# MaNGA galaxy properties – I. An extensive optical, mid-infrared photometric,
and environmental catalogue

Nikhil Arora,1 Connor Stone,1 Stéphane Courteau1 and Thomas H. Jarrett2
1Department of Physics, Engineering Physics and Astronomy, Queen’s University,
Kingston, ON K7L 3N6, Canada
2Astronomy Department, University of Cape Town, Rondebosch 7701, South Africa
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We present an extensive catalogueue of non-parametric structural properties
derived from optical and mid-infrared imaging for 4585 galaxies from the MaNGA
survey. DESI and Wide-field Infrared Survey (WISE) imaging are used to extract
surface brightness profiles in the $g,r,z,{\it W1},W2$ photometric bands. Our
optical photometry takes advantage of the automated algorithm AUTOPROF and
probes surface brightnesses that typically reach below 29 ${{{{\rm mag}~{}{\rm
arcsec}}^{-2}}}$ in the $r$ band, while our WISE photometry achieves 28
${{{{\rm mag}~{}{\rm arcsec}}^{-2}}}$ in the ${\it W1}$ band. Neighbour
density measures and central/satellite classifications are also provided for a
large subsample of the MaNGA galaxies. Highlights of our analysis of galaxy
light profiles include (i) an extensive comparison of galaxian structural
properties that illustrates the robustness of non-parametric extraction of
light profiles over parametric methods; (ii) the ubiquity of bimodal
structural properties, suggesting the existence of galaxy families in multiple
dimensions; and (iii) an appreciation that structural properties measured
relative to total light, regardless of the fractional level, are uncertain. We
study galaxy scaling relations based on photometric parameters, and present
detailed comparisons with literature and theory. Salient features of this
analysis include the near-constancy of the slope and scatter of the
size–luminosity and size–stellar mass relations for late-type galaxies with
wavelength, and the saturation of the central surface density, measured within
1 kpc, for elliptical galaxies with $M_{*}>10.7\,M_{\odot}$ (corresponding to
$\Sigma_{1}\simeq 10^{10}\,M_{\odot}\,{\rm kpc}^{-2}$). The multiband
photometry, environmental parameters, and structural scaling relations
presented are useful constraints for stellar population and galaxy formation
models.

###### keywords:

galaxies: general – galaxies: photometry – galaxies: structure – techniques:
image processing – galaxies: fundamental parameters – galaxies: spiral –
galaxies: elliptical and lenticular

††pubyear: 2021††pagerange: MaNGA galaxy properties – I. An extensive optical,
mid-infrared photometric, and environmental catalogue–A

##  1 Introduction

A comprehensive picture of galaxy formation and evolution, as well as reliable
data-model comparisons, requires access to large homogeneous photometric and
spectroscopic samples of galaxies covering a broad range of morphologies,
stellar and dynamical masses, star formation histories, environmental
conditions, and more. Previously, such measurements have been extracted from
large imaging and spectroscopic wide-field surveys such as 2MASS (Jarrett et
al., 2000), SDSS (York et al., 2000), GAMA (Driver et al., 2009), and others.
More recently, large-scale acquisition of spatially resolved structural
properties of galaxies has been achieved with integral-field spectroscopy. The
latter is especially valuable in this context since it allows the synchronous
collection of global and spatially resolved chemical and dynamical properties
such as stellar mass surface density, age, metallicities, star formation
rates, circular velocity, velocity dispersion and more, across a broad
wavelength range. Pioneering integral-field spectroscopy surveys of galaxies
such as SAURON (Bacon et al., 2001), ATLAS3D (Cappellari et al., 2011), CALIFA
(Walcher et al., 2014), and SAMI (Allen et al., 2015), provide such
properties, although for relatively small samples.

With its spatially resolved optical spectroscopic data for ${\sim}10000$
nearby galaxies ($z{\sim}0.15$), the SDSS-IV survey “Mapping Nearby Galaxy at
Apache point observatory" (MaNGA; Bundy et al., 2015; Wake et al., 2017) has
heralded a new era of large-scale galaxy studies with integral field units
(IFUs)111While the MaNGA target sample includes $\sim$10,000 objects, 4585 of
them are publicly available at the time of writing.. MaNGA uses a 127-fiber
IFU to provide high-quality spatially resolved kinematic and chemical
information for galaxies by collecting spectra at each pixel out to a maximum
of 1.5/2.5 effective radii ($R_{\rm eff}$) for 85/15 percent of the MaNGA
sample (Cano-Díaz et al., 2016; Sánchez et al., 2016, 2018; Graham et al.,
2018; Méndez-Abreu et al., 2018). The MaNGA galaxies were selected from the
NSA 222NASA Sloan Atlas, Blanton et al. (2011) catalogue with no inclination
or size selection cuts. For more details about the MaNGA sample, see Bundy et
al. (2015) and Wake et al. (2017).

Large-scale IFU surveys, such as MaNGA and CALIFA (Walcher et al., 2014), open
an avenue for the exploration of spatially resolved counterparts to global
structural drivers and scaling relations in galaxies. For instance, the MaNGA
survey has already yielded new insights about evolutionary mechanisms such as
star formation quenching; finding it to be regulated on global galaxy scales
while star formation density is controlled locally (Bluck et al., 2020). Using
the Pipe3D (Sánchez et al., 2018) output for MaNGA, Sánchez-Menguiano et al.
(2020) have also explored the relation between the average stellar age and
gas-phase metallicity for star-forming systems. While this relation had been
observed globally (Lian et al., 2015), the spatially resolved nature of the
MaNGA data also revealed a local correlation.

In addition to the published spatially resolved spectroscopic MaNGA data, a
comprehensive understanding of MaNGA galaxies requires a full suite of
structural and environmental galaxy properties. A catalogue of model-dependent
MaNGA galaxy structural parameters (effective sizes, total magnitudes, Sérsic
indices, ellipticities, position angles) already exists (Fischer et al., 2019,
hereafter F19). The MaNGA PYMORPH Photometric Value Added Catalogue (MPP-VAC)
provides structural parameters for MaNGA galaxies extracted through Sérsic and
Sérsic+Exponential fits to 2D surface brightness profiles. However, model-
dependent assumptions about the light distribution of galaxies severely bias
and limit any investigations of galaxy structure and evolution, as shown
below. Providing galaxy structural parameters in non-parametric fashion is the
main goal of this study.

In this paper, we present an extensive compilation of model-independent
galaxian structural parameters based on optical and mid-infrared (MIR) imaging
of all MaNGA galaxies extracted respectively from the Dark Energy Sky
Instrument Legacy Imaging Survey (DESI Collaboration et al., 2016; Dey et al.,
2019)333In what follows, the acronym DESI is meant to represent the Dark
Energy Sky Instrument Legacy Imaging Survey. and Wide-field Infrared Survey
Explorer (WISE) surveys. The combination of optical and MIR bands is
especially sensitive to the evolved stellar population, sites of star
formation, and distribution of dust within galaxies. Broader multiband
coverage for MaNGA galaxies is also being developed elsewhere; major imaging
campaigns of MaNGA galaxies at radio (Masters et al., 2019) and ultraviolet
wavelengths (Molina et al., 2020) are either in place or in progress. These
will expand our understanding of MaNGA galaxies with clearer views of
processes such as star formation on small spatial/time scales and the
distribution of neutral hydrogen within galaxies, the fuel for star formation.

The surface brightness (surface brightness) profiles extracted from the DESI
and WISE imaging surveys for the MaNGA galaxies allow us to extract numerous
non-parametric structural properties representing various measures of galaxy
size, surface brightness, luminosity, stellar mass, and stellar mass surface
density. Along with the structural parameters for MaNGA galaxies,
environmental demographics are also provided below. Our compilation
supplements fifth nearest-neighbour density measurements for MaNGA galaxies
(see Argudo-Fernández et al., 2015; Etherington & Thomas, 2015, for details),
with important information about the gravitational dominance of a galaxy (i.e.
central and satellite designation) within its own halo. These considerations
motivate the assembly of a catalogue of environmental properties for a large
subsample of MaNGA galaxies, in addition to the photometric catalogues. The
environmental catalogue that we present below includes measures of neighbour
densities and classification of these galaxies as a central or satellite.

A natural outcome of such an extensive data compilation is the construction
and study of galaxy scaling relations. The slope, zero-point, and scatter of
such empirical scaling relations present evidence of the underlying physics
that dictates structure formation and evolution of galaxies (Mo et al., 1998;
Courteau et al., 2007; Dutton et al., 2007; Brook et al., 2012; Hall et al.,
2012; Lange et al., 2015). The MaNGA non-parametric data sets produced in this
study allow for an analysis of various galaxy scaling relations in different
photometric bands. Among others, the size–stellar mass ($R-M_{*}$) relation
and the stellar surface density ($\Sigma_{1}$ measured within 1 kpc) - stellar
mass relations ($\Sigma_{1}-M_{*}$) are presented. As discussed below, these
relations enable constraints of the gas accretion and merger history as well
as quenching and feedback models in galaxies (Chiosi & Carraro, 2002; Shen et
al., 2003; Franx et al., 2008; Saglia et al., 2010; Fang et al., 2013; Woo &
Ellison, 2019).

This paper is organized as follows: in Section 2, we describe the procedures
used to extract surface brightness profiles in optical and MIR bands. The
extraction and correction of non-parametric galaxy structural properties are
also discussed and presented in tabular format. The environmental catalogue is
presented in Section 2.2.5. With our catalogue in place, we provide in Section
3 a broad overview of the DESI and WISE parameters for our MaNGA Public
sample. Unimodal and bimodal structural distributions are also highlighted. In
Section 4, we compare our model-independent structural parameters for MaNGA
galaxies, such as size, apparent magnitude, and stellar mass, with literature
values. Our MIR photometry and derived structural properties are compared to
optical structural properties in Section 5. With our optical and MIR
photometry validated, we combine these data sets in Section 6 to infer
structural galaxy scaling relations of MaNGA galaxies with a focus on the
size–stellar mass, $R-M_{*}$, relation in Section 6.1, and the central surface
density–stellar mass, $\Sigma_{1}-M_{*}$, relation in Section 6.3. We conclude
in Section 7.

##  2 Light Profile Extraction

Our galaxy sample consists of 4585 galaxies from the public release of the
MaNGA survey. The full MaNGA galaxy survey will yield $\sim$10 000 objects
with a uniform distribution of stellar mass $M_{*}>10^{9}{\rm M_{\odot}}$,
with no inclination or size selections.

For our optical photometry, we have cross-correlated the public MaNGA data
release with the DESI 444https://www.legacysurvey.org (DESI Collaboration et
al., 2016) and extracted $\rm 10\times 10\,{arcmin^{2}}$ images in the g, r,
and z bands for 4585 matching galaxies. The large galaxy images ensure that
the background sky level can be robustly characterized and subtracted. We use
our fully automated ‘AUTOPROF ’ code (Section 2.1) to extract azimuthally
averaged surface brightness profiles from DESI g-,r- and z- band images, with
the solution fit to the r band for its minimal dust extinction and high
signal-to-noise ratio (S/N; and for consistency with the parallel Photometry
and Rotation Curve Observations from Extragalactic Surveys, or “PROBES”,
investigation by Stone & Courteau 2019 and Stone et al. 2021). The $r$-band
isophotal solution is applied to the $g$ and $z$ images for uniformity of the
position angles, ellipticities, fluxes and color gradients. Unless otherwise
stated, all band-dependent structural parameters refer to the $z$ band
photometry. The automation of AUTOPROF is well suited to large surveys like
DESI, where interactive surface brightness extraction methods, such as those
based on the XVISTA data reduction
package555http://ganymede.nmsu.edu/holtz/xvista/, become prohibitive (see
Courteau, 1996; McDonald et al., 2011; Hall et al., 2012; Gilhuly & Courteau,
2018, for more details).

Our MIR surface brightness profiles are derived from the WISE Large Galaxy
Atlas and the Extended Source catalogue (WXSC; Jarrett et al. 2019)666In what
follows, WISE and the WISE Large Galaxy Atlas and the Extended Source
catalogue are taken as synonymous (Jarrett et al., 2019)., which features
custom image mosaic construction to produce native angular resolution products
that include both WISE and NEOWISE imaging 777(NEO)WISE data imaging and
catalogueues can be retrieved from https://irsa.ipac.caltech.edu/to improve
the sensitivity; complete details of image construction are provided in
Jarrett et al. (2012). Here we use the W1 (3.4$\rm\mu$m) and W2 (4.6$\rm\mu$m)
mosaics with 5.9$\scriptscriptstyle\prime$ $\scriptscriptstyle\prime$ and
6.5$\scriptscriptstyle\prime$ $\scriptscriptstyle\prime$ spatial resolution,
respectively. These bands are sensitive to the evolved stellar populations
(Jarrett et al., 2013), and hence the stellar mass content and distribution
for the target galaxies. We have extracted from the WISE surface brightness
profiles the same structural properties as those measured from the DESI
optical photometry, except for the stellar surface density within 1 kpc which
is not resolved for many WISE profiles. The robustness of our WISE derived
structural properties is demonstrated in Section 5. Among others, the W1 and
W2 band passes are especially sensitive to older, more mass dominant stellar
populations resulting in robust stellar mass measurements. The comparison of
stellar masses from our DESI and WISE photometry is presented in Section 5. In
what follows, all surface brightnesses used and reported are in the AB
magnitude system.

In Appendix A, we provide Table 8 and 9 to present the output format of the
public multiband surface brightness profiles.

###  2.1 AUTOPROF

Figure 1: Comparison of photometrically derived non-parametric quantities from
XVISTA interactive routines and AUTOPROF with: (panel a) effective radius
[$R_{\rm eff}$], (panel b) isophotal radius [$R_{\rm 23.5}$], (panel c)
concentration index [$C_{\rm 28}$], (panel d) effective surface brightness
[$\mu_{eff}$], (panel e) luminosity within $R_{\rm 23.5}$ [$L_{\rm 23.5}$],
(panel f) colour within $R_{\rm 23.5}$ [$(g-r)_{\rm 23.5}$], (panel g) stellar
mass within $R_{\rm 23.5}$ [$M_{*}$], and (panel h) stellar mass surface
density within 1 kpc [$\Sigma_{1}$]. The blue solid line shows the best
orthogonal linear fit and the red dashed line shows the one-to-one line. All
measurements are from DESI z-band photometry. The text in the top left-hand
panel presents root mean square (rms) of the residuals for the one-to-one
line.

The automated surface brightness profile extraction algorithm, “AUTOPROF ”
works on a combination of standard and machine learning based numerical
techniques. A complete description of the AUTOPROF pipeline is presented in
Stone et al (in preparation). What follows is a brief outline.

The AUTOPROF pipeline first computes basic image parameters such as the
background sky level, PSF, and galaxy centre. The background is determined as
the mode of the pixel flux distribution. The PSF is determined uniquely for
each image with circular apertures placed on a set of 50 non-saturated stars
found using an edge detection convolutional filter. The galaxy centre is found
by starting at the centre of the image and iteratively moving to brighter
regions until a peak is found. The centre finding iterative step works by
following the direction of increasing brightness as determined by the first
FFT coefficient phase (FFT: Cooley & Tukey, 1965) of the flux values around a
circular aperture. On the sky subtracted and centred image, a global position
angle and ellipticity is fit to the galaxy at the outer region of the galaxy
(at approximately 3$\sigma$ above the sky noise). The global fit is performed
by minimizing the power in the second FFT coefficient of the flux values along
the isophote. An elliptical isophote solution is fit to the sky-subtracted and
centred image by simultaneously minimizing the second Fourier coefficient and
a regularization term (Shalev-Shwartz & Ben-David, 2014). The regularization
term is the $l_{1}$ norm of the difference in ellipticity and position angle
between adjacent isophotes. The use of a regularization term is borrowed from
machine learning; other automated surface brightness profile extraction
techniques take advantage of machine learning for all steps (Tuccillo et al.,
2018; Smith et al., 2021).

A surface brightness profile is extracted at incremental radii corresponding
to the median flux along each isophote. For isophotes at larger radii,
AUTOPROF extracts a non-overlapping “band” of pixel flux values from the
image, thus yielding a higher S/N for each isophote. A curve of growth is then
calculated by integrating the surface brightness profile appropriately. The
surface brightness uncertainty is computed from the 68.3% quartile range of
the sampled flux along each isophote; this uncertainty is also propagated to
the curve of growth.

Other surface brightness profile extraction techniques exist, such as the
interactive package PROFILE in XVISTA (Courteau, 1996; McDonald et al., 2011;
Hall et al., 2012; Gilhuly & Courteau, 2018). Figure 1 shows a comparison of
several (uncorrected) structural properties defined in Section 2.2 for
$\sim$50 MaNGA galaxies extracted using XVISTA and AUTOPROF . A good match
between the two methods is found for $R_{\rm 23.5}$, $L_{23.5}$, $g-r$, and
$M_{*}$. Other quantities in Figure 1, such as $R_{\rm eff}$, $C_{28}$ (see
equation 1), and $\mu_{\rm eff}$ (measured at $R_{\rm eff}$), do not match as
well. The effective radius comparison has a scatter of 0.07 dex, which matches
the $R_{\rm eff}$ comparison of SDSS imaging parameters in Gilhuly & Courteau
(2018, hereafter GC18) (0.06 dex) with the photometry of Walcher et al. (2014)
for CALIFA galaxies. An equally poor match for $R_{\rm eff}$ relative to SDSS
Petrosian radii is shown in fig. 9 of Hall et al. (2012). We also find a large
rms of 0.42 dex comparing $C_{28}$ estimates which reflects the large
uncertainties involved in measuring outer radii based on total light (Graham
et al., 2001; Trujillo et al., 2001). Likewise, a large rms of 0.42 dex is
found for comparisons of $C_{28}$ estimates, reflecting the large
uncertainties involved in measuring outer radii based on total light (Graham
et al., 2001; Trujillo et al., 2001). We argue in Section 4 that the poor
reproducibility of $\mu_{\rm eff}$, $R_{\rm eff}$, and $C_{\rm 28}$, results
largely from the ambiguous definition of total integrated luminosity in a
photometric band, which these quantities all depend on. Still, we include
these quantities in our tables for comparison with the literature.

Figure 2: Lowest surface brightness levels and maximal radial extents of DESI
surface brightness profiles in the g (left-hand panel), r (center panel) and
z-bands (right-hand panel) with coloured contours in log density versus
similar quantities for SDSS surface brightness profiles (black dots in the $g$
and $r$ bands; the $z$ band is unavailable) for the same MaNGA galaxies. The
radial axis shows the extent of the last point in each surface brightness
profile scaled in units of R23.5. The text within each panel indicates the
average depth of our DESI photometry in the radius and surface brightness.

Figure 2 offers a visualization of the greater depth of the DESI imaging
(coloured contours) relative to SDSS (black dots for the $g$ and $r$ bands).
The photometric depth is chosen as the point at which a profile reaches an
surface brightness error threshold of 0.22 mag arcsec-2 . As a result, the
surface brightness levels are typically $\sim$2 mag arcsec-2 deeper where
$\sim$1.5 mag arcsec-2 is attributed to the deeper DESI imaging (over SDSS)
and $\sim$0.5 mag arcsec-2 is attributed to the isophote sampling method in
AUTOPROF (over XVISTA)888The error threshold adopted by Gilhuly & Courteau
(2018) for SDSS surface brightness profiles of CALIFA galaxies at $g$, $r$,
and $i$ bands is $0.15~{}{{{{\rm mag}~{}{\rm arcsec}}^{-2}}}$. A typographical
error in that paper incorrectly lists that threshold as $1.5~{}{{{{\rm
mag}~{}{\rm arcsec}}^{-2}}}$ (sic) in their Section 3.

The coloured contours show the surface brightness levels and radial extents at
which the surface brightness truncation occurs in the three DESI-grz bands. On
average, the DESI photometric solutions extend radially beyond
$2(z)-3.8(g)~{}R_{\rm 23.5}$ (greater radial extent at bluer wavelengths) and
can reach surface brightness levels as low as 26.7(z) to 28.5(g) ${{{{\rm
mag}~{}{\rm arcsec}}^{-2}}}$, with some profiles going down to 30 mag arcsec-2
. Comparison with the SDSS data (extracted by ourselves using XVISTA
procedures) shows that the combination of DESI images and the AUTOPROF surface
brightness extraction yields profiles that reach typically ${\sim}2~{}{{{{\rm
mag}~{}{\rm arcsec}}^{-2}}}$ deeper than SDSS analysed with XVISTA given the
same surface brightness uncertainty.

###  2.2 Parameter Extraction

We briefly describe the parameters inferred from optical and MIR imaging
presented in the photometric and environment catalogues. A complete listing of
our extracted parameters and their units is given in Table 3 and 4.

####  2.2.1 Sizes

Some galaxy sizes are calculated relative to total light or measured at
different isophotal levels. Relative sizes are calculated at 20, 50, and 80
per cent of the total light. The errors on these sizes are calculated by
standard error propagation from the curve of growth (COG). Isophotal sizes are
measured at the $\rm 22.5$, $\rm 23.5$ and $\rm 25\,{{{{\rm mag}~{}{\rm
arcsec}}^{-2}}}$ isophotes from the surface brightness profiles in their
respective band. Errors on isophotal sizes are calculated by standard error
propagation from the surface brightness profile. While surface brightness
errors tend to be larger than COG errors, the relative slope of the profiles
results in larger errors for the sizes based on the COG.

The projected sizes $(R)$ extracted from our photometry can be transformed
into 3D physical radii ($r$), i.e., $r(R)$, by modelling projection effects.
For flat discy stellar systems, the physical and projected radii are
interchangeable (e.g. $r(R)\approx R$). For trixial systems, models suggest
that $r(R)\approx(4/3)R$ (Hernquist, 1990; Ciotti, 1991; Ouellette et al.,
2017). In Section 6, we review the impact of this transformation on galaxy
scaling relations such as the size–mass relation.

####  2.2.2 Brightness, luminosities, and colours

Total apparent magnitudes and total luminosities enclosed within the $R_{\rm
23.5}$ and $R_{\rm 25}$ radii are presented. The colour terms $g-r$, $g-z$ and
$r-z$ are evaluated at $R_{\rm 23.5}$ and $R_{\rm 25}$ in the z band.

The ellipticity of the last measured isophote of a galaxy is used as the
representative ellipticity of that galaxy on the sky.

These quantities are all calculated using linear interpolations of consecutive
surface brightness profile or curve of growth data. If an interpolation is not
possible, the last 25 percent of the profile is used to extrapolate up to that
point using a linear fit. A flag for each structural parameter indicates an
interpolation or extrapolation.

####  2.2.3 Concentration

The concentration of light, $C_{\rm 28}$, is a ratio of radii that enclose 20
per cent and 80 per cent of the total light:

$C_{28}=5\log(R_{80}/R_{20}).$ (1)

A second measure of concentration, $C_{\rm 25}$, is also presented. Its use of
$R_{\rm 20}$ and $R_{\rm 50}$ is operationally similar to Eq. (1). $\rm R_{\rm
50}$ is the effective radius, equivalent to $R_{\rm eff}$.

####  2.2.4 Stellar mass and surface stellar density

Stellar masses can be inferred from observed colours using stellar mass-to-
light colour relations (MLCRs;Courteau et al. 2014). We use five different
stellar mass estimates from the MLCRs presented in Roediger & Courteau (2015,
hereafter RC15), Zhang et al. (2017, hereafter Z17), and García-Benito et al.
(2019, hereafter B19). These MLCRs differ in their choice of stellar
population synthesis model, adopted galactic extinctions, and input data used
to calibrate the MLCR (global vs. resolved SED fits ). Our stellar mass
estimates use $g-r$ and $g-z$ colours measured at R23.5 in the DESI-z band.
The use of multiple colours yields better constraints on mass-to-light ratios
(RC15, Z17, Gilhuly & Courteau 2018). The mass-to-light ratios
($\rm\Upsilon_{*}$) calculated from these colours are multiplied by the
luminosity in the g, r, and z bands measured at R23.5, which itself is
inferred in the DESI-z band. This results in 30 stellar mass estimates that
are averaged to provide a stellar mass estimate used throughout this study.
The error in the stellar mass is the standard deviation of the 30 stellar mass
measurements. MLCRs in RC15 and Z17 have only been calibrated for late-type
systems and are exclusively applied to those systems. The stellar mass
measurements for ETGs are thus measured using the MLCR presented in B19.

The stellar $\rm\Upsilon_{*}$ enable the direct conversion of COGs into
stellar surface density profiles. We calculate the stellar surface density
within 1 kpc ($\Sigma_{1}=M_{\rm*,1kpc}/\pi$) and the effective radius
($\Sigma_{\rm eff}=M_{*}/\pi R_{\rm eff}^{2}$) where $M_{*}$ is the total
stellar mass of the galaxy and $\rm M_{\rm*,1kpc}$ is the stellar mass within
the 1 kpc aperture.

The MIR stellar masses derived from ${\it W1}-W2$ colours and the MLCR of
Cluver et al. (2014) are shown as follows:

$\log(M_{*}/L_{{\it W1}})=-0.17-2.54\times({\it W1}-W2),$ (2)

where $L_{{\it W1}}=10^{-0.4(M_{{\it W1}}-M_{\odot,{\it W1}})}$ is the
luminosity, $M_{{\it W1}}$ is the absolute magnitude in the ${\it W1}$ filter,
and $M_{\odot,{\it W1}}=3.24$ is the absolute magnitude of the Sun in ${\it
W1}$ band. The same expression is used to get the luminosity for the WISE $W2$
photometric band, except that $M_{\odot,W2}=3.27$.

These MLCRs use a Chabrier IMF, star formation and AGN activity, dust content,
old stellar content, along with detailed stellar mass calibrations (Taylor et
al., 2011). The colour in eq. (2) is limited to the range $-0.05\leq({\it
W1}-W2)\leq 0.2$ as redder (bluer) sources may be contaminated by AGN or
starburst activity (Jarrett et al., 2013).

####  2.2.5 Environmental parameters

Various environmental properties for 3207 MaNGA galaxies are presented in
Table 4. The number of neighbours is extracted from the modified catalogue of
Wilman et al. (2010) based on SDSS-DR7 (Abazajian et al., 2009). Galaxies are
counted as neighbours if they fall within projected circular apertures of
varying radii (0.25-3.0 Mpc) and their heliocentric Hubble flow velocities are
within $\pm$1500 km s-1 of each other.

Central and satellite galaxies are identified via a stellar mass rank with a
cylindrical aperture. The radius of the cylindrical aperture depends on the
stellar mass of the galaxy and the depth of the cylinder is taken to be $\pm$
2000 km s-1. A galaxy with a stellar mass rank of 1 is identified as a central
galaxy, whereas a mass rank greater than 1 is associated with a satellite
galaxy. See Fossati et al. (2015) and Arora et al. (2019) for a description of
the stellar mass rank scheme to identify centrals and satellites. We have also
cross-correlated the SDSS and MaNGA catalogues to compute the probability a
galaxy being central or satellite according to the scheme of Fossati et al.
(2017).

Figure 3: Distribution of MaNGA galaxy properties separated by galaxy
morphology; LTGs in blue and ETGs in red. Shown are the stellar mass
($M_{*,23.5}$), stellar mass surface density within 1 kpc ($\Sigma_{1}$),
colour measured within $R_{\rm 23.5}$ ($(g-z)_{23.5}$), effective surface
brightness ($\mu_{\rm eff}$), effective radius ($R_{\rm eff}$), and isophotal
radius at 23.5 mag arcsec-2 ($R_{\rm 23.5}$). The grey histogram in each panel
shows the underlying data distribution. Each LTG/ETG property is fit with a
double or single Gaussian; the optimal distribution is determined via the
F-test (see the text for details). The data in each panel give the Gaussian
mean(s) of the unimodal (bimodal) distributions and the F-test confidence for
a single vs. double Gaussian distribution.

###  2.3 Parameter corrections

Our apparent magnitudes are corrected for Galactic extinction ($A_{\rm g}$),
geometric projections ($\gamma$), internal extinction ($A_{\rm i}$), and
k-correction ($A_{\rm k}$). Using the following transformation in each band:

$m_{{\rm corr},\lambda}=m_{{\rm obs},\lambda}-A_{{\rm
g},\lambda}-A_{\gamma,\lambda}-A_{{\rm k},\lambda},$ (3)

the Galactic extinction ($A_{\rm g}$) is obtained from the NSA-Sloan
Atlas999http://www.nsatlas.org/ (NSA; Blanton et al., 2011), which are
themselves taken from Schlegel et al. (1998). The cosmological k-correction
($A_{\rm k}$) uses the template from Blanton & Roweis (2007).

Correcting for internal extinction and geometric projections is more
challenging, and depends on morphological type. Note that the discussion below
applies to late-type galaxies (LTGs); ETGs are assumed dust-free and trixial
and no such corrections are applied. MaNGA LTGs are identified via the MaNGA
Deep Learning Morphological VAC (MDLM-VAC; Domínguez Sánchez et al., 2018).
The effects of projection on the sky bias the measurement of intrinsic
properties, hence our attempt to recover face-on equivalent measures with a
simple model (Holmberg, 1958; Stone et al., 2021). A common correction for the
deprojection of structural parameters involves a linear fit between the
desired projected variable and the log of the cosine of the inclination
(Giovanelli et al., 1994). This method is expressed in Eq. (4):

$\log X_{0}=\log X_{i}+\gamma\log(\cos(i)),$ (4)

where $X_{0}$ is the variable corrected to face-on, $X_{i}$ is the observed
measurement, $i$ is the inclination of the galaxy on the sky corrected for the
stellar disc thickness and calculated using eq. (5), and $\gamma$ is the
fitted correction factor:

$\cos^{2}i=\frac{(b/a)^{2}-q_{0}^{2}}{1-q_{0}^{2}};\quad(q_{0}=0.13).$ (5)

These corrections can be performed on a complete sample (Masters et al., 2010)
or applied to subsamples based on galaxy properties for which inclination
corrections are robust and known such as HI line widths (Tully et al., 1998),
galaxy morphology (Maller et al., 2009; Masters et al., 2010), or total
infrared luminosity (Devour & Bell, 2019). The correction factor, $\gamma$,
encompasses effects due to geometry (line-of-sight projection), stellar
populations, and dust extinction as a function of inclination.

T-Type | N | $R_{23.5,g}$ | $R_{23.5,r}$ | $R_{23.5,z}$ | $L_{23.5,g}$ | $L_{23.5,r}$ | $L_{23.5,z}$ | $(g-r)_{23.5}$ | $(g-z)_{23.5}$ | $\log\Sigma_{1}$
---|---|---|---|---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
0–10 | 1907 | $0.28\pm 0.03$ | $0.25\pm 0.03$ | $0.23\pm 0.03$ | $-0.34\pm 0.08$ | $-0.24\pm 0.09$ | $-0.12\pm 0.09$ | $0.22\pm 0.02$ | $0.51\pm 0.04$ | $\phantom{-}0.01\pm 0.08$
0–3 | 829 | $0.38\pm 0.05$ | $0.37\pm 0.05$ | $0.35\pm 0.05$ | $-0.05\pm 0.11$ | $\phantom{-}0.10\pm 0.12$ | $\phantom{-}0.25\pm 0.12$ | $0.34\pm 0.03$ | $0.72\pm 0.04$ | $\phantom{-}0.43\pm 0.11$
4–5 | 958 | $0.21\pm 0.04$ | $0.19\pm 0.04$ | $0.18\pm 0.04$ | $-0.42\pm 0.11$ | $-0.28\pm 0.11$ | $-0.15\pm 0.11$ | $0.26\pm 0.02$ | $0.62\pm 0.04$ | $\phantom{-}0.05\pm 0.11$
6–10 | 164 | $0.31\pm 0.08$ | $0.26\pm 0.08$ | $0.22\pm 0.08$ | $-0.28\pm 0.23$ | $-0.28\pm 0.24$ | $-0.08\pm 0.24$ | $0.01\pm 0.03$ | $0.09\pm 0.08$ | $-0.25\pm 0.18$
Table 1: Inclination correction terms, $\gamma$, for various galaxy structural
parameters in different photometry bands. Column (1) shows the T-Type bins
used for the correction; column (2) presents the number of data points used
for the fitting; and columns (3)–(11) show the correction factors for
different structural properties. The first row gives $\gamma$ for all
galaxies; the next three rows give $\gamma$ for specific morphological bins.

We solve Eq. (4) for $\gamma$ with a forward least-squares fit between the
desired variable and $\cos(i)$ in log space. For the fitting, we restrict the
sample to an inclination range of $30^{\circ}<i<80^{\circ}$ and assume an
intrinsic thickness of $q_{0}=0.13$ to convert the ellipticity to inclination
(Hall et al., 2012; Ouellette et al., 2017). Errors on $\gamma$ are calculated
using bootstrap sampling. Table 1 tabulates the correction factor, $\gamma$,
for various galaxy structural properties of the MaNGA LTG sample in the grz
bands. We present $\gamma$ for the full sample (first row of Table 1) and
split into three morphological bins done using the MLDM-VAC (last three rows
of Table 1).

The absolute value of these correction factors differ from those presented in
Masters et al. (2010) and Stone et al. (2021). However, in all cases, the
correction factors are small. For example, the correction factor for an
isophotal radius in the transparent case is $\gamma\approx 2.3$ (Giovanelli et
al., 1994), compared to our correction factor of $\rm{\sim}0.25\pm 0.02$.

Scaling relation | Uncorrected | Corrected T–Types 1-10 | Corrected 3 T-Type bins
---|---|---|---
| m | $\sigma$ | m | $\sigma$ | m | $\sigma$
(1) | (2) | (3) | (4) | (5) | (6) | (7)
$\Sigma_{1}$–$M_{\rm*,23.5}$ | $0.96\pm 0.01$ | $0.24\pm 0.01$ | $0.96\pm 0.01$ | $0.23\pm 0.01$ | $0.96\pm 0.01$ | $0.23\pm 0.01$
$R_{23.5,z}$–$M_{*,23.5}$ | $0.34\pm 0.01$ | $0.11\pm 0.01$ | $0.34\pm 0.01$ | $0.11\pm 0.01$ | $0.35\pm 0.01$ | $0.10\pm 0.01$
$R_{23.5,z}$–$\Sigma_{1}$ | $0.30\pm 0.01$ | $0.17\pm 0.01$ | $0.29\pm 0.01$ | $0.16\pm 0.01$ | $0.30\pm 0.01$ | $0.17\pm 0.01$
$R_{23.5,z}$–$L_{23.5,z}$ | $0.41\pm 0.01$ | $0.08\pm 0.01$ | $0.41\pm 0.01$ | $0.09\pm 0.01$ | $0.41\pm 0.01$ | $0.09\pm 0.01$
$\Sigma_{1}$–$L_{23.5,z}$ | $0.94\pm 0.01$ | $0.30\pm 0.01$ | $0.95\pm 0.01$ | $0.30\pm 0.01$ | $0.93\pm 0.01$ | $0.29\pm 0.01$
$(g-z)_{23.5}$–$L_{23.5,z}$ | $0.24\pm 0.01$ | $0.24\pm 0.01$ | $0.25\pm 0.01$ | $0.22\pm 0.01$ | $0.22\pm 0.01$ | $0.21\pm 0.01$
Table 2: Variation of slopes and scatters of galaxy structural scaling
relations due to inclination corrections. Column (1) indicates the scaling
relation; columns (2) and (3) give the uncorrected slope and scatter; columns
(4) and (5) give the slope and scatter with a single full-sample correction
(all T-Types); columns (6) and (7) give the slopes and scatter with
corrections applied to three morphological bins.

Ideally, an accurate inclination correction model should yield a reduction of
the observed scatter in various galaxy scaling relations. This concept is
tested in Table 2, which presents the variation of the slopes and scatter for
a suite of structural galaxy scaling relations with inclination corrections.
The slopes and scatter are found to be robust against inclination corrections
for nearly all scaling relations presented. A significant variation in the
scatter of the $(g-z)_{23.5}--L_{23.5,z}$ relation is found for both
inclination correction models, with or without binning by morphology. In light
of the null variation in the slopes and scatter of galaxy scaling relations,
we apply inclination corrections to our photometry without reducing our sample
into various morphological bins.

Column name | Description | Unit | Data yype
---|---|---|---
MANGA-ID | MaNGA Identification | – | string
PlateIFU | MaNGA Plate-IFU | – | string
ObjID | SDSS-DR15 photometric identification number | – | long int
RA | Object Right Ascension (J2000) | ∘ | float
DEC | Object Declination (J2000) | ∘ | float
Z | NSA or SDSS redshift | – | float
TTYPE | Morphological T-Type (from MDLM-VAC) | – | float
GAL_EXTINCTION | Galactic extinction (DESI grz only) | mag | float
KCORRECTION | Cosmological K-Corrections (DESI grz only) | mag | float
R20 | Radius where 20 per cent of the total light is integrated | arcsec | float
R20_E | Error in R20 | arcsec | float
Reff | Effective radius | arcsec | float
Reff_E | Error in effective radius | arcsec | float
R80 | Radius where 80 per cent of the total light is integrated | arcsec | float
R80_E | Error in R80 | arcsec | float
R22.5 | Isophotal radius calculated at $\rm 22.5\,{{{{\rm mag}~{}{\rm arcsec}}^{-2}}}$ | arcsec | float
R22.5_E | Error in R22.5 | arcsec | float
R22.5_FLAG | Method of calculation: interpolation (0) and extrapolation (1) | boolean | int
R23.5 | Isophotal radius calculated at $\rm 23.5\,{{{{\rm mag}~{}{\rm arcsec}}^{-2}}}$ | arcsec | float
R23.5_E | Error in R23.5 | arcsec | float
R23.5_FLAG | Method of calculation: interpolation (0) and extrapolation (1) | boolean | int
R25 | Isophotal radius calculated at $\rm 25\,{{{{\rm mag}~{}{\rm arcsec}}^{-2}}}$ | arcsec | float
R25_E | Error in R25 | arcsec | float
R25_FLAG | Method of calculation: interpolation (0) and extrapolation (1) | boolean | int
C25 | Concentration index measured using R20 and Reff | – | float
C28 | Concentration index measured using R20 and R80 | – | float
MU_20 | Surface brightness at R20 | ${{{{\rm mag}~{}{\rm arcsec}}^{-2}}}$ | float
MU_20_E | Error in Mu_20 | ${{{{\rm mag}~{}{\rm arcsec}}^{-2}}}$ | float
MU_20_FLAG | Method of calculation: interpolation (0) and extrapolation (1) | boolean | int
MU_EFF | Surface brightness at the effective radius | ${{{{\rm mag}~{}{\rm arcsec}}^{-2}}}$ | float
MU_EFF_E | Error in effective surface brightness | ${{{{\rm mag}~{}{\rm arcsec}}^{-2}}}$ | float
Mu_EFF_FLAG | Method of calculation: interpolation (0) and extrapolation (1) | boolean | int
MU_80 | Surface brightness at R80 | ${{{{\rm mag}~{}{\rm arcsec}}^{-2}}}$ | float
MU_80_FLAG | Error in Mu_80 | ${{{{\rm mag}~{}{\rm arcsec}}^{-2}}}$ | float
MU_80_FLAG | Method of calculation: interpolation (0) and extrapolation (1) | boolean | int
MAG23.5 | Total apparent magnitude within R23.5 | mag | float
MAG23.5_E | Error in total apparent magnitude within R23.5 | mag | float
MAG23.5_FLAG | Method of calculation: interpolation (0) and extrapolation (1) | boolean | int
MAG25 | Total apparent magnitude within R25 | mag | float
MAG25_E | Error in total apparent magnitude within R25 | mag | float
MAG25_FLAG | Method of calculation: interpolation (0) and extrapolation (1) | boolean | int
L23.5 | Total luminosity within R23.5 | $L_{\odot}$ | float
L25 | Total luminosity within R25 | $L_{\odot}$ | float
ELLIPTICITY | Ellipticity of the last isophote; $1-(b/a)$ | – | float
PA | Position angle of the last isophote measured from north to east (DESI grz only) | ∘ | float
MSTAR_235 | Stellar mass measured at the z-band R23.5 (z & W1 band only) | $\rm M_{\odot}$ | float
MSTAR_235_E | Error in stellar mass estimates measured at z band R23.5 (z band only) | $\rm M_{\odot}$ | float
MSTAR_25 | Stellar Mass measured at the z-band R25 (z band only) | $\rm M_{\odot}$ | float
MSTAR_25_E | Error in stellar mass estimates measured at z-band R25 (z band only) | $\rm M_{\odot}$ | float
SIGMA1 | Stellar mass surface density within 1 kpc (z band only) | $\rm M_{\odot}\,kpc^{-2}$ | float
SIGMA1_E | Error in SIGMA1 (z band only) | $\rm M_{\odot}\,kpc^{-2}$ | float
SIGMA_EFF | Stellar mass surface density within Reff (z band only) | $\rm M_{\odot}\,kpc^{-2}$ | float
SIGMA1_EFF_E | Error in SIGMA_EFF (z band only) | $\rm M_{\odot}\,kpc^{-2}$ | float
COLOR |  $g-r$ and $g-z$ measured at z-band R23.5 and R25 (z band only) | mag | float
Table 3: Photometric quantities for the MaNGA DESI photometric catalogue. The table includes calculated parameters along with the units and the data types. All parameters presented are uncorrected for Galactic extinction, inclination and cosmology. These parameters are available in three separate files for the DESI grz bands. The three full tables are presented as supplementary material. Column Name | Description | Unit | Data type
---|---|---|---
MANGA-ID | MaNGA Identification | – | string
PlateIFU | MaNGA Plate-IFU | – | string
ObjID | SDSS-DR15 photometric identification number | – | long int
RA | Object Right Ascension (J2000) | ∘ | float
DEC | Object Declination (J2000) | ∘ | float
Z | NSA or SDSS redshift | count | float
Dens_01 | Number of neighbours within a 0.1-Mpc aperture | count | int
Dens_02 | Number of neighbours within a 0.2-Mpc aperture | count | int
Dens_05 | Number of neighbours within a 0.5-Mpc aperture | count | int
Dens_1 | Number of neighbours within a 1-Mpc aperture | count | int
Dens_2 | Number of neighbours within a 2-Mpc aperture | count | int
Dens_3 | Number of neighbours within a 3-Mpc aperture | count | int
Mrank_AA | Identification of central or satellite galaxy; central (1) and satellite (>1) | rank | int
P_CEN | Probability of the galaxy being the central member in the halo | rank | float
P_SAT | Probability of the galaxy being a satellite in the halo | – | float
Table 4: Environmental properties for the MaNGA galaxies. The table includes
each parameter along with the units and data types. The full table is
presented as supplementary material.

##  3 Parameters Distributions

This section provides an overview of some important MaNGA galaxy properties
and their range. Figure 3 offers a broad appreciation of the distribution of
structural properties for galaxies in the MaNGA public release. For instance,
if dwarf galaxies are defined as having a stellar mass
$\log(M_{*}/M_{\odot})\leq 9.5$ (Woo et al., 2008; Ouellette et al., 2017),
only 11 percent of our galaxies are dwarfs. Our results in this section
clearly highlight the presence of distinct populations in each of the LTG and
ETG categories. The latter is made clear through the unimodal and bimodal
trends displayed by some structural and dynamical parameters (Tully &
Verheijen, 1997; McDonald et al., 2009; Sorce et al., 2013; Ouellette et al.,
2017). We define a unimodal distribution as one described by a normal
distribution. The figure of merit to distinguish a bimodal from a unimodal
distribution is the F-test that gives the probability that the observed
distributions originate from two distinct Gaussian populations rather than a
single one. These populations are represented by single or double Gaussian
fits in Figure 3. F-test confidence results for a double vs a single Gaussian
distribution and the fitted means for the double/single population(s) are
indicated in each panel. Unimodal distributions are found for LTG sizes
(effective and isophotal) and ETG effective surface brightnesses and colour.

The following properties for LTGs show bimodal signatures; stellar mass (top
left-hand panel), stellar surface density with 1 kpc (middle panel), effective
surface brightness (bottom left-hand) and colour (top right-hand) measured at
23.5 mag arcsec-2 . The notion of surface brightness bimodalities has been
addressed at some length in (Ouellette et al., 2017, and references therein).
Surface brightness bimodalities in LTGs are especially conspicuous at dust-
insensitive wavelengths such as the z band (Sorce et al., 2013).

For ETGs, stellar mass, stellar surface density within 1 kpc, isophotal radius
at 23.5 mag arcsec-2 , and effective radius show bimodal signatures. A
bimodality in the galaxian properties shown here reflects environmental
influences, varying merger and star formation histories, and different radial
dark matter fractions, which all play a key role in galaxy evolution. The
coupling of these structural bimodalities with bimodal dynamical properties
(if any) would greatly enhance galaxy formation scenarios.

The detailed investigation of bimodal trends in scaling relations, and the
identification of galaxy subclasses, will be presented elsewhere. For now, we
appreciate the need to consider one or two populations in fitting scaling
relations over a range of galaxian properties.

##  4 Literature Comparisons

The following section presents comparisons of our galaxy structural parameters
with similar values found in the literature. We first present a multifaceted
comparison of the 1D surface brightness profiles generated using model-
independent (e.g. AUTOPROF , XVISTA) and model-dependent (e.g. GALFIT, PYMORPH
) methods. Effective (half-light), isophotal radii and apparent magnitudes
from the MPP-VAC of F19 are also compared with our photometry. This comparison
recognizes that the MPP-VAC reports parameters from circularized light
profiles. We caution that this operation is especially uncertain in light of
unknown dust distributions, non-axisymmetric feature and disc thicknesses, and
the vagaries of 2D image decompositions (Gilhuly & Courteau, 2018). Total
magnitudes, and effective radii, should be the least model-biased parameters
from F19, and hence our comparison below. Stellar masses are also compared
with a PCA-based stellar mass estimation technique from Pace et al. (2019,
hereafter P19). For the sake of comparison, parameters presented in this
section are not corrected for Galactic extinction, inclination, and cosmology.

###  4.1 Surface brightness profile comparisons

Figure 4: Comparison of our DESI-based 1D r-band surface brightness profile
(black dots) with the SDSS-based surface brightness profile (red dot) of GC18.
Also compared are the 2D Sérsic + Exponential decompositions using GALFIT by
GC18 (cyan solid lines) and F19 (gold solid line). The Sérsic + Exponential
decompositions are separated by their respective bulge (dashed line) and disc
(solid line) contributions. Missing coloured lines represent failed fits by
the original authors.

Figure 4 compares 1D r-band surface brightness profiles extracted from DESI
images (black points) by us and from SDSS images by GC18 (red points). The
excellent agreement between those profiles results from quality DESI/SDSS
imaging and the robust non-parametric surface brightness profile extraction
with XVISTA and AUTOPROF . Figs. 1 and 4 compare various global properties
between XVISTA and AUTOPROF , showing that both codes reproduce local
variations in 1D surface brightness profiles with high fidelity.

Our catalogue also overlaps with F19 and GC18. The latter two studies used the
2D image fitting algorithm GALFIT to obtain Bulge-Disc decompositions for
their samples based on the MaNGA and CALIFA samples, respectively. A total of
16 galaxies overlap between the MaNGA (us and F19) and CALIFA (GC18) samples.
These overlapping galaxies enable a comparison of our independent results.

In Figure 4, the blue and gold solid line show the Sérsic + Exponential
decompositions by Gilhuly & Courteau (2018) and F19 respectively, for eight
galaxies using GALFIT. We caution that the MPP-VAC (F19) present total
apparent magnitudes in the circularized plane of the galaxy, i.e. corrected to
face-on based on the simplest assumptions of a dust-free, infinitesimally-thin
disc. The recovery of total apparent magnitudes ($m$) from the MPP-VAC in the
plane of the sky must therefore be made with the equation
$(m_{r}^{\prime}=m_{r}+2.5\log(b/a))$ for the bulge and disc components, where
$b/a$ is the axis ratio of the galaxy.

The appreciation of more complex disc systems, with their triaxial bulges,
thicker mid-planes, and sporadic dust extinction, calls for a more extensive
modelling. Stone et al. (2021) performed an extensive analysis of inclination
corrections for disc galaxies. While some correction models showed a scatter
reduction of various galaxy scaling relations, little agreement between
different correction models was found.

For six out of the eight galaxies, the two independent GALFIT decompositions
return Sérsic + Exponential models that can differ by as much as
${\sim}0.4\,{{{{\rm mag}~{}{\rm arcsec}}^{-2}}}$, demonstrating the great
subjectivity between these model-dependent solutions while our non-parametric
comparison only show differences on the order of ${\sim}0.09\,{{{{\rm
mag}~{}{\rm arcsec}}^{-2}}}$. In some cases, only one user can find a valid
solution for the GALFIT decomposition. Where both fits converge, they often
find different bulge to disc ratios with a difference of ${\sim}0.3$ dex.
Similar caveats for Bulge-Disc decompositions for the same galaxies using two
different image fitters (GALFIT and IMFIT (Erwin, 2015)) by GC18 showed
discrepant results as well.

The large variations between the solutions of GC18 and F19, as well as the
analysis presented in GC18, remind us that generic parametric solutions are
especially fragile and inconclusive. For these reasons, an analysis of galaxy
structure or scaling relation should rely on the non-parametric
characterization of surface brightness profiles.

###  4.2 Effective sizes

Figure 5: Comparison of our model-independent effective radii from DESI r-band
surface brightness profiles with those from a single Sérsic fit from F19. The
solid lines show the median for MaNGA-LTGs (blue) and MaNGA-ETGs (red) and the
shaded region shows the scatter within a bin of size 0.12 dex. The dashed line
shows the one-to-one line. The inset text shows the number of data points and
root mean square (rms) for the LTG and ETG populations. The bottom panel shows
the residual $\Delta=\log(R^{r}_{\rm eff}[PYMORPH]/R^{r}_{\rm eff})$. Figure
6: Same as Figure 5 but the y-axis uses effective radii from Sérsic and
exponential fits by F19.

Figure 5 compares our non-parametric $R_{\rm eff}$, measured in the DESI r
band, with those found in F19 for a single Sérsic fit with PyMorph. We have
used the MDLM-VAC to divide our sample into LTG and ETG categories. Size
measurements are taken in the $r$-band to enable a direct comparison with
PyMorph results. PYMORPH and AUTOPROF agree well at small radii; at larger
radii AUTOPROF yields smaller sizes than PYMORPH .

This behaviour is expected as a single Sérsic fit does not capture all the
light from the outer regions of a galaxy, with low S/N, yielding a larger
estimate for $R_{\rm eff}$. The effect is amplified for larger PYMORPH $R_{\rm
eff}$ and for the ETG sample due to their higher light concentration relative
to LTGs. For the complete population, a single Sérsic fit from F19 results in
larger effective radii by 0.21 dex compared to our results.

The agreement between our methods improves with the two-component fits from
F19. Figure 6 shows a comparison between our non-parametric effective radii
and those extracted from two-component Sérsic exponential fits. Both ETGs and
LTGs are in agreement, though at large radii the scatter increases.

While the PYMORPH two-component fit improves the overall agreement with
AUTOPROF , there remains significant random variations, especially with
quantities determined relative to the total light of the galaxy, like the
effective radius, $R_{\rm eff}$. The latter suffered from poor
reproducibility, largely due to the uncertain definition of total apparent
magnitude of a galaxy. In a similar vein, Hall et al. (2012) found that the
scatter of velocity–radius–luminosity (VRL) scaling relations is reduced with
isophotal radii and Trujillo et al. (2020) found that a stellar mass density
radius reduces scatter in the size–mass relation. Similar impressions were
echoed by GC18 who found differences as large as 0.16 dex (45%) between non-
parametric and model-dependent measures of $R_{\rm eff}$ for CALIFA galaxies
(Walcher et al., 2014). González-Samaniego et al. (2017) also used the FIRE
simulations to point out the same pathology about $R_{\rm eff}$. For the size-
dependent analyses that follow (Section 6), we limit our use of effective
radii and pay special attention to isophotal size metrics. The scatter in the
size–mass relation is discussed in Section 6.

###  4.3 Isophotal sizes

Figure 7: Comparison of our model-independent isophotal radius measured at
$23.5$ mag arcsec-2 from DESI r-band surface brightness profiles with model-
dependent PYMORPH decomposition from F19. The solid lines show the median for
MaNGA-LTGs (blue) and MaNGA-ETGs (red), and the shaded region shows the
scatter in a bin of width 0.12 dex. The dashed line is the one-to-one line.
The legend shows the number of data points and rms for the LTG and ETG
populations. The left- and right-hand panels show the Sérsic and
Sérsic+Exponential fits, respectively. The bottom panels show the residual
$\Delta=\log(R^{r}_{23.5}[PYMORPH]/R^{r}_{23.5})$.

The parameters from the MPP-VAC can be used to construct de-projected surface
brightness profiles in order to infer the isophotal radii measured at $23.5$
mag arcsec-2 . These are compared with matching size measurements from the
DESI photometry in Figure 7. Disagreements in isophotal sizes are larger for
galaxies with preferred Sérsic model (${\sim}0.05\,$dex) compared to galaxies
with preferred Sérsic+Exponential model (${\sim}0.04\,$dex). This reaffirms
the results from Section 4.2 that simple Sérsic models cannot account for all
of the galaxy light.

The comparison of model-independent isophotal radii measured with XVISTA and
AUTOPROF in Figure 1 showed more consistency ($0.02\,$dex), indicating that
non-parametric modelling of galaxies is more reproducible. The larger rms
($\sim$0.05 dex) is explained by the vagaries in parametric modelling from
GALFIT. Comparing Figure 7 and Figure 6 demonstrates that that isophotal sizes
($R_{\rm 23.5}$) are more consistent than sizes based on fraction of total
light even while comparing non-parametric with model-dependent sizes.

###  4.4 Apparent magnitudes

Figure 8: Comparison of our model-independent apparent magnitudes from DESI
r-band surface brightness profiles with those from a single Sérsic fit from
F19. For both methods, the total apparent magnitude is measured within the
$25\,{{{{\rm mag}~{}{\rm arcsec}}^{-2}}}$ isophote. The bottom panel shows the
residual.

Next, total apparent magnitudes extracted from DESI photometry are compared
with MPP-VAC magnitudes from F19. The total apparent magnitudes are both
calculated within $25\,{{{{\rm mag}~{}{\rm arcsec}}^{-2}}}$ and are not
corrected for cosmology, Galactic and inclination extinctions. While total
magnitudes are here mostly reported at the $23.5\,{{{{\rm mag}~{}{\rm
arcsec}}^{-2}}}$ levels to maximize comparisons with literature values, the
current comparisons (Figure 8 and 9) at the $25\,{{{{\rm mag}~{}{\rm
arcsec}}^{-2}}}$ isophotal level takes advantage of the superior DESI imaging
depth. Once again, the F19 total apparent magnitudes are deprojected according
to the expression, $m^{\prime}=m+2.5\log(b/a)$. Figure 8 compares apparent
r-band magnitudes from our DESI surface brightness profiles with Sérsic fit
magnitudes from F19, in various galaxy morphological bins. The rms values are
given in dex (magnitude divided by 2.5). For both ETGs and LTGS, the DESI
surface brightness profiles from AUTOPROF are $\sim 0.10$ dex brighter than
those from PYMORPH with a Sérsic fit. This further highlights that a single
Sérsic fit fails to capture all the light from the object, leading to
disagreements in effective galaxy sizes (Section 4.2).

Figure 9: Same as Figure 8 with apparent magnitude on the y-axis for a double
Sérsic and exponential fit from F19.

.

Surprisingly, the addition of a second, exponential, component in PYMORPH for
MaNGA galaxies results in poorer fits (Figure 9). While random variations
between PYMORPH and AUTOPROF for LTGs are reduced with an additional
component, PyMorph still underestimates the total light (calculated using the
analytic Sérsic function) relative to our analysis. The shaded regions for
both LTGs and ETGs in Figure 9 represent the inter-quartile range of the
residuals. With our large sample, we can estimate the random error (as
$1/\sqrt{N}\sim 0.03\,$dex) to be very small, and the rms errors are thus
largely systematic. Indeed, disagreements with our apparent magnitudes emerge
largely from the model-dependent nature of the F19 photometric analysis that
do not account for non-axisymmetric features such as bars, rings and spiral
arms. Features unaccounted for by PYMORPH will systematically yield fainter
total magnitudes relative to non-parametric estimates. Along with the surface
brightness profile comparison in Section 4.1, the size and apparent magnitude
comparisons further reinforce the benefits of using model-independent
technique for measuring galaxy structural properties.

###  4.5 Stellar masses

Figure 10: Comparisons of our stellar mass estimates from DESI photometry
measured within $\rm R_{23.5,z}$ shown on the x-axis versus those from various
literature sources. The y-axes compare stellar mass estimates from panel (a):
P19; panel (b): Pipe3D (Sánchez et al., 2016); panel (c): NSA photometry
(Blanton & Roweis, 2007); and panel (d) the MPA-JHU catalogue (Kauffmann et
al., 2003; Brinchmann et al., 2004). The colour scheme matches that of Figure
5. The solid line shows the median trends and the shaded regions represent the
scatter within a bin. The top left inset gives the number of LTG (blue) and
ETG (red) galaxies, as well as the rms for the respective stellar mass
differences.

Figure 10 presents a comparison of our stellar mass estimates on the x-axis
versus various literature sources on the y-axis. Our stellar masses are an
amalgam of 30 variants derived from optical MLCRs (RC15; Z17; B19). These
MLCRs use stellar population synthesis (SPS) models from Bruzual & Charlot
(2003, hereafter BC03) and Conroy & Gunn (2010). The MLCRs presented in B19
apply to all galaxy morphologies, while RC15 and Z17 were only calibrated for
LTGs and are here only used for those systems. The stellar masses from P19 in
panel (a) were derived using $\Upsilon_{*}$ ratios calculated with a principal
component analysis (PCA) that finds the best-fitting synthetic spectra for
each MaNGA spaxel observation. Our stellar masses are measured within $R_{\rm
23.5}$ in the z band, while those from P19 are calculated using the footprint
of the MaNGA IFU with aperture correction performed using NSA excess fluxes.

The aperture-corrected stellar masses from P19 appear to be systematically
larger than our estimates, especially for MaNGA LTGs (panel a of Figure 10).
The comparison yields an rms offset of 0.25 (0.14) dex and a scatter of 0.09
(0.08) for the LTG (ETG) populations. These systematic differences are likely
due to the adopted star formation histories (SFHs). P19 adopted smooth SFH
templates; the omission of bursts in SFHs can bias the $\Upsilon_{*}$ high
(RC15), resulting in larger stellar mass estimates. These systematic effects
are more pronounced for LTGs as these systems have more bursty and active star
formation histories. However, the reported rms offsets for this comparison are
well within the systematic errors expected for MLCRs. Panel (b) compares our
stellar masses against those calculated from Pipe3D (Sánchez et al., 2016);
these are integrated within the FOV of the MaNGA IFU. We find an even larger
rms offset and scatter range than our comparison with P19. The Pipe3D
comparison shows a large rms difference of 0.30 dex and a scatter of 0.16
(0.1) dex for the LTGs (ETGs). For both LTGs/ETGs, our stellar mass estimates
at the low (high) mass end are smaller (larger) than Pipe3D. The difference
between our respective stellar mass estimates may arise from $\Upsilon_{*}$
calculation, which is done pixel by pixel for Pipe3D whereas our
$\Upsilon_{*}$ is calculated using a global colour.

Panel (c) in Figure 10 compares stellar mass estimates inferred via
K-corrected elliptical Petrosian photometry from the NSA (Blanton & Roweis,
2007). In our stellar mass comparisons, NSA estimates present the largest
discrepancy with the our photometry. Sources for this offset include (i)
missing flux in the NSA photometry, (ii) adoption of simple stellar
populations (SSPs) for the $\Upsilon_{*}$ conversions, and/or (iii) the use of
Petrosian magnitudes. The NSA elliptical-Petrosian photometry has been shown
to yield bluer colors $(\Delta(g-r)=0.046\pm 0.008)$ that the SDSS photometry
for the complete MaNGA sample P19, thus causing systematic differences in
stellar mass estimates.

Finally, Panel (d) compares our stellar mass estimates with those from the
MPA-JHU catalogue (Brinchmann et al., 2004). Their stellar mass estimates are
calculated using the $z$-band stellar $\Upsilon_{*}$ ratio obtained using the
SDSS spectra that best model the H$\,\delta$ and D4000 absorption features
applied to $z$ band luminosities. The comparison in Panel (d) shows a superb
match between the MPA-JHU and our photometry with a median across all bins
lying close to the 1:1 line and an rms of 0.23 (0.12) dex for the LTGs (ETGs).
Comparing all stellar mass estimates presented in Figure 10, MPA-JHU has the
best agreement for both morphological types.

##  5 MIR Structural Parameters

Figure 11: Comparison of total integrated luminosity inferred from DESI and W1
images measured at $R_{23.5,z}$. The blue circles present the MaNGA-LTGs, and
red triangles present MaNGA-ETGs. The orange line shows the best fit for the
complete population and inset text presents statistics for the two
populations. Figure 12: Comparison of stellar masses inferred from DESI and W1
images measured at $R_{23.5,z}$. The format is the same as Figure 11. For
LTGs, "opt" stellar masses are an average of five MLCRs presented in Section
2.2.4. For ETGs, "opt" stellar masses are measured using the MLCR of B19.

This section presents a comparison of galaxy structural parameters extracted
from our optical and MIR photometry. We first caution that surface
brightnesses sampled with different pixel resolutions, as is the case here
with the DESI and WISE data, cannot be compared directly unless profiles are
all sampled (degraded) to the lowest resolution. Therefore, only integrated
quantities between DESI and WISE data are compared below.

Figure 11 shows the W1 and DESI z-band luminosities measured at $R_{23.5,z}$.
For the complete sample, W1 luminosities are typically larger than z-band
luminosities by $\sim$0.3 dex, as a result of a greater sensitivity of the W1
bandpass to the dominant low mass (older) stellar population and lesser dust
extinction in the W1 band. Furthermore, the W1-$z$ colour term grows
significantly with luminosity, as seen in the residual panel of Figure 11. The
scatter between DESI z and W1 luminosities is tighter for the MaNGA-ETGs (than
LTGs) largely due to their star formation activity being quenched (Cluver et
al., 2014). The larger scatter for the LTGs population is also indicative of a
more diverse stellar population and larger dust content.

Finally, Figure 12 compares stellar masses inferred from optical and MIR
photometry measured at $R_{23.5,z}$. As discussed in Section 2.2.4, we used
the average of five different MLCRs with $g-r$ and $g-z$ colours to calculate
optical stellar masses. Mass estimates of a stellar population should not
depend on the flux tracer, however dust extinction in optical bands could lead
to systematic offsets, especially in late-type systems. While a systematic
offset of 0.21 dex is detected in Figure 12, with W1 stellar masses being
larger than optical, the latter is within the bounds of typical MLCRs
systematic variations of 0.2-0.3 dex (Taylor et al., 2011; Courteau et al.,
2014; Roediger & Courteau, 2015). Our optical and MIR stellar mass
measurements are thus in good agreement RC15. This reaffirms the conclusion
that optical colours are robust tracers of the stellar mass (Taylor et al.,
2011).

The differences in luminosity, and stellar mass (11 and 12 respectively) at
different wavelengths can serve as calibrators for stellar population models
and numerical models of galaxy formation (MacArthur et al., 2004; Renzini,
2006; Zheng et al., 2020).

##  6 Galaxy Scaling Relations

In the previous sections, we have demonstrated the robustness of our optical
and MIR photometry. We have also shown that our DESI optical photometry is
$\sim$1.5 mag arcsec-2 deeper than nominal SDSS imaging, and we have used the
MLDL-VAC to define our MaNGA LTG and ETG subsamples.

We now present, in Table 5, a variety of scaling relations in DESI (g, r, z)
and WISE (W1, W2) band passes for our MaNGA data. The scaling relations are
all presented as orthogonal linear regressions (Virtanen et al., 2020, SCIPY).
This treatment facilitates comparisons with matching studies in the
literature, though we note that subtle differences in choice of fitting method
and parameter definition can affect the final scaling relation parameters (see
Table 6). As discussed in Section 3 and Figure 3 some distributions may call
for more complex modelling, such as that characterized by a slowly varying
slope or a piece-wise function. We revisit these complexities below.

Below we focus on two popular scaling relations drawn from our DESI and WISE
photometric investigations of MaNGA LTGs and ETGs, namely the size–stellar
mass ($R-M_{*}$) and $\Sigma_{1}$–stellar mass ($\Sigma_{1}$-M∗) relations. In
the following sections, all structural parameters are measured at R23.5 in the
$z$ band unless otherwise stated.

Scaling relation | Band | $y$ | $x$ | Type | Slope | Zero-point | Scatter | N
---|---|---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9)
Projected size–luminosity | g | $\log R_{23.5}^{g}$ | $\log L_{23.5}^{g}$ | LTGs | $0.44\pm 0.01$ | $-3.55\pm 0.03$ | $0.08\pm 0.01$ | 2411
|  |  |  | ETGs | $0.49\pm 0.01$ | $-4.05\pm 0.04$ | $0.06\pm 0.01$ | 1796
|  |  |  | All | $0.42\pm 0.01$ | $-3.32\pm 0.03$ | $0.10\pm 0.01$ | 4215
Projected size–luminosity | r | $\log R_{23.5}^{r}$ | $\log L_{23.5}^{r}$ | LTGs | $0.43\pm 0.01$ | $-3.40\pm 0.03$ | $0.08\pm 0.01$ | 2426
|  |  |  | ETGs | $0.52\pm 0.01$ | $-4.37\pm 0.04$ | $0.06\pm 0.01$ | 1801
|  |  |  | All | $0.44\pm 0.01$ | $-3.40\pm 0.03$ | $0.10\pm 0.01$ | 4236
Projected size–luminosity | z | $\log R_{23.5}^{z}$ | $\log L_{23.5}^{z}$ | LTGs | $0.41\pm 0.01$ | $-3.21\pm 0.03$ | $0.08\pm 0.01$ | 2456
|  |  |  | ETGs | $0.54\pm 0.01$ | $-4.56\pm 0.05$ | $0.07\pm 0.01$ | 1790
|  |  |  | All | $0.44\pm 0.01$ | $-3.41\pm 0.03$ | $0.10\pm 0.01$ | 4254
Projected size–luminosity | W1 | $\log R_{23.5}^{{\it W1}}$ | $\log L_{23.5}^{{\it W1}}$ | LTGs | $0.36\pm 0.01$ | $-2.49\pm 0.12$ | $0.10\pm 0.01$ | 168
|  |  |  | ETGs | $0.46\pm 0.02$ | $-3.59\pm 0.17$ | $0.09\pm 0.01$ | 97
|  |  |  | All | $0.40\pm 0.01$ | $-2.98\pm 0.11$ | $0.11\pm 0.01$ | 265
Projected size–luminosity | W2 | $\log R_{23.5}^{W2}$ | $\log L_{23.5}^{W2}$ | LTGs | $0.34\pm 0.02$ | $-2.32\pm 0.22$ | $0.10\pm 0.02$ | 67
|  |  |  | ETGs | $0.42\pm 0.03$ | $-3.19\pm 0.32$ | $0.08\pm 0.02$ | 32
|  |  |  | All | $0.37\pm 0.02$ | $-2.63\pm 0.17$ | $0.10\pm 0.01$ | 99
Projected size–stellar mass | g | $\log R_{23.5}^{g}$ | $\log M_{*,23.5}$ | LTGs | $0.34\pm 0.01$ | $-2.61\pm 0.03$ | $0.12\pm 0.01$ | 2408
|  |  |  | ETGs | $0.40\pm 0.01$ | $-3.39\pm 0.04$ | $0.07\pm 0.01$ | 1790
|  |  |  | All | $0.30\pm 0.01$ | $-2.22\pm 0.03$ | $0.14\pm 0.01$ | 4206
Projected size–stellar mass | r | $\log R_{23.5}^{r}$ | $\log M_{*,23.5}$ | LTGs | $0.34\pm 0.01$ | $-2.57\pm 0.03$ | $0.10\pm 0.01$ | 2408
|  |  |  | ETGs | $0.46\pm 0.01$ | $-3.88\pm 0.04$ | $0.07\pm 0.01$ | 1790
|  |  |  | All | $0.34\pm 0.01$ | $-2.53\pm 0.03$ | $0.12\pm 0.01$ | 4206
Projected size–stellar mass | z | $\log R_{23.5}^{z}$ | $\log M_{*,23.5}$ | LTGs | $0.35\pm 0.01$ | $-2.57\pm 0.03$ | $0.10\pm 0.01$ | 2408
|  |  |  | ETGs | $0.49\pm 0.01$ | $-4.17\pm 0.05$ | $0.07\pm 0.01$ | 1790
|  |  |  | All | $0.37\pm 0.01$ | $-2.73\pm 0.03$ | $0.12\pm 0.01$ | 4206
Projected size–stellar mass | W1 | $\log R_{23.5}$ | $\log M_{*,23.5}$ | LTGs | $0.34\pm 0.01$ | $-2.51\pm 0.13$ | $0.11\pm 0.01$ | 168
|  |  |  | ETGs | $0.46\pm 0.02$ | $-3.59\pm 0.16$ | $0.10\pm 0.01$ | 97
|  |  |  | All | $0.41\pm 0.01$ | $-2.98\pm 0.11$ | $0.12\pm 0.01$ | 265
Projected size–stellar mass | W2 | $\log R_{23.5}$ | $\log M_{*,23.5}$ | LTGs | $0.40\pm 0.02$ | $-2.80\pm 0.21$ | $0.10\pm 0.01$ | 67
|  |  |  | ETGs | $0.44\pm 0.02$ | $-3.38\pm 0.35$ | $0.10\pm 0.02$ | 32
|  |  |  | All | $0.42\pm 0.02$ | $-3.04\pm 0.19$ | $0.11\pm 0.01$ | 99
Physical size–stellar mass | z | $\log r_{23.5}$ | $\log M_{*,23.5}$ | LTGs | $0.36\pm 0.01$ | $-2.83\pm 0.04$ | $0.11\pm 0.01$ | 2433
|  |  |  | ETGs | $0.50\pm 0.01$ | $-4.07\pm 0.03$ | $0.07\pm 0.01$ | 1839
|  |  |  | All | $0.42\pm 0.01$ | $-3.26\pm 0.03$ | $0.10\pm 0.01$ | 4274
Physical size–stellar mass | W1 | $\log r_{23.5}$ | $\log M_{*,23.5}$ | LTGs | $0.36\pm 0.01$ | $-2.51\pm 0.12$ | $0.11\pm 0.01$ | 168
|  |  |  | ETGs | $0.46\pm 0.02$ | $-3.45\pm 0.16$ | $0.10\pm 0.01$ | 97
|  |  |  | All | $0.41\pm 0.01$ | $-3.02\pm 0.12$ | $0.12\pm 0.01$ | 265
$\Sigma_{1}$–stellar mass | grz | $\log\Sigma_{1}$ | $\log M_{*,23.5}$ | LTGs | $0.96\pm 0.01$ | $-0.86\pm 0.08$ | $0.24\pm 0.01$ | 2408
|  |  |  | ETGs | $0.66\pm 0.01$ | $\phantom{-}2.43\pm 0.11$ | $0.26\pm 0.01$ | 1790
|  |  |  | All | $0.91\pm 0.01$ | $-0.31\pm 0.07$ | $0.29\pm 0.01$ | 4206
$\Sigma_{\rm eff}$-stellar mass | grz | $\log\Sigma_{\rm eff}$ | $\log M_{*,23.5}$ | LTGs | $0.70\pm 0.01$ | $\phantom{-}1.16\pm 0.13$ | $0.36\pm 0.01$ | 2408
|  |  |  | ETGs | $-0.01\pm 0.03$ | $\phantom{-}8.85\pm 0.29$ | $0.33\pm 0.01$ | 1790
|  |  |  | All | $0.62\pm 0.01$ | $\phantom{-}2.06\pm 0.12$ | $0.43\pm 0.01$ | 4206
Table 5: MaNGA Photometric Galaxy Scaling Relations in the $g,r,z,$ W1, and W2 bands, with orthogonal linear fit results. Columns (1) and (2) give the scaling relation and the relevant photometric band(s); columns (3) and (4) give the variables on the y and x axis coordinates for the scaling relation; column (5) gives the morphological type used for the fit; columns (6)–(8) give the slope (m), zero-point (zp), and scatter ($\rm\sigma$) for our linear orthogonal distance regression; and column (9) gives the number of data points used in each fit. Scaling relation | Source | Sample | Type | Band | N | Slope | Scatter | Size metric
---|---|---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9)
$R-M_{*}$ | This Work | MaNGA | LTGs | z | 2408 | $0.35\pm 0.01$ | $0.10\pm 0.01$ | $R_{\rm 23.5}$
| Shen et al. (2003) | SDSS | LTGs | z | 99 786 | $0.40$ | $0.15$ | $R_{\rm eff}$
| Pizagno et al. (2005) | SDSS | LTGs | i | 81 | $0.242\pm 0.030$ | n/a | $R_{\rm d}$
| Lange et al. (2015) | GAMA | LTGs | z | 6151 | $0.21\pm 0.02$ | n/a | $R_{\rm eff}$
| Ouellette et al. (2017) | SHIVir | LTGs | i | 69 | $0.34\pm 0.02$ | $0.15$ | $R_{\rm 23.5}$
| Stone et al. (2021) | PROBES | LTGs | z | 1152 | $0.334^{0.009}_{0.004}$ | $0.099^{0.002}_{0.003}$ | $R_{\rm 23.5}$
| Trujillo et al. (2020) | IAC Stripe82 | LTGs | i | 464 | $0.318\pm 0.014$ | $0.087\pm 0.05$ | $R_{\rm 23.5}$
$R-M_{*}$ | This Work | MaNGA | ETGs | z | 1790 | $0.49\pm 0.01$ | $0.07\pm 0.01$ | $R_{\rm 23.5}$
| Shen et al. (2003) | SDSS | ETGs | z | 99 786 | $0.56$ | $0.15$ | $R_{\rm eff}$
| Lange et al. (2015) | SDSS | ETGs | z | 2248 | $0.46\pm 0.02$ | n/a | $R_{\rm eff}$
| Ouellette et al. (2017) | SHIVir | ETGs | i | 121 | $0.35\pm 0.04$ | $0.12$ | $R_{\rm 23.5}$
| Trujillo et al. (2020) | IAC Stripe82 | ETGs | i | 279 | $0.453\pm 0.011$ | $0.042\pm 0.004$ | $R_{\rm 23.5}$
$\Sigma_{1}-M_{*}$ | This Work | MaNGA | LTGs | grz | 2408 | $0.96\pm 0.01$ | $0.24\pm 0.01$ | $R_{\rm 23.5}$
| Barro et al. (2017) | CANDELS | LTGs | – | 1328 | $0.89\pm 0.03$ | $0.25$ | n/a
| Woo & Ellison (2019) | MaNGA | LTGs | i |  $\sim$41 000 | 0.86 | 0.24 | n/a
| Stone et al. (2021) | PROBES | LTGs | z | 1152 | $1.004^{0.021}_{0.035}$ | $0.231^{0.005}_{0.006}$ | $R_{\rm 23.5}$
$\Sigma_{1}-M_{*}$ | This Work | MaNGA | ETGs | grz | 1790 | $0.66\pm 0.01$ | $0.25\pm 0.01$ | $R_{\rm 23.5}$
| Barro et al. (2017) | CANDELS | ETGs | – | 151 | 0.65 | 0.14 | n/a
| Woo & Ellison (2019) | MaNGA | ETGs | i |  $\sim$15 000 | 0.75 | 0.17 | n/a
| Fang et al. (2013) | GALEX/SDSS | ETGs | i | 1247 | 0.64 | 0.16 | n/a
Table 6: Literature comparisons for scaling relation from our photometry.
Column (1) shows the scaling relation; column (2) presents the literature
source; column (3) shows the sample used for the scaling relation; column(4)
presents the morphological type; column (5) lists the photometric band used
for the analysis; columns (6), (7) and (8) present the number of data points,
slope and scatter for the best fit line; finally column (9) presents the size
metric used for constructing the scaling relation. "n/a" are shown where the
data are not available.

###  6.1 Size–stellar mass ($R-M_{*}$) relation

Figure 13: Size–stellar mass relation for LTGs (left-hand panel) and ETGs
(right-hand panel). In each panel, grey filled contours represent the
distribution of our DESI photometric data; the cyan (LTGs) and red (ETGs)
lines are the orthogonal best fit for the corresponding populations. The
orange triangles and solid line represent the same structural parameters
measured with the WISE (W1) data. The dotted lines in each panel correspond to
the 1$\sigma$ scatter about the best-fitting line. In the left-hand panel, the
$R-M_{*}$ relation for ${\sim}$1100 PROBES galaxies is presented as a pink
line (Stone et al., 2021). Both panels show the $R-M_{*}$ relation of Trujillo
et al. (2020) based on ${\sim}$1000 galaxies. Piece-wise linear fits to the
DESI and WISE data are also shown for the ETGs (see the text for details.)

Figure 13 shows the $R-M_{*}$ relation for LTG and ETG populations measured
from our DESI and WISE photometry. The parameter distributions are shown as
density contours, while the cyan (red) lines represent the orthogonal best
fits to the LTG (ETG) data. The pink solid line shows the best-fitting
relation from Stone et al. (2021) who used a compilation of LTG surveys with
DESI imaging for $\sim$1100 spiral galaxies. The photometric analyses for our
MaNGA and PROBES samples use the same methods (DESI photometry, AUTOPROF ,
surface brightness profile treatments, photometric band). It is therefore not
surprising that our linear regression should match the PROBES fit so well.
Stone et al. (2021) also report a scatter of $0.099^{+0.002}_{-0.003}$ which
is in perfect agreement with the observed scatter of our MaNGA galaxies.
Overall, the MaNGA and PROBES LTGs have matching $R-M_{*}$ properties measured
from a distinct sample of galaxies (though matching analysis routines).

The left-hand panel of Figure 13 (blue solid line) also presents a comparison
with the linear $R-M_{*}$ relation from Trujillo et al. (2020) who reported a
slope of $0.318\pm 0.014$ and a scatter of $0.087\pm 0.005$, based on SDSS-i
band imaging and using isophotal sizes at 23.5 mag arcsec-2 . The different
photometric band used in our respective analysis may explain the slight slope
and scatter mismatch for our respective $R-M_{*}$ relations.

For LTGs, the slope of the $R-M_{*}$ relation is independent of wavelength
(Table 5). This agrees with Lange et al. (2015) who showed minimal variations
in the slope of the $R-M_{*}$ relation for 8400 GAMA galaxies (Driver et al.,
2009) across the ugrizZYJHK photometric bands modulo random variations (see
Table 6). The actual value of our respective slopes differ on account of our
respective size metric choices (effective vs. isophotal radius).

The density map and the red solid line in the right-hand panel of Figure 13
represent the $R-M_{*}$ relation for our ETG sample. The single linear
$R-M_{*}$ relation for ETGs is steeper (larger slope) and tighter (smaller
scatter) than for LTGs. The slope and scatter of the ETGs $R-M_{*}$ relation
is likely controlled by their formation via repeated mergers on high impact
parameter orbits (Shen et al., 2003). Dry (gas-less) mergers are the most
plausible explanation for the steep size growth of the ETGs From $z\sim 1$ to
now (Huertas-Company et al., 2013).

Our linear $R-M_{*}$ relation is in general agreement with (Trujillo et al.,
2020), who found a slope of $0.453\pm 0.011$ and an observed scatter of
$0.042\pm 0.004$ for 280 galaxies. The differences in best-fitting parameters
are a result of the choice photometric band (SDSS-i) and least-square linear
regression. Lange et al. (2015) found a range of $R-M_{*}$ relation slopes of
$0.46-0.56$ (scatter not reported) for GAMA galaxies (Driver et al., 2009) in
the SDSS-z band. They also used effective radii as the size metric making
comparisons challenging. The exact value of the slope in Lange et al. (2015)
depends largely on their morphological assignments of ETGs as guided by Seŕsic
index, dust-corrected optical colour, and visual classification. We find a
general trend that the $R-M_{*}$ relation for ETGs is steeper (shallower) if
effective (isophotal) radii are used.

Figure 13 also presents the linear $R-M_{*}$ relation for our WISE W1
photometry with the orange line and triangles for the LTGs/ETGs in the
left-/right-hand panels. This relation (slope and scatter) is essentially the
same as that inferred from DESI $z$-band images for our LTGs, further
highlighting our conclusions in Table 5 that the slope and scatter for LTG
$R-M_{*}$ relation is independent of the wavelength. The scatter and slope of
the ETG WISE $R-M_{*}$ relation differ slightly from their $z$-band
counterpart. This result is similar to that of Lange et al. (2015), who found
large random variations in the slope of $R-M_{*}$ relation for ETGs.

Along with the projected $R-M_{*}$ relation (Table 5), we can calculate this
relation with physical radii (see Section 2.2.1). Table 5 presents the
physical $r_{23.5}-M_{*}$ relation for the DESI z and W1 photometric bands.
The projected and physical $r-M_{*}$ relations for LTGs are equal by
definition. For ETGs physical sizes increase by 4/3 relative to projected
values (Hernquist, 1990; Chiosi & Carraro, 2002), resulting in a predictable
change in zero-points (by 0.125 dex) of the best-fitting relation. The best
linear fits to physical relations are presented in Table 5.

Band | N | M∗ limit | Piece-wise fits
---|---|---|---
(1) | (2) | (3) | (4)
DESI-z | 1854 | $\rm\log M_{*}\leq 10.20$ | $\rm 0.31(\log M_{*}-10.20)+0.80$
|  | $\rm\log M_{*}>10.20$ | $\rm 0.55(\log M_{*}-10.20)+0.80$
W1 | 97 | $\rm\log M_{*}\leq 10.81$ | $\rm 0.41(\log M_{*}-10.81)+1.05$
|  | $\rm\log M_{*}>10.81$ | $\rm 0.52(\log M_{*}-10.81)+1.05$
Table 7: Linear piece-wise $R-M_{*}$ relations for MaNGA-ETGs. columns (1) and
(2) give the photometric band and number of data points used for the fit;
column (3) shows the stellar mass limit for the change in slope; and column
(4) presents the piece-wise fits.

Given the bimodalities in stellar mass and sizes for ETGs seen in Figure 3, we
also model the $R-M_{*}$ relation based on DESI and WISE imaging with a double
piece-wise linear fit (see Table 7). It is found that the slopes of our
$R-M_{*}$ relations for LTGs and ETGs based on DESI and WISE data agree
closely with the theoretical expectations. For LTGs, it can be shown that
$R_{opt}\propto M_{*}^{0.33}$ for virialized galaxy discs and assuming
constant $\Upsilon_{*}$ per galaxy (Courteau et al., 2007). Various scaling
arguments connecting structure formation to primordial density fluctuations
(Blumenthal et al., 1984) also suggest that massive ETGs
($\log(M_{*}/M_{\odot})\geq 10$) have $R\propto M_{*}^{0.53}$ (Burstein et
al., 1997; Chiosi & Carraro, 2002; D’Onofrio et al., 2020). The slope for
lower mass ETGs is predicted to be shallower with $R\propto M_{*}^{0.33}$;
closer to that of LTGs in the same mass range (Chiosi & Carraro, 2002; Woo et
al., 2008). The piece-wise linear fit slopes for ETGs (Table 7), with a low
and high mass transition at $\log(M_{*}/M_{\odot})\sim 10.2$ matches
theoretical expectations (0.33/0.53) in the same stellar mass bins quite
closely (Blumenthal et al., 1984; Chiosi & Carraro, 2002). The same statement
holds for the WISE data with stellar mass transition being larger than the
optical data. However, this larger stellar mass transition could be attributed
to small statistics for low-mass WISE ETGs.

The agreement between the observed and predicted $R-M_{*}$ slopes is certainly
encouraging. However, a complete data-model investigation should also match
the zero-points, and scatters of observed scaling relations. Our MaNGA data
base serves as a stepping stone for such a comparison with theoretical and
numerical models of galaxy formation and structure.

In the next section, we explore other size metrics and their effects on slopes
and scatters of the $R-M_{*}$ relation.

###  6.2 Slope and scatter variations of the $R-M_{*}$ relation

Figure 14: Variations of the slope and orthogonal scatter of the $R-M_{*}$
relation of LTGs (blue) and ETGs (red) for different size measurements. The
top panels show size measurements at various fractions of total light.
Isophotal size measurements are presented in the bottom panels. $R-M_{*}$
slopes are presented in the left-hand panels with connected squares. Observed
orthogonal scatter measurements are presented in the right-hand panels with
connected triangles. The error bars on all points correspond to bootstrap
uncertainties.

The spatially-resolved nature of our photometric solutions enables a detailed
study of the $R-M_{*}$ relation with a suite of size metrics for both LTGs and
ETGs, as shown in Figure 14.

####  6.2.1 Slope variations of the $R-M_{*}$ relation

The left-hand panels of Figure 14 show variations of the slope of the
$R-M_{*}$ relation with size metrics measured relative to the total light (top
panels) and isophotal levels (bottom panels). For both morphologies, the slope
of the $R-M_{*}$ relation increases linearly with light fraction. However, the
$R-M_{*}$ slopes for LTGs and ETGs with sizes measured at different isophotal
levels have nearly opposite behaviours, as seen in the bottom left-hand panel
of Figure 14. The $R-M_{*}$ relation slope for LTGs settles to the theoretical
value of 0.33 (Courteau et al., 2007) between 23 and 26 $z$-mag arcsec-2 . The
slope for the ETGs grows steadily before flattening to a value of $\sim$0.53
at or beyond 26 $z$-mag arcsec-2 . The value where the slope flatten agrees
with the theoretical prediction found in Burstein et al. (1997) and Chiosi &
Carraro (2002). The exact nature of the slope of the $R-M_{*}$ relation as a
function of size metric can be related to the interplay between the relative
slopes of the surface brightness profiles and COG.

For LTGs, $R-M_{*}$ slopes range from 0.13 to 0.39 (fractional) or 0.39 to
0.33 (isophotal); the slopes are always smaller if measured relative to the
total light, and the trends are opposite. For ETGs, $R-M_{*}$ slopes range
from 0.42 to 0.62 (fractional) or 0.39 to 0.63 (isophotal). The steeper
$R-M_{*}$ slope for ETGs (see Section 6.1) is expected from a high occurrence
of dry mergers and feedback from stars and supermassive black holes (Shen et
al., 2003; Huertas-Company et al., 2013). The use of $R_{\rm eff}$ also yields
a closer match to theoretical predictions of the $R-M_{*}$ slope. The
theoretical prediction can also be matched with isophotal radii by binning
galaxies in stellar mass (similar to Chiosi et al., 2020).

####  6.2.2 Scatter variations of the $R-M_{*}$ relation

The right-hand panels of Figure 14 show variations in the orthogonal scatter
of the $R-M_{*}$ relation with size metrics measured relative to the total
light (top panels) and isophotal levels (bottom panels). For both
morphologies, the $R-M_{*}$ scatter profiles (top right-hand panel of Figure
14) show different behaviours. The scatter for LTGs decreases monotonically
from 0.20 to 0.15 dex with increasing total light fraction. The tightest
$R-M_{*}$ relation is found when all the light from our photometry is taken
into account. For ETGs, the scatter of the $R-M_{*}$ relation is mostly
constant around $\sim$0.14 dex for all size metrics.

Trends with isophotal sizes differ: smallest orthogonal scatter for the
$R-M_{*}$ relation is found at 18.5 (21.6) $z$-mag arcsec-2 for LTG (ETG)
populations. Our conclusions remain the same if forward scatter was used
instead of orthogonal. This result comes as a surprise in light of the current
literature that points to the isophotal radius of 23.5 mag arcsec-2 that
minimizes the scatter of VRL scaling relations (Courteau, 1996; Hall et al.,
2012). More recently, Trujillo et al. (2020) found the radius corresponding to
a stellar surface density of $\rm 1\,M_{\odot}\,pc^{-2}$ also shows a tight
$R-M_{*}$ relation along with the added benefit of definition motivated by the
physics of star formation in galaxies. This radius corresponds to a fainter
isophote ($\sim$26 mag arcsec-2 ) which is larger than the isophotal radius of
23.5 mag arcsec-2 . Our findings contradict this as the radius giving the
tightest $R-M_{*}$ relation is found to be at 18.5 (21.5) z mag arcsec-2 for
LTGs (ETGs). Sánchez Almeida (2020) performed a similar exercise and found the
isophotal radius of $\rm 24.7\pm 0.5$ $r$-mag arcsec-2 minimizes the scatter.
The difference between our results are related to the definition of scatter of
a linear relation (half of inter-quartile range vs. rms) and the choice of the
photometric band (DESI-z vs. SDSS-r).

Scatter values are also always smaller for isophotal sizes than light fraction
sizes. This occurs because light fraction sizes encompass multiple surface
brightness levels, thus enhancing the mix of stellar populations at any radius
and yielding larger $R-M_{*}$ scatter values (see e.g. Trujillo et al., 2020).
The results in this section are further corroborated with our MIR photometry
that show similar trends [minimum scatter on 17.5(20) mag arcsec-2 for
ETGs(LTGs)]. These are not shown in Figure 14 for simplicity. It has been
noted the the isophotal level of 23.5 $i$-mag arcsec-2 minimizes scatter of
the TFR (Giovanelli et al., 1994; Hall et al., 2012). In an upcoming
publication, we investigate the radius, if any, that minimizes the scatter of
the VRL scaling relations simultaneously.

###  6.3 $\Sigma_{1}$-stellar mass ($\Sigma_{1}$–M∗) relation

Figure 15: $\Sigma_{1}$ \- stellar mass relation for the LTGs (left-hand
panel) and ETGs (right-hand panel) using our optical DESI photometry. The
density maps in grey show the data distribution. Orthogonal best fits are
represented by solid cyan (LTGs) and red (ETGs) lines; the dotted lines show 1
$\sigma$ scatter for the best-fitting relations. For LTGs, the stellar masses
are measured as the average of five MLCRs presented in Section 2.2.4. For
ETGs, the stellar masses are measured using the MLCR of B19. We compare our
LTG relation with Woo & Ellison (2019) and Stone et al. (2021), and our ETG
relation with Fang et al. (2013) and Barro et al. (2017) (see the text for the
redshift range). Both panels show the $\Sigma_{1}-M_{*}$ relation of Chen et
al. (2020a) which fits all morphological types. A piece-wise linear fit to the
DESI data is also shown for the ETGs (see the text for details).

The $\Sigma_{1}-M_{*}$ relation reveals information about the star formation
and merger histories of galaxies (Barro et al., 2017) and the physical/time
evolution of their central components of galaxies (Woo & Ellison, 2019; Chen
et al., 2020a; Chen et al., 2020b). While the calculation of the stellar
surface density at 1 kpc can be challenging given large distance errors and
saturation issues, $\Sigma_{1}$ traces properties as the bulge component with
the added advantage of being model-independent. Figure 15 shows the
$\Sigma_{1}-M_{*}$ relation for MaNGA LTGs and ETGs based on our DESI optical
photometry. Because the WISE data cannot resolve 1-kpc regions for MaNGA
galaxies, this section on $\Sigma_{1}$ only uses our optical photometry.

Our orthogonal fit parameters for the $\Sigma_{1}-M_{*}$ relation are
presented in the bottom row of Table 5. Stone et al. (2021) found a similar
$\Sigma_{1}-M_{*}$ relation with a slope of $1.005^{0.021}_{0.035}$ and a
scatter of $0.23\pm 0.01$ dex for their PROBES sample.

This relation is also fit by Woo & Ellison (2019) who found a
$\Sigma_{1}-M_{*}$ slope of 0.86 and a scatter of 0.24 dex using ${\sim}2100$
MaNGA galaxies with SDSS photometry and MPA-JHU stellar masses (Brinchmann et
al., 2004; Kauffmann et al., 2004). Their different slope may be explained by
their use of the SDSS i band, a different definition of stellar mass and a
least-square linear fit. Their fit is not a good match to our relation (Figure
15).

Our $\Sigma_{1}-M_{*}$ slope for ETGs matches closely to that of Fang et al.
(2013) whose study of ${\sim}1300$ quenched galaxies selected from the SDSS
with $z<0.075$ yielded a slope of $0.64^{+0.23}_{-0.20}$. However, their
reported scatter of 0.16 dex is significantly smaller than ours. This
disagreement could be due to sample selection, choice of MLCRs to calculate
stellar masses and the assumptions about the IMF. The conversion of light into
stellar mass is also inherently uncertain. While our study targets
morphologically selected ETGs, Fang et al. (2013) selected green valley
galaxies that are quenched. Even though there is overlap in these samples, an
ETG sample and green valley/quenched sample are different. For instance, green
valley galaxies can exhibit a range of morphologies (Mendez et al., 2011) and
ETGs can show large range in star formation histories. In principle,
$\Sigma_{1}$ should be more sensitive to the star formation history than
visual morphologies explaining our larger scatter for the relation.

The right-hand panel of Figure 15 also shows the $\Sigma_{1}-M_{*}$ relation
of Barro et al. (2017) for CANDELS GOODS-S galaxies at $0.5<z<1.0$ (Guo et
al., 2013) who reported a slope of $0.65\pm 0.03$ and a zero-point of $2.71\pm
0.05$. For quiescent galaxies, Barro et al. (2017) found that the slope of the
$\Sigma_{1}-M_{*}$ relation remains constant as a function of redshift; only
the zero-point evolves with time. For a fixed stellar mass bin, $\Sigma_{1}$
should decrease over time (Barro et al., 2017). Our similar slopes and smaller
zero-point strengthen this assertion as our local universe MaNGA ETGs
($z<0.15$) achieve the same slope and a smaller zero point.

An interesting feature of the $\Sigma_{1}-M_{*}$ relation for ETGs is its
flattening for $\log(M_{*}/M_{\odot})\geq 10.7$. As a result of this feature,
and as stated for the $R-M_{*}$ relation of ETGs Section 6.1, caution should
be taken while fitting a linear relation to the ETG $\Sigma_{1}-M_{*}$
relation (see the right-hand panel of Figure 15). Along with the linear
regression, we fit piece-wise linear function to the data distribution, with
$\log\Sigma_{1}=0.90(\log M_{*}-10.73)+9.76$ for $\log M_{*}\leq 10.73$, and
$\log\Sigma_{1}=0.12(\log M_{*}-10.73)+9.76$ for $\log M_{*}>10.73$. We note
that the transition in stellar mass at $\log M_{*}\sim 10.7$ in this piece-
wise fit is mirrored in the bimodal distribution of stellar masses for ETGs
seen in Figure 3. However, the stellar mass transition in the $R-M_{*}$
relation of ETGs is found at $\rm\log M_{*}\sim 10.2$. We are reminded that
the bivariate distributions are controlled by two random variables.

Chen et al. (2020a) also used a piece-wise function to describe the
$\Sigma_{1}-M_{*}$ relation for the complete MaNGA sample calculated to be:
$\log\Sigma_{1}=0.93(\log M_{*}-10.95)+9.44$ for $\log M_{*}\leq 10.95$, and
$\log\Sigma_{1}=0.13(\log M_{*}-10.95)+9.44$ for $\log M_{*}>10.95$. Their
piece-wise linear fit is shown in the left- and right-hand panels of Figure
15. Their slopes for the low- and high-mass ends of the fit match ours quite
well. However, the disagreement in our respective zero-points is significant
and may result from our respective stellar mass calculations and different
samples. Chen et al. (2020a) used stellar masses provided by the NSA (Blanton
et al., 2011); our procedure is described in Section 2.2.4. Indeed, a large
difference is found between the stellar masses by NSA and in this study; our
photometry results in larger stellar masses by 0.34 (0.40) dex for LTGs (ETGs)
that could be due to the systematic offsets of the MLCRs (see Figure 10). Chen
et al. (2020a) fit a linear piece-wise function to the full MaNGA sample while
our fit is restricted to ETGs. Both of these effects could cause the observed
zero point difference, although it is surprising that the slopes remain
unaffected.

For LTGs and low-mass ETGs, the slope of the $\Sigma_{1}-M_{*}$ relation near
unity (0.96 and 0.90) is suggestive of a co-evolution of the inner and outer
regions through star formation and environmental interactions. Indeed, these
galaxies may have an enhanced $sSFR(=SFR/M_{*})$ which builds up stellar mass
in their inner regions (Woo & Ellison, 2019). The shallower $\Sigma_{1}-M_{*}$
slope (0.13) at the high-mass end for ETGs likely applies to galaxies with
little star formation but ongoing overall accretion, leading to a flattening
of the $\Sigma_{1}-M_{*}$ relation at $\Sigma_{1}\sim
10^{10}\rm\,M_{\odot}kpc^{-2}$. A complimentary explanation for the saturation
of $\Sigma_{1}$ in high mass ETGs involves partially depleted central cores
due to coalescing black holes at high redshifts (King & Minkowski, 1966;
Ferrarese et al., 1994; Lauer et al., 1995; Gebhardt et al., 1996; Graham &
Guzmán, 2003). A proper appreciation of the saturation of $\Sigma_{1}$ in
galaxies will require additional data, such as SFRs, maps of neutral and
molecular gas reservoirs, environmental parameters to characterize
interactions and gas infall, and more. While some of these data still exist, a
detailed investigations of the shallower slope at the high-mass end is beyond
the scope of this study. We also caution that $\Sigma_{1}$ may be sensitive to
projection, dust extinction, and stellar population effects.

##  7 Summary and Future Work

We have presented high-quality optical and MIR surface brightness profiles and
environmental properties for the MaNGA galaxy survey. We made use of DESI
imaging and our software (AUTOPROF ; (Stone et al., 2021)) to extract
azimuthally averaged optical surface brightness profiles. On average, the DESI
photometry reaches ${\sim}2$ mag arcsec-2 deeper than the SDSS photometry in
the gr photometric bands which arises from a combination of deeper DESI
imaging and our novel technique, AUTOPROF . The WISE profiles are extracted
from the WXSC (Jarrett et al., 2019) which uses deconvolution techniques to
achieve a higher resolution than the native WISE imaging. 70 per cent (33 per
cent) of the WISE W1 (W2) surface brightness profiles are as deep in radial
extent as the DESI photometry and can be used to compute scaling relations at
the fiducial isophotal radius $R_{23.5,z}$.

Excellent agreement is found between most model-independent structural
parameters from AUTOPROF and those obtained with well-tested surface
photometry routines based on the XVISTA software package for astronomical
image processing (Courteau, 1996). Disagreements between AUTOPROF , XVISTA and
the literature, are largely found for parameters that scale with total light
such as effective radii, effective surface brightness, and concentration
indices. The bimodal nature in the distribution of some structural parameters
is also suggestive of distinct galaxy populations in the Universe.

Detailed comparisons of our surface brightness profiles and structural
parameters with other studies were presented. The non-parametric surface
brightness profiles from AUTOPROF (DESI) and GC18 (SDSS) agree well, even
reproducing small local variations. However, the reconstructed surface
brightness profiles from the bulge-to-disc decompositions of GC18 and F19
exhibit large differences (${\sim 0.4}$ mag arcsec-2 ) demonstrating the
challenges involved in such parametric modelling. Moreover, similar
disagreements are found between our model-independent surface brightness
profiles and the parametric decompositions of both GC18 and F19, highlighting
once again the fragile nature of parametric modelling.

Our comparisons of effective radii and apparent magnitudes with PYMORPH of F19
have also revealed disagreements for $R_{\rm eff}$, especially for ETGs
$(rms\sim 0.2\,$)dex. Better comparisons are found for isophotal radii
$(rms\sim 0.05\,$)dex, demonstrating the superior reproducibility of isophotal
sizes over those measured relative to total light fractions. Our apparent
magnitudes are also typically brighter than those of F19 by $\sim$0.1 dex.
This is expected as, unlike parametric models, our non-parametric surface
brightness extraction captures all the light. The GALFIT implementations of
GC18 and F19 preferentially favor high S/N regions and systematically predict
fainter magnitudes for low S/N. These systematic effects average out to
fainter total integrated light, relative to our non-parametric results.

Our stellar mass estimates, measured at $\rm M_{*}(R_{23.5}^{z})$ and obtained
from multiband photometry and various MLCRs, compare favorably with those
found in the literature, such as MPA-JHU catalogue (Kauffmann et al., 2003),
NSA photometry (Blanton & Roweis, 2007), Pipe3D (Sánchez et al., 2016), and
P19. Our stellar masses for LTGs, based on the average of multiple MLCRs from
RC15, Z17, and B19, are 0.24 dex smaller than those of P19. This offset is
explained by the modelling of SFHs by P19 that systematically biases
$\Upsilon_{*}$ high. Our stellar masses for ETGs, based on the MLCR from B19,
are 0.11 dex smaller than those of P19. The largest stellar mass differences,
found for the NSA stellar mass estimates with an rms of 0.34 (0.40) dex for
LTGs (ETGs), may stem from uncertainties in the NSA elliptical-Petrosian
photometry. The best match with our stellar mass estimates is found for the
MPA-JHU catalogue, with an rms of 0.21 (0.11) dex for LTGs (ETGs).

We also present WISE photometry for a subset of $\sim 300$ MaNGA galaxies. It
provides an independent measure of stellar masses, which agree with our
optical estimates within 0.21 dex (see also Taylor et al., 2011). Dust
extinction may explain the small systematic differences in the stellar mass
estimates of LTGs. In addition to providing accurate stellar masses,
spatially-resolved MIR fluxes are most valuable for studies of the star
formation main-sequence, SFR$-M_{*}$ (Cluver et al., 2017; Hall et al., 2018)
stellar population properties (Cluver et al., 2014, 2020).

The slope and scatter of the $R-L_{*}$ and $R-M_{*}$ relations for LTGs are
found to be independent of bandpass (from g to W2 Table 5). For ETGs, slope
variations for the $R-M_{*}$ relation from bluer to redder bands can be linked
to varying stellar populations over a range of stellar masses (Lange et al.,
2015). The $R-L_{*}$ and $R-M_{*}$ slopes and scatters for LTGs and ETGs also
agree well, within 1 $\sigma$, with published values (see Figures 13 and 15).

We have examined the variations of the slope and scatter of the $R-M_{*}$
relation for a range of size metrics. The slopes of the $R-M_{*}$ relations
for LTGs and ETGs with size metrics measured relative to total light grow
linearly with fraction of total light. Conversely, slopes calculated using
isophotal sizes decrease (increase) for LTGs (ETGs) from brighter to fainter
regions. These trends are dictated by the relative slope variations in the
surface brightness profiles and curves of growth.

Isophotal sizes also yield tighter $R-M_{*}$ relations (smaller scatter) than
sizes measured at relative fractions of total light. The isophotal radius
measured at 18.5 (21.5) mag arcsec-2 also yields the tightest $R-M_{*}$
relation for the LTG (ETG) population by orthogonal scatter. Our orthogonal
linear fits result in slopes for the LTGs abs ETGs that match theoretical
predictions of the $R-M_{*}$ relations.

The $\Sigma_{1}-M_{*}$ relation is also presented for both MaNGA LTGs and ETGs
and an excellent agreement is found with the literature. For LTGs, the slope
of the $\Sigma_{1}-M_{*}$ relation is near unity, indicating a co-evolution of
stellar mass and $\Sigma_{1}$ that is driven by enhanced star formation and
environmental effects. For ETGs, a near constant $\Sigma_{1}$ is found for
$M_{*}>10.5$. A piecewise linear function was adopted to better match the
$\Sigma_{1}-M_{*}$ distribution. The saturation of $\Sigma_{1}$ at high
stellar mass could be related to SFRs, environment, neutral/molecular gas
distribution, etc.

The multiband photometry, environmental parameters, and structural scaling
relations presented in our study may be used to constrain stellar populations
models, test semi-analytic or numerical models of galaxy formation, and test
their subgrid physics prescriptions (Dutton & van den Bosch, 2009; Brook et
al., 2012; Henriques et al., 2015). While extensive, the photometry and
scaling relations studied here only inform us about baryonic properties of
galaxies. An essential aspect of galaxy formation and evolution is
understanding the co-evolution of baryons and dark matter through a
simultaneous study of photometric and kinematic properties of galaxies
(Courteau et al., 2007; Hall et al., 2012; Ouellette et al., 2017). The MaNGA
survey includes dynamical information for all observed galaxies, making this
an exciting avenue for related investigations.

## Data Availability

All data are incorporated into this paper and its online supplementary
material.

## Acknowledgements

We are especially grateful to the Natural Sciences and Engineering Research
Council of Canada, Ontario Government, and Queen’s University for support
through various scholarships and grants. THJ also acknowledges funding from
the National Research Foundation under the Research Career Advancement and
South African Research Chair Initiative programs (SARChI), respectively.
Special thanks go to the referee for valuable suggestions, and to Arjun Dey
and the Dark Energy Sky Instrument Legacy Imaging Survey team for their
extensive and accessible database. We also thank Alister Graham for insightful
comments that led to further clarifications and judicious references, as well
as Stephanie Rendell for contributing to our study of SDSS photometry with
XVISTA. Discussions with Mariangela Bernardi enabled a confirmation that the
model-dependent PYMORPH (GALFIT) apparent magnitudes presented in F19 are
circularized and inclination corrected (assuming infinitesimally-thin
transparent discs). This research made extensive use of astropy (Astropy
Collaboration et al., 2013), as well as data products from the Wide-field
Infrared Survey Explorer, which is a joint project of the University of
California, Los Angeles, and the Jet Propulsion Laboratory/California
Institute of Technology, funded by the National Aeronautics and Space
Administration.

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##  Appendix A Surface Brightness Profiles

This Appendix shows the output format of the DESI-grz and WISE W1, W2 surface
brightness profiles that are provided as supplementary material. The DESI and
WISE surface brightness profiles are provided in the AB and Vega magnitude
systems, respectively. The conversions from Vega to AB magnitudes in the W1
and W2 bands are given by (Jarrett et al., 2013):

$\rm m_{AB}^{{\it W1}}=m_{Vega}^{{\it W1}}+2.683,$ (6)

$\rm m_{AB}^{W2}=m_{Vega}^{W2}+3.319.$ (7)

Column | Unit | Description
---|---|---
(1) | (2) | (3)
R | arcsec | Semimajor axis length of the isophote
SB | mag arcsec-2 | Median surface brightness in the AB magnitude system
SB_E | mag arcsec-2 | Error on the surface brightness
MAG | mag | Total magnitude within the isophote, computed by integrating the surface brightness profile
MAG_E | mag | Error on the total magnitude within the isophote
ELLIP | – | Ellipticity of the isophote; $\epsilon=1-b/a$, where $b$ is the semi-minor axis length of the isophote, and $a=R$.
ELLIP_E | – | Error on the ellipticity, computed by analysing the local variability within 1 PSF
PA | ∘ | Position angle of isophote measured from north to east
PA_E | ∘ | Error on the position angle, computed by analysing the local variability within 1 PSF
MAG_DIRECT | mag | Total magnitude within the isophote computed by flux summation
SB_FIX | mag arcsec-2 | Average surface brightness in the AB magnitude system along isophote with ellipticity and position angle set to global values
SB_FIX_E | mag arcsec-2 | Error on SB_FIX
MAG_FIX | mag | Total magnitude enclosed within the isophote. Computed by integrating SB_FIX profile
MAG_FIX_E | mag | Error on MAG_FIX
Table 8: Output format of the DESI grz surface brightness profiles provided as supplementary material. Column (1) refers to the column names in each galaxy surface brightness profile; Column (2) shows the units for each parameter; Column (3) describes each profile entry. All DESI-grz surface brightness profiles are named with the MaNGA-ID followed with the extension "_AP.prof" Column | Unit | Description
---|---|---
(1) | (2) | (3)
radius | arcsec | Semimajor axis length of the isophote
SBpix | – | Surface brightness in digital number along the isophote
SBmag | ${{{{\rm mag}~{}{\rm arcsec}}^{-2}}}$ | Surface brightness in mag arcsec-2 along the isophote in the Vega magnitude system
SBerr | ${{{{\rm mag}~{}{\rm arcsec}}^{-2}}}$ | Error on surface brightness in the Vega magnitude system
SBtotmod | ${{{{\rm mag}~{}{\rm arcsec}}^{-2}}}$ | Total surface brightness for the bulge+disc model in the Vega magnitude system (Jarrett et al., 2019)
SBbulge | ${{{{\rm mag}~{}{\rm arcsec}}^{-2}}}$ | Surface brightness of the bulge component in the Vega magnitude system (Jarrett et al., 2019)
SBdisk | ${{{{\rm mag}~{}{\rm arcsec}}^{-2}}}$ | Surface brightness of the disc component in the Vega magnitude system (Jarrett et al., 2019)
Table 9: Output format of the WISE W1, W2 surface brightness profiles provided
as supplementary material. Column (1) refers to the column names in each
galaxy surface brightness profile; Column (2) shows the units for the
parameter; Column (3) describes each profile entry. All WISE W1, W2 surface
brightness profiles are named with the WISE catalogue name followed with the
extension ".profile.w1/w2.txt". A separate file named "DESI-WISE-index.tbl"
provides a conversion table between the MaNGA-ID and WISE-NAME.