# Early results from GLASS-JWST. IV: Spatially resolved metallicity in a low-
mass $z\sim 3$ galaxy with NIRISS111Based on observations acquired by the JWST
under the ERS program ID 1324 (PI T. Treu)

Xin Wang School of Astronomy and Space Science, University of Chinese Academy
of Sciences (UCAS), Beijing 100049, China  National Astronomical
Observatories, Chinese Academy of Sciences, Beijing 100101, China  Infrared
Processing and Analysis Center, Caltech, 1200 E. California Blvd., Pasadena,
CA 91125, USA  Tucker Jones Department of Physics and Astronomy, University of
California Davis, 1 Shields Avenue, Davis, CA 95616, USA  Benedetta Vulcani
INAF Osservatorio Astronomico di Padova, vicolo dell’Osservatorio 5, 35122
Padova, Italy  Tommaso Treu Department of Physics and Astronomy, University of
California, Los Angeles, 430 Portola Plaza, Los Angeles, CA 90095, USA
Takahiro Morishita Infrared Processing and Analysis Center, Caltech, 1200 E.
California Blvd., Pasadena, CA 91125, USA  Guido Roberts-Borsani Department of
Physics and Astronomy, University of California, Los Angeles, 430 Portola
Plaza, Los Angeles, CA 90095, USA  Matthew A. Malkan Department of Physics and
Astronomy, University of California, Los Angeles, 430 Portola Plaza, Los
Angeles, CA 90095, USA  Alaina Henry Space Telescope Science Institute, 3700
San Martin Drive, Baltimore MD, 21218  Center for Astrophysical Sciences,
Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD,
21218  Gabriel Brammer Cosmic Dawn Center (DAWN), Denmark  Niels Bohr
Institute, University of Copenhagen, Jagtvej 128, DK-2200 Copenhagen N,
Denmark  Victoria Strait Cosmic Dawn Center (DAWN), Denmark  Niels Bohr
Institute, University of Copenhagen, Jagtvej 128, DK-2200 Copenhagen N,
Denmark  Maruša Bradač University of Ljubljana, Department of Mathematics and
Physics, Jadranska ulica 19, SI-1000 Ljubljana, Slovenia  Department of
Physics and Astronomy, University of California Davis, 1 Shields Avenue,
Davis, CA 95616, USA  Kristan Boyett School of Physics, University of
Melbourne, Parkville 3010, VIC, Australia  ARC Centre of Excellence for All
Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia  Antonello Calabrò INAF
Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone,
Rome, Italy  Marco Castellano INAF Osservatorio Astronomico di Roma, Via
Frascati 33, 00078 Monteporzio Catone, Rome, Italy  Adriano Fontana INAF
Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone,
Rome, Italy  Karl Glazebrook Centre for Astrophysics and Supercomputing,
Swinburne University of Technology, PO Box 218, Hawthorn, VIC 3122, Australia
Patrick L. Kelly School of Physics and Astronomy, University of Minnesota, 116
Church Street SE, Minneapolis, MN 55455, USA  Nicha Leethochawalit School of
Physics, University of Melbourne, Parkville 3010, VIC, Australia  ARC Centre
of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia
National Astronomical Research Institute of Thailand (NARIT), Mae Rim, Chiang
Mai, 50180, Thailand  Danilo Marchesini Department of Physics and Astronomy,
Tufts University, 574 Boston Ave., Medford, MA 02155, USA  P. Santini INAF
Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone,
Rome, Italy  M. Trenti School of Physics, University of Melbourne, Parkville
3010, VIC, Australia  ARC Centre of Excellence for All Sky Astrophysics in 3
Dimensions (ASTRO 3D), Australia  Lilan Yang Kavli Institute for the Physics
and Mathematics of the Universe, The University of Tokyo, Kashiwa, Japan
277-8583

###### Abstract

We report the first gas-phase metallicity map of a distant galaxy measured
with the James Webb Space Telescope (JWST). We use the NIRISS slitless
spectroscopy acquired by the GLASS Early Release Science program to spatially
resolve the rest-frame optical nebular emission lines in a gravitationally
lensed galaxy at $z=3.06$ behind the Abell 2744 galaxy cluster. This galaxy
(dubbed GLASS-Zgrad1) has stellar mass $\sim 10^{8.6}M_{\odot}$, instantaneous
star formation rate $\sim 8.6$ $M_{\odot}$/yr (both corrected for lensing
magnification), and global metallicity one-fourth solar. From its emission
line maps ([O iii], H$\beta$, H$\gamma$, [Ne iii], and [O ii]) we derive its
spatial distribution of gas-phase metallicity using a well-established
forward-modeling Bayesian inference method. The exquisite resolution and
sensitivity of JWST/NIRISS, combined with lensing magnification, enable us to
resolve this $z\sim 3$ dwarf galaxy in $\gtrsim$50 resolution elements with
sufficient signal, an analysis hitherto not possible. We find that the radial
metallicity gradient of GLASS-Zgrad1 is strongly inverted (i.e. positive):
$\Delta\log({\rm O/H})/\Delta r$ = $0.165\pm 0.023$
$\mathrm{dex\leavevmode\nobreak\ kpc^{-1}}$. This measurement is robust at
$\gtrsim$4-$\sigma$ confidence level against known systematics. This inverted
gradient may be due to tidal torques induced by a massive nearby ($\sim$15 kpc
projected) galaxy, which can cause inflows of metal-poor gas into the central
regions of GLASS-Zgrad1. These first results showcase the power of JWST wide-
field slitless spectroscopic modes to resolve the mass assembly and chemical
enrichment of low-mass galaxies in and beyond the peak epoch of cosmic star
formation ($z\gtrsim 2$). Reaching masses $\lesssim 10^{9}\leavevmode\nobreak\
M_{\odot}$ at these redshifts is especially valuable to constrain the effects
of galactic feedback and environment, and is possible only with JWST’s new
capabilities.

galaxies: abundances — galaxies: evolution — galaxies: formation — galaxies:
high-redshift — gravitational lensing: strong

##  1 Introduction

A central challenge in galaxy evolution is to understand how galaxies assemble
their baryonic mass, and cycle their gas and heavy elements in and around
themselves. Deep imaging and spectroscopic surveys with Hubble Space Telescope
(HST), the Sloan Digital Sky Survey (SDSS), and other facilities have provided
a census of the cosmic star formation rate (SFR) and hence metal enrichment
history, which peak at $1\lesssim z\lesssim 3$ (the “cosmic noon” epoch; e.g.,
Madau & Dickinson, 2014). Dedicated observational campaigns have established
tight correlations among various physical properties of star-forming galaxies
at this epoch, e.g., stellar mass ($M_{\ast}$), SFR, gas-phase metallicity,
size, morphology, kinematics, and dust and gas content (see recent reviews by
Kewley et al., 2019; Maiolino & Mannucci, 2019). These integrated scaling
relations are largely reproduced by theoretical semi-analytic models and
simulations which incorporate accretion and merging, star formation, and
feedback in the form of gaseous outflows powered by star formation and
supermassive black hole accretion (e.g., Somerville & Davé, 2015). However,
key properties of galactic outflows such as their mass loss rates and
recycling timescales have proven extremely challenging to discern, especially
at intermediate and high redshifts. A variety of assumptions and “sub-grid”
physical models are able to reproduce global galaxy scaling relations. Hence,
additional observational constraints are needed to better understand how
feedback redistributes baryons within and around galaxies.

Gas-phase metallicity gradients are sensitive probes of the complex gas flows
driven by galactic feedback and tidal interactions. The value of gas
metallicity maps as a diagnostic of galaxy formation has been demonstrated by
numerous integral field spectroscopy (IFS) surveys at $z=0$ (e.g., Sanchez et
al., 2014; Belfiore et al., 2017; Poetrodjojo et al., 2018; Franchetto et al.,
2021). Theoretical models and simulations make differing predictions for
metallicity gradient evolution, depending on the strength of feedback and the
outflow properties at high redshifts (Gibson et al., 2013). Predictions
diverge the most at low stellar masses ($M_{\ast}$ $\lesssim$
$10^{9}M_{\odot}$), especially at $z$>2 (Mott et al., 2013; Mollá et al.,
2018; Gibson et al., 2013; Hemler et al., 2021). This is a key regime where
feedback may be important for dynamical evolution and is even a candidate to
resolve the longstanding “cusp-core” problem (and related challenges to the
cold dark matter paradigm; e.g., Bullock & Boylan-Kolchin, 2016). However,
observations are challenging due to small angular sizes of high-$z$ galaxies,
and ground-based adaptive optics studies have yielded limited samples (e.g.,
Jones et al., 2013; Yuan et al., 2013; Leethochawalit et al., 2016; Curti et
al., 2020). Meanwhile, HST grism surveys have made substantial progress in
charting resolved chemical enrichment at high redshifts (Jones et al., 2015;
Wang et al., 2017, 2020; Simons et al., 2021; Li et al., 2022). Combining WFC3
grism spectroscopy with gravitational lensing magnification, Wang et al.
(2020) assembled a large sample of galaxies with (sub-kiloparsec) sub-kpc
resolution metallicity radial gradients at cosmic noon. While this progress is
encouraging, results from HST are limited by wavelength coverage to $z\lesssim
2.3$ and typically probe $M_{\ast}\gtrsim 10^{9}\leavevmode\nobreak\
M_{\odot}$.

The Near-infrared Imager and Slitless Spectrograph (NIRISS; Willott et al.
2022) onboard the James Webb Space Telescope (JWST) now enables a tremendous
leap forward with its superior sensitivity, angular resolution, and longer
wavelength coverage compared to HST/WFC3. This allows resolved metallicity
studies probing higher redshifts and lower mass galaxies, which are a powerful
discriminant of feedback and outflow models (e.g., Ma et al., 2017; Hemler et
al., 2021). This Letter presents the first study of gas-phase metallicity maps
at $z>3$, a regime not yet explored observationally, based on the NIRISS data
acquired by the Early Release Science (ERS) program GLASS-JWST (ID
ERS-1324222https://www.stsci.edu/jwst/science-execution/approved-programs/dd-
ers/program-1324; Treu et al., 2022). These observations also take advantage
of the gravitational lensing magnification by the galaxy cluster Abell 2744,
to study background high-$z$ sources in high definition.

This Letter is structured as follows. We briefly describe the observations in
Section 2. In Section 3 we describe the extraction of emission line maps and
subsequent measurements of gas-phase metallicity (both the global value and
spatial map). We discuss the results in Section 4 and summarize the main
conclusions in Section 5. We adopt a standard cosmology with $\Omega_{m}=0.3$,
$\Omega_{\Lambda}=0.7$, and $\mathrm{H_{0}}=70$ $\rm km\leavevmode\nobreak\
s^{-1}\leavevmode\nobreak\ Mpc^{-1}$, and a Chabrier (2003) Initial Mass
Function (IMF).

##  2 Observations

In this Letter we use JWST/NIRISS data from GLASS-ERS, whose observing
strategy is described by Treu et al. (2022), and data reduction in Roberts-
Borsani et al. (Paper I 2022). In brief, the Abell 2744 cluster core was
observed with $\sim$15 hours with NIRISS wide field slitless spectroscopy and
direct imaging in three filters (F115W, F150W, F200W). This provides low
resolution $R\sim 150$ spectra of all objects in the field of view with
continuous wavelength coverage from $\lambda\in[1.0,2.2]$ $\mu\textrm{m}$
(rest-frame [0.24, 0.54] $\mu\textrm{m}$ at $z$=3.06). This includes the
strong rest-frame optical emission lines [Mg ii], [O ii], [Ne iii], H$\gamma$,
H$\beta$, and [O iii]. Spectra are taken at two orthogonal dispersion angles
(using the GR150C and GR150R grism elements) which helps to minimize the
effects of contamination by overlapping spectral traces.

##  3 Data analysis

Here we focus on the NIRISS observations of one galaxy (GLASS-Zgrad1) at
$z=3.06$, whose measured properties are given in Table 1. GLASS-Zgrad1 has
highly secure grism redshift determination given by Grizli, with $\left(\Delta
z\right)_{\rm posterior}/(1+z_{\rm peak})=1.7\times 10^{-4}$, ascribed to its
extremely strong rest-frame optical emission lines. Its data benefit from low
contamination from neighboring sources, so its spectrum is suitable to measure
emission line maps. The synergy of JWST’s resolving power and its lensing
magnification (estimated to be $\sim$3, Johnson et al., 2014; Wang et al.,
2015; Bergamini et al., 2022) reveals its detailed physical properties on
scales as small as $\sim$200 pc. These characteristics make our target a
textbook case to showcase the capabilities of JWST in spatially resolving the
properties of high-$z$ galaxies. The upper left panel of Fig. 1 shows its
color composite image, made by combining the three NIRISS filters (F115W,
F150W and F200W). The galaxy shows a smooth light profile, with no clear signs
of clumpy structures. The location of GLASS-Zgrad1 on the mass-excitation
diagram (Juneau et al., 2014; Coil et al., 2015) indicates negligible emission
line contamination from an active galactic nucleus (AGN), such that we can
apply standard gas-phase metallicity diagnostics for Hii regions.

While GLASS-Zgrad1 itself shows no clear signs of interaction, it is located
only $\sim$15 kpc in projection from a $\sim 100\times$ more massive galaxy
($M_{\ast}\approx 10^{10.6}\leavevmode\nobreak\ M_{\odot}$) at a consistent
redshift (Wu et al., 2022; Sun et al., 2022). This massive companion shows
potentially spiral structure which may be induced by interaction with GLASS-
Zgrad1 (Wu et al., 2022). Such interaction may affect the metallicity gradient
via torques on the gas; we discuss this possibility in Section 4.

Galaxy |  GLASS-Zgrad1
---|---
R.A. [deg] | 3.585943
Dec [deg] | -30.382102
$z_{\rm spec}$ | 3.06
$\mu$ | $3.00^{+0.03}_{-0.03}$
Observed emission line fluxes
$f_{[\textrm{O}\leavevmode\nobreak\ \textsc{iii}]}$ [$10^{-19}$$\rm erg\leavevmode\nobreak\ s^{-1}\leavevmode\nobreak\ cm^{-2}$ ] | 913.77 $\pm$ 9.65
$f_{\textrm{H}\beta}$ [$10^{-19}$$\rm erg\leavevmode\nobreak\ s^{-1}\leavevmode\nobreak\ cm^{-2}$ ] | 161.68 $\pm$ 8.89
$f_{\textrm{H}\gamma}$ [$10^{-19}$$\rm erg\leavevmode\nobreak\ s^{-1}\leavevmode\nobreak\ cm^{-2}$ ] | 40.71 $\pm$ 12.73
$f_{[\textrm{Ne}\leavevmode\nobreak\ \textsc{iii}]}$ [$10^{-19}$$\rm erg\leavevmode\nobreak\ s^{-1}\leavevmode\nobreak\ cm^{-2}$ ] | 101.65 $\pm$ 14.76
$f_{[\textrm{O}\leavevmode\nobreak\ \textsc{ii}]}$ [$10^{-19}$$\rm erg\leavevmode\nobreak\ s^{-1}\leavevmode\nobreak\ cm^{-2}$ ] | 207.43 $\pm$ 9.65
Rest-frame equivalent widths
EW${}_{[\textrm{O}\leavevmode\nobreak\ \textsc{iii}]}$ [Å] | 749.37 $\pm$ 25.23
EW${}_{\textrm{H}\beta}$ [Å] | 156.92 $\pm$ 10.18
EW${}_{\textrm{H}\gamma}$ [Å] | 31.66 $\pm$ 9.39
EW${}_{[\textrm{Ne}\leavevmode\nobreak\ \textsc{iii}]}$ [Å] | 47.80 $\pm$ 6.51
EW${}_{[\textrm{O}\leavevmode\nobreak\ \textsc{ii}]}$ [Å] | 130.52 $\pm$ 6.70
Nebular emission diagnostics
$12+\log({\rm O/H})$ global | $8.11^{+0.07}_{-0.06}$
$\Delta\log({\rm O/H})/\Delta r$ [$\mathrm{dex\leavevmode\nobreak\ kpc^{-1}}$] | $0.165\pm 0.023$
SFRN [$M_{\sun}\leavevmode\nobreak\ {\rm yr}^{-1}$] | $8.64^{+6.35}_{-2.48}$
log(sSFRN/[${\rm yr}^{-1}$]) | $-7.68^{+0.34}_{-0.22}$
$A_{V}^{\rm N}$ | $0.54^{+0.63}_{-0.39}$
Broad-band photometry SED fitting
$\log(M_{\ast}/M_{\sun})$ | $8.62^{+0.07}_{-0.10}$
SFRS [$M_{\sun}\leavevmode\nobreak\ {\rm yr}^{-1}$] | $4.28^{+0.43}_{-0.44}$
log(sSFRS/[${\rm yr}^{-1}$]) | $-7.97^{+0.07}_{-0.10}$
$A_{V}^{\rm S}$ | $0.60^{+0.03}_{-0.04}$
Table 1: Physical properties of galaxy GLASS-Zgrad1. The values of $M_{\ast}$
and SFR have been corrected for lensing magnification.

Figure 1:  Galaxy GLASS-Zgrad1, a $z\sim$3 star-forming dwarf galaxy
($M_{\ast}$$\simeq$$10^{8.6}$$M_{\odot}$) with a strongly inverted metallicity
radial gradient presented in this work: the first metallicity map obtained
with the JWST and first ever such measurement secured by sufficient spatial
resolution ($\lesssim$kpc) at $z\geq 3$. Top, from left to right: the color
composite stamp (made using the 3-band JWST/NIRISS pre-imaging on 30 mas plate
scale), stellar surface density ($\Sigma_{\ast}$) map (derived from the pixel-
by-pixel SED fitting), and surface brightness maps of emission lines ([O ii],
H$\gamma$, H$\beta$ and [O iii]), measured from the NIRISS slitless
spectroscopy acquired by GLASS-JWST. The black contours mark the de-lensed de-
projected galacto-centric radii with 1 kpc interval, given by our source plane
morphological reconstruction using the public lens model. The orientation
(north up and east to the left) and spatial extent remain unchanged throughout
all the 2D maps. Middle: the optimally extracted 1D observed $F_{\lambda}$
flux and its 1-$\sigma$ uncertainty, represented by the blue solid lines and
cyan shaded bands, respectively, combined from the two orthogonal dispersion
directions (GR150C and GR150R). In total, the exposure time _per_ filter
combined from both dispersions reaches 2.9 hours. The forward-modeled spectra
(source continuum + nebular emission), based on the best-fit intrinsic SED
with source morphological broadening taken into account, is shown in the red
dashed line. Bottom: the _continuum-subtracted_ 2D grism spectra covered by
the three filters (F115W, F150W, and F200W) respectively, showcasing the
quality of our GLASS-JWST slitless spectroscopy.

###  3.1 Emission line map and metallicity measurements

We rely on the latest version the Grism Redshift & Line software (Grizli
333https://github.com/gbrammer/grizli; Brammer & Matharu, 2021) to extract and
model the grism spectra, following the procedure described in Paper I. Grizli
provides contamination subtracted 1D and 2D grism spectra, along with the
best-fit spectroscopic redshifts, as shown in Fig. 1 (also see Appendix A of
Wang et al., 2019, for the full descriptions of the redshift fitting procedure
employed by Grizli). We follow the procedures described by Wang et al. (2020)
to extract un-contaminated line maps from the 2D grism spectra, also shown in
Fig. 1. The maps shown here are encompassed by the boundary of the Grizli
segmentation map (for details see Roberts-Borsani et al., 2022) defined using
conventional source detection parameters largely following the 3D-HST survey
(Brammer et al., 2012; Momcheva et al., 2016). We restrict our analysis to
this region, where the stellar continuum is detected at high significance. We
additionally use the spatially integrated line fluxes measured by Grizli to
estimate global physical properties as presented in Table 1. When drizzling
the 2D grism spectra and emission line maps, we adopt a plate scale of 30 mas,
to Nyquist sample the FWHM of the JWST point spread function at these
wavelengths.

We jointly constrain ionized gas metallicity ($12+\log({\rm O/H})$), nebular
dust extinction ($A_{v}^{\rm N}$), and de-reddened H$\beta$ line flux
($f_{\textrm{H}\beta}$), using our forward-modeling Bayesian inference method,
largely described in Wang et al. (2017, 2019, 2020, 2022). The likelihood
function is defined as

$\displaystyle\mathrm{L}\propto\exp\left(-\frac{1}{2}\cdot\sum_{i}\frac{\left(f_{\textrm{EL}_{i}}-R_{i}\cdot
f_{\textrm{H}\beta}\right)^{2}}{\left(\sigma_{\textrm{EL}_{i}}\right)^{2}+\left(f_{\textrm{H}\beta}\right)^{2}\cdot\left(\sigma_{R_{i}}\right)^{2}}\right).$
(1)

where $f_{\textrm{EL}_{i}}$ and $\sigma_{\textrm{EL}_{i}}$ represent the de-
reddened emission-line (e.g. [O ii], H$\gamma$, H$\beta$, [O iii]) flux and
its uncertainty (measured from the flux-calibrated error array; see Roberts-
Borsani et al. 2022), corrected using the Calzetti et al. (2000) dust
extinction law with $A_{v}^{\rm N}$ as a free parameter.
$R_{i}=\frac{f_{\textrm{EL}_{i}}}{f_{\textrm{H}\beta}}$ is the expected flux
ratio of each line with respect to H$\beta$, based on the adopted metallicity
calibrations and intrinsic Balmer decrements, while $\sigma_{R_{i}}$ is the
intrinsic scatter in $R_{i}$. To compute metallicity we adopt the purely
empirical strong line diagnostics prescribed by Bian et al. (2018), calibrated
against a sample of local analogs of high-$z$ galaxies according to their
location on the BPT (Baldwin et al., 1981) diagram. We note that dust
extinction $A_{v}^{\rm N}$ is constrained by the metallicity diagnostics in
addition to H Balmer line ratios, as described in our earlier work. For
example, the characteristic locus of R23 versus O32 (see, e.g., Shapley et
al., 2015) and the intrinsic [O iii]/[Ne iii] line ratios (Jones et al., 2015)
provide constraints on $A_{v}^{\rm N}$ along with traditional diagnostics such
as H$\beta$/H$\gamma$. The effect of uncertainty in $A_{v}^{\rm N}$ is
included in our metallicity uncertainties. To estimate the instantaneous star
formation rate (SFRN), we use the Balmer line luminosity assuming the
Kennicutt (1998) calibration scaled to the Chabrier (2003) IMF, i.e., ${\rm
SFR^{N}}=1.6\times
10^{-42}\frac{L(\textrm{H}\beta)}{\rm[erg\leavevmode\nobreak\
s^{-1}]}\leavevmode\nobreak\ [M_{\odot}{\leavevmode\nobreak\ \rm yr^{-1}}]$.

The forward-modeling Bayesian inference described above is first performed on
the integrated emission line fluxes to yield global values of $12+\log({\rm
O/H})$, $A_{v}^{\rm N}$, and SFRN (with results listed in Table 1). We then
utilize Voronoi tessellation (Cappellari & Copin, 2003; Diehl & Statler, 2006)
as in Wang et al. (2019, 2020) to construct spatial bins with nearly uniform
signal-to-noise ratio (SNR) of [O iii], the strongest emission line available.
We apply the Bayesian inference with line fluxes in each Voronoi bin, yielding
maps of metallicity and other properties at sub-kpc resolution. Overall, we
are able to resolve this $z\sim 3$ dwarf galaxy with $\gtrsim$50 resolution
elements at a signal-noise ratio threshold of 10 in [O iii].

As this work relies on emission lines spanning multiple spectroscopic filters,
we have examined the relative flux calibration accuracy as a potential source
of error. Comparing the spectra with both broadband photometric colors and
best-fit spectral templates, we estimate that the relative calibration is
accurate to within $\lesssim$10% near the center of each filter (F115W, F150W,
and F200W). This applies to the strong lines of [O ii], [Ne iii], H$\beta$,
and [O iii] in our $z=3.06$ target. Calibration uncertainty for [Ne iii]/[O
ii] and [O iii]/H$\beta$ appears to be negligible. However, fluxes near band
edges appear to be underestimated in some cases, possibly due to slight
misalignment of the expected and actual spectral trace positions. This
potentially affects the H$\gamma$ line such that its true flux may be
$\sim$20% larger than we report here. We note that systematic error of this
magnitude is smaller than the statistical uncertainty for spatial Voronoi bins
(where line ratio uncertainties are $\gtrsim$10% and H$\gamma$ is undetected).
Any relative calibration error between the F150W and F200W spectra would
appear similar to a change in $A_{v}$; in this case our methodology would
produce a bias in $A_{v}$ but not in $12+\log({\rm O/H})$. Absolute flux
calibration is not needed since our results rely entirely on line ratios. Flux
calibration errors therefore may bias the derived $A_{v}$ but should not
substantially affect the spatial trends in metallicity. While more detailed
examination is beyond the scope of this work, for now we caution that modest
NIRISS flux calibration uncertainties may exist and that wavelengths near the
bandpass edges should be treated carefully. We anticipate that calibrations
will improve over time, as the calibration plan is executed during Cycle-1.

###  3.2 SED fitting and stellar mass map

There has been a wealth of deep multi-wavelength imaging in broad bands
covering 0.2–5 $\mu\textrm{m}$ wavelengths in the field of A2744. We rely on
the photometric catalog compiled by the ASTRODEEP project (Merlin et al.,
2016), which performs aperture-matched and blending-corrected photometry of
the HFF 7-band, Hawk-I Ks, and Spitzer IRAC images (Brammer et al., 2016; Lotz
et al., 2017). We use the BAGPIPES software (Carnall et al., 2018) to fit the
BC03 models (Bruzual & Charlot, 2003) of galaxy spectral energy distributions
(SEDs) to the ASTRODEEP photometry. BAGPIPES is capable of adding the nebular
emission component into galaxy spectra, so the emission line fluxes are taken
into account in the fit simultaneously. Basic assumptions and parameter ranges
include the Chabrier (2003) IMF, a stellar metallicity range of
$Z/Z_{\odot}\in(0,2.5)$, the Calzetti et al. (2000) dust extinction law with
$A_{v}^{\rm S}$ in the range of (0, 3), and an exponentially declining star
formation history with $\tau$ in the range of (0.01, 10) Gyr. We fix the
spectroscopic redshift of our galaxy to its best-fit grism value ($z=3.06$),
with a conservative uncertainty of $\Delta z/(1+z)\approx 0.003$, following
Momcheva et al. (2016). The obtained physical properties are presented in
Table 1. The measured stellar mass and SFRS are
$\log(M_{\ast}/M_{\odot})=8.62^{+0.07}_{-0.10}$ and ${\rm
SFR^{S}}=4.28^{+0.43}_{-0.44}$, respectively, indicating that our galaxy lies
0.14 dex above the star-forming main sequence (Speagle et al., 2014). We also
note that our derived values of the dust reddening for the nebular and stellar
component are consistent with E(B-V)stars $\sim$ E(B-V)gas (Reddy et al.,
2015).

Broad-band image morphology is not necessarily a good tracer of the underlying
stellar mass distribution in star forming galaxies (e.g., Wuyts et al., 2012).
We, therefore, construct stellar mass maps using spatially resolved SED
fitting. We use the same method as in Wang et al. (2020), applied to Hubble
Frontier Field imaging (Lotz et al., 2017). The F606W, F814W, F105W, F125W,
F140W, and F160W HST images are used for this analysis. F435W is not used as
it corresponds to the Lyman $\alpha$ forest region at $z=3.06$. Images from
each filter are aligned and convolved to a common angular resolution of
0$.\\!^{\prime\prime}$22 FWHM, ensuring good sensitivity at low surface
brightness reaching beyond the effective radius. The photometry in each
0$.\\!^{\prime\prime}$06-square pixel is then fit using FAST (Kriek et al.,
2009) with an exponentially declining star formation history, Chabrier (2003)
IMF, and Bruzual & Charlot (2003) stellar population synthesis models (for
full details see Wang et al., 2020). The resulting stellar mass map is shown
in Fig. 1. We fit the stellar mass map with a 2-D elliptical Gaussian in order
to determine the galactocentric radius at each point (Jones et al., 2015). The
stellar mass surface density is indeed smoother than the luminosity
distribution, and we consider morphological parameters based on this mass map
to be more reliable.

Future JWST photometry with NIRCam, especially in filters relatively
unaffected by strong nebular emission, will enable improved SED fitting
results via spatially resolved photometry at longer wavelengths. Our spatial
SED fitting is currently based on HST photometry sampling only $\lesssim 4100$
Å in the rest frame. NIRISS F200W imaging would extend the wavelength
coverage, but it contains strong emission lines which account for $\sim$55% of
the total broad-band flux based on the H$\beta$ and [O iii] equivalent widths.
While this can be corrected using the emission line maps (Figure 1), the
effect of including this additional photometry is small and comparable to the
uncertainty. We therefore do not use it for this initial study.

###  3.3 Source plane morphology

We perform a source plane reconstruction of GLASS-Zgrad1 to recover its
intrinsic morphology based on public lens models (Johnson et al., 2014; Wang
et al., 2015; Bergamini et al., 2022). Each pixel in the image-plane stellar
mass map is ray-traced back to its source-plane position based on the
deflection fields from the macroscopic cluster lens model. We then fit a 2D
Gaussian profile to galaxy’s intrinsic stellar mass spatial map to pinpoint
its axis ratio, orientation and inclination, so that we obtain the intrinsic
source morphology (corrected for lensing distortion). The centroid of this 2D
fit is adopted as the galaxy center ($r=0$). As a result, we establish the
delensed deprojected galactocentric distance scale for each Voronoi bin, as
displayed by the black contours in Figs. 1 and 2.

Figure 2:  The metallicity spatial maps and radial gradient of GLASS-Zgrad1 at
$z\sim 3$. In the left and central panels, we adopt the weighted Voronoi
tessellation method (Cappellari & Copin, 2003; Diehl & Statler, 2006) to
divide the galaxy surface into spatial bins with a uniform SNR of 10 on [O
iii]. The black contours represent the delensed, deprojected galactocentric
radii with 1 kpc intervals from our source-plane morphological reconstruction.
In the right panel, we show the radial gradient of the metallicity inferences
in all individial Voronoi cells, with a slope of $\Delta\log({\rm O/H})/\Delta
r=0.165\pm 0.023\leavevmode\nobreak\ [\mathrm{dex\leavevmode\nobreak\
kpc^{-1}}]$ represented by the magenta dashed line.

##  4 The first metallicity map from JWST/NIRISS wide-field slitless
spectroscopy

Here we present the main results of our analysis. The top panels of Fig. 1
show the maps of the most prominent emission lines of GLASS-Zgrad1: [O ii],
H$\gamma$, H$\beta$, [O iii]. Its optimally extracted 1D spectrum, covered by
all three grism filters (F115W, F150W and F200W) combined from both dispersion
elements (GR150C and GR150R), is shown in the central row, while the
_continuum-subtracted_ 2D grism spectrum is shown in the bottom row. All
nebular emission features used in this work are clearly seen. This 1D/2D
spectrum showcases the quality of our NIRISS spatially resolved spectroscopy
of high-$z$ emission line galaxies.

The emission line maps unveil how most of the emission is concentrated in the
galaxy core, sharply decreasing at radii $>$1 kpc. In the outskirts the
emission looks quite smooth, especially for [O iii]. The only exception is
H$\gamma$, which appears patchy due to the lower SNR of this line.

Fig. 2 shows the 2D metallicity map of GLASS-Zgrad1. We note that variations
in the derived metallicity result directly from the intrinsic emission line
flux ratios via Equation 1 (e.g., as shown for the R23 and O32 indices for two
examples in Figure 2 of Wang et al. 2019). Clearly, the galaxy outskirts on
average display highly elevated metallicities, i.e., more metal-enriched by
$\sim$0.2 dex than the center. To quantify the radial gradient, we conduct a
linear regression using a simple least-squares method, with the functional
form $12+\log({\rm O/H})=\theta_{1}r+\theta_{0}$. Here $\theta_{1}$ and
$\theta_{0}$ are the radial gradient and the intercept, respectively, and $r$
is the source-plane galactocentric radius in kpc. We obtain the best-fit and
1-$\sigma$ uncertainty results as $\theta_{1}\equiv\Delta\log({\rm
O/H})/\Delta r=0.165\pm 0.023\leavevmode\nobreak\
[\mathrm{dex\leavevmode\nobreak\ kpc^{-1}}]$ and $\theta_{0}=8.140\pm 0.019$.
The central metallicity is roughly one-third of the solar value (adopting
solar $12+\log({\rm O/H})$ =8.69; Asplund et al., 2009) with a significant
positive radial gradient. The positive metallicity gradient in GLASS-Zgrad1 is
even steeper than those measured by Wang et al. (2019) for two similarly low-
mass $z\sim 2$ galaxies, which also show extremely high emission line
equivalent widths, and which have gradients of $\sim 0.1$ dex/kpc.

We performed several tests to verify that the positive gradient slope is
robust against potential systematic errors. Firstly, we have binned the data
in radial annuli to obtain a gradient measurement which is independent of the
Voronoi tesselation. Using radial bin sizes such that each has SNR $>10$ in [O
iii], we find $\theta_{1}=0.14\pm 0.03$ dex kpc-1 which is fully consistent
with our fiducial result (see also similar tests in Wang et al., 2017).
Secondly, we consider whether spurious noise features could bias the results.
The largest possible effect is from the highest-metallicity region which is
also at the largest radius ($r\simeq 2$ kpc). Repeating the analysis with this
point removed still results in a significant positive gradient
$\theta_{1}=0.076\pm 0.019$ dex kpc-1, albeit smaller than our fiducial result
by design. Thirdly, we vary the galaxy center (i.e., $r=0$ position) by up to
0$.\\!^{\prime\prime}$1 and find no significant difference in the results.
Finally, to test the statistical significance of the positive slope, we also
calculated the Pearson correlation coefficient $r_{P}$ for metallicity as a
function of radius. The result is $r_{P}=0.43$ (p-value 0.001) which confirms
the significance of the positive slope independent of statistical uncertainty
estimates. Taken together, we conclude from these tests that the metallicity
gradient slope is indeed positive and on the order of $\gtrsim$0.1 dex kpc-1
at $\gtrsim 4\sigma$ significance.

In addition to the steeply rising metallicities indicated by the strong and
highly significant ($\geq$7-$\sigma$) inverted radial gradient in GLASS-
Zgrad1, there also exist some hints of azimuthal metallicity variations. In
particular the local metallicity shows large variations at radii $r\simeq 1$–2
kpc. This azimuthal structure and deviation from a smooth radial gradient, if
further confirmed in numerous high-$z$ galaxies, can shed light upon the
timescales for chemical enrichment relative to diffusion and mixing via
measurements of the metallicity correlation length scale. This would represent
a valuable new constraint for models of galaxy formation at high redshifts
(e.g., Metha et al., 2021, 2022).

Figure 3:  The redshift evolution of sub-kpc resolution metallicity gradients
measured from observations and predicted by hydrodynamic simulations. Using
the deep NIRISS slitless spectroscopy acquired by GLASS-JWST, we present
hitherto the first metallicity gradient measurement with sub-kpc resolution at
$z\gtrsim 3$, highlighted by the star color-coded in sSFR. Before this work,
all previous observational efforts at similar resolution ($\lesssim$kpc scale)
primarily come from ground-based AO-assisted integral-field spectroscopy
(marked by the magenta diamonds, Swinbank et al., 2012; Jones et al., 2013;
Leethochawalit et al., 2016; Schreiber et al., 2018) and space-based slitless
spectroscopy with HST/WFC3 (marked by the circles also color-coded in sSFR if
such information is publicly available, Jones et al., 2015; Wang et al., 2020;
Simons et al., 2021; Li et al., 2022). In particular, we highlight the first
measurements of metallicity radial gradients in high-$z$ overdense
environments conducted by the MAMMOTH-Grism survey (HST-GO-16276, P.I. Wang,
Li et al., 2022) using color-coded circles with maroon edges. In comparison,
we show the predictions made by state-of-the-art cosmological hydrodynamic
simulations: the 1-$\sigma$ spread of FIRE (Ma et al., 2017) and Illustris-
TNG50 (Hemler et al., 2021), as well as two Milky Way analogs with normal and
enhanced feedback strengths but otherwise identical numerical setups
(corresponding to MUGS and MaGICC, respectively, Gibson et al., 2013). Despite
the wide differences among the numerical recipes implemented, these
simulations make indistinguishable predictions at $z\lesssim 1$. However,
their predictions diverge more significantly at higher redshifts, leaving a
potential breakthrough at $z\gtrsim 2.6$, where the JWST spatially resolved
spectroscopy can be highly efficient in deriving metallicity gradients and
thus test these theoretical predictions.

In Fig. 3, we show the redshift evolution of radial metallicity gradients in
high-$z$ galaxies secured with sub-kpc spatial resolution. This sub-kpc
resolution is crucial in ensuring the results are robust against beam-smearing
effects (e.g., Yuan et al., 2013). The vast majority of the galaxies shown
here reside in blank fields, with the exceptions of those identified by the
MAMMOTH-Grism survey (HST-GO-16276, P.I. Wang, Wang et al., 2022) residing in
the core regions of one of the most massive galaxy protoclusters at $z\sim
2.24$ (marked by the maroon edges, Li et al., 2022). The current existing
sample in the literature consists of essentially two types of measurements
driven by the available infrared spectroscopic instrumentation: ground-based
IFS assisted with adaptive optics (AO) (Swinbank et al., 2012; Jones et al.,
2013; Leethochawalit et al., 2016; Schreiber et al., 2018) and space-based
slitless spectroscopy (Jones et al., 2015; Wang et al., 2020; Simons et al.,
2021; Li et al., 2022). The latter method only refers to HST WFC3 spectroscopy
before this work. Limited by the wavelength coverage of the WFC3/G141 grism
and the H/K-band AO Strehl ratios, there have not yet been _any_ sub-kpc
resolution measurements of metallicity maps at $z\geq 3$. Using the deep
NIRISS slitless spectroscopy acquired by GLASS-JWST, we for the first time
secure an inverted gradient in the redshift range of $z\gtrsim 2.6$. This
opens up a new key window on accurate characterization of the chemical
profiles of galaxies in and beyond the cosmic noon epoch, to constrain the
effect of galactic feedback. Notably, we can see from Fig. 3 that the
theoretical predictions by a number of state-of-the-art cosmological
hydrodynamic simulations — FIRE (Ma et al., 2017), Illustris-TNG50 (Hemler et
al., 2021), MUGS and MaGICC (Gibson et al., 2013) — significantly diverge at
high redshifts, as a consequence of diverse feedback prescriptions. They also
struggle to reproduce the fraction of inverted (positive slope) gradients
currently observed.

The existence of a relatively steep positive metallicity gradient in GLASS-
Zgrad1 is at first surprising, given the predominantly flat or moderately
negative radial gradients in Fig. 3. However, GLASS-Zgrad1 has a massive
companion which may be gravitationally interacting (Section 3; Wu et al.
2022). Such an interaction can induce torques on the gas, causing metal-poor
gas at large radii to lose angular momentum and migrate toward the center of
the galaxy. This process can result in flattened or inverted metallicity
gradients (e.g., Kewley et al., 2006). Indeed, close gravitational interaction
is the primary driver of positive gradients in $z\simeq 0$ galaxies (e.g.,
Rupke et al., 2010; Torrey et al., 2012). We therefore consider it likely that
the gradient in our target is indeed steeply positive and is induced by
interaction with the nearby object.

Figure 4:  The mass dependence of sub-kpc resolution metallicity gradients
measured from observations and predicted by hydrodynamic simulations. All
symbols remain the same as in Fig. 3, except that the solid lines now
represent the predictions by the EAGLE simulations assuming weak or strong
feedback prescriptions (Tissera et al., 2019). The $z=2$ results of the
Illustris-TNG50 simulations are shown here. The latest EAGLE results extending
to $M_{\ast}\sim 10^{9}M_{\odot}$ at $z=2$ are denoted by the purple shaded
regions bracketing the [25th, 75th] percentiles of the simulation predictions,
which shows a better agreement with the observed scatters in metallicity
gradients (Tissera et al., 2021). As compared to the MAMMOTH-Grism metallicity
gradients measured in overdense environment having a sample median of
$0.014\pm 0.022\leavevmode\nobreak\ [\mathrm{dex\leavevmode\nobreak\
kpc^{-1}}]$ (Li et al., 2022), GLASS-Zgrad1 shows a much more pronounced
inverted gradient, indicating stronger environmental effects. This is
consistent with the theoretical prediction that tidal torques, stemming from
close gravitational interaction, induce cold gas infalls into the inner disk
to invert metallicity radial gradient (Torrey et al., 2012; Jones et al.,
2013, 2015).

In Fig. 4, we show the metallicity gradients of these field galaxies in terms
of their $M_{\ast}$. This correlation is highly sensitive to galactic
feedback. For instance, the two suites of EAGLE simulations using different
feedback prescriptions predict widely dissimilar mass dependence (Tissera et
al., 2019). Observationally there is considerable scatter in the metallicity
gradient slopes, which the current state-of-the-art numerical hydrodynamic
simulations (e.g. Ma et al., 2017; Hemler et al., 2021) struggle to reproduce
(but see Tissera et al., 2021).

Recently, there is growing evidence for the existence of inverted metallicity
gradients in distant galaxies (Cresci et al., 2010; Wang et al., 2019; Li et
al., 2022). Wang et al. (2019) interpreted this phenomenon as an indication of
the metal-enriched gas outflows triggered by central starbursts that disrupt
galaxy out of equilibrium (also see Sharda et al., 2021), whereas other groups
have suggested centrally directed low-metallicity gas infall as the physical
cause (Cresci et al., 2010; Mott et al., 2013). The latter scenario has been
adopted to explain the inverted gradients observed in protocluster
environments where gas inflows are easily drawn by the underlying large
gravitational potentials (Li et al., 2022). Here our analysis confirmed a
third scenario where strongly inverted gradients at high redshifts can be
caused by the inflow of metal-poor gas into inner disks as a result of close
gravitational interactions. Furthermore, as shown in Figs. 3 and 4, the
magnitude of the positive radial slope measured in GLASS-Zgrad1 is
significantly more dramatic than the sample median of $0.014\pm
0.022\leavevmode\nobreak\ [\mathrm{dex\leavevmode\nobreak\ kpc^{-1}}]$
measured in the MAMMOTH-Grism galaxies residing in extreme overdensities (Li
et al., 2022). This likely suggests that gravitational interactions impose
stronger environmental effects on the chemical profiles of high-$z$ galaxies
than large-scale overdensities.

##  5 Conclusions

In this Letter, we present the first spatially resolved analysis of a high-$z$
emission line galaxy using the wide-field slitless spectroscopic modes
provided by JWST. We first showcase the quality of our NIRISS grism data
acquired by the GLASS-JWST ERS program, presenting the extracted and cleaned
1D/2D grism spectra of a $z\simeq 3$ dwarf galaxy, GLASS-Zgrad1. Via SED
fitting to the broad-band photometry fully covering its rest-frame UV through
optical spectrum, we obtain $\log(M_{\ast}/M_{\odot})=8.62^{+0.07}_{-0.10}$
and ${\rm SFR^{S}}=4.28^{+0.43}_{-0.44}\leavevmode\nobreak\
[M_{\sun}\leavevmode\nobreak\ {\rm yr}^{-1}]$ corrected for lensing
magnification ($\mu=3.00{\pm}0.03$), $\sim$0.14 dex above the SFMS at $z\sim
3$. From the optimally extracted 1D grism spectrum (in particular the rest-
frame optical nebular emission lines: [O iii], H$\beta$, H$\gamma$, and [O
ii]), we measure its global physical properties to be $12+\log({\rm O/H})_{\rm
global}=8.11^{+0.07}_{-0.06}$, ${\rm
SFR^{N}}=8.64^{+6.35}_{-2.48}\leavevmode\nobreak\
[M_{\sun}\leavevmode\nobreak\ {\rm yr}^{-1}]$, and $A_{V}^{\rm
N}=0.54^{+0.63}_{-0.39}$, consistent with E(B-V)stars $\sim$ E(B-V)gas.

Importantly, the new capabilities afforded by JWST/NIRISS (e.g. exquisite
sensitivity, resolution, and wavelength coverage, etc.), coupled with
gravitation lensing magnification, enable us to spatially resolve GLASS-Zgrad1
into $\gtrsim$50 individual resolution elements with source-plane resolution
reaching $\sim$200 pc scales. Using its multiple nebular emission line maps,
we determine its metallicity radial gradient to be highly inverted (positive),
i.e., $\Delta\log({\rm O/H})/\Delta r$ = $0.165\pm 0.023$
[$\mathrm{dex\leavevmode\nobreak\ kpc^{-1}}$]. This is the first-ever
metallicity map from JWST spectroscopy, and the first sub-kpc resolution
metallicity gradient ever measured at $z\gtrsim 3$. We also verified this
positive gradient slope through extensive tests. In particular, by removing
the outermost spatial bin at $r\simeq 2$ kpc showing significant metal
enhancement, we rederived the gradient slope to be $0.076\pm 0.019$ dex kpc-1,
vindicating our finding that in GLASS-Zgrad1 the abundance of metals increases
with galacto-centric radius.

This strongly inverted metallicity gradient of GLASS-Zgrad1 likely stems from
the close gravitational interaction with a nearby object — a dusty galaxy
$\sim 100\times$ more massive than GLASS-Zgrad1 at a projected separation of
$\sim$15 kpc. This close encounter results in powerful tidal torques to induce
metal-poor gas inflows to the inner regions of GLASS-Zgrad1, inverting its
radial metallicity gradient. We thereby confirm a third channel for high-$z$
galaxies showing strongly inverted metallicity gradient, in addition to cold-
mode accretion and metal-enriched gas outflows. Moreover, in light of the more
pronounced inverted gradient measured in GLASS-Zgrad1 than any of the MAMMOTH-
Grism gradient sources, we deduce that close gravitational interactions are
more capable of producing strong environmental effects that modulate the
chemical profiles of galaxies than large-scale overdensities (e.g.
protocluster cores) at high redshifts. Our subsequent analysis of a larger
sample within the GLASS-JWST data set will enable more comprehensive
investigations of the true chemical profiles of galaxies at $z\sim 3$, so that
we can make a quantitative comparison to simulations and hence cast more
meaningful constraints on the effects of mergers, galactic feedback, and
environments. This work marks the beginning of a new era for spatially
resolved analysis on galaxy chemo-structural evolution in and beyond the
cosmic noon epoch.

We would like to thank the anonymous referee for careful reading and
constructive comments that help improve the clarity of this paper. This work
is based on observations made with the NASA/ESA/CSA James Webb Space
Telescope. The data were obtained from the Mikulski Archive for Space
Telescopes at the Space Telescope Science Institute, which is operated by the
Association of Universities for Research in Astronomy, Inc., under NASA
contract NAS 5-03127 for JWST. These observations are associated with program
JWST-ERS-1324. We acknowledge financial support from NASA through grant JWST-
ERS-1324. XW is supported by CAS Project for Young Scientists in Basic
Research, Grant No. YSBR-062. XW thanks Zach Hemler for kindly providing his
compilations of gradient measurements in the literature, and Patricia Tissera
for providing the tabulated results of the latest EAGLE simulations. KG
acknowledges support from Australian Research Council Laureate Fellowship
FL180100060. MB acknowledges support from the Slovenian national research
agency ARRS through grant N1-0238.

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