
massive galaxies. The colors are in the observed frame at $z=0.73$ and the
filters correspond to rest-frame wavelengths of $\sim$0.7, 0.95 and 1.3$\mu
m$. In the right-hand panel we show the $i_{p}-Y$ and $Y-J$ colors for the
same sample (rest-frame: $\sim$0.44, 0.6, and 0.7$\mu$m). The majority of
these galaxies have been shown on the basis of their high-quality optical
spectra from LEGA-C to have little or no star formation in the past few Gyr
and ages typically in the range of 3-5 Gyr (Chauke et al., 2018): their colors
should resemble those of single stellar populations (SSPs). We compare these
colors with synthesized photometry for a variety of SPS models with ages in
the range of 2 to 6 Gyr. The FSPS models (Conroy et al., 2009) and the BC03
models use different Padova evolutionary tracks: Marigo & Girardi (2007) and
Bertelli et al. (1994), respectively. Neither solar nor super-solar models
match the observed $H-K_{s}$ colors, and attenuation is unlikely to explain
the offset both due to mismatched ‘direction’ in color-color space and the
direct evidence for low attenuation even at shorter wavelengths for this type
of galaxy. Considering this set of photometric measurements in isolation, both
the Maraston and FSPS models can match the data by adopting high
metallicities, younger ages (0.5 - 1 Gyr) and a significant amount of
attenuation, but these parameter ranges are firmly ruled out by independent
constraints on age (from the LEGA-C spectra) and attenuation. In the rest-
frame optical wavelength range (probed by the colors used in the right-hand
panel of the figure) no such wholesale offsets are apparent and the model
colors generally correspond well with the observed colors. The result that no
large changes in metallicity, age, and attenuation are required to match the
optical spectral energy distribution (SED) suggests that the problems lie with
the models in the near-IR.

In order to analyse the near-infrared offsets further we use the fitting code
Prospector (Leja et al., 2019). We provide the photometry in the wavelength
range $B$ to $K_{s}$ for the filter set given in Table 3 but $H$ and $K_{s}$
are not used in the fit; instead, residuals are calculated based on the models
that are fit to the $B$ through $J$ photometry. 101010Note that the MIPS
24$\mu$m data are also used in this fit in order to constrain the star-
formation rate. In Figure 17 we show the residuals in $H-K$ across redshift.
These differences between observed and inferred $H-K_{s}$ colors are to first
order independent of galaxy type (star-formation activity) but strong change
with redshift. The implication is that the color offsets seen for old galaxies
(Figure 16) are present in all galaxies in the redshift range $z=0.6-1$: the
models systematically underpredict the $H-K_{s}$ colors. The redshift
dependence suggest that the photometric measurements are not the problem:
these would be redshift independent.

We conclude that using photometry longward of rest-frame $\sim 0.8\mu\rm{m}$
leads to systematic errors in fits to the spectral energy distribution of
$\sim 20\%$, which will propagate into small but systematic errors in the
stellar mass, star-formation rate, attenuation, and other parameters that are
inferred. For the purpose of calibrating our spectra we choose the $BVrizYJ$
filter set. We note that if $H$ and $K_{s}$ are included in the fits, then the
attenuation parameters are adjusted to accommodate for the systematic effect.
We do not fully explore this here, but one illustrative result is that passive
galaxies typically require $A_{V}\sim 0.5$, which is ruled out by other means
(optical depth estimates; attenuation measurements from spectra, …). However,
stellar mass estimates differ by no more than $\sim$0.05 dex on average if $H$
and $K_{s}$ are included in SED fits.

Figure 14: $J-H$ vs. $H-K_{s}$ colors of stars (black) in the UltraVISTA
catalog from Muzzin et al. (2013b) compared with synthesized colors of stars
(red) from the Pickles library. The left-hand panel shows the star colors with
the original zero points; the right-hand stars show the colors with the
revised zero points. The red points are idential in both panels.  Figure 15:
$B-V$ vs. $V-r$ colors of stars (black) in the UltraVISTA catalog from Muzzin
et al. (2013b) compared with synthesized colors of stars (red) from the
Pickles library. The left-hand panel shows the star colors with the original
zero points; the right-hand stars show the colors with the revised zero
points. The red points are identical in both panels.

Figure 16: $J-H$ vs. $H-K_{s}$ (left-hand panel) and $i_{p}-Y$ vs. $Y-J$ colors (all with revised zero points) of massive, passive galaxies at $z=0.72-0.74$ selected from LEGA-C, compared with synthesized photometry for three SPS models (Maraston, FSPS and BC03) and two metallicities (solar and $2\times$ solar) in the age range 2-6 Gyr.  Figure 17: Difference between observed $H-K_{s}$ color and inferred $H-K_{s}$ based on fits to the $BVrizYJ$ photometry. Color coding is with specific star formation rate: red colors indicate passive galaxies; blue colors indicate high star-formation activity. The strong redshift dependence indicates the offsets are not due to a simple calibration error in the photometry (which would lead to a redshift-independent offset). The small difference between young (star-forming) and old (quiescent) galaxies that the offsets are not strongly age dependent.  Table 3: Zero points shifts in magnitude for 9 filters. A positive number corresponds with decreasing the flux density / increasing the magnitude. The shift in $K_{s}$ is zero by construction.  Filter | $B$ | $V$ | $r$ | $i$ | $z$ | $Y$ | $J$ | $H$ | $K_{s}$
---|---|---|---|---|---|---|---|---|---
Zero point shift | 0.12 | 0.05 | 0.04 | 0.04 | 0.05 | 0.07 | 0.07 | 0.07 | 0.00

##  Appendix C Uncertainties in Spectral Properties: Comparing Duplicate
Observations

The formal uncertainties, based on the noise spectra, may not fully capture
the full random error budget due to correlations in the noise spectra and
systematics in the spectra that propagate to random errors. For specific
measurements there may be specific contributions: template mismatch for
$\sigma_{*}$, the quasi-random wavelength coverage of emission lines for
$\sigma_{g}$, flux calibration uncertainties for spectral index measurements,
and so forth.

By design, LEGA-C targeted hundreds of galaxies multiple times, providing an
automatic assessment of the complete budget of spectrum-to-spectrum random
uncertainties. We compare the variance in the differences between duplicate
measurements to the expected variance inferred from the formal measurement
uncertainties, and correct the latter if necessary. This approach was already
used in DR2 – here we show that due to improvements in the data reduction and
analysis techniques such corrections are generally smaller than before. For
the analysis we choose the sample of 205 galaxies for which we have duplicate
spectra with $S/N>5$ and successful redshift measurements. (We omit galaxies
in mask 101, which were taken with the slits perpendicular to the rest of the
survey. This leads to physically different velocity dispersions due to
projection effects along the slit.) The scatter between the duplicate
measurements is compared with the random uncertainty (added in quadrature),
producing a $\sqrt{\chi^{2}/N}$ value to parameterize the excess scatter
compared to the scatter that can be expected on the basis of the formal
measurement uncertainties. This number serves as the correction factor on our
measurement uncertainties, propagated into our published catalog.

We first examine the duplicate measurements of
$\sigma^{\prime}_{\star,\rm{int}}$ (Figure 18, left-hand side), and conclude
that the true uncertainties are 50% higher than the formally derived
uncertainties. There are several possible causes: template mismatch,
correlated noise, and wavelength coverage. For $\sigma^{\prime}_{g,\rm{int}}$
(Figure 18, right-hand side) we infer a similar correction of 1.5, bearing in
mind the 15% systematic uncertainty discussed in Figure 3.3 due to emission
line-specific slit losses.

Figure 18: Comparison of duplicate measurements of
$\sigma^{\prime}_{\star,\rm{int}}$ (left) and $\sigma^{\prime}_{g,\rm{int}}$
(right). The grey scaling reflects the measurement uncertainties, which serves
to increase the focus on high-precision measurements isntead of uncertain
outliers. The factor $\sqrt{2}$ on the y axis serves to convert the difference
between the duplicate measurements into a number that reflects the uncertainty
on the individual measurements. The dashed lines indicate the scatter; the
error bar represents the typical formal uncertainty. The upward correction
factor on the formal uncertainties serve to match those with the observed
scatter among the duplicate obserations.

Figure 19 shows the results for duplicate index measurements for three
spectral features. In all cases the formal uncertainties, indicated with the
error bars, are somewhat smaller than the scatter among duplicates. Analogous
to the correction factors on the velocity dispersion uncertainties we measure
correction factors for all absorption indices of a factor 1.3. Only
LICK_H$\beta$ (1.8) and DN4000 (2.0) receive larger correction factors. The
measurement of the former is complicated by the often-bright emission line
that is subtracted before the absorption strength is measured. The precision
of the measurement of the latter is limited by imperfections in the wavelength
dependence of the flux calibration.

Formal uncertainties on the emission line fluxes and equivalent widths are
more difficult to determine due to the aforementioned systematic problems with
variable slit losses. The analysis of the LICK_H$\beta$ absorption and
emission uncertainties, driven in a large part by the decomposition of the
spectrum into ionized gas emission and stellar light, led us to adopt a
correction factor of 1.8. This correction factor is applied to all emission
line measurements in the catalog, again keeping in mind a 15% systematic
uncertainty that is not propagated. These results compare well with similar
tests on emission lines in the Sloan Digital Sky Survey (Brinchmann et al.,
2008). They find typical corrections to the uncertainty estimates are a factor
$1.2-1.5$ for forbidden lines and a factor of $2.0$ for Balmer lines and
OII_3727.

Figure 19:  Comparison of duplicate measurements of 3 absorption line indices
(LICK_H$\delta$_A, LICK_H$\beta$, LICK_FE4383). See Fig. 18 caption and text
for details.