# Rest-Frame Near-Infrared Radial Light Profiles up to $z=3$ from JWST/NIRCam:
Wavelength Dependence of the Sérsic Index

Marco Martorano Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281
S9, 9000 Gent, Belgium  Arjen van der Wel Sterrenkundig Observatorium,
Universiteit Gent, Krijgslaan 281 S9, 9000 Gent, Belgium  Eric F. Bell
Department of Astronomy, University of Michigan, 1085 South University Avenue,
Ann Arbor, MI 48109-1107, USA  Marijn Franx Leiden Observatory, Leiden
University, P.O. Box 9513, 2300 RA, Leiden, The Netherlands  Katherine E.
Whitaker Department of Astronomy, University of Massachusetts, Amherst, MA
01003, USA  Cosmic Dawn Center (DAWN), Niels Bohr Institute, University of
Copenhagen, Jagtvej 128, Kø benhavn N, DK-2200, Denmark  Angelos Nersesian
Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281 S9, 9000 Gent,
Belgium  Sedona H. Price Department of Physics and Astronomy and PITT PACC,
University of Pittsburgh, Pittsburgh, PA 15260, USA  Maarten Baes
Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281 S9, 9000 Gent,
Belgium  Katherine A. Suess Department of Astronomy and Astrophysics,
University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA 95064
USA  Kavli Institute for Particle Astrophysics and Cosmology and Department of
Physics, Stanford University, Stanford, CA 94305, USA  Erica J. Nelson
Department for Astrophysical and Planetary Science, University of Colorado,
Boulder, CO 80309, USA  Tim B. Miller Department of Astronomy, Yale
University, 52 Hillhouse Avenue, New Haven, CT 06511, USA  Rachel Bezanson
Department of Physics and Astronomy and PITT PACC, University of Pittsburgh,
Pittsburgh, PA 15260, USA  Gabriel Brammer Cosmic Dawn Center (DAWN), Niels
Bohr Institute, University of Copenhagen, Jagtvej 128, Kø benhavn N, DK-2200,
Denmark Marco Martorano<EMAIL_ADDRESS>
(Received January 1, 2999; Revised January 2, 2999; Accepted January3, 2999)

###### Abstract

We examine the wavelength dependence of radial light profiles based on Sérsic
index $n$ measurements of 1067 galaxies with M${}_{*}\geq$ 109.5M⊙ and in the
redshift range $0.5<z<3$. The sample and rest-frame optical light profiles are
drawn from CANDELS$+$3D-HST; rest-frame near-infrared light profiles are
inferred from CEERS JWST/NIRCam imaging. $n$ shows only weak dependence on
wavelength, regardless of redshift, galaxy mass and type: on average, star-
forming galaxies have $n=1-1.5$ and quiescent galaxies have $n=3-4$ in the
rest-frame optical and near-infrared. The strong correlation at all
wavelengths between $n$ and star-formation activity implies a physical
connection between the radial stellar mass profile and star-formation
activity. The main caveat is that the current sample is too small to discern
trends for the most massive galaxies (M${}_{*}>10^{11}~{}M_{\odot}$ ).

galaxies: Sérsic index – galaxies: structure

††journal: ApJ

##  1 Introduction

James Webb Space Telescope (JWST) NIRCam imaging is providing us for the first
time with spatially resolved, rest-frame near-infrared structural information
of galaxies at high redshift (up to z$\sim$3) with an angular resolution
unachievable from ground-based observatories. Previous, extensive Hubble Space
Telescope (HST) surveys have produced a detailed picture of the rest-frame UV
and optical structural properties and their correlations with other galaxy
properties such as stellar mass and star-formation rate (i.e., van der Wel et
al., 2014a, b; Lang et al., 2014; Shibuya et al., 2015; Nelson et al., 2016),
but only at longer wavelengths is the stellar body revealed without being
significantly hampered by the effects of stellar population and attenuation
variations across galaxies.

The broad wavelength coverage together with the high angular resolution
offered by the synergy between HST and JWST observations in the near-IR allows
one to examine the wavelength dependence of the Sérsic index ($n$). For the
first time we can determine for galaxies at large look-back time whether any
trends in the rest-frame near-IR with stellar mass and star-formation activity
are substantially different from those seen in the rest-frame optical/UV.

Both non-parametric and parametric methods have been widely used to examine
galaxy structure: see Conselice (2014) for a comprehensive review on non-
parametric methods and Whitney et al. (2021) for a recent application to high-
redshift galaxies. Among parametric methods, Sérsic profile fits have become
the standard as they are conveniently measured with codes such as galfit (Peng
et al., 2002, 2010); this is the approach we use in this study.

As stellar populations and dust attenuation determine the light distribution,
the measured structural properties are generally observed to depend on
wavelength (e.g, de Jong, 1996a, b; Kelvin et al., 2012; Häußler et al., 2013;
Vika et al., 2013; Pastrav et al., 2013; Vulcani et al., 2014; Kennedy et al.,
2015; Baes et al., 2020; Nersesian et al., 2023). Kelvin et al. (2012) used
the low-redshift ($z<0.3$) GAMA survey (Driver et al., 2009) to examine the
dependence of the Sérsic index on wavelength, splitting the galaxy sample by
visual morphology (disc galaxies and spheroidal galaxies). They find a mild
dependence on wavelength for spheroidal galaxies and a somewhat stronger
correlation for disc galaxies. Kelvin et al. (2012) argue that the trend is to
be expected, as spiral galaxies will have redder bulges, which tend to have
$n>1$. Despite this trend, the difference in Sérsic index between disc and
spheroidal galaxies persists even in the $K_{s}$ band ($n\lesssim 2$ vs.
$n\approx 3.5$).

Since the morphological class and structure/concentration (as parameterized by
Sérsic index) are intrinsically connected and, from an empirical perspective,
derived from the same information, we will instead examine the wavelength
dependence of Sérsic $n$ separating galaxies by star-formation activity, which
is estimated independently from the Sérsic profile. Moreover, thanks to the
revolutionary NIRCam imaging we can for the first time extend such an analysis
to redshift $z=2$ and beyond. The goal of this study is to measure the
evolution of the Sérsic index with redshift in the rest-frame near-infrared
and examine the wavelength dependence of the Sérsic index across the redshift
range $0.5<z<3$. One question of specific interest is whether the difference
between the Sérsic index for quiescent and star-forming galaxies, seen in the
rest-frame optical (e.g., Blanton et al., 2003; Blanton & Moustakas, 2009;
Bell et al., 2012), persists in the rest-frame near-IR. If not, then the star-
formation activity itself is the cause of the apparent difference in structure
(while the underlying mass profile shows no such difference). Alternatively,
if the difference persists, then there is a physical correlation between the
shape of the radial stellar mass profile and star-formation activity.

In this work we take advantage of the JWST/NIRCam (Rieke et al., 2005) imaging
provided by the CEERS program (Finkelstein et al., 2023) and model the light
profiles of 1067 galaxies in the redshift range $z=0.5-3$ with stellar masses
$M_{*}\geq 10^{9.5}$M⊙. We also compare our results with previous studies
(Kelvin et al., 2012; van der Wel et al., 2012) to exploit strengths and
weaknesses of our study.

The paper is structured as follows: in section 2 we describe the datasets used
in this paper, section 3 contains the results of this work divided into the
different dependencies of Sérsic indices and a comparison with literature
results. This will be followed by a discussion in section 4 and finally, in
section 5, we will sum up the content of the paper and draw our conclusions.

We assume a flat $\Lambda$CDM cosmology with H0=70km s-1 Mpc-1 and
$\Omega_{\rm{m}}$=0.3.

##  2 Data and Sample Selection

In this section we construct a redshift and stellar mass-selected sample from
pre-existing catalogs in the Extended Groth Strip (EGS, Davis et al., 2007),
and derive Sérsic profile fits from the recently acquired JWST/NIRCam imaging
from CEERS (Finkelstein et al., 2023).

###  2.1 Imaging and Photometry

Skelton et al. (2014) and Whitaker et al. (2014) presented HST, Spitzer and
ground-based imaging data to construct a widely used, homogeneous photometric
catalog from the UV to 24$\mu$m for the five extragalactic deep fields
targeted by CANDELS (Koekemoer et al., 2011; Grogin et al., 2011) and 3D-HST
(Brammer et al., 2012) which Leja et al. (2020) used to estimate redshift,
stellar masses, star-formation rates and dust attenuation parameters with the
Prospector SED fitting code (Johnson & Leja, 2017; Johnson et al., 2021). In
this paper we use the Leja et al. (2020) catalog of redshifts, stellar masses
and star-formation rates for galaxies at redshift $0.5<z<3$.

We first cross-match this catalog with van der Wel et al. (2012) which will be
used as a reference for comparisons, and then with sources in the recent
JWST/NIRCam data taken as part of the Cosmic Evolution Early Release Science
Survey (CEERS) program (Finkelstein et al., 2017, 2023) in the EGS, one of the
5 CANDELS fields. We note (and correct for) a systematic shift in declination
of $+0.19"$ between the Skelton et al. (2014) coordinates and the coordinates
in the CEERS mosaics, which we identified with the Python library for Source
Extraction and Photometry sep (Bertin & Arnouts, 1996; Barbary, 2016, 2018).
We identify 2684 out of 63,413 galaxies in the Leja et al. (2020) catalog
falling within the NIRCam footprint, of which 1216 are above our adopted
stellar mass limit of $M_{*}=10^{9.5}$M⊙, which is the stellar mass
completeness limit of the photometric catalog at $z\sim 3$ (Tal et al., 2014).
97% of these objects have signal-to-noise ratio $>$50 in all JWST/NIRCam
filters, which is the requirement for unbiased Sérsic index measurements (van
der Wel et al., 2012). This is not the case for the shallower HST/WFC3 data,
but those data do not play a major role in this work.

CEERS provides imaging in seven near-IR filters, specifically F115W, F150W,
F200W in the Short Wavelength channel of NIRCam and F277W, F356W, F410M, F444W
through the Long Wavelength channel. We use Stage 2b calibrated images already
background subtracted available on the MAST archive additionally processed
with the Grizli software (Brammer, 2019) to obtain aligned imaging, weight and
segmentation mosaics out of the 4 pointings available when we started this
work (also see Naidu et al., 2022).

For convenience, the available HST/ACS (F606W and F814W) and HST/WFC3 (F125W,
F140W and F160W) data are re-reduced with Grizli to produce mosaics that are
aligned with the NIRCam mosaics from CEERS.

###  2.2 Sérsic Profile Fits

For each of the 1216 target galaxies with NIRCam imaging and for each of the
seven JWST filters and five HST filters, we create square cutouts with size
ten times the effective radius in pixels measured from the F160W CANDELS
imaging (van der Wel et al., 2012). We set a lower limit of 63 pixels
($\sim$2.5”) and an upper limit of 200 pixels for sources with
$m_{\rm{F160W}}>22.5$. The upper limit is doubled for sources brighter than
this threshold to ensure accurate background estimates. All objects in the
cutout that are brighter than or less than 1 magnitude fainter than the target
are assigned their own Sérsic profile and simultaneously fitted. All other
sources in the van der Wel et al. (2012) catalog or in the CEERS segmentation
map are masked.

We use GalfitM (Häußler et al., 2013; Vika et al., 2013) to perform the
profile fits simultaneously for all JWST/NIRCam filters and simultaneously for
all HST/ACS and HST/WFC3 filters. The model Sérsic profiles are convolved with
the publicly available model PSFs111https://github.com/gbrammer/grizli-psf-
library/tree/main/ceers drizzled with the same drizzle parameters as those
used to create the mosaics. The square root of the inverse of the weight map
is used as the noise map in GalfitM. The background, as well as the center of
the galaxy, the total magnitude, Sérsic index and effective radius are left as
free parameters of the fit, allowing those to vary independently from filter
to filter. The axis ratio and position angle are the additional free
parameters, but these are constrained to have the same value for all filters
in the simultaneous fits.

We set the following constraints on the fit’s parameters:

  * •

$0.2\leq$ Sérsic index $\leq 12$

  * •

$0.01\leq$ Re [pix] $\leq 150$

  * •

x and y coordinates have to be within 5 pixels from the van der Wel et al.
(2012) corrected position.

Following van der Wel et al. (2012) we assign a formal random uncertainty of
0.1 dex on the Sérsic index for objects with signal-to-noise ratio S/N$=50$,
and scale the (linear) uncertainty with (S/N)-1/2. The S/N is calculated by
summing the image and inverse weight maps across the object segment in the
segmentation map.

In Figure 1 we show the data, model and residual of four
$10^{9.5}-10^{9.8}M_{\odot}$ galaxies respectively at redshift 0.74, 0.98,
2.49 and 2.98. Even these low-mass galaxies are detected with high
significance and are well resolved by JWST/NIRCam filters, even when HST does
not.

Figure 1: _First panel:_ Galaxy 5751 in Leja et al. (2020) catalog with
M=109.84M⊙ and redshift z=0.74, _Second panel:_ Galaxy 11438 with M=109.60M⊙
and redshift z=0.98, _Third panel:_ Galaxy 10662 with M=109.53M⊙ and redshift
z=2.49, _Fourth panel:_ Galaxy 14128 with M=109.60M⊙ and redshift z=2.98. For
each of the four sets, the first row shows the original image, the second row
the model used and the third row the residuals. Per each galaxy the color of
the panels spans the same scale in all the filters. Cutouts have been cropped
with respect to those adopted for the fit to enhance galaxy visibility.
Together with the model, in the bottom right corner, is shown the measured
Sérsic index in each filter. In case the fit of a filter failed, the value of
Sérsic index reported is _nan_.

In order to calculate the Sérsic index at specific rest-frame wavelength
values we fit for each object a 2nd-order Chebyshev polynomial to the
independently measured Sérsic $n$ values across all filters (but separately
for JWST and HST to exploit differences between the instruments) with the
uncertainties as weight factors. For each galaxy we fit the polynomial only to
those filters where the galaxy was detected (i.e. does not fall in gaps of the
NIRCam detectors) and with a converged value of $n$. We reject from our sample
galaxies for which less than 3 filters are available to fit the polynomial.
Among the JWST fits, just one galaxy does not satisfy this condition, while
for the HST fits we reject 35 galaxies.

The adopted uncertainty for Sérsic indices at specific rest-frame wavelength
recovered from the Chebyshev polynomial is that of the filter nearest in pivot
wavelength. The differences between the directly measured Sérsic index values
and the polynomial values are small, typically $<5\%$ and within the error
bar.

We also remove from our sample those 113 objects for which the Sérsic index
reached the $n=0.2$ or $n=12$ constraint for either of the JWST/NIRCam or
HST/ACS filters. The WFC3 filters overlap in wavelength with the NIRCam/SW
channel, so that such a rejection is not needed.

This leaves us with a final sample of 1067 galaxies in the redshift range
$0.5<z<3$ and M${}_{*}\geq 10^{9.5}$M⊙. The rejected galaxies do not severely
bias the sample as they do not occupy a particular region of the parameter
space in terms of redshift or stellar mass (in the appendix A we show the
stellar mass and sSFR distribution of the selected sample and of the rejected
galaxies as a function of redshift).

Figure 2: _Upper panel:_ Comparison between HST/F160W Sérsic indices from van
der Wel et al. (2012) (y-axis) and HST/F160W Sérsic indices derived in this
paper (x-axis) color-coded by the $log_{10}(SNR)$. _Lower panel:_ Comparison
of Sérsic indices from JWST/NIRCam filter F150W and HST/WFC3 filter F160W
(this paper). Filled circles represent F150W estimates with the WebbPSF-based
model-psf while open circles show F150W estimates with the empirical psf.
Dark-grey and light-grey solid lines show linear fits respectively on the
model-psf and empirical psf datasets after 3-sigma clipping. In the lower
right corner of each panel are reported the median ratios and the 16-84
percentile intervals. Next to the legends we show the median uncertainties.
The first panel shows the agreement with literature results is remarkable,
while the second highlights how differences between empirical and model-PSF
arise mostly for high values of $n$.

To check whether the size adopted for cutouts is large enough to properly
retrieve Sérsic profiles, we compare our size measurements with those
presented in van der Wel et al. (2012) finding no systematic differences.

To ensure that the background estimate converges for the sizes of the cutouts,
we compare the magnitudes with those obtained from cutouts half the size and,
for a subset of the 50 most massive galaxies, the magnitudes obtained with
cutouts double the size. From this exercise we conclude that the magnitudes
are accurate to within 0.05 mag (and Sérsic indices to within 0.03 dex),
indicating the systematic uncertainties in the background estimates do not
play a significant role. To check for spatial variations of the background
within cutouts we compared the standard deviation of pixels in the residuals
with the median value in the noise-maps finding a good agreement between the
two. This confirms that background spatial variations due to close bright
sources or diffuse halos do not contribute significantly to the uncertainties.

Likewise we test whether constraining the position angle and axis ratio to the
same value for all filters leads to systematic errors. With those parameters
free to vary from filter to filter we find only small scatter in Sérsic $n$.

To test the reliability of our new HST-based Sérsic profile fits we compare in
the upper panel of Figure 2 our measurements of Sérsic index in the HST/WFC3
filter F160W with the previously published values from van der Wel et al.
(2012) inferred from the same data. Due to slight differences in the
segmentation of objects and in methodology there is scatter and a fair number
of outliers appear ($\approx 30\%$ of the sample have $\Delta$log($n$)
$>0.08$dex with no preferred properties, where $\Delta$log($n$) is defined as
$|log_{10}(n_{F160W(vdw2012)})-log_{10}(n_{F160W})|$), but the systematic
offset is negligible and the 1$\sigma$ scatter small ($\sim 16\%$). Galaxies
with $\Delta$log($n$) $>0.08$dex are characterized by a median S/NF160W that
is half of that of galaxies with smaller $\Delta$log($n$), suggesting low S/N
might be an important source of scatter in this plot.

In the bottom panel of Figure 2 we show a comparison of NIRCam/F150W and
HST/F160W Sérsic indices retrieved in this work. From this figure, we can
infer that despite being shallower than JWST/F150W, HST/F160W was already deep
enough to properly recover Sérsic indices for the whole population (van der
Wel et al., 2012; Nedkova et al., 2021). Indeed, quantitatively, $n_{F150W}$
is just $\sim$7% systematically larger than $n_{F160W}$. However, the large
scatter observed reflects how the improved depth of F150W highlights new
features that can change the Sérsic index of some galaxies. An example of such
differences can be observed in the last two panels of Figure 1.

The scatter is larger by about a factor 2 compared to what one expects based
on the formally adopted measurement uncertainties: the total uncertainty (on
the ratio of the two independently measured Sérsic indices shown in the
figure) is as much as 50%. That said, the random uncertainties on the CEERS-
based measurements are typically a factor 3-4 smaller than those from CANDELS
due to the increased S/N, leading us to conclude that the CEERS-based
measurements have a variance that is one-quarter of the total variance seen in
Fig. 2. The error budget is an important issue that needs to be examined in
detail, but it is also beyond the scope of this paper. Future improvements in
the PSF model and background subtraction techniques are certain to improve the
data analysis.

To test whether the choice of the PSF used to fit NIRCam mosaics affects our
results, we repeat the profile fits with an empirical PSF: a star visually
identified in the NIRCam mosaics. The star is chosen to be faint (and
therefore noisy) in order to avoid the well-known saturation issues in the
NIRCam imaging (for an in-depth analysis of the JWST/NIRCam PSF see e.g.,
Nardiello et al., 2022; Weaver et al., 2023; Zhuang & Shen, 2023). The
difference between the model-PSF and the empirical-PSFs is most pronounced in
the Short Wavelength channel, where we see a decrease of $\sim 25\%$ in $n$
for objects with $n>3$. Low-$n$ and Long Wavelength channel estimates are not
systematically affected. This bias does not introduce large significant
uncertainties in the following analysis and our conclusions do not depend on
the choice of PSF. Solid dark(light)-grey lines show linear regression fits to
the $n$ values inferred with the model (empirical) PSF, using 3$\sigma$
clipping. The empirical PSF results shows systematic offsets at low and high
$n$, whereas the model PSF results do not, implying that they suffer less from
systematic uncertainties. The results based on the model PSF are used in the
remainder of this paper.

###  2.3 Local Comparison Sample from GAMA

A $z\leq 0.3$ comparison sample is drawn from GAMA. For the GAMA I dataset we
use the GalfitM profile fits obtained from the SDSS _ugriz_ imaging and the
UKIDSS-LAS YJHK imaging (Lawrence et al., 2007, 2012).222http://www.gama-
survey.org/dr4/schema/table.php?id=578

MAGPHYS (da Cunha et al., 2008) stellar mass and star-formation rate estimates
from GAMA II 333http://www.gama-survey.org/dr4/schema/table.php?id=545 are
used to construct the comparison sample of $\sim 23600$ galaxies with
$M_{*}\geq 10^{9.5}$M⊙ and redshift $z\leq 0.3$. There may be systematic
differences between MAGPHYS and Prospector-based parameter estimates, for the
purpose of this study these are not significant: we study trends with mass and
bulk redshift evolution so that 0.1-0.2 dex differences in $M_{*}$ and SFR do
not matter.

Figure 3: Median Sérsic index (and 16-84 percentile ranges as shaded areas) of
the quiescent and star-forming population as a function of rest-frame
wavelength. Errorbars indicate the statistical uncertainty on the median
($\sigma_{n}/\sqrt{N}$) at log-spaced wavelengths. Solid lines show an spline
regression to the medians as outlined in the text. Dashed gray horizontal
lines represent the overall median, integrating over wavelength. The dotted
lines show the low-$z$ GAMA comparison sample. For both star-forming and
quiescent galaxies we see no strong change in $n$ with $\lambda_{REST}$ from
the nUV to the nIR.

##  3 Results

In this section we investigate the wavelength and mass dependence and redshift
evolution of the Sérsic index, based on the 1067 galaxies in the redshift
range $0.5<z<3.0$ and with stellar masses $M_{*}\geq 10^{9.5}$M⊙, and the
low-$z$ comparison from GAMA. We often use the rest-frame 0.5$\mu$m and
1.1$\mu$m Sérsic index, $n_{0.5\mu m}$ and $n_{1.1\mu m}$, to examine the
differences between rest-frame optical and rest-frame near-IR trends, choosing
0.5$\mu$m to avoid the larger scatter at shorter wavelength, and choosing
1.1$\mu$m to have common wavelength coverage across the entire redshift range.

###  3.1 Wavelength dependence of Sérsic n

We divide the sample into quiescent and star-forming galaxies defining the
former as those galaxies that are located $0.8$dex below the $SFR-M_{*}$ ridge
defined by Leja et al. (2022) (see also Appendix A). The ridge definition
presented in Leja et al. (2022) applies to $0.2<z<3$ galaxies. The SFRs of
GAMA galaxies at $z<0.2$ are compared with the cutoff value for $z=0.2$ to
avoid extrapolation.

Figure 3 shows the median Sérsic index $n$ as a function of rest-frame
wavelength. The medians (and percentile ranges) are constructed as follows. At
a specific rest-frame wavelength all galaxies (minimum 10) with coverage from
either HST or JWST are included using the Chebyshev polynomial value (see Sec.
2.3). If both HST and JWST cover that wavelength, JWST is preferred on account
of its higher S/N. Lines are drawn using the cobs (Ng & Maechler, 2007, 2022)
library which allows for a combination of a spline regression and quantile
regression (the smoothing factor is chosen using the Schwarz-type information
criterion automatically computed by the code.).

We recover a clear, overall difference in the median Sérsic index of star-
forming and quiescent galaxies: $1.36\pm 0.01$ vs. $3.28\pm 0.03$,
respectively (as indicated by the grey dashed lines in Fig. 3). Uncertainties
are computed as standard deviation of 1000 replica of the medians computed at
different wavelength and gaussian distributed according to their own
statistical uncertainty (represented by the errorbars in Figure 3). Neither
the quiescent nor the star-forming population shows a strong wavelength
dependence across $0.3\mu$m to $2\mu$m. The scatter in $n$ among all the
galaxies, shown in the figure by means of shaded areas that extend from the
$16^{th}$ to the $84^{th}$ percentiles, is constant with wavelength for
quiescent galaxies, but for star-forming galaxies the scatter decreases with
wavelength, likely due to a reduced variation in radial profiles due to
stochasticity in the distribution of young stars and dust. This reduced
scatter at long wavelengths implies that the contrast between quiescent and
star-forming galaxies is, statistically speaking, more significant in the
near-IR than in the UV/optical.

Figure 4: _Upper panel:_ Sérsic index at $0.5\mu m$ against Sérsic index at
$1.1\mu m$ color-coded with $A_{V}$ (from the Prospector SED fits). Blue and
red solid lines show the median for star-forming and quiescent galaxies
respectively computed as explained in the text. Error bars show the
statistical uncertainty (84-16percentiles$/\sqrt{N}$). In the lower right
corner is shown the median (and 16-84percentiles) ratio $n_{0.5\mu
m}/n_{1.1\mu m}$ for the whole sample, the star-forming population and the
quiescent population. In the upper left corner in black are shown the median
uncertainties. _Lower panel:_ Ratio between Sérsic index at $0.5\mu m$ and
$1.1\mu m$ against $A_{V}$. Only galaxies with $SNR>100$ are included in this
figure to highlight the trend with $A_{V}$. In the lower right corner in black
is shown the median uncertainty propagated to the ratio of Sérsic indices.

The fact that the wavelength dependence is weak for the ensemble of galaxies
does not necessarily imply that individual galaxies have similar Sérsic
indices at all wavelengths. In Figure 4 we investigate the direct comparison
between $n_{1.1\mu m}$ and $n_{0.5\mu m}$. The comparison shows only 0.1dex
(26$\%$) scatter, which is a combination of observational uncertainties and
physical variations. $19\%$ of galaxies change their Sérsic index by more than
a factor 1.5 (up or down) from $0.5\mu$m to $1.1\mu$m. The vast majority of
galaxies have similar radial light profiles at different wavelengths. The
fractions of galaxies with $n_{1.1\mu m}/n_{0.5\mu m}>1.5$ and $n_{0.5\mu
m}/n_{1.1\mu m}>1.5$ are similar: 8% and 11%, respectively. At low $n$ there
is a small but significant deviation in the sense that $n_{0.5\mu m}$ is
smaller than $n_{1.1\mu m}$, driven by galaxies with large $A_{V}$. We
performed a Cramér-test (Baringhaus & Franz, 2004) to asses whether $n_{0.5\mu
m}$ and $n_{1.1\mu m}$ share the same distribution. For quiescent galaxies the
test results 0.34 with an estimated p-value of 0.89 (with 1-$\sigma$
confidence interval) confirming the absence of wavelength dependence on Sérsic
index for quiescent galaxies. On the contrary, for star-forming galaxies, we
find an observed statistic of 3.75 with a p-value of $10^{-3}$, suggesting the
Sérsic index indeed shows a mild dependence on wavelength. However, as shown
in the bottom panel of Figure 4, $n_{0.5\mu m}/n_{1.1\mu m}$ becomes
systematically smaller than unity for rising $A_{V}$. To statistically confirm
this observation we performed a Cramér-test on those star-forming galaxies
with Av$<0.3$ finding that $n_{0.5\mu m}$ and $n_{1.1\mu m}$ for these
galaxies are distributed the same (test result 0.64, p-value 0.36). This is
consistent with the recent results from Gillman et al. (2023) who find that
sub-mm-selected galaxies (expected to be dusty) have more concentrated
profiles in the rest-frame near-IR than in the rest-frame optical/UV.

Figure 3 shows also the wavelength dependence of the Sérsic index for the
$z\leq 0.3$ comparison sample drawn from GAMA (Sec. 2.3). Although the star-
forming galaxies show an increase with wavelength from $n=1$ to almost $n=2$
in the rest-frame $H$ band, or $\approx$$45\%$ higher than seen in the
high-$z$ sample, the quiescent population shows a milder evolution with its
peak in the nUV. The trend shown by the star-forming galaxies echos the
findings by Kelvin et al. (2012) for GAMA, but they divided the sample into
Disk and Spheroidal classes, presenting a different look compared to our
separation by star-formation activity. It is worth pointing out that the
definition of quiescence can be important: different definitions can affect
the strength of the increase(decrease) in the nIR(nUV) shown by star-
forming(quiescent) galaxies. Definitions like that presented in Tacchella et
al. (2022) (where a galaxy starts its quiescent phase when
sSFR$<$$1/(3t_{H}(z))$, with $t_{H}(z)$ being the age of the universe at the
galaxy’s redshift) lead to much shallower slopes for both the GAMA quiescent
and star-forming population leaving almost unaffected our high redshift
sample.

Nonetheless, the good agreement between the two datasets suggests a lack of
dependence on redshift for the quiescent population and a mild evolution in
the median $n$ for the star-forming population.

The trends shown in Figure 3 are for the full galaxy sample, with a wide range
in redshift and stellar mass. Correlations with star-formation activity,
stellar mass and redshift will be examined in further detail in Section 3.2
and 3.3.

###  3.2 Correlations with Star Formation Activity

Figure 5: Sérsic index at $1.1\mu m$ rest-frame against the sSFR in two
redshift bins, color-coded with the ratio between the Sérsic indices at
$1.1\mu m$ and at $0.5\mu m$. The solid line shows the median for the whole
sample in sSFR bins while the dashed lines show the 16-84 percentiles. In the
upper left corner of each panel a black errorbar shows the median uncertainty
of $n_{1.1\mu m}$. Low sSFR galaxies have systematically larger Sérsic indices
in the rest-frame near-IR.

Figure 3 suggests that star formation activity shows a strong correlation with
Sérsic index, regardless of wavelength. In Figure 5 we show
$n_{1.1\mu\rm{m}}$, the Sérsic index at rest-frame $1.1\mu$m, as a function of
the sSFR. Lines are drawn with the technique presented in section 3.1. The
smoothing factor is chosen using the Schwarz-type information criterion.
Galaxies with low sSFR have systematically larger $n_{1.1\mu m}$ than galaxies
with high sSFR. For both $n_{1.1\mu\rm{m}}$ and $n_{0.5\mu\rm{m}}$ the Cramér
test excludes with very high confidence $<5\sigma$ that star-forming and
quiescent galaxies are drawn from the same $n$ distribution. However, star-
forming galaxies show a tail of high-$n$ galaxies. This echoes earlier results
obtained in the rest-frame optical by Bell et al. (2012) and Whitaker et al.
(2017), who argued that having a high Sérsic index is a necessary, but not
sufficient, condition for a galaxy to be quiescent.

Interestingly, the Sérsic index does evolve with redshift at fixed sSFR:
galaxies with log(sSFR)$\sim-10$ have $n_{1.1\mu m}\lesssim 2$ at $z\sim 1$
and $n_{1.1\mu m}\sim 3$ at $z\sim 2$. But rather than indicating a physical
decrease in $n_{1.1\mu m}$ with cosmic time, this should be interpreted in the
context of a decline in SFR with cosmic time, which is of course well
documented (Leja et al., 2022, and references therein).

We also see that galaxies with low sSFR do not show a difference between
$n_{1.1\mu m}$ and $n_{0.5\mu m}$. On the contrary, at $z<1.5$ (left-hand
panel of Fig. 5) high sSFR galaxies show positive values of $n_{1.1\mu
m}/n_{0.5\mu m}$. At $z>1.5$ there is no such trend, but there is a
significant scatter in $n_{1.1\mu m}/n_{0.5\mu m}$, which is mostly due to
variations in $n_{0.5\mu m}$ (rather than $n_{1.1\mu m}$), otherwise this
would result in a vertical gradient in the color coding. This scatter does not
reflect difficulties in estimating Sérsic profiles at $0.5\mu m$ at high
redshift since these come from high-$S/N$ JWST/NIRCam imaging, but rather a
wider variety of $n_{0.5\mu\rm{m}}$ values at high redshift, likely due to
variance induced by bright star-forming regions and/or dust-obscured areas.

###  3.3 Correlations with Stellar Mass

Figure 6: Sérsic indices at $1.1\mu m$ (top row), $0.5\mu m$ (mid row) and
their ratio (bottom row) vs. stellar mass, color-coded as star-forming (blue)
and quiescent (red). The left column shows galaxies at $0.5\leq z<1.5$; the
right column shows galaxies at $1.5\leq z\leq 3$. Blue and red lines show the
medians for the star-forming and quiescent galaxies, respectively, while the
black lines represent the full (combined) sample. Median lines are computed as
described in section 3.1 with a smoothing factor of 0.3 for the quiescent
population and 1 for the star-forming and the whole sample. Errorbars show the
statistical uncertainty (84-16percentiles$/\sqrt{N}$) in bins of width 0.5dex
for the quiescent population and 0.25dex for the others. In the lower right
corner of each panel a black errorbar represents the median uncertainty for
the whole sample. We see a clear dependence of $n$ on stellar mass, regardless
of wavelength and redshift, and no significant evidence for a mass- or
redshift dependence for $n_{1.1\mu m}/n_{0.5\mu m}$.

The wavelength and sSFR dependence of the Sérsic index shown above do not
consider any correlation with stellar mass. Figure 6 shows $n_{1.1\mu m}$,
$n_{0.5\mu m}$ and their ratio as a function of stellar mass. Regardless of
wavelength, the Sérsic index increase with stellar mass is in part due to the
underlying correlations between, on the one hand, stellar mass and sSFR, and
on the other hand sSFR and Sérsic index. But also among quiescent galaxies the
Sérsic index increases with stellar mass, while for star-forming galaxies such
an increase is less evident. Here we should keep in mind that the current
sample has only a few massive star-forming galaxies with significant bulge
components.

Regardless of the detailed mass-dependencies that may exist, the main point is
that the Sérsic index - stellar mass distribution looks very similar in the
rest-frame optical and rest-frame near-IR, and that these patterns exist
across the entire redshift range $0.5<z<3$. This is further elucidated by the
bottom panels, that show $n_{1.1\mu m}/n_{0.5\mu m}$, which does not deviate
much from unity across the sampled stellar mass range. The only significant
departure is seen, somewhat surprisingly, for lower-$M_{*}$ star-forming
galaxies at $z<1.5$, which have slightly higher $n_{1.1\mu m}$ than $n_{0.5\mu
m}$. These galaxies often have $n_{0.5\mu m}<1$ whereas $n_{1.1\mu m}\approx
1$, which may suggest that these galaxies have diffusely distributed young
populations and/or somewhat attenuated centers, while the underlying
populations have approximately exponential profiles.

In the highest redshift bin we observe the median $n_{1.1\mu m}/n_{0.5\mu m}$
is compatible with unity for star-forming galaxies with $M_{*}<10^{10.3}$M⊙
followed by an increase that peaks at $M_{*}\sim 10^{10.7}$M⊙ and a sharp
decline for higher masses. The quiescent population shows no significant
trend. However, the sample is too small at these high masses to claim a
physical difference in $n_{1.1\mu m}/n_{0.5\mu m}$.

##  4 Discussion

While light profiles in the optical/UV can be strongly affected by young stars
and dust absorption, the near-IR is more representative of the stellar mass
distribution. But the striking absence of a strong wavelength dependence of
the Sérsic index $n$ for both quiescent and star-forming galaxies over the
redshift range $0<z<3$ suggests that the curvature of the radial light profile
in the optical does not deviate much from that of the underlying stellar mass
distribution across most of cosmic time: an exponential profile at short
wavelengths predicts an exponential profile at long wavelengths, and a De
Vaucouleurs-like profile generally also persists across the UV-to-near-IR
wavelength regime. Our findings reinforce the results from Bell et al. (2012)
who found no wavelength dependence for $n$ across the rest-frame UV and
optical wavelength regime for galaxies up to $z\sim 2.5$.

The absence of a striking wavelength dependence on Sérsic index does not imply
that light profiles do not systematically change with wavelength. Galaxies
have smaller scale radii at longer wavelengths at both low and high redshift
(Kelvin et al., 2012; van der Wel et al., 2014a). At low redshift we
understand this to be due to gradients in attenuation (e.g., Popescu et al.,
2000; Graham & Worley, 2008) and stellar population properties (e.g., Sánchez-
Blázquez et al., 2007; Zibetti et al., 2020). At large look-back time, thanks
to JWST, such analysis is now becoming possible (Miller et al., 2022; Suess et
al., 2022; Shen et al., 2023), and it is already clear that the stellar mass
distribution is smoother (Wuyts et al., 2012) than the clumpier distribution
seen in the UV and optical (e.g., Guo et al., 2015).

The key result presented here is that the radial profiles of star-forming and
quiescent galaxies are different even in the rest-frame near-infrared If star
formation and/or dust were responsible for the different structure seen at
shorter wavelengths, then the Sérsic indices of star-forming and quiescent
galaxies would become more similar at longer wavelengths. In fact, the reduced
scatter in $n$ of star-forming galaxies at longer wavelengths
($\lambda_{\rm{rest}}\approx 1.5\mu$m, see Figure 3) implies that the
difference in structure is _more_ pronounced in the rest-frame NIR than the
rest-frame UV/optical. The absence of such a trend implies, at first sight,
that stellar mass profiles are similar to stellar light profiles, but since
galaxy sizes decrease with wavelength, and stellar half-mass radii are
generally found to be smaller than half-light radii (e.g., Szomoru et al.,
2013; Fang et al., 2013; Suess et al., 2017; Mosleh et al., 2017; Suess et
al., 2019; Miller et al., 2023), the interpretation is not straightforward.
Clearly, the outshining effect of young, bright, blue populations (Wuyts et
al., 2012; Reddy et al., 2012; Lilly & Carollo, 2016) plays a significant
role. In particular, Fang et al. (2013) find that, for galaxies in the
present-day Universe, the difference between half-mass and half-light radii is
larger for star-forming galaxies than for quiescent galaxies and that stellar
mass profiles in the range $3<R<10$ kpc are rather similar for quiescent and
star-forming galaxies.

But a high Sérsic index is driven by the combination of deviations from an
exponential profile at both small radius, where Fang et al. (2013) indeed find
a significant difference between the mass profiles of star-forming and
quiescent galaxies, and large radius, which Fang et al. (2013) do not examine.
In general, a decline in galaxy size with wavelength and a lack of such
dependence for the Sérsic index are not necessarily in tension, and we
conclude that there is a physical difference in the radial curvature of the
stellar mass profiles when comparing star-forming and quiescent galaxies.

The strong correlation between galaxy structure and star-formation activity
seen at high redshift (Franx et al., 2008; Wuyts et al., 2011; Bell et al.,
2012; Barro et al., 2017; Whitaker et al., 2017) is now verified to be
physical in nature and builds on well-documented correlations seen for
present-day galaxies (e.g., Kauffmann et al., 2003; Brinchmann et al., 2004).
A more in-depth discussion of the causal connection between structural
evolution and star-formation history/quenching (e.g., van der Wel et al.,
2009; Bell et al., 2012; Fang et al., 2013; van Dokkum et al., 2015; Lilly &
Carollo, 2016; Tacchella et al., 2016; Barro et al., 2017; Bluck et al., 2020;
Chen et al., 2020; Dimauro et al., 2022) is beyond the scope of this paper.

At $z\lesssim 1.5$, $M_{*}<10^{10.3}$M⊙ star-forming galaxies do show a mild
increase in $n$ with wavelength, while this trend disappears at higher
redshift. Because of the lack of a significant number of high-mass galaxies in
the sample, we can not argue the same for higher masses. However, the hint of
a gradual trend of $n$ with redshift (Fig. 6) at first sight echoes the usual
line of thought that older bulges and a lack of attenuation in the center lead
to an increased Sérsic index at longer wavelengths, but our measurements are
not consistent with this picture. Instead, the trend is driven by galaxies
with $M_{*}\lesssim 10^{10}$M⊙ which display a slight decrease in $n$ from
high to low redshift in the rest-frame optical (mid row of Fig.6) while their
rest-frame near-IR $n$ shows a weaker and less significant evolution (top row
of Fig.6). Similar trends were found at low redshift by Vulcani et al. (2014)
and at $z\sim$2-3 by Shibuya et al. (2015) comparing UV and optical
wavelengths. We speculate this is, at least partially, due to an increase in
attenuation with cosmic time for galaxies in this mass range, associated with
an increase in gas-phase metallicity (e.g., Sanders et al., 2021).

##  5 Conclusions and Outlook

We present rest-frame optical and near-IR Sérsic index $n$ measurements for a
sample of 1067 galaxies at $0.5<z<3$ with stellar masses $M_{*}$$\geq$109.5M⊙
selected from recent JWST/NIRCam imaging that was collected as part of the
CEERS program (Finkelstein et al., 2023). The wavelength dependence of $n$ is
weak (Fig.3). As a result, the near-IR light profiles of galaxies do not, on
average, strongly differ from those in the optical (Fig.4). The large spread
in $n$ at any given wavelength is strongly correlated with star-formation
activity (Fig.5), across redshift and stellar mass. Indeed, after controlling
for star-formation activity, star-forming galaxies show just a weak evolution
in $n$ with redshift, as previously shown by Shibuya et al. (2015) in the
rest-frame optical, and a mild dependence on stellar mass. The remaining
scatter is mostly driven by variations in the optical profile driven by dust
absorption (Fig.4). Regardless of wavelength, stellar mass, and redshift we
see that star-forming galaxies have $n\sim 1-1.5$, and quiescent galaxies have
$n\sim 3.5$ (Figs. 3 and 6).

The fact that the well-documented correlation between galaxy structure and
star-formation activity (see Sec. 3.2) persists in the rest-frame near-
infrared implies a physical connection between radial stellar mass
distribution and growth through star-formation. In other words, it is not a
mere perception caused by young, bright, star-forming disks that fade after
the cessation of star formation.

The lack of a strong wavelength dependence in the Sérsic index at all
redshifts $z<3$ also implies a plausible lack of such a dependence at even
higher redshifts. As JWST/NIRCam explores the rest-frame optical up to $z\sim
10$ (Kartaltepe et al., 2022) and UV at $z>10$, we can have some confidence
that the observed radial light profiles inform us about the underlying stellar
mass profiles even if $M/L$-gradient corrections are needed to reconstruct
those.

Our conclusions hold for $0.1<L/L_{*}<1$ galaxies across the redshift range
$0.5<z<3$ and the main weakness of the current study is the small number of
high-mass star-forming galaxies (as discussed in section 3.3), especially at
high $z$: there are only 11(9) $M_{*}\geq 10^{11}$M⊙ star-forming(quiescent)
galaxies at $1.5<z<3$ investigated with JWST in our sample. For these galaxies
the structure may be expected to vary the strongest with wavelength due to
centrally concentrated, dust-obscured star-formation activity. As larger areas
are observed with NIRCam by, for example, JADES (Williams et al., 2018),
UNCOVER (Bezanson et al., 2022) and COSMOS-Web (Casey et al., 2022), this
challenge will be addressed.

## Acknowledgments

This project has received funding from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No. 683184). MM and MB acknowledge the financial support of
the Flemish Fund for Scientific Research (FWO-Vlaanderen), research project
G030319N.

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##  Appendix A Sample Selection and Characteristics

Figure 7 shows the sample distribution and selection of galaxies used in this
work. In the left panel we show the SNR in the HST/WFC3 filter F160W (empty
circles) and JWST/NIRCam filter F150W (filled circles) as a function of
redshift. The dashed horizontal line shows the SNR=50 limit suggested by van
der Wel et al. (2012) to accurately measure Sérsic indices. The central panel
of Figure 7 shows the mass distribution of our galaxies across redshift. The
right panel of the figure shows the sSFR against the redshift distribution of
our galaxies. In the last two panels star-forming galaxies are color-coded in
blue while quiescent are red. The distinction between star-forming and
quiescent is done as outlined in section 3.1. We used circles for galaxies
included in the sample and stars for galaxies that are rejected as outlined in
section 2 and 2.2. Black squares represent galaxies that despite having a
SNR$<50$ in F150W are not removed from the sample.

Figure 7: _Left panel:_ Signal-to-Noise Ratio (SNR) in the HST/ACS filter
F160W (empty circles) and JWST/NIRCam F150W (filled circles) against redshift.
The horizontal dashed black line shows the reference SNR=50. _Central panel:_
Stellar mass against redshift. _Right panel:_ specific Star Formation Rate
against redshift. In the central and right panels colors red and blue are used
to identify quiescenet and star-forming galaxies. Circles define galaxies used
in this work while stars show galaxies rejected according to section 2 and
2.2. Black squares are galaxies with SNR$<50$ in F150W that are not rejected.