# Diagnosing DASH: A Catalog of Structural Properties for the COSMOS-DASH
Survey

Sam E. Cutler Department of Astronomy, University of Massachusetts, Amherst,
MA 01003, USA  Katherine E. Whitaker Department of Astronomy, University of
Massachusetts, Amherst, MA 01003, USA  Cosmic Dawn Center (DAWN), Copenhagen,
Denmark  Lamiya A. Mowla Dunlap Institute for Astronomy and Astrophysics,
University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada
Gabriel B. Brammer Cosmic Dawn Center (DAWN), Copenhagen, Denmark  Niels Bohr
Institute, University of Copenhagen, Lyngbyvej 2, 2100 Copenhagen, Denmark
Arjen van der Wel Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan
281 S9, B-9000 Gent, Belgium  Danilo Marchesini Department of Physics and
Astronomy, Tufts University, Medford, MA 02153, USA  Pieter G. van Dokkum
Astronomy Department, Yale University, New Haven, CT 06511, USA  Ivelina G.
Momcheva Space Telescope Science Institute, 3700 San Martin Dr., Baltimore, MD
21211, USA  Mimi Song Department of Astronomy, University of Massachusetts,
Amherst, MA 01003, USA  Mohammad Akhshik Department of Physics, University of
Connecticut, Storrs, CT 06269, USA  Erica J. Nelson Department for
Astrophysical and Planetary Science, University of Colorado, Boulder, CO
80309, USA  Rachel Bezanson University of Pittsburgh, Department of Physics
and Astronomy, 100 Allen Hall, 3941 O’Hara St., Pittsburgh, PA 15260, USA
Marijn Franx Leiden Observatory, Leiden University, P.O. Box 9513, NL-2300 AA
Leiden, The Netherlands  Mariska Kriek Astronomy Department, University of
California, Berkeley, CA 94720, USA  Joel Leja Department of Astronomy &
Astrophysics, The Pennsylvania State University, University Park, PA 16802,
USA  Institute for Computational & Data Sciences, The Pennsylvania State
University, University Park, PA 16802, USA  Institute for Gravitation and the
Cosmos, The Pennsylvania State University, University Park, PA 16802, USA
John W. MacKenty Space Telescope Science Institute, 3700 San Martin Dr.,
Baltimore, MD 21211, USA  Adam Muzzin Department of Physics and Astronomy,
York University 4700 Keele St., Toronto, Ontario, Canada MJ3 1P3  Heath
Shipley  Department of Physics, McGill University, 3600 Rue University,
Montréal, QC H3P 1T3, Canada  Daniel Lange-Vagle  Department of Physics and
Astronomy, Tufts University, Medford, MA 02153, USA

(Received 2021 August 18; Revised 2021 October 18; Accepted 2021 October 26)

###### Abstract

We present the $H_{\mathrm{160}}$ morphological catalogs for the COSMOS-DASH
survey, the largest area near-IR survey using HST-WFC3 to date. Utilizing the
“Drift And SHift” observing technique for HST-WFC3 imaging, the COSMOS-DASH
survey imaged approximately 0.5 deg2 of the UltraVISTA deep stripes (0.7 deg2
when combined with archival data). Global structural parameters are measured
for 51,586 galaxies within COSMOS-DASH using GALFIT (excluding the CANDELS
area) with detection using a deep multi-band HST image. We recover consistent
results with those from the deeper 3D-HST morphological catalogs, finding
that, in general, sizes and Sérsic indices of typical galaxies are accurate to
limiting magnitudes of $H_{160}<23$ and $H_{160}<22$ ABmag, respectively. In
size-mass parameter space, galaxies in COSMOS-DASH demonstrate robust
morphological measurements out to $z\sim 2$ and down to
$\log(M_{\star}/M_{\odot})\sim 9$. With the advantage of the larger area of
COSMOS-DASH, we measure a flattening of the quiescent size-mass relation below
$\log(M_{\star}/M_{\odot})\sim 10.5$ that persists out to $z\sim 2$. We show
that environment is not the primary driver of this flattening, at least out to
$z=1.2$, whereas internal physical processes may instead govern the structural
evolution.

catalogs – galaxies: evolution – galaxies: statistics – galaxies: structure –
surveys

††journal: the Astrophysical Journal

##  1 Introduction

Balancing resolution, depth, and area of optical/near-infrared (NIR)
observations is critical in sampling the properties of galaxies across a wide
range of redshifts and masses. From the ground, many surveys have been able to
cover areas in the hundreds or thousands of square degrees (e.g., the 5000
deg2 optical Dark Energy Survey and the deep two deg2 NIR UltraVISTA survey;
The Dark Energy Survey Collaboration, 2005; McCracken et al., 2012) and have
been important in advancing the study of galaxy formation and evolution. For
example, UltraVISTA (UVISTA) has contributed to our understanding of massive
galaxy structure, color, and mass out to $z\sim 5$ (Hill et al., 2017), as
well as the evolution of the stellar mass function out to $z\sim 4$ (Muzzin et
al., 2013a). Despite the many achievements of ground based surveys, the
spatial resolution of these observations is limited by seeing, so deblending
becomes important at higher redshift (Mowla et al., 2019b; Marsan et al.,
2019). For high spatial resolution, the Hubble Space Telescope (HST) is
excellent, but its narrow FOV is not ideal for wide area surveys. The largest
area observed with HST is the 1.7 square degree Cosmic Evolution Survey
(COSMOS) field imaged using the optical F814W filter of the Advanced Camera
for Surveys (ACS; Scoville et al., 2007; Koekemoer et al., 2007). Until
recently, the largest HST survey in the NIR by comparison is the 0.25 square
degree Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey
(CANDELS) survey in the F160W and F125W filters of the Wide Field Camera 3
(WFC3) (Koekemoer et al., 2011).

The CANDELS survey in particular has led to a wealth of important results,
many of which make full use of the HST-resolution morphological catalogs
presented in van der Wel et al. (2012) (e.g., Bell et al., 2012; Wuyts et al.,
2012; Barro et al., 2013; van der Wel et al., 2014; van Dokkum et al., 2015;
Barro et al., 2017; Marsan et al., 2019; Mowla et al., 2019a, b; Suess et al.,
2019a, b; Chen et al., 2020), as well as other morphological and structural
measurements (e.g., van Dokkum et al., 2011; Kartaltepe et al., 2012; Shibuya
et al., 2015; Holwerda et al., 2015; Nelson et al., 2016; Dimauro et al.,
2018, 2019; Nedkova et al., 2021). To name a few, this data yields clear
evidence for inside out disk growth (Wuyts et al., 2012; Nelson et al., 2016),
establishes correlations between quiescence and galaxy morphology (Bell et
al., 2012), and uncovers the striking diversity of morphologies among massive
galaxies at high redshift (van Dokkum et al., 2011). Structural measurements
from van der Wel et al. (2012) are also fundamental to establishing
significant correlations between the surface mass densities of star-forming
and quiescent galaxies (e.g., Whitaker et al., 2017); these results inspired
astronomers to coin a new term, the structural main sequence, that
hypothesizes a universal evolution track of compaction among star-forming
galaxies (Barro et al., 2013, 2017).

Combining procedures and imaging utilized in the CANDELS morphological
catalogs by van der Wel et al. (2012) with analysis from 3D-HST (Brammer et
al., 2012; Skelton et al., 2014; Momcheva et al., 2016), van der Wel et al.
(2014) perform the first comprehensive investigation of the size-mass
distribution of galaxies out to $z=3$. van der Wel et al. (2014) definitively
establish that both quiescent and star forming galaxies of the same stellar
mass are smaller in size at higher redshift, with the number density of
compact, quiescent galaxies peaking around $z\sim 1.5-2$ (see also Cassata et
al., 2011). Building a sample of ultra-massive galaxies with HST-resolution
morphologies, Mowla et al. (2019b) extend the study of the evolution of the
size-mass relation to $\log(M_{\star}/M_{\odot})>11.3$ and $z=3$ (see also
Marsan et al., 2019; Nedkova et al., 2021). Contrary to scaling relations
measured for less massive galaxies (e.g., van der Wel et al., 2014), the most
massive quiescent galaxies instead have similar sizes to star-forming galaxies
of similar stellar mass at all redshifts explored (Mowla et al., 2019b).
Moreover, by combining the COSMOS-DASH and 3D-HST surveys, Mowla et al.
(2019a) show that the galaxy size-mass relation is best represented by a
broken power law. These studies obtain comprehensive samples of galaxies owing
to the combination of the deep, CANDELS-depth observations with the wide area
observations of optical ($I_{814}$) COSMOS ACS (Scoville et al., 2007;
Koekemoer et al., 2007) and NIR ($H_{160}$) COSMOS-DASH imaging, the latter of
which is possible due to the “Drift And SHift” (DASH) imaging technique
(Momcheva et al., 2017).

While Mowla et al. (2019b) analyzed only the most massive galaxies in COSMOS-
DASH, the motivation for this work is to augment earlier work by releasing a
full COSMOS-DASH morphological catalog. The focus here will be on testing and
quantifying the stellar mass and redshift limits of this moderately shallow
imaging. In the following sub-sections, we first intro the DASH technique
(Section 1.1), followed by the COSMOS-DASH survey itself in more detail
(Section 1.2).

Figure 1: Image of the COSMOS-DASH mosaic, which roughly covers the UVISTA
deep stripes. The left panel shows the science image of the COSMOS-DASH field
with CANDELS and other archival exposures included. The inset shows the
“calibration field”, which is the region of COSMOS-DASH that overlaps with
CANDELS. The overlap itself is highlighted in teal, and facilitates a direct
comparison of DASH and CANDELS depth morphologies.

###  1.1 Drift And SHift (DASH) Technique

Surveying large areas with HST is observationally expensive for two reasons.
The first is the small, 4.6 arcmin2 field-of-view (FOV), requiring roughly 750
pointings to map degree scale areas on the sky. However, just as significant,
especially in the NIR, are the large overheads stemming from guide star
acquisition. Standard HST observations require guide star acquisitions that
take over 300s, often limiting observations to a single pointing per orbit.
Hence, in the case of one orbit per pointing, covering degree-scale areas
would require approximately 25% of the annual pool available to the community,
assuming 3000 orbits per HST cycle. The novel DASH technique (Momcheva et al.,
2017) turns off guide star acquisition between pointings to allow up to eight,
300s pointings to be observed in a single orbit. In DASH, a single guide star
is acquired for the first pointing after which the fine guidance sensors (FGS)
are disabled and the gyros are used to slew to subsequent pointings. Without
the use of the FGS, gyro bias introduces an instrument drift of 0.001″-0.002″
per second. This drift smears exposures exceeding 60s, rendering them
unusable. However, exposures from the WFC3 IR detector are composed of several
zero-overhead reads, whose exposure times can be set to $<25$s, corresponding
to a drift of $\lesssim 0.05$″. A full 300s DASH exposure consists of 12 reads
of 25s, which can be treated as 12 individual, dithered exposures. The
independent reads are then shifted and drizzled in post-processing to restore
the full HST resolution with high fidelity (see Fig. 1 of Momcheva et al.,
2017).

###  1.2 COSMOS-DASH

Using the DASH technique, Mowla et al. (2019b) present COSMOS-DASH, a 0.66
deg2 NIR survey of the COSMOS field in the F160W filter of WFC3, 0.49 deg2 of
which are taken with 57 DASH orbits. With the first four COSMOS-DASH orbits,
Momcheva et al. (2017) demonstrate that HST resolution is recovered and the
structural parameters are consistent with those from 3D-HST (van der Wel et
al., 2012, 2014) for objects brighter than $H_{160}=22$ ABmag. Mowla et al.
(2019b) also fit the morphologies of 910 galaxies with $M_{\star}>2\times
10^{11}M_{\odot}$ in COSMOS-DASH and COSMOS ACS (Scoville et al., 2007;
Koekemoer et al., 2007) and supplemented these with lower mass galaxies from
the 3D-HST morphological catalogs (van der Wel et al., 2014) to measure the
size-mass relation.

While DASH allows for high resolution, wide-field imaging in fewer orbits, it
does so at the cost of image depth. Since DASH exposures are limited to around
300s per pointing, the image depth is subsequently lower: the $5\sigma$ point
source depth is 25.1 ABmag, compared to $\sim 27$ ABmag for CANDELS (Koekemoer
et al., 2011). Moreover, shifting the individual reads in post-processing
could also impact the ability to accurately measure morphologies of all but
the most massive galaxies. The intermediate depth, combined with the unusual
data reduction techniques suggest that DASH observations may be unsuitable for
obtaining galaxy morphologies for fainter low-mass or extended galaxies. The
exact parameter space in which morphological fits become unreliable is the
study of this work.

In this paper, we present the COSMOS-DASH morphological catalog, inclusive of
sources in Mowla et al. (2019b) but extending toward lower masses to yield a
magnitude limited sample. Section 2 describes the COSMOS-DASH survey and
observations used to build this catalog. In Section 3, we describe methods
employed to fit the morphological parameters and to determine the uncertainty
on these parameters. Section 4 discusses the format and layout of the
morphological catalog itself. Our key results are presented in Section 5,
where we compare COSMOS-DASH morphologies to other samples and discuss the
mass dependence of the size-mass relation and the roles galactic environment
and internal physical processes play in it. A summary of results and future
directions for this study are given in Section 6. We assume a flat
$\Lambda$CDM cosmology with $\Omega_{m}=0.3$, $\Omega_{\Lambda}=0.7$, and
$H_{0}=70\mathrm{~{}km~{}s}^{-1}~{}\mathrm{Mpc}^{-1}$, as well as a Chabrier
IMF (Chabrier, 2003) for stellar masses. All magnitudes are in the AB system.

##  2 Observations and Data

###  2.1 COSMOS-DASH Mosaic

The Cycle 23 COSMOS-DASH program (Program ID: GO-14114) is a 0.49 deg2 survey
of the COSMOS field using the HST-WFC3 F160W filter. It consists of 456
pointings in 57 orbits (8 pointings per orbit) obtained between 2016 November
and 2017 June using the aforementioned DASH technique. Each exposure consists
of 11 or 12 25s reads which are shifted and drizzled to remove the effect of
instrument drift to thereby restore HST resolution (see Momcheva et al.,
2017). The data set additionally includes all available archival F160W data in
COSMOS, including CANDELS, resulting in a total F160W area of 0.66 deg-2. We
use an updated, redrizzled mosaic (containing more archival data) that has a
pixel scale of 0.1″ pix-1, centered at R.A.=10:00:20.2, decl.=+2:11:03.7,
shown in Fig. 1, main panel.

###  2.2 COSMOS-DASH Sample

For this project, we select galaxies from an HST-selected photometric catalog
of sources in COSMOS-DASH. Sources are detected by running SExtractor v2.19.5
(Bertin & Arnouts, 1996) on a combined WFC3 (F105W, F110W, F125W, F140W, and
F160W) and ACS (F814W) noise-equalized HST image, where available. We identify
galaxies following the standard settings of e.g., Skelton et al. (2014) and
Shipley et al. (2018). The catalog aperture is 0.7″ in diameter and all
catalog sources are required to have coverage in at least one WFC3 band;
sources with F814W coverage only are therefore not included. The catalog is
generated from a global, deep detection segmentation map that is used to mask
objects for GALFIT (see Sec. 3.4). The primary purpose of this catalog herein
is for source detection to facilitate the goal of measuring robust structural
parameters and deblending lower-resolution ground based data. We therefore
focus on the F160W photometry alone. Kron radii from SExtractor are also used
in determining image cutout size (see Sec. 3.1).

Cross-matching this catalog with the UltraVISTA catalog of Muzzin et al.
(2013b), we identify 51,586 galaxies covered by COSMOS-DASH with significant
signal to noise (SNR$>5$) in F160W. The SNR threshold ensures accurate GALFIT
measurements for most of the galaxies. This sample excludes all galaxies from
CANDELS in the 3D-HST morphological catalogs of van der Wel et al. (2014) to
avoid duplicate effort. This catalog can therefore be used directly alongside
the COSMOS 3D-HST morphological catalog from van der Wel et al. (2014). Masses
in this sample are from the Muzzin et al. (2013a) UVISTA catalog, and are
derived using the FAST code (Kriek et al., 2009). The mass-completeness limits
for the UVISTA catalogs are shown in Table 1 (adapted from Muzzin et al.,
2013a; Mowla et al., 2019b).

$z$ | $\log(M/M_{\odot})$
---|---
$<0.5$ | 9
0.5 - 1 | 9.6
1 - 1.5 | 10.2
1.5 - 2 | 10.6
2 - 2.5 | 10.9
2.5 - 3 | 11.1
Table 1: Table of 100% mass-completeness limits for the UltraVISTA catalogs
(Muzzin et al., 2013a), adapted from Figure 3 of Mowla et al. (2019b).

Due to the limited spatial resolution of ground-based UVISTA observations
(K-band FWHM$\sim 0.8$″ vs. HST F160W FWHM$\sim 0.151$″), some sources
cataloged as a single object in UVISTA will be deblended into two or more
objects in COSMOS-DASH. Of the 51,586 galaxies in DASH, 2,345 are split into
pairs or triplets when searching within the UVISTA FWHM. Adapting from Mowla
et al. (2019b), for each deblended UVISTA ID we compute F160W total fluxes
using GALFIT (Peng et al., 2002, 2010a), making sure to mask the other
deblended objects. The brightest galaxy is retained, with the stellar mass
weighted by its flux relative to the total flux of all of the blended
components:

$\displaystyle
M_{\star,i}~{}=~{}M_{\star,\mathrm{tot}}~{}\times~{}\frac{F_{i}}{F_{\mathrm{tot}}},$
(1)

where $M_{\star,\mathrm{tot}}$ is the total mass of the blended object from
the UVISTA catalog, $F_{i}$ is the model flux of the brightest component and
$F_{\mathrm{tot}}$ is the total summed fluxes of all the components. The mass
corrections are provided in the catalog of this sample (see Sec. 4).

The deblending status of the galaxies in the sample is indicated with a
blending flag. HST-selected galaxies that have no close pairs are given a flag
of 0, and are labeled “not blended”. Galaxies whose components can be properly
deblended and fit with GALFIT are flagged with 1, indicating they are
“deblended”. Deblended galaxies whose $U-V$ and $V-J$ colors do not change
likely have robust masses and morphologies, but significant color changes may
suggest that stellar masses and/or photometric redshifts are incorrect.
Galaxies that remain “blended”, meaning the deblending procedure failed, are
given a flag of 2. Lastly, a flag of 4 is given to galaxies that are in the
UVISTA catalogs, but have “no coverage” with COSMOS-DASH. This flag value is
chosen to match with the “no coverage” GALFIT flag (see sec. 3.1). Since later
analyses in this work use rest-frame colors from UVISTA to classify galaxies
as star-forming or quiescent, deblended galaxies with significantly differing
colors must be excluded. The difference in the our analyses is negligible when
all deblended galaxies (flag_deb=1) are discarded. As such, we require a
deblending flag of 0 in future analyses to avoid contamination from deblended
galaxies with potentially incorrect colors, stellar masses, and redshifts.

###  2.3 COSMOS-DASH Calibration Field

We define a region of the mosaic as the “calibration field”; this region
contains roughly 12 overlapping pointings of CANDELS and COSMOS-DASH imaging.
Since this calibration field contains both CANDELS F160W pointings and the new
DASH pointings by design, we separate this data to create two versions:
exposures from (1) the COSMOS-DASH program only, and (2) the CANDELS program
only. The CANDELS-only reduction overlaid on the DASH-only reduction is shown
in the zoom panel of Fig. 1, with the regions where the two images overlap
highlighted. The calibration field is useful for testing morphological fitting
methods and comparing those results to the 3D-HST morphological catalogs, as
it provides a reasonable sample size to run tests on and contains sources that
have both DASH and CANDELS imaging. Through crossmatching the COSMOS-DASH HST-
selected photometric catalog (see Sec. 2.2) with the 3D-HST morphological
catalog (van der Wel et al., 2014), we find 483 galaxies with significant
F160W detection (SNR$>5$), comprising our calibration sample. Morphologies for
this sample of calibration field galaxies are compared to the 3D-HST
morphologies from van der Wel et al. (2014). This smaller sample allows for an
in-depth error analysis and direct comparison of our measured errors relative
to those of the corresponding galaxies in 3D-HST. The morphology and error
analysis, as well as comparisons between the calibration field and 3D-HST, are
discussed in more detail in the next section. For clarity, all figures using
solely calibration field data are labeled in the top left.

Figure 2: Normalized curve of growth for PSFs determined at positions of
calibration field galaxies. The gray transparent lines are the growth curves
for each of the 483 galaxies in the calibration field. The solid black line
shows the running mean of the individual growth curves, with error from the
standard deviation of the individual growth curves. The dashed line shows the
F160W reference growth curve. The reference curve and each individual growth
curve is normalized to unity at 2″. The middle panel shows the fractional
error in the growth curve and the bottom panel shows the ratio between the
reference curve and the running mean.

##  3 Analysis

###  3.1 GALFIT Fitting Methodology

We closely follow the fitting methods laid out in van der Wel et al. (2012)
and Mowla et al. (2019b), with a few notable changes made in our morphology
fitting pipeline. We fit the list of COSMOS-DASH objects laid out in Section
2.2. A simple square cutout of each object and the corresponding location in
the weight map is made using Montage v6.0111http://montage.ipac.caltech.edu.
The cutouts have a size equal to 7 times the semi-major axis Kron radius,
which is measured when making the photometric catalog (Sec. 2.2). SExtractor
is used to identify all sources in each cutout, masking all objects except for
the galaxy of interest. This segmentation map is made in two ways: (1) using
the SExtractor detection of the F160W cutout itself, and (2) from the “global”
segmentation map created when building the deep, HST-selected catalog. The
selection of which type of segmentation map we use is an important
consideration which we will discuss more in Section 3.4. We also implement a
position-dependent point spread function (PSF), the specifics of which will be
discussed in Section 3.2. Lastly, we include a noise map with the same
dimensions as the image cutout, determined identically to Mowla et al.
(2019b). The noise calculations for DASH assume sky background is the dominant
component and include Poisson noise. Noise is calculated via

$\displaystyle\sigma=\sqrt{\frac{|1+f|}{w}},$ (2)

where $f$ is the image cutout and $w$ is the cutout weight image.

The image cutout, noise map, segmentation map, and position-dependent PSF are
given to GALFIT (Peng et al., 2002, 2010a) which fits a Sérsic model. The
free-parameters GALFIT changes are the magnitude ($m$), the semi-major axis
effective radius ($r_{\text{eff}}$), the Sérsic index ($n$), axis ratio ($q$),
the position angle (PA), and the central position ($x_{0},y_{0}$). GALFIT can
also fit a constant sky background to the input image; a discussion of
background fitting is saved for Appendix A. Following van der Wel et al.
(2012) and Mowla et al. (2019b), initial guesses for the parameters are taken
from SExtractor detection of the target galaxy. Boundary constraints are also
placed on certain parameters: Sérsic index is held between 0.1 and 6,
effective radius between 0.03″ and 40″ (0.3 and 400 pixels at the pixel scale
of COSMOS-DASH), axis ratio between 0.0001 and 1, and magnitude between $-3$
and $+3$ magnitudes of the SExtractor magnitude, as in van der Wel et al.
(2012).

Galaxies are flagged for suspicious parameter values or for failed fits,
similar to van der Wel et al. (2012). Objects that are fit without problems
are assigned a flag of zero and are deemed “good” fits. “Suspicious” fits,
sources whose GALFIT magnitudes deviate by more than $3\sigma$ (as determined
in Section 3.5) from the expected magnitude, are given a flag of 1. The
expected magnitudes are measured in Section 3.3 and are corrected for
previously noted systematic offsets between GALFIT and SExtractor magnitudes,
which range from roughly 0.1 dex at bright magnitudes to 0.3 dex at faint
magnitudes (see e.g., Häussler et al., 2007; van der Wel et al., 2012).
Galaxies that have a best-fit parameter at the constraint limits are
considered “bad” and flagged with a value of 2. When GALFIT fails to converge
at all, the fit is marked with a flag of 3 and we indicate the fit as
“failed”. Moreover, galaxies that have a negative aperture flux are also given
a flag of 3, as the signal-to-noise ratio (SNR) is crucial in estimating
parameter errors (see Sec. 3.5). These galaxies account for only 0.5% of all
51,586 galaxies with coverage. Lastly, we assign a flag of 4, differing from
van der Wel et al. (2012), to galaxies in UVISTA that are not covered by
COSMOS-DASH imaging. Though analysis is not possible for galaxies without
COSMOS-DASH coverage, we still include these objects in order to present a
complete list of IDs in the catalog (see Sec. 4). In total, 39.5% of galaxies
with coverage are “suspicious”, 12.7% are “bad”, and 0.5% are “failed”.
“Suspicious” galaxies are not necessarily poorly fit or reporting inaccurate
magnitudes. In most cases, these are galaxies with very small GALFIT magnitude
errors, so there is less of a deviation required for a flag to be applied. On
average, “good” galaxies had a magnitude error that was 70% larger than
“suspicious” galaxies.

Figure 3: Grid of all 72 empirical PSFs for the COSMOS-DASH mosaic. Empirical
PSFs are inserted in the frame of each exposure that covers a given position
within the mosaic, and the PSFs are then drizzled with the same parameters as
the science exposures. Black squares show regions where there is no PSF
available because there are no dithering parameters. Figure 4: Empty aperture
photometry on the background COSMOS-DASH calibration field. The top panel
shows histograms of the summed flux in different aperture sizes from empty
regions in the image. The solid lines are the best fit Gaussians to these
histograms. The bottom panel compares the means of these Gaussians divided by
the number of pixels in the aperture (black points) to the mean background
measured by GALFIT (solid line). The shaded region shown is the standard
deviation in the GALFIT measured background.

(a)  (b)

Figure 5: Empty aperture errors for CANDELS-only (left) and DASH-only (right)
reductions of the COSMOS-DASH mosaic. The measured best fit Gaussian width to
the flux distribution of $2000$ apertures are indicated with triangles for a
range of aperture sizes. The solid line indicates the best fit power law given
by Eq. 3. Dashed lines show uncorrelated and perfectly correlated noise below
and above the best fit line, respectively. The dotted line shows the PSF FWHM.
The best fit power law parameters for each reduction are shown in the top left
of each figure.

###  3.2 PSF Models

We obtain PSFs for COSMOS-DASH using Grizli222https://grizli.readthedocs.io/
to shift and drizzle HST empirical PSFs (Anderson, 2016) to (1) the location
of every source, or (2) a coarser grid of positions throughout the mosaic when
running GALFIT. Using the Grizli determined PSFs for all 483 galaxies in the
COSMOS-DASH calibration field, we obtain growth curves for each galaxy (Fig.
2). The running mean and the standard deviation of the 483 individual growth
curves is also calculated at each aperture size. We compare the running mean
to the HST F160W reference curve and determine that there is no significant
difference for aperture radii $\gtrsim 0.25$″. Similarly, scatter in the
position dependent PSFs is also negligible for a given aperture size.
Moreover, there is no significant difference in structural measurements
between galaxies fit with position dependent PSFs and those fit with PSFs
determined over a larger area of the mosaic, even at $z>2$. This suggests that
further corrections to the PSF at each individual location in the mosaic are
unnecessary.

Due to the time it takes to determine each individual PSF and the minimal
effect of individual position dependent PSFs, we alternatively opt for a set
of empirical PSFs evaluated on a coarse grid across the mosaic. The 72 PSFs
for the COSMOS-DASH mosaic are shown in Figure 3. These are empirical PSFs
that are altered to match the mosaic pixel scale and the dither grid at each
position. In regions where there are no dithering parameters (due to the image
being empty), the PSFs are also empty. These PSFs have an average FWHM of
0.2″, compared to 0.18″ in CANDELS. For each galaxy, the closest PSF by RA and
Dec is chosen, excluding empty PSFs. Further corrections (such as 2D
interpolations) are not done due to the added computational time and
negligible change in fit quality. This PSF is then used by GALFIT when fitting
a 2D Sérsic model like in van der Wel et al. (2012) and Mowla et al. (2019b).

###  3.3 Photometry and Noise Properties

We compute the flux density of all 51,586 galaxies within a 0.7″ diameter
aperture using SExtractor. This aperture size is chosen to maximize the SNR of
HST observations (Skelton et al., 2014). The Kron radius and Kron radius flux
(AUTO flux) are also computed by SExtractor. The aperture flux is scaled to a
total flux by correcting first to the flux within the Kron radius. We then
interpolate the value of the growth curve (normalized to unity at 2″) at the
Kron radius, and multiply the inverse of this value to obtain the total flux.
If the AUTO flux is less than the aperture flux or the Kron radius is greater
than 2″, then that scaling is kept at one following Skelton et al. (2014).

Photometric errors are estimated using an empty apertures approach (e.g.,
Whitaker et al., 2011; Skelton et al., 2014). For a diameter in the range of
0.2″ to 2.1″, 2000 circular apertures are placed in empty regions of the
noise-equalized, background-subtracted image. Apertures that overlap with
objects based on the segmentation map or regions outside of the image are
moved to different random coordinates until satisfactory. The distribution of
the summed fluxes obtained for 6 aperture diameters ranging from 0.5″ to 2″ is
shown in Figure 4 (top). The shifts in the Gaussian means indicate a small,
per-pixel background, as shown in Figure 4 (bottom), which gets larger in
magnitude as more pixels are included in the aperture. The figure also
demonstrates that the widths of the best fit Gaussians increase with larger
aperture sizes, which implies an increase in standard deviation with linear
aperture size $N=\sqrt{A}$, where $A$ is the area of the aperture. This
relation is modeled by a power law of the form

$\displaystyle\sigma_{\mathrm{nmad}}=\sigma_{1}\alpha N^{\beta},$ (3)

where $\sigma_{1}$ is the standard deviation of the pixels of background
pixels, $\alpha$ is the normalization, and $\beta$ is the power law index
which falls between 1 and 2 (see Whitaker et al., 2011). A power law index of
1 indicates uncorrelated noise and a power law index of 2 indicates perfectly
correlated noise. The combined COSMOS-DASH mosaic (outside the nominal CANDELS
footprint) contains shallower DASH-mode pointings alongside deeper standard
HST observations (from archival imaging); we fit a separate power law for
DASH- and standard-depth observations. The distinction in depth is determined
from the weight maps, with a boundary set at a weight of 100, corresponding to
a 5$\sigma$ depth of 26.7 ABmag (as calculated directly from the weight map).
The resulting fit is shown in Figure 5. The standard-depth (CANDELS) imaging
shows a higher level of correlation due to the finer spatial grid (when
compared to DASH). To convert this standard deviation into a physical error,
the noise equalization factor ($\sqrt{w}$, where $w$ is the weight) must be
divided out.

To find the photometric error of each source, empty aperture error at the Kron
radius is computed and added in quadrature to Poisson noise as follows:

$\displaystyle\sigma_{\text{Kron}}^{2}=\left(\frac{\sigma_{1}\alpha\left(\pi
R_{\text{Kron}}^{2}\right)^{\frac{\beta}{2}}}{\sqrt{w}}\right)^{2}+\frac{F_{\text{AUTO}}}{g},$
(4)

where $w$ is the weight of the source, $F_{\text{AUTO}}$ is the Kron radius
flux of the source, and $g$ is the effective gain (detector gain times
exposure time) of the data. This is then scaled to a total error using the
growth curve in the same way as the flux.

Figure 6: Scatter in the best fit Sérsic parameters obtained using a deep-
detection (Catalog) segmentation map is slightly smaller than with a DASH-
depth (SExtractor) segmentation map. The top and middle rows show the
effective radii, Sérsic indices, and axis ratios of the best fit Sérsic models
determined with the DASH-depth segmentation map (top) and with the catalog
segmentation map (middle), respectively, compared to those from CANDELS/3DHST
(van der Wel et al., 2012). Transparent points are those with flag=2 parameter
values (see Section 3.1). The bottom row shows the difference in the
parameters when measured both with and without fitting background. The large
black points are the running median in each bin, with errorbars showing the
scatter determined by the median absolute deviation (MAD) of the bin. The
color scale indicates the $H_{160}$ magnitude of the source in AB magnitudes.
Points with black x’s are those that are greater than 0.3 dex from the one-to-
one line in radius. The grey shaded region shows radii less than the PSF FWHM
and points with black +’s are sources whose best fit radius falls in this
region. The median and MAD of the offset between parameters derived with the
two segmentation maps and CANDELS is shown in the each panel of the top and
middle row. Figure 7: GALFIT parameter errors of calibration field galaxies
derived from bootstrapping are in agreement with errors the CANDELS/3D-HST
catalog. The top row shows, from left to right, the bootstrapping error in
effective radius, Sérsic index, and magnitude plotted against the same errors
from the CANDELS/3D-HST. Bootstrapping is run on galaxies in the CANDELS-only
reduction of the calibration field. The dashed line shows the one-to-one line.
The bottom row shows the difference between the CANDELS/3D-HST and
bootstrapping errors plotted against the CANDELS/3D-HST effective radius,
Sérsic index, and magnitude. The running median in each panel is shown with
black points, and error bars are determined with the median absolute
deviation. The dashed line shows a difference of zero. The color scale
indicates the AB magnitude of each galaxy, as reported in the COSMOS-DASH
catalog. The median and MAD of the offset between bootstrapping and CANDELS
errors are indicated in each of the bottom panels.

###  3.4 Segmentation Map

Due to the uncertain depth and structural fidelity of DASH imaging, we choose
to mask objects in lieu of simultaneously fitting neighboring objects with
GALFIT. This is done to circumvent any issues with poorly modeled neighboring
objects impacting the structural fits to the target galaxy. When fitting
structural parameters with masking, the effect of different size segmentation
maps resulting from detection images of varying depth becomes an important
consideration. The deeper images used in the COSMOS-DASH photometric catalog
are able to detect more of the fainter, extended flux of galaxies. Thus, the
segmentation map from these images is larger than when detected in DASH-depth
imaging. When objects surrounding the target galaxy are masked by GALFIT, a
larger area mask of surrounding objects could remove flux from the faint,
extended wings of large Sérsic index target galaxies, especially in crowded
regions of the mosaic. This could suggest that sources fit using segmentation
maps built from DASH-depth imaging have systematically larger Sérsic indices
than those with deeper detection images.

To test the effect of two different size segmentation maps on the best-fit
parameters, we first use the COSMOS-DASH photometric catalog segmentation map,
which is made from deep imaging: this segmentation map uses all available HST
imaging that overlaps with the HST-WFC3 F160W observations of COSMOS-DASH
field, most notably HST-ACS F814W data (Scoville et al., 2007; Koekemoer et
al., 2007) and HST-WFC3 F160W and F125W data from CANDELS (Koekemoer et al.,
2011). A cutout of this catalog segmentation map is made with Montage and
given to GALFIT, similar to the image cutout. Next we generate segmentation
maps from DASH-depth data. To do this, SExtractor (Bertin & Arnouts, 1996) is
run on the individual COSMOS-DASH cutouts (Sec. 3.1), similar to Mowla et al.
(2019b), and the resulting segmentation maps are used with GALFIT. We run the
GALFIT pipeline on the 483 calibration field galaxies using both segmentation
maps.

In Figure 6, we compare the measured morphologies of both scenarios. The first
row compares parameters measured using the DASH-depth segmentation map to the
morphologies of corresponding galaxies in the CANDELS/3D-HST morphological
catalog. The second row makes a similar comparison showing parameters measured
using the deep-detection (catalog) segmentation maps. Galaxies with a flag
value $\geq 3$ are excluded from the plot and objects with a flag of 2 are
indicated with higher transparency and excluded from the bottom row of the
figure. For the comparison, CANDELS/3D-HST galaxies with flags $\geq 2$ (see,
van der Wel et al., 2012) are also excluded. Objects that deviate
significantly in radius (more than 0.3 dex) from CANDELS/3D-HST are indicated
with black x’s. If a source has a measured radius less than the PSF FWHM
(0.18″), it is marked with a black “+”, as radius measurements may be
unreliable below the FWHM.

On average, both scenarios have morphologies consistent with those from the
CANDELS/3D-HST catalog. We observe a 22% larger scatter in the measured radii
and an 11% larger scatter in Sérsic indices for fits obtained with the DASH-
depth segmentation map. Given the factor of two decrease in standard deviation
when using the deeper-detection segmentation map, we adopt the deep-detection
segmentation map for masking, as this best represents the full extent of
detected sources. In the case where deeper data isn’t available, it may be
advisable to “grow” the DASH-only segmentation maps in size, though this was
not implemented in this analysis due to the existence of deeper data
throughout COSMOS from HST-ACS F814W (Scoville et al., 2007; Koekemoer et al.,
2007).

Figure 8: Size, Sérsic index, and magnitude comparison between calibration
field galaxies in CANDELS/3D-HST and COSMOS-DASH, showing overall agreement
between parameter values and random uncertainties consistent with scatter. In
the top row, CANDELS/3D-HST parameters with GALFIT flags $\leq 1$ (see van der
Wel et al., 2012) are plotted against COSMOS-DASH paramters with GALFIT flags
$\leq 1$. The running median and one-to-one line are shown with open circles
and dashed lines, respectively. $1\sigma$ error bars show the average
parameter error (from bootstrapping) in each running median bin. The bottom
row shows the difference between CANDELS/3D-HST and COSMOS-DASH structural
parameters plotted against the COSMOS-DASH parameters. The open circles again
indicate the running median, while the dashed line shows a difference of zero.
The black error bars are the median absolute deviation in the running median,
while the red error bars show the average parameter error. The median and MAD
of the difference in the structural parameters, as well as the average
parameter error is also displayed in the top left of each panel.

###  3.5 Bootstrapping and Error Estimation

In order to discern where DASH-depth morphologies become unreliable,
consistent parameter errors must be measured. To estimate the error in each
GALFIT parameter, we run a bootstrapping analysis on the 483 galaxy
calibration field sample. A random array the same dimensions as the image
cutout is drawn from a normal distribution. The random perturbation is
multiplied element-wise by the noise image (see Section 3.1) and by a scalar
empty aperture error $\sigma(A)$, see Eq. 3, where $A$ is the aperture area in
square pixels. This error-scaled random perturbation is added to the image,
which is then fit using GALFIT. The initial parameter guesses given to GALFIT
are the best fit results of the GALFIT routine run without perturbation. This
is repeated for 50 iterations with a different random perturbation for each
iteration. The mean of the 50 best fit parameters are taken as the parameter
value and the standard deviation is used as the error in the parameter
measurement.

We test the bootstrapping method on the calibration field sample of galaxies
using the CANDELS-only reduction. This allows us to make direct comparisons to
the CANDELS/3D-HST morphological catalog errors, as these analyze the same
sources at the same depth. In lieu of extrapolating to a single pixel, we
adopt the empty aperture error within 3 pixels when running the bootstrapping
simulations. We find this is consistent with CANDELS/3D-HST errors within
$1\sigma$. Figure 7 shows this comparison of CANDELS-only calibration field
errors (from COSMOS-DASH) to CANDELS/3D-HST errors. Brighter sources have
smaller errors, as these are more easily fit. There is also strong agreement
between the photometric catalog magnitudes and the morphological catalog
magnitudes (Fig. 7, bottom right). Galaxies with smaller errors have less
scatter around the one to one line than those with larger errors, which is
expected as well. The parameter error difference is also less than 0.3 dex for
most galaxies in both radius and Sérsic index and not significant in magnitude
error for all but the faintest galaxies. This is confirmed by the median
offsets between the errors, as well as the scatter in this offset (bottom
panels, Fig. 7).

We also directly compare the parameter values of calibration field galaxies in
CANDELS/3D-HST and COSMOS-DASH in Figure 8. The running median (open circles)
is in agreement with a one-to-one relationship within the error bars, which
are given by the median absolute deviation. Moreover, the random uncertainties
from bootstrapping are consistent with the scatter in the CANDELS/3D-HST and
COSMOS-DASH relation, as shown by the red and black $1\sigma$ error bars,
respectively. This is also reflected by quantitative measurements of the
difference between the parameters and parameter error that are indicated in
the top left of the panels in Figure 8. This indicates that there are no
systematic effects in both our structural measurements and our error analysis.

Figure 9: Evolution of relative uncertainty in effective radius (top) and
Sérsic index (bottom) with increasing depth, resulting in the parameter
magnitude limits of Figure 10. For each depth bin ($m_{5\sigma}$) given in the
top left of each panel, relative errors in effective radius and Sérsic index
(Sections 3.1 and 3.5) are plotted against the best fit GALFIT magnitude. A
$3\sigma$ clipped running mean is shown with a solid line. A relative error of
20% is marked by a dotted line. The running median is linearly interpolated to
find the magnitude where the fractional error reaches 20%. This value is
indicated with a dashed vertical line and explicitly stated by the limit in
the top left of each panel. The color bar shows the SNR of each galaxy as
computed in Section 3.3. Figure 10: Magnitude limit-depth relation for
effective radius and Sérsic index used in generating parameter robustness
flags in the COSMOS-DASH morphological catalog. The GALFIT $H_{160}$ limits
derived in Section 3.6 and Figure 9 are compared to the $5\sigma$ depths
computed in Section 3.6. Effective radius limits are shown with circles and
Sérsic index limits are shown with squares. Limits from COSMOS-DASH (this
study) are indicated by filled points while open points indicate values
derived from the CANDELS/3D-HST morphological catalog (van der Wel et al.,
2014). The expression describing the relation between the parameter limits and
the magnitude depths is a piecewise function that is constant for depths
$<24.5$ and linear for depths $>24.5$. The dotted line indicates a $5\sigma$
depth of 24.5, illustrating the two regimes of the relation. The resulting
best fit constant and linear relations are shown in the bottom left and right
of the figure and the curves are indicated with a solid line for radius and a
dashed line for Sérsic index.

Computational constraints prevent us from determining parameter errors using
bootstrapping for all 51,586 galaxies in our sample. Instead, we adapt the
empirical error estimation approach from Section 5.1 of van der Wel et al.
(2012) that will use our calibration field errors obtained from bootstrapping.
For each galaxy in the COSMOS-DASH morphological catalog with GALFIT flag
$\leq 1$, we find the 25 most structurally “similar” galaxies in the
calibration field. This is done by computing the “position” of each galaxy in
the three-dimensional parameter space given by

$\displaystyle\vec{p}_{i}=(m_{i}/\sigma(\vec{m}),~{}\log
n_{i}/\sigma(\log\vec{n}),~{}\log r_{i}/\sigma(\log\vec{r})),$ (5)

where $\sigma$ is the standard deviation in a parameter for the entire sample
set.

We compute $\vec{p}_{i}$ for each galaxy in the calibration field and use the
bootstrapping results to calculate the signal-to-noise ratio (SNR) equalized
parameter error vector:

$\displaystyle\vec{\delta}_{i}=(\delta m_{i},~{}\delta\log n_{i},~{}\delta\log
r_{i},~{}\delta q_{i},~{}\delta\text{PA}_{i})\cdot(S/N)_{i},$ (6)

where $(S/N)_{i}$ is the SNR of the galaxy. The multiplication by SNR removes
first-order SNR dependence. The set of $\vec{p}_{i}$ and $\vec{\delta}_{i}$
can then be used as a representative sample of galaxies and errors from which
we can estimate the parameter error of similar galaxies.

For each galaxy in the full mosaic with position $\vec{p}_{i}$, we compute the
“distance” to each galaxy in the calibration field via
$\vec{p}_{i}-\vec{p}_{j}$, where $\vec{p}_{j}$ is the position of galaxies in
the calibration field. Following van der Wel et al. (2012), the 25333We find
no significant change in uncertainties if the number of galaxies is reduced to
10 or increased to 50, in agreement with van der Wel et al. (2012). most
similar galaxies (i.e. galaxies with the shortest distance) in the calibration
field are selected and $\vec{\delta}_{i}$ is computed by taking the average of
$\vec{\delta}_{j}$. We then divide $\vec{\delta}_{i}$ by $(S/N)_{i}$ to
properly normalize the parameter error. Log errors are converted to linear
errors in the standard way, i.e. $\delta r=\ln(10)~{}r~{}\delta\log r$, and
these errors are given in the morphological catalog. The relative errors of
the full DASH sample are shown in Figure 9 compared to the corresponding
GALFIT magnitudes.

###  3.6 Parameter Limits

Fainter and more noisy sources are expected to yield less robust structural
diagnostics than bright, high SNR galaxies. Thus, we can directly relate the
depth of the data to the magnitude limit at which morphologies become
unreliable. We measure the depth of the entire COSMOS-DASH mosaic (Fig. 1)
using empty apertures on the noise-equalized image (see Section 3.3). We
separately place 2000 apertures in empty regions of DASH and CANDELS depth
areas of the full mosaic. The width of the best-fit gaussians for both
aperture flux distributions is computed and used with the weight map to find a
$5\sigma$ depth ($m_{5\sigma}$).

For CANDELS depth data ($m_{5\sigma}\sim 26.5$), galaxies brighter than
$H_{F160W}\sim 24.5~{}(23.5)$ had average fractional errors of 20% or lower
for the parameters $m,~{}r_{e},$ and $q$ ($n$) (see also van der Wel et al.,
2012). We find similar values for the CANDELS/3D-HST morphological catalog
(24.9 and 23.7, respectively) using a $3\sigma$ clipped running mean. A
similar analysis is done on the 51,586 DASH galaxies, shown in Figure 9.
Fractional errors for both effective radius and Sérsic index are computed
using the errors derived in Section 3.5 and the best fit parameters from
GALFIT (3.1). We compute the $5\sigma$ depth of each object and separate each
galaxy in to 0.25 AB magnitude bins based on the depth of the image at their
location. The fractional errors are plotted against the GALFIT best-fit
magnitudes and color-scaled by the total SNR (i.e. the aperture SNR scaled to
total using the curve of growth). A running mean over the respective GALFIT
magnitudes is computed for each depth bin with outliers $>3\sigma$ clipped
(solid line in Fig. 9). We interpolate the running mean to find the magnitude
at which it equals a fractional error of 0.2 (marked with a dashed-dotted line
in Fig. 9) and quote that magnitude in the top left of each panel.

These values are then plotted against the corresponding $5\sigma$ depth in
Figure 10 (solid points) along with the limits from CANDELS/3D-HST (open
points). We separate the limits into two regimes, shown with a dotted line in
Fig. 10: $m_{5\sigma}<24.5$, where the parameter limit is constant with
changing depth, and $m_{5\sigma}>24.5$, where there is a linear relationship
between depth and magnitude limit. For the former, we measure the mean
parameter limit for all bins with $m_{5\sigma}<24.5$ and use this as the
constant limit for this regime444While all of these exposures are taken with
the DASH method, varying zodiacal light impacts the noise level and pointing
depth.. For $m_{5\sigma}>24.5$, ensuring continuity at $m_{5\sigma}=24.5$, we
fit a linear relation to the data. The resulting depth-parameter limits are

$\displaystyle m_{lim,r}$
$\displaystyle=\begin{cases}23.40&[m_{5\sigma}<24.5],\\\
0.88m_{5\sigma}+1.91&[m_{5\sigma}>24.5],\end{cases}$ (7)

for effective radius and

$\displaystyle m_{lim,n}$
$\displaystyle=\begin{cases}21.87&[m_{5\sigma}<24.5],\\\
0.82m_{5\sigma}+1.70&[m_{5\sigma}>24.5],\end{cases}$ (8)

for Sérsic index. They are also shown as solid and dashed lines, respectively,
in Figure 10. These limits can be useful for future planned observations using
DASH. If a survey with an expected imaging depth needs robust morphologies for
galaxies of a certain magnitude, these magnitude limits can be used as checks
to ensure this is feasible.

Table 2: Summary of Morphological Catalog Contents Column No. |  Column Title |  Description
---|---|---
1 |  ID |  Object identifier from UVISTA catalogs of Muzzin et al. (2013b)
2,3 |  RA,DEC |  Right ascension and declination (J2000; decimal degrees)
4 |  flag |  GALFIT flags (see Sec. 3.1); 0=good, 1=suspicious, 2=bad, 3=failed, 4=no coverage
5 |  use |  General use flag (see Sec. 4); 1=GALFIT flag<2, $r_{e}>$FWHM
6 |  mag |  GALFIT best-fit magnitude
7 |  dmag |  Uncertainty in GALFIT magnitude (see Sec. 3.5)
8 |  re |  GALFIT best-fit effective (half-light) radius in arcsec
9 |  dre |  Uncertainty in GALFIT effective radius in arcsec
10 |  n |  GALFIT best-fit Sérsic index
11 |  dn |  Uncertainty in GALFIT Sérsic index
12 |  q |  GALFIT best-fit axis ratio
13 |  dq |  Uncertainty in GALFIT axis ratio
14 |  pa |  GALFIT best-fit position angle
15 |  dpa |  Uncertainty in GALFIT position angle
16 |  kron |  Kron radius from SExtractor in arcsec
17 |  f_F160W_auto |  F160W AUTO flux (SExtractor measured flux within Kron radius); zeropoint=25
18 |  e_F160W_auto |  Error in F160W AUTO flux; zeropoint=25
19 |  f_F160W_tot |  F160W total flux (scaled from AUTO flux); zeropoint=25
20 |  e_F160W_tot |  Error in F160W total flux (scaled from AUTO flux error); zeropoint=25
21 |  snr |  Total signal-to-noise ratio (f_F160W_tot/e_F160W_tot)
22,23 |  flag_limit_r, flag_limit_n |  Parameter robustness flags (see Sec. 4); 0=not robust, 1=robust
24 |  flag_deb |  Deblending flag (see Sec. 2.2); 0=not blended, 1=deblended, 2=blended, 4=no coverage
25 |  Mcorr |  Mass correction for deblended galaxies (see Sec.2.2)
26 |  5_sigma_depth |  Total $5\sigma$ depth measured from COSMOS-DASH mosaic (see Sec. 3.6)
27 |  chi |  GALFIT chi-squared
28 |  chi_nu |  GALFIT chi-squared per degree of freedom

##  4 Morphological Catalog

This paper is accompanied by the public release of the COSMOS-DASH
morphological catalog, available at MAST as a High Level Science Product via
10.17909/T96Q5M (catalog 10.17909/T96Q5M). Of the 262,615 objects identified
in the UVISTA catalogs of Muzzin et al. (2013b), 51,586 have coverage with the
COSMOS-DASH F160W observations. The catalog contains object IDs from Muzzin et
al. (2013b). Best-fit GALFIT parameters and errors from this study are also
given in the catalog, when available, as well as photometric fluxes and errors
measured in Section 3.3 and $5\sigma$ depths measured in Section 3.6. The
catalog fluxes can be converted into total magnitudes using a photometric
zeropoint of 25. The information included in the catalog for each object is
listed and described in Table 2.

The catalog contains 4 types of flags. The first flag is the modified GALFIT
flag (flag) from van der Wel et al. (2012), described in Section 3.1. We also
include a general use flag (use) with values of 1 for “good” and 0 for “bad”.
An object is given a flag of 1 if it has a GALFIT flag $\leq 1$ (i.e. “good”
or “suspicious” fits) and the effective radius is greater than the PSF FWHM.
Otherwise it is flagged with a 0. The third type of flag is a “parameter
robustness limit” flag (flag_limit_r, flag_limit_n). There are two of these
flags, one for radius and one for Sérsic index. A galaxy is given a radius
robustness flag of 0 if its GALFIT magnitude exceeds (i.e. is fainter than)
the radius magnitude limit inferred by its $5\sigma$ depth using Eq. 7 (see
Fig. 10). Similarly, a Sérsic index flag of 0 is assigned by comparing the
GALFIT magnitude to the limit from Eq. 8. Otherwise, these flags are 1. These
flags indicates whether or not an object’s effective radius or Sérsic index
can be robustly measured given its magnitude and $5\sigma$ depth. The last
type of flag is the deblending flag (flag_deb), described in Section 2.2.

A standard selection is obtainable with use=1, though more stringent cuts on
the GALFIT flag (flag=0), SNR cuts, and use of the parameter robustness flags
(flag_limit_r, flag_limit_n=0) may be desirable. It is recommended that only
non-blended galaxies (flag_deb=0) are used when pairing COSMOS-DASH
morphologies with rest-frame colors from UVISTA, as corrections for blended
galaxy colors are not included in the catalog. Blending is most significant at
high redshifts and for the most massive galaxies (e.g.
$\log(M/M_{\odot})>11$). Blended galaxies may have contaminated colors,
stellar masses, and/or photometric redshifts, as these quantities are measured
from the ground. We recommend that any sample using high mass galaxies,
especially at high redshifts, exclude galaxies that are blended.

##  5 Quantifying the Utility of DASH Imaging

Owing to the moderately shallow depth of DASH imaging relative to traditional
HST imaging, we expect the structural fidelity to diminish for fainter and/or
lower stellar mass objects. To probe the parameter space where COSMOS-DASH
morphologies are robust, as well as the overall utility of DASH observations,
we make direct comparisons to a combined sample of morphologies from other
studies. This sample is made up of independent size measurements of galaxies
in both the COSMOS-DASH and CANDELS imaging. The bulk of this sample is
comprised of a mass-limited galaxy sample selected from all five fields of the
CANDELS survey (Koekemoer et al., 2011), adopting measurements from the 3D-HST
morphological catalogs (van der Wel et al., 2014, hereafter referred to as
vdW14). This is augmented by morphologies from COSMOS-DASH imaging for ultra-
massive galaxies555This high mass sample is available at
https://archive.stsci.edu/hlsp/cosmos-dash ($\log(M_{\star}/M_{\odot})>11.3$;
Mowla et al., 2019b, hereafter referred to as M19). In the M19 sample, COSMOS-
DASH morphologies are only measured at $z>1.5$, resulting in a sample size of
203 galaxies. 18 of the galaxies in this sample are split into pairs, and 14
of those remain above the $\log(M_{\star}/M_{\odot})>11.3$ cut. Stellar
masses, redshifts, and rest-frame $U-V$ and $V-J$ colors are taken from the
UVISTA and are assigned to COSMOS-DASH galaxies based on matching UVISTA ID.
In order to maintain consistency between the stellar masses from 3D-HST and
the sample from Mowla et al. (2019b), we adopt a $+0.1\,$ dex correction to
the UVISTA masses (see appendix B.1 in Mowla et al., 2019b). However, further
stellar mass corrections done in Mowla et al. (2019b) may contribute to
differing numbers of high-mass galaxies in the COSMOS-DASH measurements of M19
and the COSMOS-DASH morphological catalog. Moreover, we remove $\sim 2\%$ of
the ultra-massive COSMOS-DASH galaxies due to deblending flags.

Figure 11: Evolution of quiescent (red) and star-forming (blue) galaxy size
with redshift using morphologies from COSMOS-DASH is consistent with size-
evolution trends from other studies. Galaxies are separated into mass bins
(indicated in the top right of each panel). The distribution of quiescent and
star-forming galaxies are shown with colored kernel density estimate contours.
The running mean and median for both galaxy types are shown with solid and
open points, respectively, and the size of the running mean/median points in
each bin varies to reflect the fraction of DASH galaxies in that redshift-mass
bin that have a GALFIT flag of 0 or 1 (see Sect. 3.1). Error bars are
determined by the standard error of the mean within each redshift bin. The
running means are fit with power laws, see Eq. 10, and the corresponding best
fit line is shown as a dotted blue or dashed red line for star-forming and
quiescent populations, respectively. The same fits are made to the combined
sample of galaxies from 3D-HST (van der Wel et al., 2014) (vdW14) and massive
($\log(M_{\star}/M_{\odot})>11.3$) COSMOS-DASH morphologies (Mowla et al.,
2019b) (M19). These are shown with black dotted and dashed lines for star-
forming and quiescent galaxies, respectively. The number of star-forming (in
blue) and quiescent (in red) galaxies in each mass bin in the combined sample
and COSMOS-DASH (C-D) are listed in the upper right of each panel. Note that
vdw14/M19 includes both COSMOS-DASH (at $z>1.5$) and 3D-HST morphologies for
the highest mass bin whereas we consider COSMOS-DASH alone. This therefore
explains the lower number of galaxies in our analysis.

###  5.1 Size-Evolution

Figure 11 compares the size-redshift evolution relations determined from the
COSMOS-DASH morphological catalog to the combined vdW14/M19 sample. Galaxies
are separated into star-forming and quiescent classifications using rest-frame
$U-V$ and $V-J$ colors. Quiescent galaxies are defined using a modified,
redshift-independent version of the Whitaker et al. (2012) rest-frame color
separation (van der Wel et al., 2014; Whitaker et al., 2015), given by

$\displaystyle U-V~{}$ $\displaystyle>~{}1.3\text{ \hskip 5.69046pt and \hskip
5.69046pt }U-V~{}>~{}0.8~{}(V-J)~{}+~{}0.7.$ (9)

We limit the galaxies in the sample to those with GALFIT flags $\leq 1$ (see
Sec. 3.1). In Figure 11, we separate the data into four mass bins and measure
the mean (solid points) and median (open points) size evolution of quiescent
(red) and star forming (blue) galaxies in. Errors in the mean galaxy size are
computed using the standard error of the mean (SEM).

In each redshift bin we also keep track of the ratio of “good” or “suspicious”
fits (flag=0 or 1) to the total number of covered galaxies (flag$\leq 3$).
This is indicated by the size of each running mean/median point: small points
have a fraction $<0.5$, medium points have a fraction between 0.5 and 0.75,
and large points have a ratio greater than 0.75. This measurement acts as a
proxy for the completeness of the bin. A higher fraction of galaxies with
“usable” morphologies implies the mean size of that bin better conveys the
true average size, while the average size of bins with a lower fraction should
be treated with caution. Moreover, we only include redshift bins that have 10
or more galaxies in them, so a sufficient sample size is established. The size
evolution with redshift is parameterized with a power law relation (van der
Wel et al., 2014; Mowla et al., 2019b), given by

$\displaystyle r_{e}=B_{z}~{}\times~{}(1+z)^{-\beta_{z}}.$ (10)

This power law is fit to the running mean quiescent and star-forming galaxy
size and is shown as the dashed red and dotted blue lines in Figure 11,
respectively.

We compare these power law fits to similar fits to the vdW14/M19 sample. van
der Wel et al. (2014) and Mowla et al. (2019b) use morphological K-corrections
to determine “rest-frame” sizes, utilizing F125W and F814W below $z=1.5$,
respectively, and F160W above (see Appendix B.2 in Mowla et al., 2019b). Our
COSMOS-DASH morphological catalog only contains F160W sizes666Though F814W
data exists in the COSMOS-DASH area, adding this data is outside of the scope
of this particular work, which trace rest-frame wavelengths redward of the
Balmer break for the full redshift range (ranging from 4,000Å at $z=3$ to
16,000Å at $z=0$). To mitigate concerns with K-corrections, we compare
observed sizes (without K-corrections) between COSMOS-DASH and vdW14/M19. The
vdW14/M19 sample is refit in order to account for these uncorrected sizes.
Using rest-frame $U-V$ and $V-J$ colors from the 3D-HST catalogs (Brammer et
al., 2012; Momcheva et al., 2016) and the UltraVISTA catalog (Muzzin et al.,
2013b), we separate galaxies into star-forming and quiescent selections. The
3D-HST sample is limited to objects with GALFIT flags $\leq 1$ (Sec. 3.1) from
the 3D-HST catalogs. The mean size for each mass and redshift bin is then
computed and Eq. 10 is fit to the running mean size for both quiescent and
star-forming galaxies, shown with dashed and dotted black lines in Figure 11,
respectively. The number of galaxies used to measure the size-evolution of
quiescent and star-forming galaxies for each mass bin and each data set is
also indicated in each panel of Figure 11.

Table 3: Best fit star-forming and quiescent size-evolution relations for both COSMOS-DASH and the vdW14/M19 sample, shown in Figure 11. Relations are given by Eq. 10, as described in Section 5.1. $\log(M/M_{\odot})$ | Star-forming
---|---
COSMOS-DASH | vdW14/M19
$B_{z}$ | $\beta_{z}$ | $B_{z}$ | $\beta_{z}$
9.8-10.3 | 3.96$\pm$0.41 | 0.29$\pm$0.14 | 4.60$\pm$0.43 | 0.54$\pm$0.10
10.3-10.8 | 5.22$\pm$0.36 | 0.47$\pm$0.09 | 4.71$\pm$0.35 | 0.34$\pm$0.08
10.8-11.3 | 7.75$\pm$0.40 | 0.71$\pm$0.07 | 7.90$\pm$0.41 | 0.68$\pm$0.06
$>$11.3 | 10.66$\pm$1.40 | 0.68$\pm$0.13 | 10.53$\pm$1.49 | 0.64$\pm$0.14
$\log(M/M_{\odot})$ | Quiescent
COSMOS-DASH | vdW14/M19
$B_{z}$ | $\beta_{z}$ | $B_{z}$ | $\beta_{z}$
9.8-10.3 | 1.79$\pm$0.03 | 0.37$\pm$0.03 | 1.74$\pm$0.21 | 0.40$\pm$0.19
10.3-10.8 | 3.12$\pm$0.19 | 0.84$\pm$0.09 | 3.22$\pm$0.21 | 1.08$\pm$0.09
10.8-11.3 | 5.78$\pm$0.51 | 1.06$\pm$0.12 | 6.44$\pm$1.02 | 1.21$\pm$0.20
$>$11.3 | 10.42$\pm$1.78 | 1.00$\pm$0.25 | 9.53$\pm$2.00 | 0.83$\pm$0.24

In general, the size evolution measured from COSMOS-DASH is remarkably
consistent with that from M19, despite that sample being supplemented with
deeper data from 3D-HST/CANDELS and COSMOS ACS. This is especially true for
star-forming galaxies (see Table 3). We note one regime where the average
relations deviate by $\sim 3\sigma$ in $\beta_{z}$: intermediate mass
quiescent galaxies (i.e. $10.2<\log(M_{\star}/M_{\odot})<10.8$). Whereas the
vdW14 measurements are based on all five deep CANDELS fields in this stellar
mass regime, the COSMOS-DASH data covers a significantly shallower but wider
area on-sky for the single COSMOS field. The M19 sample uses COSMOS-DASH data
in the most massive bin only, whereas we extend the analysis here to
significantly lower stellar masses to test the limits of this data. Within
this $10.2<\log(M_{\star}/M_{\odot})<10.8$ quiescent sample, which shows a
slightly higher average size evolution at $0.8<z<2$, we also find a higher
quiescent fraction. The large, contiguous coverage of the COSMOS-DASH survey,
as well as known overdensities within the COSMOS field (e.g., Spitler et al.,
2012; Chiang et al., 2014) may account for these larger quiescent fractions
found in the COSMOS-DASH sample. Overall, despite some limitations, DASH data
is sufficient for recovering these relations down to significantly lower
stellar mass limits than previously explored when compared to standard HST
observations like 3D-HST.

Figure 12: The size-mass relations for star-forming (top row) and quiescent
(bottom row) galaxies show COSMOS-DASH sizes are robust for much of the
available parameter space. Each column shows galaxies separated into one of
three redshift bins: $0<z<1$ (left), $1<z<2$ (center), and $2<z<3$ (right).
The underlying distribution of star-forming and quiescent galaxies is shown
with contours. Size-mass relations from Nedkova et al. (2021) are included for
comparison (dotted lines) alongside re-fit size-mass relations (to avoid
K-corrections) to 3D-HST morphologies (van der Wel et al., 2014). Mass-radius
bins are defined by boxes whose colors identify the fraction of galaxies in
the bin with fractional size errors less than 20% ($\delta r_{e}/r_{e}<0.2$).
Green squares represent a fraction greater than 80%, yellow show a fraction
between 50% and 80%, and red indicate a fraction less than 50%, as shown in
the legend in the top right of the right panel. Dashed borders around these
boxes indicate a significant fraction of galaxies in that bin have an
effective radius less than the PSF FWHM (0.2″). The color of the dashed border
conveys the fraction of galaxies in that bin with $r_{e}>$FWHM: red if the
fraction is less than 0.5 and yellow if it is between 0.5 and 0.8.

###  5.2 The Size-Mass Relation

Another useful test of COSMOS-DASH is examining where in size-mass space DASH
morphologies are robust via the fraction of galaxies with low uncertainty
($\delta r_{e}/r_{e}<20\%$). Figure 12 shows the size-mass relation, limiting
our sample to non-blended objects (flag_deb=0) with GALFIT flags $\leq 1$.
Using Eq. 9 we classify galaxies in the sample as star-forming and quiescent.
Sources are separated into 3 redshift bins and the mean quiescent and star-
forming size is measured. Median sizes are only shown in Figure 12 if there
are more than 10 objects in the mass bin and $\geq 80\%$ of the galaxies in
the bin have robust size measurements (flag_limit_r=0). Requiring a majority
of robust sizes ensures bins with magnitudes fainter than the magnitude limits
inferred from Eq. 7 on average are excluded and removes an already known
sample of sizes potentially dominated by uncertainties.

We investigate the robustness of galaxy structural parameters in 0.5 dex size
and stellar mass bins, ranging from $\sim 0.3$ to 100 kpc and
$9\leq\log(M_{\star}/M_{\odot})\leq 12$, respectively. For each region in
size-stellar mass parameter space with more than 10 objects, the fraction of
galaxies with $(\delta r_{e}/r_{e})<0.2$ is computed. Regions are then ranked:
fractions greater than 0.8 are “usable” and the regions are shaded green in
Figure 12, between 0.5 and 0.8 are labeled “problematic” and shaded yellow,
and below 0.5 are “unsuitable” and shaded red. Some galaxies with $(\delta
r_{e}/r_{e})<0.2$ may still not have robust morphologies if the effective
radius is smaller than the PSF FWHM (0.2″). To account for PSF limitations, we
also compute the fraction of galaxies in each region with $r_{e}$[″]$<$FWHM.
This fraction is reflected in the border of the region. Fractions greater than
0.8 have a solid border the same color as the shaded region, while fractions
between 0.5 and 0.8 and less than 0.5 have yellow and red dashed borders,
respectively.

For low redshift galaxies, most of the size-mass parameter space explored is
usable, with the exception of very large, low mass galaxies, which are likely
nonphysical. These galaxies (as well as intermediate redshift galaxies in a
similar parameter space) are likely very faint or noisy, which GALFIT is
unable to distinguish from the sky background itself, even after background
fitting. The resulting fits attempt to model this, leading to unfeasibly large
sizes. For galaxies smaller than 1 kpc the PSF FWHM becomes an issue as well.
This is expected, as lower redshift ($z<1$) galaxies, even low mass galaxies,
are usually bright and as such are not limited by the depth of DASH
observations. At intermediate redshifts $1<z<2$, the usable parameter space is
similar to low redshifts, though the FWHM becomes more of an issue owing to
the smaller angular sizes. At high redshifts ($z>2$), most of the low mass
parameter space becomes problematic and only galaxies with the highest masses
yield robust structural parameters. This is likely due to the fact that higher
redshift galaxies are fainter (due to distance), causing the shallower DASH
depth to become a limiting factor. In general, large, low mass galaxies are
unreliable due to GALFIT failing to establish a reasonable fit, while the
uncertainty in low mass, high redshift galaxies is due to shallower imaging as
a result of the DASH observation technique. Overall, much of the size-mass
parameter space remains usable with DASH, with most issues showing up at
$z>2$.

At all redshifts where galaxies are detectable, DASH imaging complements
deeper, smaller area surveys. Due to the shape of the mass function, there are
fewer massive galaxies in a given area relative to fainter, lower mass
galaxies. Since a large sample of lower mass galaxies is obtainable with
deeper, narrow field imaging, standard HST observations are suitable, whereas
DASH observations may struggle. Likewise, a large sample of massive galaxies
requires a larger area survey, though the depth of standard observations is
not required, so DASH observations are better suited. This is utilized in
Mowla et al. (2019b), where a combined sample of galaxies with a large mass
range is assembled using CANDELS/3D-HST morphologies for lower masses
($\log(M_{\star}/M_{\odot})<11.3$) and COSMOS-DASH morphologies for high mass
galaxies.

Our analysis of the robustness of structural parameter from COSMOS-DASH
suggest that the DASH morphological catalog can be used for lower stellar
masses than previously explored in the literature. Mowla et al. (2019b)
restrict the selection of COSMOS-DASH galaxies to
$\log(M_{\star}/M_{\odot})>11.3$ with morphologies from deeper CANDELS/3D-HST
catalogs used for lower masses, however our results imply morphologies from
COSMOS-DASH, and presumably DASH observations in general, are usable to even
$\log(M_{\star}/M_{\odot})\sim 9$ for $z<1$.

We also examine the size-mass relation resulting for both quiescent and star-
forming galaxies in each redshift range. For star-forming galaxies we
parameterize this equation with a single power law, given by

$\displaystyle r_{e}~{}[\text{kpc}]=A~{}\times~{}m_{\star}^{\alpha},$ (11)

where $m_{\star}\equiv M_{\star}/7\times 10^{10}~{}M_{\odot}$ (van der Wel et
al., 2014; Mowla et al., 2019b). We then fit Eq. 11 to the median star-forming
sizes and show the best fit lines with dashed lines (Fig. 12). The best fit
parameters for Eq. 11 are listed in the top of Table 4. The behavior of
COSMOS-DASH quiescent galaxy sizes at $z<2$ is better described by a broken
power law, given by

$\displaystyle r_{e}~{}[\text{kpc}]$
$\displaystyle=\begin{cases}A~{}\times~{}m_{\star}^{\alpha_{1}}&M_{\star}\leq
M_{p}\\\ A\times
m_{p}^{(\alpha_{1}-\alpha_{2})}~{}\times~{}m_{\star}^{\alpha_{2}}&M_{\star}>M_{p},\end{cases}$
(12)

where $m_{\star}$ is the same as in Eq. 11, $M_{p}$ is the pivot mass in solar
masses, and $m_{p}\equiv M_{p}/7\times 10^{10}~{}M_{\odot}$. We fit this
relation to the median quiescent galaxy sizes for the two bins with $z<2$. Due
to a lack of low mass galaxies in the high redshift bin ($z>2$) no fit is
made. The best fit relations from Eq. 12 are shown with dashed lines in each
panel of Figure 12 and the best fit parameters are given in the bottom of
Table 4.

For comparison, we also fit Eq. 11 and 12 to the full sample of galaxies from
the 3D-HST morphological catalogs (van der Wel et al., 2014), again using
uncorrected sizes. These relations, as well as the size-mass relations from
Nedkova et al. (2021), are shown with dotted and dashed-dotted lines in Figure
12, respectively. In general, there is good agreement between star-forming
size-mass relations at all redshifts. Quiescent size-mass relations are also
in agreement at low masses, but the high-mass end shows noticeable deviations.
This is discussed in Mowla et al. (2019b), who compare size-mass relations
using high-mass COSMOS-DASH galaxies to those from van der Wel et al. (2014).
The larger sample of high-mass galaxies obtained with DASH observations may
provide a more accurate measurement of the size-mass relation in this mass
range, and thus explain the discrepancy. However, it may also to some degree
be due to contamination when identifying star-forming and quiescent galaxy
populations (as noted in Mowla et al., 2019b).

Table 4: Results from fits to star-forming and quiescent size-mass distributions given by Eq. 11 and 12, as described in Section 5.2 shown in Figure 12. z | Star-forming
---|---
| $A$ | $\alpha$ |
0-1 |  | 4.84$\pm$0.08 | 0.17$\pm$0.01 |
1-2 |  | 4.12$\pm$0.15 | 0.15$\pm$0.02 |
2-3 |  | 3.20$\pm$0.09 | 0.12$\pm$0.02 |
z | Quiescent
$A$ | $\alpha_{1}$ | $\alpha_{2}$ | $\log(M_{p}/M_{\odot})$
0-1 | 1.73$\pm$0.04 | 0.04$\pm$0.01 | 0.45 $\pm$ 0.02 | 10.37 $\pm$ 0.03
1-2 | 1.23$\pm$0.03 | -0.01$\pm$0.02 | 0.50 $\pm$ 0.01 | 10.50 $\pm$ 0.01
Figure 13: Quiescent galaxies of different mass have different structural
properties, as shown in the covariances of various parameters. The included
structural and environmental parameters are effective radius, Sérsic index,
axis ratio, $U-V$ and $V-J$ color, and galaxy field overdensity
($\delta=\Sigma/\Sigma_{\mathrm{median}}$). Low mass
($\log(M_{\star}/M_{\odot})<10$) and high mass
($\log(M_{\star}/M_{\odot})>11$) galaxies are shown with black and orange 1D
and 2D histograms, respectively. Dashed contours and 1D histograms indicate
intermediate mass galaxies ($10<\log(M_{\star}/M_{\odot})<11$). The number of
galaxies in each mass bin is shown in the legend.

The result of this broken power law relation is a flattening of the size-mass
relation for quiescent galaxies below $\sim 3\times 10^{10}~{}M_{\odot}$. This
behavior has been noted previously in the literature (e.g., Dutton et al.,
2011; Cappellari et al., 2013; Norris et al., 2014; Whitaker et al., 2017;
Nedkova et al., 2021). Broken power-law relations for all galaxies are also
found in Mowla et al. (2019a), with the pivot proposed to mark the transition
from star-formation to the dry merger dominated mode of growth for galaxies.
This earlier study also compares the size-mass relation to the stellar mass-
halo mass relation and finds comparable slopes and pivots between the two
relations. Further theoretical support of the flattening of the low-mass
quiescent size-mass relation is found in results of simulations (Shankar et
al., 2014; Furlong et al., 2017; Genel et al., 2018). This flattening is
likely to be physical and not a result of inaccurate size measurements for
small, low mass galaxies (e.g., van der Wel et al., 2014; Whitaker et al.,
2017). We perform a comparative analysis of quiescent galaxy sizes (observed
F160W frame) relative to the 3D-HST morphological catalog (van der Wel et al.,
2014), which yields a similar flattened size-mass relation at low stellar
masses.

(a)  Figure 14: The flattening of the size-mass relation for quiescent
galaxies at $z<1.2$ may disappear in galaxies with high Sérsic indices.
Galaxies are separated by axis ratio (top) and Sérsic index (bottom) into
approximately equal number quartiles indicated in each panel. Empty KDE
contours show the underlying distribution of sizes. For each quartile, running
medians are shown with solid points and error bars show the $1\sigma$ SEM.
Hexagonal bins indicate the average overdensity
($\delta=\Sigma/\Sigma_{\mathrm{median}}$) of points within the bin, as
indicated by the color bar.

A potential cause of this phenomenon could be the environment in which these
low mass galaxies are embedded. There are many ways to form and quench
galaxies, and likely different physical processes for cluster and field
galaxies (e.g., Peng et al., 2010b; Tal et al., 2014; van Dokkum et al., 2015;
Bluck et al., 2020; McNab et al., 2021). Thus, the morphologies of galaxies in
different environments could vary. Moreover, as galaxies evolve, their
morphologies may change as well (Dressler, 1980; Postman et al., 2005). For
example, dry mergers can significantly increase the size of quiescent galaxies
(Bezanson et al., 2009; Cappellari, 2013), while gas-rich mergers or violent
disk instabilities are proposed physical drivers reducing the effective radius
of compact star-forming galaxies (Barro et al., 2013). We explore the role of
environment on quiescent galaxy size in the next section.

###  5.3 Environmental Effects

To investigate the environmental dependence of the flattening of the quiescent
size-mass relation, COSMOS-DASH galaxies with $z<1.2$ and GALFIT flags $\leq
1$ are matched within a 0.5″ radius to the publicly available COSMOS density
field catalog (Darvish et al., 2015, 2017). Since redshift precision is
important in determining the galactic density field, we cross match first
spatially (using RA and Dec) and then with photometric redshift, discarding
galaxies that exhibit a redshift difference of $\Delta z>0.1$ between the two
catalogs. This second check removes $\sim 5\%$ of galaxies that are cross
matched by RA and Dec alone. We then examine the correlation between a number
of structural and environmental parameters available for this sample of
quiescent galaxies. The parameters used are the size, Sérsic index, axis
ratio, $U-V$ and $V-J$ color, and the overdensity
($\delta=\Sigma/\Sigma_{\mathrm{median}}$). These correlations are examined
for three mass bins: low mass ($\log(M/M_{\odot})<10$), intermediate mass
($10<\log(M/M_{\odot})<11$), and high mass ($\log(M/M_{\odot})>11$), indicated
with solid black histograms, dashed black histograms/contours, and orange
histograms, respectively, in Figure 13.

Figure 13 highlights different structural parameter distributions (size,
Sérsic index, and axis ratio) for low- and high-mass quiescent galaxies. Lower
mass galaxies preferentially have smaller sizes overall, as expected, though
these sizes are also similar to intermediate-mass galaxies. This reinforces a
flattening of the size-mass relation at low masses. We also find low-mass
quiescent galaxies have morphologies similar to star-forming galaxies (smaller
Sérsic index and axis ratio), while their high-mass counterparts are more
elliptical in nature (larger Sérsic index and axis ratio). In general, the
distribution of overdensity should be centered around $\delta=1$, since
overdensity is defined relative to the median density at a given redshift.
However, the distribution of overdensities for low- and high-mass galaxies are
skewed, with low-mass quiescent galaxies being more abundant in field
($\delta\lesssim 1$) environments and high-mass galaxies being more abundant
in cluster ($\delta\gtrsim 3$) environments.

One explanation for the deficit of low mass quiescent galaxies in the highest
overdensities could be the preferential destruction of satellite galaxies in
clusters via tidal interactions and/or mergers with other cluster galaxies.
Matharu et al. (2019) found that a significant fraction of compact quiescent
cluster galaxies must be destroyed in order to maintain the observed
consistency between field and cluster size-mass relations (see also, e.g.,
Weinmann et al., 2009; Maltby et al., 2010; Cebrián & Trujillo, 2014). We
separate our sample of quiescent galaxies into quartiles of increasing axis
ratio (top) and Sérsic index (bottom) and show the resulting size-mass
relations in Figure 14.

A flattening in the size-mass relation of quiescent galaxies is observed for
all Sérsic index bins except for the most centrally concentrated galaxies. The
size-mass relation for quiescent galaxies with $4<n<6$ results because the
lowest mass galaxies are slightly more compact, while galaxies close to the
pivot mass are slightly larger on average, thereby returning the relation to a
power-law. Interestingly, the flattening is still present in the 50% galaxies
with high axis ratios ($q>0.62$). This is driven by face-on disky galaxies,
which dominate the low-mass quiescent population: when removing galaxies with
$n<2.5$ from the axis ratio analysis, the flattening disappears for $q>0.62$.
Quiescent galaxies with lower Sérsic indices ($n<2.5$) have been measured with
a wide range axis ratios, as well as a roughly even distribution over this
range (see Fig. 3 in Chang et al., 2013). Thus, it is feasible that this
sample contains a significant amount of high axis ratio, low Sérsic index
galaxies. These face-on disky galaxies will have comparable axis ratios to
centrally concentrated galaxies ($n>2.5$), but are noticeably larger in size.
Likewise, when galaxies with $n>2.5$ are removed, the flattening becomes
significantly stronger. With the mean overdensity of the galaxies shown within
hexagonal bins, we also find that these higher Sérsic index galaxies inhabit
denser environments on average. We note that separating the sample into finer
redshift bins does not change the general results of this analysis.

Figure 15: The constant evolution of low ($\log(M/M_{\odot})<10$),
intermediate ($10<\log(M/M_{\odot})<11$), and high ($\log(M/M_{\odot})>11$)
mass galaxy properties with density suggests environmental effects aren’t a
dominant mechanism behind the flattening of the quiescent size-mass relation.
The three mass regimes are represented with solid black, dashed black, and
solid orange lines, respectively. The left panel shows the change in quiescent
fraction for each mass bin. The other panels show the change in size (middle
column) and Sérsic index (right column) for both quiescent (top row) and star-
forming galaxies (bottom row). The total distributions of quiescent and star-
forming sizes and Sérsic indices are shown with shaded contours.

The over-representation of high Sérsic index galaxies in the densest
environments (Figure 13), as well as the existence of compact, centrally
concentrated quiescent galaxies in clusters (e.g., right panel in Figure 14;
see also Matharu et al., 2019), may result if disky quiescent galaxies are
either preferentially destroyed via mergers or prevented from maintaining a
stable disk due to tidal interactions.

Since cluster galaxies do not exhibit a significant increase in size due to
minor mergers (Matharu et al., 2019), compact cluster galaxies that are not
destroyed would retain their smaller sizes. Together, this could explain the
disappearance of the flattening at the highest Sérsic indices; compact
elliptical quiescent galaxies are less likely to be destroyed in clusters, and
the dynamics of the cluster effectively “freeze” their sizes, leading to a
single power law quiescent size-mass relation.

However, the preferential destruction of diskier quiescent galaxies in dense
environments should also manifest with increasing Sérsic index with density.
Likewise, if the larger low Sérsic index galaxies are destroyed in the dense
environments, we would expect that low-mass sizes decrease with increasing
density. We see no evidence for such a trend in Figure 15, which shows the
dependence of quiescent fraction (left), size (middle) and Sérsic index
(right) on overdensity. For the lowest mass bin (black solid line), the
quiescent fraction remains relatively constant with overdensity, suggesting
that the environment does not play a significant role in the quenching of the
least massive galaxies. Moreover, both the size and Sérsic index of similar
mass quiescent (top) and star-forming galaxies (bottom) is constant with
density for all mass bins. These results imply environment is not the dominant
effect producing the flattening of the quiescent size-mass relation at low
masses. Though environmental effects may still be significant for some
galaxies, universally other processes must drive this behavior. This agrees
with the results of Huertas-Company et al. (2013), who find that the size-mass
relation of massive ($\log(M_{\star}/M_{\odot})>10.5$) early type galaxies has
no significant dependence on environment at $z<0.09$ (see also, Maltby et al.,
2010; Fernández Lorenzo et al., 2013; Shankar et al., 2014).

If environment is not driving the flattening, it may instead be related to in
situ physical processes. Studies have shown that the flattening of the size-
mass relation is correlated with growth due to star formation, whereas high
mass growth is thought to be merger driven (e.g., van Dokkum et al., 2015;
Mowla et al., 2019a). This sets up a narrative where internal processes
dominate at lower mass scales whereas extrinsic factors dominate the evolution
of the most massive galaxies. The resulting size-mass relation for quiescent
galaxies could thus be explained by quenching of low-mass galaxies via the
depletion of gas reservoirs, with no replenishment. Another alternative is
that this gas is instead stabilized due to the formation of a bulge and
thereby inefficient at forming new generations of stars (e.g., Martig et al.,
2009), under the assumption that a Sérsic index of 2 corresponds to a bulge
that is sufficiently large. In both instances, the quenching process occurs
without mergers, so galaxies remain in a similar location in size-mass
parameter space and the shallower slope of the star-forming size-mass relation
is retained. While we cannot discern the physical process responsible for this
flattening in the quiescent sample within the data set at hand, we can rule
out environment as the primary driving factor.

##  6 Summary

We present a public release of the morphological catalog for the COSMOS-DASH
survey obtained with 2D-Sérsic fits using GALFIT (Peng et al., 2002, 2010a)
for 51,586 galaxies. Using a combination of bootstrapping with GALFIT and
comparing morphologies of galaxy analog populations, we obtain parameter
errors consistent with those from the CANDELS/3D-HST morphological catalog
(van der Wel et al., 2012, 2014). We analyze the various limits and parameter
space for which these structural measurements and their errors are robust. The
wider area, albeit shallower, imaging attainable with DASH is useful for
observing a significant sample of high mass, bright galaxies, which are less
common in a given area of the sky. This allows DASH observations to work in
tandem with standard HST observations: the deeper, standard imaging can obtain
significant samples of low-mass, faint sources while wider area DASH
observations obtain a sample of high mass galaxies.

However, DASH observations are also capable of producing results for a wide
range of galaxy masses and sizes, as shown in Figure 12. Analysis of the
limits of COSMOS-DASH morphologies suggests sizes and Sérsic indices are
usable to a limiting magnitude of roughly 23 and 22 ABmag for the shallowest
DASH observations, respectively. We find DASH sizes at $z<2$ are usable for
$\log(M_{\star}/M_{\odot})>9$ and at higher redshifts for
$\log(M_{\star}/M_{\odot})>10.5$. Our analysis also indicates that large,
unphysical sizes are mainly due to issues with GALFIT, while unusable sizes at
higher redshifts are primarily driven by the shallower depth of the COSMOS-
DASH survey due to the DASH technique. Overall, the shallower depth and
complex data reduction of DASH observations does not prevent high fidelity
measurements of galaxy morphology using DASH data.

With the COSMOS-DASH morphological catalog, we observe a flattening of the
size-mass relation for quiescent galaxies at low masses
($\log(M_{\star}/M_{\odot})<10.5$), similar to existing results from
observations (e.g., Cappellari et al., 2013; Norris et al., 2014; Lange et
al., 2015; Whitaker et al., 2017; Nedkova et al., 2021) and simulations (e.g.,
Shankar et al., 2014; Furlong et al., 2017). Combining COSMOS-DASH
morphologies with galaxy density field measurements (Darvish et al., 2015,
2017), we investigate the dependence of this low mass flattening on
environment. Correlations between structural and environmental parameters
suggest distinct morphological populations for low- and high-mass quiescent
galaxies, with low-mass galaxies having significantly smaller Sérsic indices
and axis ratios. Moreover, these correlations also indicate that these low-
mass quiescent galaxies are more prevalent in underdense environments,
relative to their high-mass counterparts.

Analyzing the evolution of the quiescent size-mass relation with Sérsic index
and environment, we find a disappearance of the low-mass flattening for the
highest Sérsic index galaxies. These centrally concentrated objects are also
more likely to inhabit denser environments than their lower Sérsic index
counterparts. Results from other studies (e.g., Weinmann et al., 2009; Maltby
et al., 2010; Cebrián & Trujillo, 2014; van der Wel et al., 2014; Matharu et
al., 2019) imply the majority of satellite galaxies in clusters (dense
environments) must be destroyed by $z\sim 0$ to match observed size-mass
relations. Preferential destruction of compact low Sérsic index galaxies
through tidal interactions or mergers would lead to both an over-
representation of compact centrally concentrated galaxies in clusters, as well
as a disappearance in the size-mass flattening for high Sérsic index galaxies.
However, the average quiescent fractions, sizes, and Sérsic indices for both
quiescent and star-forming galaxies are all roughly constant with overdensity.
Taken together, this suggests that the main driver of the flattening of the
quiescent size-mass relation at low stellar masses is not environment (see
also Maltby et al., 2010; Huertas-Company et al., 2013; Fernández Lorenzo et
al., 2013; Shankar et al., 2014). Instead, internal physical processes are
likely the cause of the flattening, though exactly which processes are
responsible is outside the scope of this work.

This paper is based on observations made with the NASA/ESA HST, obtained at
the Space Telescope Science Institute, which is operated by the Association of
Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.
These observations are associated with program HST-GO-14114. Support for
GO-14114 is gratefully acknowledged. S.C. and K.W. wish to acknowledge funding
from the Alfred P. Sloan Foundation grant No. FG-2019-12514, HST-AR-15027, and
HST-GO-16259. MA acknowledges support by NASA under award No 80NSSC19K1418.
M.S. and K.W. acknowledge support under NASA grant No. 80NSSC20K0416. This
research made use of Montage. It is funded by the National Science Foundation
under grant No. ACI-1440620 and was previously funded by the National
Aeronautics and Space Administration’s Earth Science Technology Office,
Computation Technologies Project, under Cooperative Agreement No. NCC5-626
between NASA and the California Institute of Technology. The Cosmic Dawn
Center is funded by the Danish National Research Foundation under grant No.
140.

##  Appendix A Background Pedestal

Figure 16: Comparison of the DASH-only reduction of the calibration field
before (left) and after (right) background subtraction. The images have the
same scale limits, which highlights the slightly negative background in the
left panel. The inset histograms show the distribution of background pixels
(i.e., any pixel with a value of 0 in the segmentation map). A slight
background of $-0.0252$ cts/s is apparent in the histogram in the left panel.
This background is much smaller than the standard deviation in background
pixels ($0.1465$ cts/s) and is successfully subtracted in the right inset
histogram.

Previous studies have shown it is important to let GALFIT fit a constant sky
background as a free parameter (Häussler et al., 2007). In order to understand
the effects of allowing GALFIT to fit the background in more detail we conduct
a series of tests. First, estimates of the mean background in the total
COSMOS-DASH mosaic are made. Sources are excluded using a combination of the
segmentation map and sigma clipping. Bad pixels and empty regions are excluded
by removing pixels where the weight map is zero. Separate estimates are made
for the DASH and CANDELS regions of the mosaic using a second weight map
selection. Low weight pixels are attributed to DASH-obtained data and high
weight pixels to CANDELS. The estimated mean DASH background is $-0.0252\pm
0.1465$, while CANDELS is $0.0011\pm 0.0694$, indicating this DASH data has a
more significant background than CANDELS and more variation in the background.
This is likely due to the shallower depth of DASH observation caused by
shorter exposure times. The DASH background also does not vary significantly
as a function of the location in the image.

Figure 17: Comparison of the best fit GALFIT parameters of the 483 calibration
galaxies in the DASH-only reduction using two different methods to deal with
the background; the small scatter in the middle row implies that the
background should be treated as a free parameter in GALFIT. The top and middle
rows show the effective radii, Sérsic indices, and axis ratios of the best fit
Sérsic models determined with (top) and without (middle) fixed backgrounds,
respectively, compared to those from CANDELS/3DHST (van der Wel et al., 2014).
Transparent points are those with flag=2 parameter values (see Section 3.1).
The bottom row shows the difference in the parameters when measured both with
and without fitting background. The large black points are the running median
in each bin, with errorbars showing the scatter determined by the MAD of the
bin. The color scale indicates the $H_{160}$ magnitude of the source in AB
magnitudes. Points with black x’s are those that are greater than 0.3 dex from
the one-to-one line in radius. The grey shaded region shows radii less than
the PSF FWHM and points with black +’s are sources whose best fit radius falls
in this region. Text in the top and middle row indicates the median and
scatter in the offset between CANDELS/3D-HST parameters and parameters derived
using the two methods to deal with the background.

We perform a standard background subtraction on both the DASH- and CANDELS-
only calibration field reductions. Background meshes with bin sizes of 200,
400, 600, 800, 1000, and 1200 pixels are applied to both reductions and the
distribution of background fluxes are computed. The 1000 bin mesh is chosen,
as the background-subtracted image for this mesh has a mean background closest
to zero. A comparison of the DASH-only reduction before (left) and after
(right) background subtraction is shown in Figure 16. First, the GALFIT
pipeline is run on the 483 galaxies in the background-subtracted calibration
field with the GALFIT sky background fixed to zero. Comparing the resulting
best-fit effective radii and Sérsic indices to the CANDELS/3D-HST
morphological catalog (van der Wel et al., 2012) and high mass galaxies from
COSMOS-DASH (Mowla et al., 2019b), shows that both the radius and Sérsic
indices are roughly 0.1 and 0.2 dex smaller in DASH, respectively. We then run
GALFIT with sky background as a free parameter on the background-subtracted
calibration field, finding good agreement with CANDELS/3D-HST. The mean
GALFIT-determined sky background is $-0.0206\pm 0.0108$, despite measuring a
negligible background when the 1000 bin mesh background is subtracted (see
also Fig. 4, bottom). Similar negligible backgrounds are also measured with
the other subtractions. This suggests that this small background value is
leading to the significant difference in our measured morphologies.

To further characterize the background of the DASH-only reduction, we use the
empty apertures approach from Section 3.3 on the background subtracted image.
This is done in the DASH-only reduction of the calibration field, which allows
for direct comparison with CANDELS (see Fig. 17). Of interest to this section
is the change in the average background as indicated with the shift in the
peak of the distribution toward slightly negative values at larger aperture
sizes. An increased average background for larger apertures could indicate
that measuring the background with a smaller aperture size underestimates the
actual background level. However, Figure 4 (bottom) shows that the average
background per pixel is roughly (but not quite) constant with aperture size,
and is approximately zero. This behavior is also independent of the overall
bin size used to perform the background subtraction. A comparison with the
GALFIT background pedestal is also shown, consistent within $2\sigma$. A
potential cause of the discrepancy between the GALFIT and empty aperture
backgrounds could be that the empty apertures are not empty and contain faint
wings from galaxies (potentially due to inadequate masking).

Next, we investigate whether or not this GALFIT background is something that
GALFIT consistently measures from the data, or if GALFIT will only produce
reasonable fits if it is allowed to fit a constant sky background. To check
this, we run GALFIT twice on calibration field galaxies using the background
subtracted DASH-only reduction. In the first run, we allow GALFIT to fit the
background. In the second run, we remove the GALFIT-measured constant sky
background (see bottom panel of Fig. 4) from the data and fix the background
parameter to zero. In Figure 17, the radius, Sérsic index, and axis ratio of
these two fitting methods are compared to each other and the CANDELS/3D-HST
Sersic parameters (van der Wel et al., 2012, 2014). The top and middle rows of
Figure 17 compare the parameters from the run with a fixed and variable (fit
by GALFIT) background to the CANDELS/3D-HST morphological parameters, in a
similar layout to Figure 6. The bottom row compares the difference between the
parameters both with and without fixing the background relative to
measurements from CANDELS/3D-HST. All panels indicate no systematic offset,
both between the different methods to deal with background and between
CANDELS/3D-HST and our morphologies.

In general, both methods show consistency with the measured CANDELS/3D-HST
morphologies, suggesting that the small background value measured by GALFIT
(see bottom panel of Fig. 4) is the root cause of the offset we observed
prior. The largest scatter is in Sérsic index, as this parameter is the most
sensitive to the measure of the background. With an incorrect background
estimate, the combination of a low Sérsic index and faint background flux can
appear similar to a large Sérsic index with faint wings. The scatter in the
parameters is smaller for radius when we allow GALFIT to fit a background: the
fixed background approach has a 9% larger scatter in radius and a 20% larger
scatter in Sérsic index. Moreover, 12% of galaxies with the fixed background
are more than 0.3 dex from CANDELS/3D-HST, while only 8% with a variable
background deviate by this much. The median offset from CANDELS/3D-HST (Fig.
17, text in top and middle rows) also prefers a variable background. This
suggests it is preferable to allow GALFIT to deal with the background.
Similarly, Häussler et al. (2007) conclude that GALFIT performs significantly
better when allowed to internally measure a sky background, as opposed to
being provided a fixed background (e.g. from SExtractor in their case). Given
the smaller spread in morphological parameters and the findings of Häussler et
al. (2007), we therefore adopt the background fitting in GALFIT to ensure
consistent fits that aren’t biased by the choice of constant background
pedestal. Moreover, this analysis also shows that GALFIT consistently recovers
morphological parameters when fitting a background regardless of the initial
background subtraction. As such, we do not use a background subtracted version
of the full COSMOS-DASH mosaic when determining morphologies for the full
sample, since GALFIT needs to fit a background regardless of prior subtraction
and the background pedestal in the calibration field is roughly constant.

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