# Characterizing Dust Extinction and Spatially Resolved Paschen-$\alpha$
Emission within 97 Galaxies at $1<z<1.6$ with JWST NIRCam Slitless
Spectroscopy

Zhaoran Liu Astronomical Institute, Graduate School of Science, Tohoku
University, 6–3 Aoba, Sendai 980-8578, Japan  Takahiro Morishita IPAC,
California Institute of Technology, MC 314-6, 1200 E. California Boulevard,
Pasadena, CA 91125, USA  Tadayuki Kodama Astronomical Institute, Graduate
School of Science, Tohoku University, 6–3 Aoba, Sendai 980-8578, Japan

###### Abstract

We present results on the Paschen-$\alpha$ (${\rm Pa\alpha}$) emitting
galaxies observed as part of the JWST FRESCO survey in the GOODS-North and
GOODS-South fields. Utilizing the JWST NIRCam wide field slitless spectroscopy
(WFSS), we analyze emission line fluxes, star formation rates (SFRs), and
spatially resolved flux distributions of 97 ${\rm Pa\alpha}$ emitters at
$1<z<1.6$. To assess dust extinction within our sample, we combine ${\rm
Pa\alpha}$ fluxes with archival ${\rm H\alpha}$ data taken with the Hubble
Space Telescope (HST) WFC3 G141 grism. Our analysis reveals a significant
correlation between dust extinction and galaxy stellar mass, where more
massive galaxies exhibit greater dust extinction. We employ two-dimensional
${\rm Pa\alpha}$ and F444W mapping to trace the distributions of star
formation and stellar mass, respectively. Our observations indicate that lower
mass galaxies are almost dust free in ${\rm Pa\alpha}$ and exhibit smaller
sizes both in star formation and underlying stellar continuum. In contrast,
galaxies with a stellar mass greater than $10^{9.5}M_{\odot}$ display diverse
dust extinction and star formation patterns. This variation suggests that the
structures and properties of massive galaxies evolve through different phases,
which involve, e.g., star formation in massive clumps, compaction, and inside-
out quenching. This study demonstrates the capabilities of JWST WFSS in
conducting systematic investigations of emission line galaxies and highlights
the pivotal role of ${\rm Pa\alpha}$ in advancing our understanding of dust
extinction and obscured star formation in the early universe.

Galaxy evolution (594); Interstellar medium (847); Galaxy structure (622)

††software: Astropy (Astropy Collaboration et al., 2013, 2018), SExtractor
(Bertin & Arnouts, 1996), CIGALE (Boquien et al., 2019)

##  1 Introduction

Galaxies are vast, diverse systems evolving through complex processes over the
cosmic time, with their formation and structural development significantly
dependent on baryonic processes occurring within dark matter halos and
interacting with molecular gas reservoirs. Understanding star formation, which
is the fundamental process that shapes galaxies, is crucial for determining
their structural build-up, thereby enhancing our comprehension of how galaxies
are constructed and evolve.

Over the past decades, various tracers of star formation across a broad
spectrum of wavelengths, from ultraviolet (UV) and optical to infrared (IR)
and sub-millimeter, have been intensively studied. These multi-wavelength
studies have provided invaluable insights into how galaxies form, evolve, and
eventually quenched across various redshifts and environments. Previous
studies have demonstrated that a large fraction of local galaxies formed most
of their current stellar mass during the epoch between redshift $z=1$ and
$z=3$ (e.g., Madau & Dickinson, 2014; Behroozi et al., 2019). However, a
prominent question remains unanswered: how exactly do galaxies assemble their
stellar mass via star formation? Spatially resolved emission line mapping
inside galaxies has played a crucial role in addressing this question,
offering deeper insights into the mechanisms behind stellar accumulation in
galaxies.

Prior to the JWST era, cutting-edge instruments with sub-kiloparsec resolving
power had made it possible to resolve the star formation processes within
galaxies. HST grism enabled studies of ${\rm H\alpha}$ line maps, uncovering
extended star-forming HII regions. Combined with stellar mass maps, these
observations helped elucidate the processes of galaxy mass assembly (e.g.,
Nelson et al., 2012; Wuyts et al., 2013; Vulcani et al., 2015; Nelson et al.,
2016a; Matharu et al., 2021). FIR and (sub)millimeter facilities such as the
Atacama Large Millimeter/submillimeter Array (ALMA) expanded this view into
longer wavelength, offering high-resolution insights into the dust continuum
and molecular gas dynamics, revealing the compact continuum of dusty sub-mm
galaxies (e.g., Simpson et al., 2015; Hodge et al., 2016; Barro et al., 2016;
Tadaki et al., 2017; Elbaz et al., 2018; Calistro Rivera et al., 2018;
Fujimoto et al., 2018; Tadaki et al., 2020; Chen et al., 2020; Cheng et al.,
2020; Ikeda et al., 2022; Gómez-Guijarro et al., 2022). When ionized gas, dust
continuum, and molecular gas observations are combined, we see a detailed
picture of galactic mass assembly as a blend of extended, young star-forming
disk and a centrally concentrated, extremely dusty bulge. However,
interpreting ${\rm H\alpha}$ data presents challenges due to non-uniform dust
extinction across different parts of a galaxy, with ongoing investigations
into how this spatial variation evolves with redshifts, stellar masses, and
SFRs (e.g., Tadaki et al., 2014; Nelson et al., 2016b; Matharu et al., 2023;
Liu et al., 2023). Furthermore, studies aimed at resolving gas and dust
components also face limitations — they are often restricted to relatively
bright sources or require significant allocation of facility’s resources.
Moreover, applying these observations to understand star formation relies on
assumptions about dust temperature and the relationships between gas mass and
star formation, which can vary not only from one galaxy to another but also
within individual galaxies (Shetty et al., 2013; Liang et al., 2019; Feldmann,
2020).

With the launch of the JWST (Gardner et al., 2006, 2023), many previous
constraints have been overcome, enabling us to study star formation using a
broader array of tracers and in greater detail thanks to its high-quality
imaging from the optical to the MIR (0.6 – 28.3 $\mu$m) and the spatial and
spectral resolving power of its spectrograph. A significant advancement
includes improved determination of dust extinction; the Near Infrared
Spectrograph (NIRSpec) facilitates the study of multiple Balmer and Paschen
lines, allowing for more accurate dust extinction measurements in high-$z$
galaxies (e.g., Shapley et al., 2023; Reddy et al., 2023; Sandles et al.,
2023; Bunker et al., 2023; Morishita et al., 2024a).

Spatially resolving dust extinction within galaxies has also been greatly
enhanced by the Near Infrared Imager and Slitless Spectrograph (NIRISS) and
NIRCam Wide Field Slitless Spectrograph (WFSS). These advanced instruments can
obtain spectra for all galaxies within their fields, enabling detailed
observation of the nebular emission line distribution inside galaxies without
pre-selection. The breakthrough extends not only to high-redshift observations
but also to the study of longer-wavelength hydrogen recombination lines, which
are less affected by extinction, such as the ${\rm Pa\alpha}$ line at 1.875
$\mu$m. With the NIRCam WFSS F444W, we can resolve ${\rm Pa\alpha}$ emission
lines up to $z=1.7$ (Neufeld et al., 2024). As an independent star formation
tracer, ${\rm Pa\alpha}$ stands out because it closely tracks the intrinsic
SFRs compared to the Balmer lines, thus providing constraints on dust
extinction models and offering a more robust tracer of star formation (Reddy
et al., 2023).

In this work, we utilize the JWST NIRCam WFSS grism to study dust extinction
and spatially resolved star formation in galaxies at $1.0<z<1.6$. Our goal is
to evaluate the degree of dust extinction in our galaxy sample, assess the
effects of dust on the ${\rm Pa\alpha}$ emission line, and employ ${\rm
Pa\alpha}$ as a star formation tracer to study galaxy mass assembly. We detail
our data reduction methods and sample selection in Sec. 2. Our techniques for
analyzing stellar mass, dust extinction, and size measurements are detailed in
Sec. 3. We present our results in Sec. 4 and compare them with the existing
literature in Sec. 5. We summarize our key conclusions in Sec. 6.

In this paper, we adopt the AB magnitude system (Oke & Gunn, 1983; Fukugita et
al., 1996), cosmological parameters of $\Omega_{m}=0.3$,
$\Omega_{\Lambda}=0.7$, $H_{0}=70$ km s${}^{-1}\,{\rm Mpc}^{-1}$, and the
Chabrier (2003) initial mass function (IMF).

##  2 DATA AND SAMPLE SELECTION

The observational dataset utilized in this work encompasses three primary
components: (1) extensive optical imaging from HST and detailed broad- and
medium-band imaging obtained with the JWST/NIRCam; (2) JWST/NIRCam WFSS F444W
grism; and (3) HST/WFC3 G141 grism. We detail the photometric and
spectroscopic data and our sample selection as follows.

###  2.1 NIRCam+HST Photometry and Photmetric Redshift

For source identification, we start with a catalog generated in Morishita et
al. (2024b). The work retrieved the fully processed images and spectroscopic
catalogs made available by the JADES team (Rieke et al. 2023). A photometric
catalog was then constructed following the method described in Morishita &
Stiavelli (2023), using borgpipe (Morishita, 2021). In our following analysis,
we adopt the aperture flux from the catalog, which was corrected to represent
the total fluxes of the galaxies. For further details regarding the catalog,
the readers are referred to Morishita et al. (2024b).

###  2.2 NIRCam WFSS Reduction

In this analysis, we utilize publicly available NIRCam WFSS data from the
First Reionization Epoch Spectroscopic Complete Survey (FRESCO; GO-1895; PI:
P. Oesch; Oesch et al. 2023). FRESCO is a JWST cycle-1 program which features
comprehensive deep NIRCam imaging and slitless spectroscopic observations
using the F444W filter. The obtained spectra achieve a resolution of R $\sim$
1600 and covers a wavelength range from 3.8 to 5.0 $\mu$m, which enables us to
study multiple hydrogen recombination lines across a wide range of cosmic time
with a spatially resolved view.

We follow the methodology outlined in Sun et al.
(2023)111https://github.com/fengwusun/nircam_grism/ and reduce the WFSS data
using a combination of the official JWST pipeline and several customized steps
as detailed below. We retrieve the stage-1 products (rate.fits) from the MAST
archive and assign the world coordinate system (WCS) for each frame. Our
background subtraction process involves two steps: we first subtract a median
background that is separately generated for each module and pupil. To further
enhance data quality and eliminate any potential residual background, we
employ additional subtraction using SExtractor (Bertin & Arnouts, 1996). To
isolate the emission line from the continuum, we follow the method described
in Kashino et al. (2023). This involves using a median filter technique that
models the continuum with a sliding window, or “kernel”. By subtracting this
modeled continuum from the original data, we effectively extract the emission
line image.

With the fully calibrated images, we then measure the astrometry offset
between the short wavelength (SW) direct images and the reduced F444W mosaic
to align each grism exposure with the direct image, this step is essential to
allow the spectral tracing models work properly. The spectral tracing, grism
dispersion and sensitivity models are produced from multiple JWST/NIRCam
Cycle-1 programs (PID: 1076/1536/1537/1538), the details are described in Sun
et al. (2023). We extract the 1d spectra with optimal extraction (Horne,
1986), and fit the emission line flux with a single Gaussian profile.

###  2.3 HST G102 and G141 Grisms

We utilize the archival HST grism observations from the CANDELS Lyman Alpha
Emission At Reionization (CLEAR) survey (PI: Casey Papovich), as detailed in
Simons et al. (2023), which provided 12-orbit depth observations with the
HST/WFC3 using the G102 grism, covering 12 fields across both the GOODS-N and
GOODS-S. Simons et al. (2023) expanded the original CLEAR survey dataset by
incorporating observations from additional HST projects that utilize the G102
and G141 grisms overlapping with the CLEAR footprint. This approach achieved
complete spectral coverage from 0.8 to 1.7 $\mu$m throughout the observed
areas. Leveraging this rich dataset, Simons et al. (2023) have compiled two
spectroscopic catalogs that present emission line fluxes and redshifts,
derived from a combination of photometry and grism spectroscopy.

In our analysis, we use the redshifts and combined ${\rm H\alpha}$ \+ [N ii]
flux from the CLEAR catalog. To correct for [N ii] contamination, we apply the
[N ii]/${\rm H\alpha}$ ratios as a function of stellar mass at $z\sim 1.5$, as
calibrated by the $\text{KMOS}^{3D}$ program (Wuyts et al., 2016). For an in-
depth understanding of the CLEAR survey’s methodology, including survey
design, data reduction processes, and the galaxy catalog compilation, we refer
readers to Simons et al. (2023).

Figure 1: Histogram showing the distribution of the F444W magnitude of our
parent sample (gray) and final sample (red). The blue dashed line indicates
our magnitude cut.

###  2.4 Sample Selection

We start with the NIRCam + HST catalog as described in Sec. 2.1 and select
sources for further analysis as follows:

  * •

First, we perform a cross-match between the NIRCam+HST catalog (Sec. 2.1) with
the CLEAR spectroscopic catalog (Sec. 2.3) using a matching radius of
$0.\\!^{\prime\prime}5$, and retain only the galaxies with available
spectroscopic redshift from the CLEAR survey.

  * •

We further refine our selection to include only those galaxies within the
redshift range of $1<z<1.6$, which aligns with the coverage of the NIRCam WFSS
F444W filter for capturing the ${\rm Pa\alpha}$ line and the HST G141 grism
for capturing the ${\rm H\alpha}$ line. The collection of galaxies that pass
this phase of selection is referred to as our parent sample.

  * •

Additionally, selected galaxies must have an AB magnitude brighter than 25 in
F444W and both ${\rm H\alpha}$ and ${\rm Pa\alpha}$ detections with a SNR
greater than 5.

  * •

Lastly, we conduct spectral energy distribution (SED) fitting for the selected
galaxies in the previous step. To ensure reliable results, we further restrict
our sample by including only those with the SED fitting results with a reduced
$\chi^{2}_{\nu}$ value of less than 3.

Our final sample consists of 42 galaxies from GOODS-S and 55 from GOODS-N. The
distribution of F444W magnitudes for both our parent and final samples is
displayed in Fig. 1.

##  3 ANALYSIS

Figure 2: (left): Stellar mass versus SFR for our samples. Stellar mass is
derived from SED fitting, SFR is calculated based on the ${\rm Pa\alpha}$ line
flux without correction for dust extinction. Error bars for SFRs reflect flux
uncertainties.The blue dashed line represents the SFR limit of 1.42
$\mathrm{M}_{\odot}\,\mathrm{yr}^{-1}$ at $z=1.5$, using a Pa$\alpha$ flux of
$2\times 10^{-18}\,\mathrm{erg\,s^{-1}\,cm^{-2}}$. The green-shaded region
illustrates the $\pm 0.5$ dex range of the star formation main sequence at
$1<z<1.5$ derived by Whitaker et al. (2014). (right): Analogous to the left
panel, yet here SFRs are adjusted for dust extinction. Error bars incorporate
uncertainties from both flux measurements and dust extinction A(${\rm
Pa\alpha}$).

###  3.1 SED Fitting

We conduct SED fitting using the photometric data to estimate stellar masses.
We use Code Investigating GALaxy Emission (CIGALE, Boquien et al. 2019).
CIGALE is particularly well-suited for analyzing data across a broad
wavelength range, extending from X-ray to radio frequencies. Our SED fitting
employs a delayed exponential model for star-formation history (sfhdelayed),
mathematically represented as ${\rm SFR}(t)\propto t\exp(-t/\tau)$. For the
stellar population synthesis, we utilize the model from Bruzual & Charlot
(2003), assuming solar metallicity. The model incorporates dust attenuation
based on the Calzetti et al. (2000) extinction law. A comprehensive
description of the parameters used in our SED fitting can be found in Liu et
al. (2023).

###  3.2 ${\rm Pa\alpha}$ and ${\rm H\alpha}$ Constraints on Nebular Reddening
and SFRs

In this work, we adopt Case B recombination assumption with ${\rm
T_{e}=10^{4}}$ K and ${\rm n_{e}=10^{2}}$ ${\rm cm^{-3}}$ as determined by
photoionization models using CLOUDY version 17.02 (Ferland et al., 2017).
Under these conditions, the model predicts intrinsic intensity ratios of ${\rm
H\alpha}$/${\rm H\beta}$ = 2.79 and ${\rm Pa\alpha}$/${\rm H\beta}$ = 0.305.
By applying the Calzetti et al. (2000) reddening curve ($R_{\rm{v}}$ = 4.05)
and comparing the observed ${\rm Pa\alpha}$ to ${\rm H\alpha}$ flux ratios
with Case B predictions, we calculate $E(B-V)_{\text{neb}}$ for our sample:

$E(B-V)_{neb}=\frac{2.5}{k(H\alpha)-k(Pa\alpha)}\log_{10}\left(\frac{Pa\alpha/H\alpha}{0.109}\right)$

Here, $k(\lambda)$ represents the extinction coefficient at wavelength
$\lambda$, as prescribed by Calzetti et al. (2000). From the calculated color
excess, we derive the extinction values A(${\rm H\alpha}$) and A(${\rm
Pa\alpha}$) using:

$A(\lambda)=k(\lambda)\cdot E(B-V)$

Subsequently, with the estimated dust extinction from the ${\rm Pa\alpha}$ and
${\rm H\alpha}$ line flux ratios, we compute the intrinsic SFRs. The selection
of the parent sample in this study relies on the ${\rm Pa\alpha}$ detection,
which is sensitive to HII regions that signal active star formation. Thus, we
expect the majority of our selected sources to be star-forming galaxies. To
assess their star-forming activities more accurately, we derive dust-corrected
SFRs using ${\rm Pa\alpha}$ line flux and color excess $E(B-V)_{\text{neb}}$.
The ${\rm Pa\alpha}$ flux is determined by fitting a single Gaussian profile
to continuum-subtracted 1D spectra (Sec. 2.2). Upon determining the intrinsic
${\rm Pa\alpha}$ flux using the Calzetti et al. (2000) approach, we convert it
to the ${\rm H\alpha}$ flux based on the line ratio predicted under Case B
recombination. SFRs are then estimated from the ${\rm H\alpha}$ luminosity
following the SFR-$L_{\mathrm{H\alpha}}$ relation established by Kennicutt
(1998):

$\frac{\mathrm{SFR}}{\mathrm{M_{\odot}}\,\mathrm{yr^{-1}}}=7.9\times
10^{-42}\,\,\mathrm{L}_{\mathrm{H\alpha}}(\mathrm{erg\,s}^{-1})$ (1)

To align with the Chabrier (2003) IMF, we scale the SFRs by dividing them by a
factor of 1.53 (Driver et al., 2013). As illustrated in Fig. 2, most of our
sample galaxies are located on or near the star formation main sequence
predicted by Whitaker et al. (2014). Our analysis indicates that the ${\rm
Pa\alpha}$ line is a robust indicator of SFRs, relatively unaffected by dust
extinction and offers a more direct measure of the ionizing radiation from
young O and B stars. This is particularly true for less massive galaxies with
a stellar mass below $\rm{10^{10}~{}M_{\odot}}$, which are less affected by
dust extinction, as demonstrated in the comparison between the left and right
panels of Fig. 2.

Figure 3: Sequence from left to right illustrating intrinsic profile
reconstruction: (1) The observed two-dimensional spectra. (2) The best-fit
Sérsic model convolved with the PSF. (3) Residuals derived from the difference
between the observed spectra (1) and the PSF-convolved Sérsic model (2). (4)
The reconstructed intrinsic light distribution, obtained by adding the
residuals to the best-fit Sérsic model prior to PSF convolution. This
reconstructed profile is used for subsequent galaxy size analysis.

###  3.3 Size Measurements

In our redshift range of interest, the F444W grism captures the ${\rm
Pa\alpha}$ emission line, a robust tracer of SFRs, while the F444W image
captures the rest-frame K-band image ($\sim$ 2 $\mu$m), providing an accurate
measure of the galaxy’s stellar mass unaffected by star formation history
(e.g., Kauffmann & Charlot, 1998; Bell & de Jong, 2001; Drory et al., 2004).
Therefore, comparing the flux distributions from the F444W image and the F444W
grism enables us to study the mechanisms governing star formation and mass
assembly within galaxies, with minimal impact from dust extinction.

However, the NIRCam grism achieves a high resolution of R $\sim$ 1600 at 3.95
$\mu$m, which corresponds to a velocity dispersion of $\sigma$ $\sim$ 80 km/s
(Nelson et al., 2023). This resolution will lead to morphological distortion
of emission-line maps along the spectral axis of galaxies having velocity
dispersion greater than 80 km/s. Therefore, the 2D spectra we extract are not
purely emission line maps; they also incorporate kinematic properties along
the spectral axis. Overcoming such degeneracy is possible with an additional
medium-band filter that serves to extract emission line map (e.g., Nelson et
al., 2023). Yet, this approach significantly narrows the applicable redshift
range due to the coverage of medium filters. Recognizing these constraints,
our analysis in this study is thus focused on examining the light profile
distribution in the cross-dispersion direction, which remains unaffected by
velocity dispersion. Our method involves the following steps:

  * •

Model fitting: We employ the technique outlined in Szomoru et al. (2010),
which involves using a Sérsic $R^{1/n}$ profile (Sérsic, 1963) to model the
observed galaxy images and 2D spectra. We first select an unsaturated star
within the same field of view to represent the PSF. Subsequently, we begin the
Sérsic $R^{1/n}$ fitting process using the initial parameters derived from
SExtractor. To refine our model, we employ optimization techniques to adjust
the parameters. The best-fit PSF-convolved Sérsic model is determined by the
minimal residual.

  * •

Intrinsic Profile Reconstruction: Using the previously identified best-fit
parameters, we construct a Sérsic profile and incorporate the residuals
obtained from comparing the observed data with the PSF-convolved model. This
profile, enhanced with the residuals, is considered the intrinsic flux profile
for further size measurement analysis. Although the residuals are still
affected by the PSF, this technique has proven to accurately reconstruct the
true flux distribution, even for galaxies poorly described by a Sérsic profile
(Szomoru et al., 2010). Fig. 3 schematically illustrates the reconstruction
process.

  * •

Flux Distribution Analysis: With the reconstructed intrinsic profiles for both
2D spectra and images, we compute the one-dimensional cross-dispersion light
intensity profile by summing pixel values across each row. Specifically, we
begin by creating cutouts of the 2D spectra and images, each with dimensions
of $3.\\!^{\prime\prime}0\times 3.\\!^{\prime\prime}0$; we then rotate F444W
images to align with the 2D spectra, ensuring the horizontal direction is set
as the dispersion direction. Additionally, we mask out pixels identified in
the segmentation maps as belonging to other galaxies and those with negative
values from the continuum removal process, thereby effectively minimizing the
effects of nearby galaxies and artifacts from bad pixels.

Based on the method above, we obtain flux profiles for both the stellar and
star formation components in the cross-dispersion direction. To quantitatively
compare the distributions of stellar mass and star formation in individual
galaxies, we measure the half-light radius along the cross-dispersion
direction. Given the different depths of the grisms and direct images, the SNR
of the stellar components is higher than that of the SFR components. For a
fair comparison, we define the total flux as the amount captured within a
specified radius in the flux profile, with this boundary determined by the
point at which the SNR of the 2D spectra drops to 1, thereby accounting for
the spectra’s shallower depth. The half-light radius is then calculated by
locating the point where the cumulative flux reaches half of the total flux.
This point, measured from the center of the cutout along the y-axis, is
defined as the half-light radius. Although this diverges from the traditional
definition of half-light radius, this method facilitates a direct comparison
of the spatial distributions of star formation and stellar mass within
galaxies, based on their light profiles in the cross-dispersion direction.

###  3.4 Stacking

To enhance the SNR and measure the average properties of ${\rm Pa\alpha}$ and
F444W profiles, our sample is divided into two sets of bins: one based on
stellar mass and another based on specific star formation rate (sSFR). For
each categorization, galaxies are classified into low, medium, and high bins,
with 32, 32, and 33 galaxies in each respective category. Following the
methodology described in Nelson et al. (2016a), we stack the ${\rm Pa\alpha}$
spectra and F444W images in each bin to create the mean profiles. Before
proceeding with the stacking, we mask nearby sources using segmentation maps,
deconvolve the PSF, and rotate the F444W images to ensure that the horizontal
direction corresponds to the dispersion direction, as detailed in 3.3. To
prevent the final stacked profile from being dominated by brighter sources, we
apply weights based on their F444W flux. According to Nelson et al. (2016a),
deprojecting, rotating, or scaling the images does not significantly affect
our main conclusions; therefore, we do not apply additional rotation to the
dispersion axis-aligned profiles. Furthermore, we calculate the half-light
radius in the cross-dispersion direction of the stacked profiles using the
same method applied to individual galaxies.

##  4 Results

In this section, we present the results of our analyses. First, we discuss the
nebular reddening values derived from the ${\rm Pa\alpha}$ and ${\rm H\alpha}$
line ratio. Additionally, we present the dust extinction and SFRs inferred
from ${\rm Pa\alpha}$ and ${\rm H\alpha}$ emission lines. We then explore
differences in flux distribution between the F444W and ${\rm Pa\alpha}$, and
examine how size measurements correlate with stellar mass and sSFR to
understand the structural build-up of galaxies. Finally, we discuss the
average properties for stacked profiles of ${\rm Pa\alpha}$ and F444W.

###  4.1 Dust Extinction

Figure 4: Stellar mass versus ratio of observed SFR predicted using ${\rm
Pa\alpha}$ and ${\rm H\alpha}$ respectively (left y-axis), and stellar mass
versus A(${\rm H\alpha}$) (right y-axis). A(${\rm H\alpha}$) is calculated
based on the observed ratio of ${\rm Pa\alpha}$ and ${\rm H\alpha}$ flux, and
is thus proportional to the observed SFR ratio.

We examine the nebular reddening within our sample galaxies and investigate
the relationship between dust extinction and stellar mass. In Sec. 3.2, we
derive the $E(B-V)_{\text{neb}}$ using the ratio of the ${\rm Pa\alpha}$ and
${\rm H\alpha}$ emission lines. We then calculate the dust extinction A(${\rm
H\alpha}$) and A(${\rm Pa\alpha}$) from these ratios. We present our findings
in Fig. 4, with error bars indicating the flux measurement uncertainties.

Our results reveal a positive correlation between stellar mass and dust
extinction, as inferred from ${\rm Pa\alpha}$-to-${\rm H\alpha}$ line flux
ratios. This is consistent with previous studies that employed Balmer-line
ratios to assess dust extinction, as well as those using far-IR and UV
continuum measurements (e.g., Garn & Best, 2010; Zahid et al., 2013; Reddy et
al., 2015; Fudamoto et al., 2020; Shapley et al., 2023). Based on the model
predictions by Calzetti et al. (2000), A(${\rm Pa\alpha}$) is significantly
smaller than A(${\rm H\alpha}$) due to the much smaller k($\lambda$). Our
results indicate that at our target redshift, A(${\rm Pa\alpha}$) is typically
around $\sim$ 0.1 mag, with the median value increasing to only $\sim$ 0.2 mag
in the most massive bin. While ${\rm Pa\alpha}$ is intrinsically fainter than
${\rm H\alpha}$ (IPaα/IHα = 0.11 under Case B), this results demonstrate the
robustness of ${\rm Pa\alpha}$ as a star formation indicator, less attenuated
by dust extinction and more sensitive to the intrinsic SFR. Such conclusions
are broadly in agreement with Reddy et al. (2023), who investigated the
Paschen lines of 63 galaxies at redshifts $z=1.0$–$3.1$ using NIRSpec. We note
that a small fraction of galaxies in our sample exhibit a negative extinction.
This happens when the observed ratio of ${\rm Pa\alpha}$ to ${\rm H\alpha}$ is
less than the dust-free minimum value of 0.109, which is not physical. Such
observations could be attributed to the relative faintness of the ${\rm
Pa\alpha}$ line in comparison to the ${\rm H\alpha}$ line, possibly leading to
incomplete detection of the galaxy’s fainter regions in the 2D spectra.
Furthermore, our reliance on empirical calibration for ${\rm H\alpha}$ flux,
based on the [N ii]/${\rm H\alpha}$ ratio, introduces additional uncertainties
into the ${\rm H\alpha}$ flux determination.

Figure 5: (left): Effective radius measured at cross-dispersion direction of
F444W images versus stellar mass. (middle): Effective radius measured at
cross-dispersion direction of ${\rm Pa\alpha}$ 2d spectra versus stellar mass.
(right): Size ratio of this two components versus stellar mass. The red dashed
line corresponds to $\mathrm{R_{Pa\alpha}}/\mathrm{R_{F444W}}=1$, which
suggests a coherent distribution of star formation and stellar. Larger data
points denote median values within three defined stellar mass bins: $10^{8.5}$
to $10^{9.5}$, $10^{9.5}$ to $10^{10.5}$, $10^{10.5}$ to $10^{11.5}$ solar
masses. Figure 6: Same as Fig. 5 but as a function of sSFR

###  4.2 ${\rm Pa\alpha}$ as a Star Formation Indicator

Thanks to the HST grism, previous studies (e.g., Nelson et al., 2016a; Vulcani
et al., 2016; Nelson et al., 2019; Matharu et al., 2022) have significantly
advanced our understanding of star formation regions within galaxies through
spatially resolved ${\rm H\alpha}$ emission line maps. As one of the most
prominent hydrogen recombination lines, ${\rm H\alpha}$ is closely linked to
ionized regions and serves as a reliable tracer of star formation. However,
even ${\rm H\alpha}$ is susceptible to significant dust extinction. This
presents a challenge for studying star formation locations as the dust amount
may differ significantly across various regions of a galaxy (Nelson et al.,
2016b; Tacchella et al., 2018; Matharu et al., 2023). Such variability
introduces notable uncertainties in quantifying galaxy sizes and analyzing
morphological features. The utilization of spatially resolved ${\rm Pa\alpha}$
emission line map offers a solution to overcome these challenges. In this
section, we present the galaxy sizes derived from ${\rm Pa\alpha}$ 2D spectra
and F444W continuum data, offering insights into the spatial distributions of
star formation activities and existing stellar mass within galaxies. In order
to better understand the observed size difference in our galaxies, we
investigate the relationship between the SFR-to-stellar size ratio, sSFR, and
stellar mass.

####  4.2.1 Half-light Radius of Individual Galaxies

The size of galaxies serves as a fundamental metric for characterizing their
structure, shedding light on bulge and disk growth and the properties of the
encompassing dark matter halos (e.g., Mo et al., 1998; Kravtsov, 2013; van der
Wel et al., 2014). By comparing half-light radii measured for different
components of galaxies, such as the stellar component and star formation
component, we can gain vital information on how galaxies build their massive
structures through vigorous star formation and how these activities vary
across different evolutionary stages. Due to the limitation by the nature of
our data, this study compares the half-light radius measured in the cross-
dispersion direction. The calculation process for half-light radius is
detailed in Sec. 3.3. We observe that the half-light radii of ${\rm Pa\alpha}$
generally exceed those of the F444W images, indicating SFR regions are
relatively more extended than the stellar mass distributions.

Furthermore, not only does galaxy size itself offer important clues about mass
assembly, but its correlations with stellar masses, SFRs, and redshifts are
equally crucial and have been extensively investigated. One of the key
discoveries is the galaxy size-mass relation. Previous studies have shown that
two main classes of galaxies, star-forming and quiescent, follow distinctly
different size-mass relations (e.g., Kauffmann et al., 2003; Baldry et al.,
2006). One possible scenario to explain this discrepancy is that star-forming
and quiescent galaxies accumulate their stellar populations through different
processes (van Dokkum et al., 2015). However, this is still a topic under much
debate. To further investigate the origin, we here study the correlation
between size measurements and stellar mass to pinpoint the star formation
regions within galaxies and track how these regions shift during various
evolutionary stages.

Fig. 5 depicts how the half-light radius varies with stellar mass. The size of
both ${\rm Pa\alpha}$ traced star-forming disks and continuum-traced stellar
components shows a weak increasing trend with stellar mass. However, it is
noted that discussions about the mass-size relationship for these components
based on this ‘effective radius’ is not appropriate. This limitation arises
because our measurement is one-dimensional, taken in the cross-dispersion
direction, which means galaxy orientation could significantly affect the size
measurements, especially for those with small axis ratios ($b/a$). Although
this measurement for galaxy size may seem arbitrary, our goal is to compare
the flux distribution between SFR and stellar components. Even with data
extracted from one direction, this comparison remains feasible. We observe
that galaxies within the lower mass bin show similar sizes for both their SFR
and stellar components. However, the ratio between these sizes tends to
increase towards the higher mass bins. This observation aligns with findings
reported by Nelson et al. (2016a), who examined the ${\rm H\alpha}$
distribution using HST grism observations. Nelson et al. (2016a) reported that
more massive galaxies are likely to have more extended ${\rm H\alpha}$
emissions; in contrast, for galaxies in the lower mass range, the size of the
${\rm H\alpha}$ region and the stellar continuum region is rather consistent.
The trends found here and in Nelson et al. (2016a) both consistently suggest
ongoing star formation activities occurring at larger radii compared to the
distribution of existing stars, supporting the inside-out growth model of
galaxies.

We further examine if the size ratio evolves with star formation per solar
mass, specifically sSFR, as presented in Fig. 6. For calculating sSFR, we
adopt the dust-corrected SFRs as described in Sec. 3.2, taking into account
uncertainties from both flux measurements and dust extinction. Galaxies within
the highest sSFR bin display compact structures in both their stellar and star
formation components, with their size ratios indicating remarkably similar
sizes.

Figure 7: Stacks of ${\rm Pa\alpha}$ (red) and F444W images (blue). From left
to right, the sequence represents the stacked profiles of low, medium, and
high stellar mass/sSFR bins. The dimensions of the stacked images are
$1.\\!^{\prime\prime}5\times 1.\\!^{\prime\prime}5$ for both $\text{Pa}\alpha$
and F444W. Figure 8: (left): Half-light radius of stacked profiles binned by
stellar mass. (right): Similar to the left but binned by sSFR.

####  4.2.2 Average Properties From Stacked Profiles

As discussed in the Sec. 4, the relatively faint nature of ${\rm Pa\alpha}$
emission line may lead to missing flux at the fainter part of ${\rm Pa\alpha}$
2d spectra. To mitigate this issue, we categorize galaxies according to their
stellar mass and sSFR, and perform stacking analysis. Our stacked profiles for
the three different bins of stellar mass (top two rows) and sSFR (bottom two
rows) are illustrated in Fig. 7. We subsequently measured the half-light
radius of these stacked profiles in the cross-dispersion direction, with our
results displayed in Figure 8. The stacked ${\rm Pa\alpha}$ profiles exhibit a
more extended structure compared to the F444W images in the high and medium
stellar mass bins, as evidenced by their larger effective radii. This trend is
consistent with observations in individual galaxies, as shown in Fig. 5.
However, when analyzing the stacked profiles binned by sSFR, it becomes
apparent that these bins are predominantly influenced by stellar mass rather
than SFRs. This results in a correlation that is almost identical but opposite
to what is observed with the stellar mass plot.

Nevertheless, these results do not necessarily imply that galaxy mass assembly
does not evolve with different SFRs. Our sample mainly consists of main
sequence galaxies; therefore, their stellar mass-SFR correlations are
relatively well-established. Consequently, sSFR may not effectively classify
galaxies into different star formation stages. To better understand where star
formation occurs in galaxies with varying star-forming modes, it is essential
to examine more extreme cases, such as starburst and quiescent galaxies.

##  5 Discussions

###  5.1 Dust, Star Formation, and Galaxy Mass Assembly

In Sec. 4.2, we investigated the half-light radius of ${\rm Pa\alpha}$ and
F444W, and their potential correlation with stellar mass. Our main findings
are illustrated in Fig. 5 and 8, which show that galaxies, especially those
with high stellar masses, exhibit ${\rm Pa\alpha}$ extent notably larger than
their stellar continuum. These observations align with the findings of Nelson
et al. (2016a), who reported a larger effective radius for ${\rm H\alpha}$
compared to F140W in a study of 3200 galaxies at $0.7<z<1.5$. Notably, the
size difference was more pronounced with increasing stellar mass. While Nelson
et al. (2016a) observed a steeper size evolution with stellar mass than our
results suggest, this difference could be attributed to the different tracers
used, i.e., ${\rm H\alpha}$ and F140W in their study versus ${\rm Pa\alpha}$
and F444W in ours. Given that our tracers are expected to be more sensitive to
attenuated emissions, the difference indicates that galaxy central regions of
our galaxies systematically host more attenuated emissions.

It should be noted that the half-light radius, determined from the integrated
profile along the cross-dispersion axis, may not directly reflect the overall
size of the galaxy due to the significant impacts of orientation and
ellipticity. This factor might also contribute to the observed scatter in the
relationship between size and stellar mass as shown in Fig. 5. Nevertheless,
despite these limitations, the analysis of the ratio of galaxy sizes remains a
robust metric.

The observed increase in galaxy size ratio with stellar mass necessitates
further investigation into the underlying physical processes that govern
galaxy structural formation. It remains a challenging question to understand
how galaxies form their central mass concentrations, particularly massive
bulges, and evolve into mature, passive systems, given the presence of active
star formation regions surrounded by dust. Our study provides a direct probe
of star-forming regions, minimizing reliance on assumptions required for dust
extinction corrections, such as UV slope and SED fitting techniques.
Consequently, we anticipate that the regions traced by ${\rm Pa\alpha}$ will
predominantly represent ionized hydrogen areas within the galaxies. Based on
this foundation, and the positive correlation between ${\rm Pa\alpha}$-to-
stellar size ratio and increasing stellar mass (Fig. 5), our finding that most
galaxies exhibit larger ${\rm Pa\alpha}$ sizes supports the inside-out growth
model of galaxies (e.g., van Dokkum et al., 2010). This model suggests that
galaxies gradually build up their outer regions while the inner regions have
completed their evolution more rapidly.

Our study distinguishes itself from previous research that utilized ${\rm
H\alpha}$, which faces significant uncertainties due to dust-obscured central
regions. Our research confirms the scenario of extended star-forming regions,
employing an independent tracer made feasible for the first time by NIRCam
WFSS. Although ${\rm Pa\alpha}$ may still be significantly affected by dust
extinction in extremely dusty starburst galaxies, as inferred from a recent
study by Bik et al. (2023) that studied a galaxy with AV = 17.2, our sample
primarily consists of normal star-forming galaxies, most of which have A(${\rm
Pa\alpha}$) $<$ 0.2, with the dustiest having A(${\rm Pa\alpha}$) $\sim$ 0.6.

Figure 9: Cutout stamps showing ${\rm Pa\alpha}$ 2D spectra (top) and RGB
images (bottom) for three galaxies in our sample, each measuring
$2.\\!^{\prime\prime}5\times 2.\\!^{\prime\prime}5$. We also note the SFR
($\rm{M_{\odot}/yr}$) and the stellar mass (log $\rm{M_{*}/M_{\odot}}$).

###  5.2 Spatial Distribution of Star Formation in Massive Galaxies: Clumpy,
Extended, and Compact

As discussed in Sec. 5.1, we observe considerable scatter in the measurements
of galaxy size ratios, particularly among medium-mass to massive galaxies
(i.e. galaxies with stellar mass $\rm{M_{*}>10^{9.5}\,M_{\odot}}$). Within our
sample, we identify three distinct flux distributions in the emission line
maps of these galaxies. Even among galaxies with similar stellar masses and
SFRs, their ${\rm Pa\alpha}$ flux profile can vary significantly. For example,
as illustrated in Fig. 9, the galaxy on the left displays extended and clumpy
star-forming regions, whereas the middle one shows centrally concentrated
star-forming regions; the right galaxy, however, exhibits expanded star-
forming regions, suggesting inside-out growth. The diverse star formation
regions observed in our massive galaxies are interesting. The overall trend
revealed by stacked profiles in Fig. 8 shows that massive galaxies exhibit
larger star formation regions, in good agreement with findings from previous
studies. However, the larger scatter in the size ratio observed in individual
massive galaxies (right panel of Fig. 5), which originates from galaxies with
different star formation patterns, warrants further investigation. Swinbank et
al. (2012) studied nine ${\rm H\alpha}$-selected galaxies at $0.8<z<2.2$ using
SINFONI/VLT and reported a variety of ${\rm H\alpha}$ morphologies; at least
six of these galaxies exhibited extended or clumpy features, while two
displayed compact features. In a related study, Förster Schreiber et al.
(2018) analyzed 35 star-forming galaxies and found that the majority were
late-type, disk-dominated systems, with eight displaying prominent rings or
off-center clumps. The diversity observed in ${\rm H\alpha}$ is consistent
with the variety of morphologies we have seen in ${\rm Pa\alpha}$. In this
section, we delve into the underlying physics behind the formation of clumpy,
extended, and compact star formation regions in these galaxies.

Both the clumps distributed at the outskirts of galaxies and the extended
${\rm Pa\alpha}$ can lead to a higher effective radius measured with ${\rm
Pa\alpha}$ compared to that of the stellar continuum. Gaseous clumps, often
contributing to the formation of bulges and disks, are regarded as key drivers
of galaxy structure formation and evolution and are commonly observed in star-
forming galaxies at $z>1$ (e.g., Dekel et al., 2009a, b). The existence of
massive clumpy galaxies can be attributed to dynamically unstable gas, which
leads to the formation of giant star-forming clumps within the disk (Krumholz
et al., 2018), or it could be indicative of gas-rich minor merger events
(Agertz et al., 2009).

To further understand the formation mechanisms of these complex structures,
observations of both ionized and molecular gas are essential. There are only a
handful of studies focusing on clumpy galaxies; recently, Bik et al. (2023)
analyzed the dusty, star-forming galaxy GN20 at $z\sim 4$ using MIRI/MRS,
detecting spatially resolved ${\rm Pa\alpha}$. Their emission line map
revealed that ${\rm Pa\alpha}$ emissions are concentrated in four distinct
clumps. Additionally, GN20 was observed with ALMA (Hodge et al., 2012, 2016),
where the CO(2-1) emission also revealed a similar clumpy structure. These
findings suggest that the galaxy is in the late stages of a major merger,
implying that the clumps in the gas-rich disk are a result of this merger,
while the central starburst is directly driven by the event. Similarly,
Cochrane et al. (2021) reported bright, extended structures in a $z=2.2$
galaxy, with clear clumps in ${\rm H\alpha}$ and extended dust continuum
emissions. This disordered morphology and extreme star formation are linked to
a merger event. Although our sample primarily consists of main sequence
galaxies, it is possible that some of the clumpy structures we observed are
triggered by merger activities. Such sub-structures remain an active area of
exploration, and our study indicates that clumpy star-forming populations can
be efficiently studied with WFSS. To fully comprehend the impact of dust and
molecular gas in shaping the characteristics of HII regions, further
investigations using sub-mm observations are crucial. The extended star
formation region observed in the middle panel of Fig. 9 has been well-studied
in previous ${\rm H\alpha}$ observations utilizing HST grism and adaptive
optics (e.g., Nelson et al., 2016a, b; Vulcani et al., 2016; Matharu et al.,
2022). Unlike rest-frame UV-optical light, ${\rm H\alpha}$ emission suffers
less attenuation by dust and is closely linked to the star formation
activities of massive stars. Given the relatively short lifespans of massive
stars, their observed population offers a direct measure of the current SFR
(e.g., Kennicutt, 1998; Pflamm-Altenburg et al., 2007). It was reported that
when galaxies assemble their massive structures, star formation typically
starts in the central region and then spreads outward. This process helps
build up the galaxy’s outskirts, leading to the larger size of star formation
regions observed in massive galaxies.

Compact star formation presents another intriguing scenario for further
investigation. One hypothesis for the most massive galaxy populations is that
they undergo a process known as “compaction”, which leads to the evolution of
massive bulges over cosmic time (Dekel & Burkert, 2014; Zolotov et al., 2015;
Lacerda et al., 2020; Marques-Chaves et al., 2022). Subsequent starbursts
and/or AGN feedback may then drive these galaxies toward quiescence (Genzel et
al., 2014; Yesuf et al., 2014), resulting in quenched, dense cores (Damjanov
et al., 2009; van Dokkum et al., 2009; Szomoru et al., 2012; Morishita &
Ichikawa, 2016). Recent studies have elucidated the formation mechanisms of
compact galaxies. Franco et al. (2020) highlighted the significant role of
compact galaxies at z $\sim$ 2.5 - 3, associating them with short depletion
timescales. Simulations such as Illustris suggest that these galaxies often
form early in extreme environments characterized by an abundance of gas and/or
in (post-)merging systems where large inflow of gas trigger intense starbursts
(Wellons et al., 2015). The acquisition of external gas is believe to be
responsible for initiating secondary star formation within the core regions of
these galaxies that result in their compact morphology (Chen et al., 2016).
Importantly, such populations might be underrepresented or even missed in
previous ${\rm H\alpha}$ analyses, at redshifts $z=1-2$, our target epoch
corresponding to the peak of cosmic star formation activity, dust extinction
affecting ${\rm H\alpha}$ can vary significantly, with magnitudes ranging from
$\sim 1$, to $>3$ (e.g., Förster Schreiber et al., 2009; Sobral et al., 2012;
Kashino et al., 2013; Koyama et al., 2019). Moreover, dust extinction can vary
widely across a galaxy. As discussed in Matharu et al. (2023), dust
attenuation is not a constant value within galaxies; instead, the spatial
distribution of dust attenuation can vary across different stellar masses. A
recent study by Cochrane et al. (2021) investigated a massive galaxy at
$z=2.2$ using multi-wavelength data and found A(${\rm H\alpha}$) values
ranging from $\sim 2-3$ in the outskirts to $>$ 5 in the central region.
Interestingly, their ${\rm H\alpha}$ emission line map, obtained using
SINFONI/VLT, showed a clear offset from the peak of the dust continuum
emission traced by ALMA. Tadaki et al. (2014) also reported color gradients in
galactic clumps, with central clumps being redder, indicating that dusty star-
formation activity is concentrated in these nuclear regions. Such dust
gradients introduce significant complexity to the analysis of ${\rm
H\alpha}$-traced HII regions, potentially biasing detections toward galaxies
with extended star formation regions. Galaxies featuring compact, yet dusty,
star formation regions might remain undetected in ${\rm H\alpha}$
observations. Therefore, compact star-forming galaxies might still be
understudied in previous ${\rm H\alpha}$-based work. Future surveys using
better tracers less affected by dust, such as ${\rm Pa\alpha}$, will be
crucial to provide a comprehensive view of the different paths of galaxy
structure formation.

Figure 10: Comparative distribution of half-light radii derived from F444W
images (x-axis) and modeled continuum (y-axis) in the cross-dispersion
direction.

###  5.3 Robustness of Size Measurements Across Imaging Depths

One might question our size measurements due to the differing depths of the
F444W imaging and WFSS spectroscopy, with the former being significantly
deeper. Such a depth discrepancy could result in an underestimation of the
size of star formation regions, as the fainter outskirts of galaxies may
remain undetected. Ideally, a comparison between the continuum captured by
WFSS and the observed emission lines would help to mitigate these
discrepancies. However, practical implementation of this method faces
significant challenges as the continuum captured in dispersed spectra is
frequently contaminated by nearby continua, thereby complicating the accuracy
of measurements. This issue is particularly pronounced for larger galaxies,
where the continuum is more likely to overlap with other sources. Therefore,
our analysis relies on direct images from F444W. To further assess the
potential effects of this depth difference, we carefully inspect each source
and select those without significant contamination from nearby galaxies. We
measure their sizes using the modeled continuum (see Sec. 2.2 for the
continuum modeling process), applying the same measurement method as used for
F444W images and 2D spectra. The results, illustrated in Fig. 10, show that
measurements based on the modeled continuum and F444W are generally
consistent. Therefore, we assert that the depth difference does not
significantly impact our conclusions. Even if the sizes of the 2D spectra are
underestimated, our findings that the star formation regions traced by 2D
spectra are more extended remain unaffected.

The inherent complexities in galaxy morphology and kinematics, particularly
the elongation of morphologies along the spectral axis due to kinematic
distortions, prevent us from obtaining accurate and separate information on
spatial and spectral information. As discussed in Nelson et al. (2023), for
high EW emission lines, such as ${\rm H\alpha}$, a combination of medium-band
filters and WFSS can provide insights into both the velocity and morphology of
the emission line maps. However, this approach may be challenging for weak
lines or for fields without medium-band filters on the targeted line. To apply
this method to our research objectives, specifically using ${\rm Pa\alpha}$ to
trace dust-free star formation, a larger sample size would be required. A
future joint analysis involving multiple programs with available medium-band
and WFSS observations will offer more opportunities to study galaxies with
strong ${\rm Pa\alpha}$ emission lines.

##  6 Summary and Future Prospect

This paper presented a comprehensive analysis of resolved ${\rm Pa\alpha}$
emissions within 97 galaxies at $1<z<1.6$ in the GOODS-North and GOODS-South
fields utilizing JWST NIRCam WFSS. By combining this new dataset with the
previous legacy HST grism observations, we were able to not only secure the
redshift determination but also robustly determine the dust extinction for our
sample galaxies. The main findings of our research are summarized below:

  * •

We calculated the dust extinction values, A(${\rm H\alpha}$) and A(${\rm
Pa\alpha}$), for our sample of 97 galaxies and confirmed that ${\rm Pa\alpha}$
is an excellent tracer for star formation activities in Hii regions, as it is
not significantly attenuated by dust. We observed a maximum A(${\rm
Pa\alpha}$) of less than 0.6, and noted that low-mass galaxies are almost
attenuation-free. This establishes a solid basis for analyzing spatially
resolved star-forming activities within galaxies with minimal impact from
dust.

  * •

We utilized HST and JWST photometric data to estimate stellar masses through
SED fitting and derived SFRs from ${\rm Pa\alpha}$ emission line flux. Our
sample predominantly features main sequence galaxies, and the ${\rm
Pa\alpha}$-derived SFRs exhibit minimal variation before and after dust
extinction correction, with the exception of a few of the most massive
galaxies.

  * •

From the analysis of individual and stacked emission maps of ${\rm Pa\alpha}$
and F444W, we found that for galaxies with medium and high stellar mass, the
${\rm Pa\alpha}$ show a larger size compared to the stellar size, whereas for
galaxies with low stellar mass, the dimensions remain comparable.

  * •

We explored the size evolution of stellar and star-forming regions, and their
ratios, across different stellar mass bins. In low-mass galaxies, star
formation is concentrated centrally, resulting in compact sizes with stellar
and star-forming regions being similar in dimension. In contrast, medium- and
high-mass galaxies show more diverse star formation regions that can be
extended, clumpy, or compact. This diversity indicates varying star formation
mechanisms, potentially driven by external gas inflow or mergers, which become
more prominent as stellar mass increases.

We acknowledge the teams of the JWST observation programs #1180, #1895, and
the HST observation program #14227 for their hard work in designing and
planning these programs, and for generously making their data publicly
available. The data presented in this paper were retrieved from the Mikulski
Archive for Space Telescopes (MAST) at the Space Telescope Science Institute,
the specific observations analyzed can be accessed via
http://dx.doi.org/10.17909/z0sb-mk09 (catalog DOI: 10.17909/z0sb-mk09). We
thank Fengwu Sun for helping with the data reduction. We thank Jasleen
Matharu, Yongda Zhu and Yunjing Wu for the valuable discussion. This work was
supported by the KAKENHI Grant Numbers 22K21349 and 24KJ0394 through the Japan
Society for the Promotion of Science (JSPS). This work was supported by JST
SPRING (Grant Number JPMJSP2114). Support for this study was provided by NASA
through grants HST-GO-15804 and HST-GO-17231 from the Space Telescope Science
Institute, which is operated by the Association of Universities for Research
in Astronomy, Inc., under NASA contract NAS 5-26555.

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