A Census of Sub-kiloparsec Resolution Metallicity Gradients in Star-forming Galaxies at Cosmic Noon from HST Slitless Spectroscopy

Metallicity is one of the most fundamental proxies of galaxy evolution at the peak of cosmic star formation and metal enrichment (1 ≲ z ≲ 3), i.e., the cosmic noon epoch (Madau & Dickinson 2014). The interstellar medium oxygen abundance relative to hydrogen—metallicity¹² —has been shown to correlate strongly with stellar mass (${M}_{* }$), star formation rate (SFR), and gas fraction (see the recent review by Maiolino & Mannucci 2019, and references therein). The cumulative history of the baryonic mass assembly, e.g., star formation, gas accretion, mergers, feedback, and galactic winds, altogether governs the total amount of metals remaining in gas (Finlator & Davé 2008; Davé et al. 2012; Lilly et al. 2013; Dekel & Mandelker 2014; Peng & Maiolino 2014). Moreover, these baryon cycling processes also tightly regulate the spatial distribution of metals in galaxies (Ho et al. 2015; Sanchez-Menguiano et al. 2016; Belfiore et al. 2019). Thus, a powerful way to learn about the baryon cycle is to use spatially resolved information.

The conventional way to obtain spatially resolved information is through integral field spectroscopy (IFS). This process has dramatically expanded our vision of galaxies from spectroscopic measurements integrated through single slits/fibers to panoramic two-dimensional (2D) views across their full surfaces, allowing for spatial variations of physical properties (including metallicity). This facilitates several large ground-based surveys (e.g., CALIFA, MaNGA, SAMI) to constrain the radial profile of metallicity in hundreds of galaxies, successfully capturing the dynamic signatures of the baryon cycle (see, e.g., Sanchez et al. 2014; Belfiore et al. 2017; Poetrodjojo et al. 2018). Meanwhile, numerical simulations are now capable of making useful predictions for metallicity radial gradients and their evolution with redshift (e.g., Ma et al. 2017; Tissera et al. 2019). The main challenge for observations is that sub-kpc spatial resolution is required for accurate results and meaningful comparison with theoretical predictions. While this spatial sampling is readily achieved for nearby galaxies (z ≲ 0.3), seeing-limited data are insufficient for galaxies at moderate to high redshift. Therefore, we need an effective approach to achieve sub-kpc resolved spectroscopy for statistically representative samples of high-z galaxies to compare meaningfully with cosmological zoom-in simulations.

The approach we take is space-based slitless spectroscopy. Building upon our previous efforts (Jones et al. 2015; Wang et al. 2017, 2019), we exploit grism spectroscopy from the Hubble Space Telescope (HST). The HST's diffraction limit in near-infrared wavelengths is equivalent to a physical scale of ∼1 kpc at z ∼ 2. Additional gains in resolution can be provided by gravitational lensing by foreground galaxies and/or galaxy clusters to fully satisfy the requirement for sufficiently resolving the chemical profiles of galaxies at that epoch. Lensing is thus essential for resolving the lowest-mass galaxies at high redshifts. Recently, Curti et al. (2020) derived metallicity maps and radial gradients in a sample of 28 lensed galaxies with stellar masses as low as 10⁹ ${M}_{\odot }$. In this work, we measure radial gradients of metallicity in 76 star-forming galaxies at 1.2 ≲ z ≲ 2.3 gravitationally lensed by foreground galaxy clusters, further extending to even lower stellar masses. Our sample enables a detailed comparison between observed and simulated chemostructural properties of galaxies, offering valuable insights into galaxy evolution.

This paper is organized as follows. In Section 2, we describe the data and galaxy sample analyzed in this work. The measurements of various physical quantities for our sample galaxies are presented in Section 3. Then, two major pieces of our analysis results, i.e., the redshift evolution and mass dependence of sub-kpc resolution metallicity gradients, are shown in Sections 4 and 5, respectively. We finally conclude in Section 6. Throughout this paper, the AB magnitude system and standard concordance cosmology (${{\rm{\Omega }}}_{{\rm{m}}}$ = 0.3, ${{\rm{\Omega }}}_{{\rm{\Lambda }}}$ = 0.7, ${H}_{0}=70\,\mathrm{km}\,{{\rm{s}}}^{-1}\,{\mathrm{Mpc}}^{-1}$) are used. Forbidden lines are indicated as $[{\rm{O}}\,{\rm\small{III}}]$ λ5008 := $[{\rm{O}}\,{\rm\small{III}}]$, $[{\rm{O}}\,{\rm\small{II}}]$ λλ3727, 3730 := $[{\rm{O}}\,{\rm\small{II}}]$, $[{\rm{N}}\,{\rm\small{II}}]$ λ6585 := $[{\rm{N}}\,{\rm\small{II}}]$, $[{\rm{S}}\,{\rm\small{II}}]$ λλ6718,6732 := $[{\rm{S}}\,{\rm\small{II}}]$, if presented without wavelength values.

The spectroscopic data analyzed in this work are acquired by the Grism Lens-Amplified Survey from Space¹³ (GLASS; Proposal ID 13459, PI: Treu; Schmidt et al. 2014; Treu et al. 2015). It is a cycle 21 HST large program allocated 140 orbits of Wide-Field Camera 3 (WFC3) near-infrared slitless spectroscopy on the centers of 10 strong-lensing galaxy clusters. For each cluster center field, we have 10 orbits of G102 (covering 0.8–1.15 $\mu {\rm{m}}$) and four orbits of G141 (covering 1.1–1.7 $\mu {\rm{m}}$) exposures, amounting to ∼22 ks of G102 and ∼9 ks of G141 in total, together with ∼7 ks of F105W+F140W direct imaging for wavelength/flux calibration and astrometric alignment. This exposure time is divided equally into two orients with almost orthogonal light dispersion directions, designed to disentangle contamination from neighbor objects. As a result, we obtain two suites of G102+G141 spectra for each object in an uninterrupted wavelength range of 0.8–1.7 $\mu {\rm{m}}$ with nearly uniform sensitivity, reaching a 1σ surface brightness of 3 × 10⁻¹⁶ $\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}\,{\mathrm{arcsec}}^{-2}$. The 10 cluster fields are listed in Table 1 and shown in Figure 1. Among these clusters, six have ultradeep seven-filter imaging from the Hubble Frontier Fields (HFF) initiative (Lotz et al. 2017). The other four have multiband imaging from the Cluster Lensing And Supernova survey with Hubble (CLASH; Postman et al. 2012).

Zoom In Zoom Out Reset image size

Table 1.  Summary of the HST Observations Presented in This Work

Cluster Field	Cluster Alias	Cluster Redshift	R.A.	Decl.	Grism PAa	HST Imaging	${N}_{\mathrm{source}}$ b
			(deg)	(deg)	(deg)
Abell 370	A370	0.375	02:39:52.9	−01:34:36.5	155, 253	HFF	7
Abell 2744	A2744	0.308	00:14:21.2	−30:23:50.1	135, 233	HFF	13
MACS 0416.1–2403	MACS 0416	0.420	04:16:08.9	−24:04:28.7	164, 247	HFF/CLASH	9
MACS 0717.5+3745	MACS 0717	0.548	07:17:34.0	+37:44:49.0	020, 280	HFF/CLASH	5
MACS 0744.9+3927	MACS 0744	0.686	07:44:52.8	+39:27:24.0	019, 104	CLASH	6
MACS 1423.8+2404	MACS 1423	0.545	14:23:48.3	+24:04:47.0	008, 088	CLASH	9
MACS 2129.4–0741	MACS 2129	0.570	21:29:26.0	−07:41:28.0	050, 328	CLASH	10
RX J1347.5–1145	RX J1347	0.451	13:47:30.6	−11:45:10.0	203, 283	CLASH	2
RX J2248.7–4431	RX J2248	0.348	22:48:44.4	−44:31:48.5	053, 133	HFF/CLASH	5
MACS 1149.6+2223c	MACS 1149	0.544	11:49:36.3	+22:23:58.1	032, 111, 119, 125	HFF/CLASH	10

Notes. Here we only list the primary pointings of the analyzed HST slitless spectroscopy covering the cluster centers with WFC3/NIR grisms.

^aThe PAs are represented by the "PA_V3" values reported in the corresponding raw image headers. The PA of the actual dispersion axis of slitless spectroscopy, in degrees east of north, is given by ${\mathrm{PA}}_{\mathrm{disp}}\approx \mathrm{PA}\_{\rm{V}}3-45.2$. For each of the GLASS PAs (i.e., excluding PAs 111 and 119 for MACS 1149), two orbits of G141 and five orbits of G102 exposures have been taken, amounting to ∼4.5 and ∼11 ks science exposure times for G141 and G102, respectively. ^bThe number of galaxies in which we secure sub-kpc resolution metallicity gradient measurements from HST spectroscopy. ^cThe detailed analyses of gradient measurements have already been presented in our earlier paper (Wang et al. 2017). Here we update the SED fitting results associated with these galaxies.

Download table as:  ASCIITypeset image

We base our source selection on the redshift catalogs made public by the GLASS collaboration. From these catalogs, we select 327 galaxies with secure spectroscopic redshifts in the range of z ∈ [1.2, 2.3] with the redshift quality flag ≥3. This redshift range is chosen to enable the grism coverage of the oxygen collisionally excited lines and the Balmer lines in the rest-frame optical (i.e., $[{\rm{O}}\,{\rm\small{III}}]$, Hβ, $[{\rm{O}}\,{\rm\small{II}}]$), which are the most promising and frequently used metallicity diagnostics at extragalactic distances. We also visually inspect the spatial extent and grism data quality of each source to remove sources with compact morphology (i.e., with half-light radius R₅₀ <025 measured in ${H}_{160}$-band imaging) and/or severe grism defects not suitable for our analysis. As a consequence, we compile a list of 93 objects with secure spectroscopic redshifts, relatively extended spatial profiles, and no severe defects or lack of data in their grism spectra. After further removing the sources with low signal-to-noise ratio (S/N) detections of emission lines (see Section 3.1) and ionization contamination from the active galactic nucleus (AGN; see Section 3.4), we obtain the final sample, comprising a total of 76 star-forming galaxies at z ∈ [1.2, 2.3], on which we present the subsequent measurements.

3.1. Emission Line Flux

We adopt the Grism Redshift and Line Analysis software (Grizli;¹⁴ G. Brammer et al. 2020, in preparation) to handle wide-field slitless spectroscopy data reduction. Grizli is state-of-the-art software that performs "one-stop shopping" processing of paired direct and grism exposures acquired by space telescopes. The entire procedure consists of five steps: (1) preprocessing raw grism exposures,¹⁵ (2) forward modeling full field-of-view (FoV) grism images, (3) redshift fitting via spectral template synthesis, (4) refining the full FoV grism model, and (5) extracting 1D/2D spectra and emission line maps of individual targets.

In step (3), we derive the best-fit redshift of our sources from spectral template fitting based on a library of spectral energy distributions (SEDs) of stellar populations with a range of characteristic ages (see Appendix A in Wang et al. 2019, for more details). We also fit the intrinsic nebular emission using 1D Gaussian functions centered at corresponding wavelengths and estimate the line fluxes. The morphological broadening is taken into account with respect to the dispersion direction associated with each exposure. Figure 2 shows the typical 1D and 2D spectra of one of our target galaxies. The majority (61/76) of our sample galaxies have $[{\rm{O}}\,{\rm\small{III}}]$ detected with S/N ≳ 10. Within the entire sample, 55, 35, and 15 have S/N ≳ 5 detections of $[{\rm{O}}\,{\rm\small{II}}]$, Hβ, and Hγ, respectively. For galaxies at z ≤ 1.6, we also typically have access to their Hα¹⁶ and $[{\rm{S}}\,{\rm\small{II}}]$, which help constrain metallicity and nebular extinction. The best-fit redshifts and observed emission line fluxes for all of our sources are presented in Table A1.

Zoom In Zoom Out Reset image size

3.2. Emission Line Maps

In addition to the measurements of integrated emission line fluxes, another key piece of information that we need to retrieve from grism spectroscopy is the spatial distribution of emission line surface brightnesses, i.e., the emission line maps. The HST WFC3 near-infrared grisms have limited spectral resolution; for point sources, R ∼ 210 and 130 for G102 and G141, respectively. Yet this is actually an advantage in obtaining emission line maps. Since the instrument FWHM is equivalently ∼700 km s⁻¹ for G102 and ∼1200 km s⁻¹ for G141, it is reasonable to assume that the source 1D spectral shapes and 2D emission line maps are not affected by any kinematic motions of gas ionized by the star-forming regions, where outflows typically have speeds <500 km s⁻¹ (see, e.g., Erb 2015, for a recent review). However, our sample galaxies are selected to be spatially extended, having their half-light radius R₅₀ ≳ 025, measured from their continuum morphology in the ${H}_{160}$-band imaging acquired by HFF or CLASH. Their spatial profiles along the light dispersion direction are convolved onto the wavelength axis, resulting in severe morphological broadening of the line-spread function FWHM (van Dokkum et al. 2011). This morphological broadening effect is already taken into account when estimating the best-fit grism redshift from the spectral template synthesis process described in Section 3.1. It also poses a great challenge for obtaining spatial 2D maps of emission lines that have very close rest-frame wavelengths, in particular the line complex of Hβ + $[{\rm{O}}\,{\rm\small{III}}]$ λλ4960, 5008 doublets.

We hence develop a custom technique to deblend the line complex as follows. First, we measure the source broadband isophotes that encompass over 90% of the surface brightness in the ${{JH}}_{140}$ and ${Y}_{105}$ bands and overlay them on the source 2D G141 and G102 spectra, respectively. The 2D grism spectra are standard data products produced by our Grizli reduction with contamination and source continuum removed. The positions of the overlaid isophotes on the 2D grism spectra mark the locations of the redshifted emission lines (see the middle and bottom rows of Figure 3). We rely on the preimaging (i.e., ${{JH}}_{140}$ and ${Y}_{105}$) paired with the grism (i.e., G141 and G102) observations to measure the isophotes because they cover a similar wavelength range, share comparable point-spread function (PSF) properties, and are acquired at the same position angle (PA) of the telescope. In this step, the grism spectra taken at different PAs have to be processed separately, since the morphological broadening varies drastically among different PAs if the source has asymmetric radial profiles. This broadband isophote is used as an aperture for emission line map extraction. Since the red (i.e., more to the right on the wavelength axis in 2D spectra) portion of the aperture centered at redshifted $[{\rm{O}}\,{\rm\small{III}}]$ λ5008 is not contaminated by $[{\rm{O}}\,{\rm\small{III}}]$ λ4960, and the flux ratio between the $[{\rm{O}}\,{\rm\small{III}}]$ doublets is fixed (${f}_{[{\rm{O}}{\rm\small{III}}]5008}/{f}_{[{\rm{O}}{\rm\small{III}}]4960}=2.98:1$; calculated by Storey & Zeippen 2000), we can obtain the same red portion of the clean $[{\rm{O}}\,{\rm\small{III}}]$ λ4960 2D map. This red part of the $[{\rm{O}}\,{\rm\small{III}}]$ λ4960 map is contaminating the slightly bluer part of the $[{\rm{O}}\,{\rm\small{III}}]$ λ5008 map and can be subtracted off, with flux errors properly propagated, therefore yielding cleaned $[{\rm{O}}\,{\rm\small{III}}]$ λ5008 flux in those slightly bluer areas within the extraction aperture. This procedure is then conducted iteratively, until the $[{\rm{O}}\,{\rm\small{III}}]$ λ4960 fluxes in all spatial pixels within the aperture have been removed and clean 2D maps of $[{\rm{O}}\,{\rm\small{III}}]$ λ5008 and Hβ can be obtained at individual PAs. Finally, we use AstroDrizzle (Gonzaga 2012) to combine the clean $[{\rm{O}}\,{\rm\small{III}}]$λ5008 and Hβ maps extracted at multiple PAs. The resultant 2D stamps are drizzled onto a 006 grid, Nyquist sampling the FWHM of the WFC3 PSF, and astrometrically matched to the corresponding broadband images. Notably, our custom deblending technique does not rely on any models of the spatial profiles of $[{\rm{O}}\,{\rm\small{III}}]$ emission.¹⁷ This is a critical procedure to account for the orient-specific contaminations of $[{\rm{O}}\,{\rm\small{III}}]$ λ4960, which can be over 2σ in some spatial areas within the extraction aperture (see the top right panel of Figure 3).

Zoom In Zoom Out Reset image size

3.3. Stellar Mass

3.4. AGN Contamination

Before carrying out the metallicity inference on our sample, we check for contamination of AGN ionizations. In Figure 4, we rely on the mass-excitation diagram to exclude AGN candidates from our sample. The demarcation scheme (Juneau et al. 2014) aims to separate AGNs from star-forming galaxies based on the SDSS DR7 emission line galaxies at z ∼ 0. This scheme has been shown to reproduce the bivariate distributions seen in a number of high-redshift galaxy samples out to z ∼ 1.5 (Juneau et al. 2014). We therefore discard sources in our sample that are 2σ away from the star-forming region in the diagram, given the measurement uncertainties on ${M}_{* }$ and $[{\rm{O}}\,{\rm\small{III}}]$/Hβ. To examine possible redshift-dependent trends in future sections, we subdivide our sample into three bins: 37, 24, and 15 galaxies at z ∈ [1.2, 1.6], [1.6, 1.9], and [1.9, 2.3], respectively, marked by different symbols in Figure 4.

Zoom In Zoom Out Reset image size

Moreover, Coil et al. (2015) found that a +0.75 dex shift in ${M}_{* }$ of the demarcation curves is necessary to match the loci of AGNs and star-forming galaxies in the MOSDEF surveys at z ∼ 2.3 to account for the redshift evolution of the mass–metallicity relation (MZR). On part of the sample, we also obtained Hα gas kinematics from the ground-based Keck OSIRIS observations (Hirtenstein et al. 2019). The integrated measurement of ${f}_{[{\rm{N}}{\rm\small{II}}]}/{f}_{{\rm{H}}\alpha }$ is typically ≲0.1 at a 3σ confidence level, indicative of star-forming regions with no significant AGN contamination. We thus verify that there is no sign of significant AGN ionization in our sample.

3.5. SFR

We have two methods for estimating the SFR. First of all, the SFR can be obtained from the stellar continuum SED fitting outlined in Section 3.3. This method is sensitive to the underlying assumptions of star formation history and stellar population synthesis models adopted in the fitting procedure. Hereafter, we refer to these measurements as SFR^S.

Second, the SFR can be derived from nebular emission after correcting for dust attenuation. From our Bayesian inference method presented in Section 3.6, we obtain posterior probability distributions of the dereddened Hβ flux, which can be converted to the intrinsic Hα luminosity given a source redshift. As a consequence, the SFR (hereafter denoted as SFR^N) can then be calculated following the widely used calibration (Kennicutt 1998), i.e.,

$$\begin{eqnarray}&&{\mathrm{SFR}}^{{\rm{N}}}=4.6\times {10}^{-42}\displaystyle \frac{L({\rm{H}}\alpha )}{\mathrm{erg}\,{{\rm{s}}}^{-1}}\,\,\,\,({M}_{\odot }\,{\mathrm{yr}}^{-1}),\end{eqnarray} \tag{ 1 }$$

appropriate for the Chabrier (2003) initial mass function. Unlike the measurements from SED fitting, this method provides a proxy of instantaneous star-forming activities on a timescale of ∼10 Myr. This short timescale is relevant to probe the highly dynamic feedback processes that are effective in redistributing metals (see, e.g., Hopkins et al. 2014). Therefore, we quote the values of SFR^N as our fiducial SFR measurements if not stated otherwise.

We note that for our low-z sample (37 galaxies at z ∈ [1.2, 1.6]), Hα is covered by the WFC3/G141 grism. However, due to the low spectral resolution, it is heavily blended with $[{\rm{N}}\,{\rm\small{II}}]$. We hence rely on the empirical prescription of Faisst et al. (2018) to subtract the contribution of $[{\rm{N}}\,{\rm\small{II}}]$ fluxes from the measured Hα flux based on the stellar mass and redshift of our galaxies (see Table A1 for the calculated $[{\rm{N}}\,{\rm\small{II}}]$/Hα flux ratios). This ensures a more reliable estimate of SFR^N that is less impacted by dust than the Hβ-based measurements.

In the left panel of Figure 5, we show the loci of our galaxies in the diagram of SFR versus ${M}_{* }$. By selecting lensed galaxies via their nebular emission line flux, our sample reaches an instantaneous SFR limit of ∼1 ${M}_{\odot }$ yr⁻¹ at z ∼ 2. In comparison to mass-complete samples (from, e.g., the KMOS^3D survey; Wuyts et al. 2016) and galaxies from the star-forming main sequence (SFMS; Speagle et al. 2014; Whitaker et al. 2014), we push the exploration of star-forming galaxies at cosmic noon by 1–2 dex deeper into the low-mass regime. We also show the loci of the spectral stacks from the WFC3 Infrared Spectroscopic Parallel (WISP) Survey (Henry et al. 2013), very close to that of our galaxies given similar observing strategies. We gain over 1 dex in ${M}_{* }$ thanks to lensing magnification and the 14-orbit depth of the GLASS data in each field.

Zoom In Zoom Out Reset image size

3.6. Metallicity and Its Radial Gradient

Following our previous work (Wang et al. 2017, 2019), we adopt a forward-modeling Bayesian method to simultaneously infer metallicity ($12+\mathrm{log}({\rm{O}}/{\rm{H}})$), nebular dust extinction (${A}_{{\rm{V}}}^{{\rm{N}}}$), and dereddened Hβ flux (f_Hβ) based on observed emission line fluxes directly, as measured in Section 3.1. We use flat priors for $12+\mathrm{log}({\rm{O}}/{\rm{H}})$ and ${A}_{{\rm{V}}}^{{\rm{N}}}$ in the ranges of [7.0, 9.3] and [0, 4], respectively, which are appropriate for the Maiolino et al. (2008) strong-line calibrations adopted in our inference. For f_Hβ, we use the Jeffreys prior in the range of [0, 1000] in units of ${10}^{-17}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$. The Markov Chain Monte Carlo (MCMC) sampler Emcee is used to explore the parameter space, with the likelihood function defined as

$$\begin{eqnarray}&&\begin{array}{l}L\propto \exp (-{\chi }^{2}/2)\\ \ =\,\exp \left(-\displaystyle \frac{1}{2}\cdot \displaystyle \sum _{i}\displaystyle \frac{{\left({f}_{{\mathrm{EL}}_{i}}-{R}_{i}\cdot {f}_{{\rm{H}}\beta }\right)}^{2}}{{\left({\sigma }_{{\mathrm{EL}}_{i}}\right)}^{2}+({f}_{{\rm{H}}\beta }^{2})\cdot {\left({\sigma }_{{R}_{i}}\right)}^{2}}\right).\end{array}\end{eqnarray} \tag{ 2 }$$

Here ${\mathrm{EL}}_{i}$ represents each of the available emission lines among the set of $[{\rm{O}}\,{\rm\small{II}}]$, Hγ, Hβ, $[{\rm{O}}\,{\rm\small{III}}]$, Hα, and $[{\rm{S}}\,{\rm\small{II}}]$, and ${f}_{{\mathrm{EL}}_{i}}$ and ${\sigma }_{{\mathrm{EL}}_{i}}$ denote the ${\mathrm{EL}}_{i}$ flux and its uncertainty, dereddened given a value of ${A}_{{\rm{V}}}^{{\rm{N}}}$ drawn from the MCMC sampling. The Cardelli et al. (1989) galactic extinction law with ${R}_{{\rm{V}}}$ = 3.1 is adopted to correct for dust reddening, and R_i is the expected flux ratio between ${\mathrm{EL}}_{i}$ and Hβ, with ${\sigma }_{{R}_{i}}$ being its intrinsic scatter. The content of R_i varies from strong-line diagnostic to Balmer decrement depending on the associated ${\mathrm{EL}}_{i}$. In practice, if ${\mathrm{EL}}_{i}$ is one of the Balmer lines, R_i is given by ${\rm{H}}\alpha /{\rm{H}}\beta =2.86$ and ${\rm{H}}\gamma /{\rm{H}}\beta =0.47$, i.e., the Balmer decrement ratios assuming case B recombination under fiducial ${\rm{H}}\,{\rm\small{II}}$ region situations. Instead, if ${\mathrm{EL}}_{i}$ is one of the oxygen collisionally excited lines, we take the strong-line flux ratios (i.e., ${f}_{[{\rm{O}}{\rm\small{III}}]}/{f}_{{\rm{H}}\beta }$ and ${f}_{[{\rm{O}}{\rm\small{II}}]}/{f}_{{\rm{H}}\beta }$) calibrated by Maiolino et al. (2008) as R_i. Last, if ${\mathrm{EL}}_{i}$ is $[{\rm{S}}\,{\rm\small{II}}]$, we rely on our strong-line calibration of $[{\rm{S}}\,{\rm\small{II}}]$/Hα presented in Wang et al. (2017).

This forward-modeling approach is superior to converting emission line flux ratios (e.g., R₂₃, O₃₂) to metallicity because it properly takes into account any weak nebular emission that falls short of the detection limit and avoids double-counting information, as happens when combining multiple flux ratios that involve the same line. All sources in our sample have S/N ≳ 10 in at least one of the oxygen collisionally excited lines and/or Hα (if the source redshift is z ≲ 1.6), yet the Hβ detection is usually not as strong given its intrinsic faintness. By not calculating observed emission line flux ratios but forward modeling observed line fluxes directly, we avoid compromising the high-S/N detections of the bright $[{\rm{O}}\,{\rm\small{III}}]$ and $[{\rm{O}}\,{\rm\small{II}}]$ lines by the faint Hβ lines. As a result, our forward-modeling methodology improves our ability to infer an accurate metallicity based on high-S/N detections of strong nebular lines (i.e., $[{\rm{O}}\,{\rm\small{III}}]$ and $[{\rm{O}}\,{\rm\small{II}}]$) and does not necessarily require high-S/N detections of faint emission lines. In the left panel of Figure 6, we show the joint constraints on ($12+\mathrm{log}({\rm{O}}/{\rm{H}})$, ${A}_{{\rm{V}}}^{{\rm{N}}}$, f_Hβ) derived from the observed integrated emission line fluxes for the exemplary object MACS 0416–ID 00955, whose 1D/2D spectra are shown in Figures 2 and 3. Together, we also simulate a scenario for this observation with much worse S/N detection of Hβ, i.e., artificially increasing the observed Hβ uncertainty by a factor of 10 while keeping other measurements unchanged. It is found that the resultant constraint on $12+\mathrm{log}({\rm{O}}/{\rm{H}})$ for this simulated scenario stays similar. This test demonstrates that our metallicity inference method can still ensure reasonable constraints on $12+\mathrm{log}({\rm{O}}/{\rm{H}})$, even in cases where some emission lines, such as Hβ, are only marginally detected. In the right panel of Figure 6, we show the histograms of metallicity inferences (median values) given by our forward-modeling technique in all individual Voronoi cells from our entire galaxy sample. We divide all of these metallicity measurements in terms of the observed S/N of Hβ in the corresponding Voronoi cells. Regardless of the Hβ S/N, the three histograms all peak at $12+\mathrm{log}({\rm{O}}/{\rm{H}})$ ∼8.0, consistent with the integrated metallicity measurements from other work in similar ranges of redshift and mass (see, e.g., Figure 5 and Maiolino et al. 2008; Henry et al. 2013). From this test, we show that there is no systematic offset of the distribution of inferred metallicities among the three groups divided by Hβ S/N, and our metallicity estimates do not simply revert to the prior used in our Bayesian inference.

Zoom In Zoom Out Reset image size

Our forward-modeling Bayesian inference is first performed on the integrated emission line fluxes measured for each galaxy to yield global metallicity. In the right panel of Figure 5, we show the MZR from our sample, color-coded by the specific SFR ($\mathrm{sSFR}=\mathrm{SFR}/{M}_{* }$) obtained from the aforementioned analyses. We also overlay the MZR from the WISP survey derived using the same strong-line calibrations (Henry et al. 2013). It is encouraging to see that the two MZRs follow similar trends due to similar source selection techniques and observing strategies. Notably, our galaxies at the extreme low-mass end (${M}_{* }\lesssim {10}^{9}\,{M}_{\odot }$) show both elevated metallicity and specific SFR (sSFR). This is consistent with the hypothesis that these low-mass systems are in the phase of early mass assembly with efficient metal enrichment and minimum dilution from pristine gas infall.

In addition to the integrated emission line fluxes, from the procedures described in Section 3.2, we also obtain 2D spatial distributions of emission line surface brightnesses. We utilize Voronoi tessellation as in Wang et al. (2019) to divide spatial bins with nearly uniform S/Ns of the strongest emission line available (usually $[{\rm{O}}\,{\rm\small{III}}]$). Our spatially resolved analysis based on Voronoi tessellation is superior to averaging the signals in radial annuli because of azimuthal variations (as large as 0.2 dex) in metallicity spatial distribution in nearby spiral galaxies (Berg et al. 2015; Ho et al. 2017). Our Bayesian inference is then executed in each of the Voronoi bins for all sources, yielding their metallicity maps at sub-kpc resolution.

To get the intrinsic deprojected galactocentric distance scale for each Voronoi bin, we conduct detailed reconstructions of the source-plane morphology of each galaxy in our sample. We first obtain a 2D map of the stellar surface density (${{\rm{\Sigma }}}_{* }$; e.g., as shown in Figure 7) for each source through pixel-by-pixel SED fitting following the prescription described in Section 3.3. Then the pixels in this map are ray-traced back to their source-plane positions according to the deflection fields given by the macroscopic cluster lens models. For all HFF clusters, we use the Sharon & Johnson version 4corr models (Johnson et al. 2014). For the CLASH-only clusters, except RX J1347, we use the Zitrin PIEMD+eNFW version 2 model. For RX J1347, we use our own model built closely following the approach in Johnson et al. (2014). To this delensed 2D ${{\rm{\Sigma }}}_{* }$ map, we fit a 2D elliptical Gaussian function to determine the galaxy's inclination, axis ratio, and major-axis orientation so that the source intrinsic morphology is recovered from lensing distortion.

Zoom In Zoom Out Reset image size

Since we have measured both metallicity and source-plane deprojected galactocentric radius for each Voronoi bin, we can estimate a radial gradient slope via linear regression (see Appendix A for the gradient measurements based on metallicities derived in source-plane Voronoi bins and related discussions about the effect of anisotropic lensing distortion). Figure 7 demonstrates the entire process for measuring the metallicity radial gradient of a z ∼ 2 star-forming dwarf galaxy. As a sanity check, we also measure its radial gradient using metallicity inferences derived in each individual spatial pixel and radial annulus. We verified that the differences among the three methods are ≲0.03 dex kpc⁻¹, within the measurement uncertainties.

In the end, we secure a total of 76 galaxies in the redshift range of 1.2 ≲ z ≲ 2.3 with sub-kpc resolution metallicity gradients (see Table 1 for the number of sources in individual cluster center fields). This is hitherto the largest sample of such measurements in the distant universe. This sample enables robust measures of both average gradient slopes and scatter in the population.

In this section, we collect published results on radial gradients of metallicity measured in the distant universe. We focus on the measurements that are derived with sub-kpc resolution because insufficient spatial sampling is shown to cause spuriously flat gradient measurements (Yuan et al. 2013). This poses a real challenge for ground-based observations, given that the optimal seeing condition is ∼06, equivalent to 5 kpc at z ∼ 2. There have been a number of attempts to overcome this beam smearing through correcting the distorted light wave front with the adaptive optics (AO) technique. Using the SINFONI instrument on the Very Large Telescope under the AO mode, Swinbank et al. (2012) measured seven gradients at z ∼ 1.5. Following the same strategy, Förster Schreiber et al. (2018) expanded the sample by adding 21 new measurements at z ∼ 2 from the SINS/zC-SINF survey.¹⁸ Lensing can also help increase the spatial sampling rate. Jones et al. (2010, 2013) brought forward this approach by securing four gradients at z ∼ 2 in galaxy–galaxy lensing systems using the AO-assisted OSIRIS instrument on the Keck telescope, with resolution further boosted ≳3× by lensing magnification. Leethochawalit et al. (2016) carried out similar analyses and measured 11 new gradients at similar redshifts. To recap, there existed a total of 43 metallicity gradient measurements with sub-kpc spatial resolution at cosmic noon before our work.

In this work, we triple the sample size by presenting 76 sub-kpc resolution metallicity radial gradients in star-forming galaxies at cosmic noon. This is by far the largest homogeneous sample with sufficient spatial resolution, which enables a uniform analysis. In Figure 8, our results are highlighted by three sets of symbols—corresponding to the three z subgroups—color-coded in sSFR. From a total of 76 galaxies in our sample with sub-kpc resolution gradient measurements, there are 15 and seven sources showing negative and positive (i.e., inverted) gradients greater than 2σ away from being flat, respectively. At a 3σ confidence level, the number of galaxies showing negative and inverted gradients is seven and three, respectively. Notably, two of the three inverted gradients (A370–ID 03751 and MACS 0744–ID 01203) have already been reported in detail in Wang et al. (2019). All individual ground-based measurements at similar resolution (≲kpc scale) are represented by magenta squares. Recently, Curti et al. (2020) analyzed the KMOS observations in the field of RX J2248 and measured metallicity gradients in 12 background galaxies lensed by RX J2248, of which three are in overlap with our sample (i.e., ID 00206, ID 00428, and ID 01205). We verified that the gradient results measured from both works are compatible at a 1σ confidence level. It is encouraging to see that the metallicity gradients derived using different methods and data sets are in good agreement.

Zoom In Zoom Out Reset image size

Some theoretical trends are overlaid in Figure 8. In particular, two numerical simulations with different galactic feedback strengths but otherwise identical settings by Gibson et al. (2013) are shown as orange curves. The comparison between these two trends demonstrates that enhanced feedback can be highly efficient in erasing metal inhomogeneity. Therefore, resolved chemical properties, if measured accurately, can shed light on the strength of galactic feedback in the early phase of disk growth.

Figure 8 also shows the spread of the KMOS^3D gradient measurements by Wuyts et al. (2016), which is highly clustered to flatness. Without AO support or lensing magnification gain on the spatial sampling rate, these gradients are usually obtained at an FWHM angular resolution of ∼06, imposed by the natural seeing. For a z ∼ 1.5 star-forming galaxy with intrinsically negative metallicity gradient (${\rm{\Delta }}\mathrm{log}({\rm{O}}/{\rm{H}})/{\rm{\Delta }}r\,=-0.16\pm 0.02\,[\mathrm{dex}\,{\mathrm{kpc}}^{-1}]$), Yuan et al. (2013) showed that from seeing-limited observations with an FWHM angular scale of ∼05, its radial metallicity gradient is instead measured to be ${\rm{\Delta }}\mathrm{log}({\rm{O}}/{\rm{H}})/{\rm{\Delta }}r=-0.01\pm 0.03\,[\mathrm{dex}\,{\mathrm{kpc}}^{-1}]$, significantly biased toward flatness caused by beam smearing. To mitigate the potential bias from beam smearing, Carton et al. (2018) conducted a forward-modeling analysis to recover 65 gradients at 0.1 ≲ z ≲ 0.8 from the seeing-limited MUSE observations (marked in green in Figure 8).

The 2σ interval of the FIRE simulations (Ma et al. 2017) is shown as the gray shaded region in Figure 8. We see that the scatter predicted by the FIRE simulations matches well that from low-z observations (at z ≲ 1; e.g., from Carton et al. 2018), but it is smaller by a factor of 2 at higher redshifts, especially at z ≳ 1.3. This likely reflects that galaxies display more diverse chemostructural properties at the peak epoch of cosmic structure formation and metal enrichment, when star formation is more episodic and vigorous (see, e.g., Hopkins et al. 2014).

With the sample statistics greatly improved, we can quantify the mass dependence of reliably measured metallicity gradients at high redshifts as a test of theoretical predictions. The combined sample includes our 76 measurements at z ∈ [1.2, 2.3] and 35¹⁹ others, as given in Section 4. Following the same color/marker styles as in Figure 8, we plot these high-resolution gradient measurements as a function of their associated ${M}_{* }$ in Figure 9. It is remarkable that now the observational data cover 4 orders of magnitude in ${M}_{* }$. Notably, over half of our gradient measurements reside in the dwarf mass regime (${M}_{* }\lesssim 2\times {10}^{9}\,{M}_{\odot }$), probing ≳2 dex deeper into the low-mass end compared with the ground-based AO results (magenta squares).

Zoom In Zoom Out Reset image size

We perform linear regression on all of these measurements of metallicity gradient and stellar mass, with errors on both quantities taken into account, using the following formula:

$$\begin{eqnarray}&&\begin{array}{l}{\rm{\Delta }}\mathrm{log}({\rm{O}}/{\rm{H}})/{\rm{\Delta }}r\,[\mathrm{dex}\,{\mathrm{kpc}}^{-1}]\\ \quad =\,\alpha +\beta \mathrm{log}({M}_{* }/{M}_{\mathrm{med}})+N(0,{\sigma }^{2}).\end{array}\end{eqnarray} \tag{ 3 }$$

Here α and β are the intercept and slope of the linear function, respectively; $N(0,{\sigma }^{2})$ represents a normal distribution, with σ being the intrinsic scatter in units of $\mathrm{dex}\,{\mathrm{kpc}}^{-1}$; and M_med is the median of the input stellar masses taken as normalization. For the entire mass range (where ${M}_{\mathrm{med}}={10}^{9.4}\,{M}_{\odot }$), we obtain the following estimates: α = −0.020 ± 0.007, β = −0.016 ± 0.008, and σ = 0.060 ± 0.006 (see the result of case I in Table 2). This shows a weak negative correction between metallicity gradient and stellar mass for these 111 high-z star-forming galaxies.

Table 2.  Linear Regression Results of the Mass Dependence of Metallicity Radial Gradients at Cosmic Noon

Case	α	β	σ	${M}_{\mathrm{med}}({M}_{\odot })$	${N}_{\mathrm{source}}$	Notes
I	$-{0.0203}_{-0.0068}^{+0.0070}$	$-{0.0156}_{-0.0077}^{+0.0076}$	${0.0601}_{-0.0057}^{+0.0065}$	${10}^{9.4}$	111	All metallicity gradients measured at sub-kpc resolution
II	$-{0.0128}_{-0.0097}^{+0.0099}$	$-{0.0025}_{-0.0181}^{+0.0181}$	${0.0677}_{-0.0077}^{+0.0091}$	${10}^{9.0}$	76	All metallicity gradients from HST spectroscopy
IIIa	$-{0.0430}_{-0.0085}^{+0.0078}$	$-{0.0009}_{-0.0179}^{+0.0186}$	${0.0342}_{-0.0060}^{+0.0075}$	${10}^{10.4}$	27	High-mass bin: ${M}_{* }/{M}_{\odot }\gtrsim {10}^{10}$
IIIb	$-{0.0082}_{-0.0137}^{+0.0134}$	$-{0.0520}_{-0.0552}^{+0.0565}$	${0.0785}_{-0.0104}^{+0.0122}$	${10}^{9.5}$	47	Medium-mass bin: ${10}^{9}\lesssim {M}_{* }/{M}_{\odot }\lesssim {10}^{10}$
IIIc	$-{0.0198}_{-0.0139}^{+0.0140}$	${0.0270}_{-0.0512}^{+0.0524}$	${0.0607}_{-0.0125}^{+0.0154}$	${10}^{8.6}$	31	Low-mass bin: ${10}^{8}\lesssim {M}_{* }/{M}_{\odot }\lesssim {10}^{9}$
IVa	$-{0.0129}_{-0.0132}^{+0.0128}$	${0.0207}_{-0.0166}^{+0.0164}$	${0.0823}_{-0.0108}^{+0.0125}$	${10}^{8.9}$	50	High-sSFR bin: $\mathrm{sSFR}\gtrsim 5\,{\mathrm{Gyr}}^{-1}$
IVb	$-{0.0344}_{-0.0080}^{+0.0078}$	$-{0.0074}_{-0.0094}^{+0.0094}$	${0.0464}_{-0.0062}^{+0.0074}$	${10}^{9.7}$	61	Low-sSFR bin: $\mathrm{sSFR}\lesssim 5\,{\mathrm{Gyr}}^{-1}$

Note. The linear regression is performed using the linmix software (https://github.com/jmeyers314/linmix), taking into account the measurement uncertainties on both stellar mass (${M}_{* }$) and metallicity gradient (${\rm{\Delta }}\mathrm{log}({\rm{O}}/{\rm{H}})/{\rm{\Delta }}r$), following the Bayesian method proposed by Kelly (2007). The following function form (Equation (3)) is adopted: Δlog(O/H)/${\rm{\Delta }}r\,[\mathrm{dex}\,{\mathrm{kpc}}^{-1}]=\alpha +\beta \mathrm{log}({M}_{* }/{M}_{\mathrm{med}})+N(0,{\sigma }^{2})$. As given in the seventh column, case I corresponds to the linear regression result based on all sub-kpc-scale metallicity gradient measurements at the cosmic noon epoch, whereas case II shows the results from our gradient measurements only. We divide the entire sample into three ${M}_{* }$ bins and conduct linear regressions separately, with results represented by cases IIIa, b, and c. Cases IVa and b show the results if the entire sample is divided based on sSFR, instead of ${M}_{* }$. The number of sources (${N}_{\mathrm{source}}$) involved in each case is shown in the sixth column.

Download table as:  ASCIITypeset image

To understand this negative mass dependence, we show two theoretical predictions from the EAGLE simulations in Figure 9, corresponding to two suites of numerical simulations implementing different strengths of supernova feedback (Tissera et al. 2019). We see a drastic difference in the slope of the mass dependence of metallicity gradients predicted by different feedback settings in EAGLE, albeit the short ${M}_{* }$ coverage. This difference is largely caused by the bifurcations seen in the temporal evolution of radial chemical profiles for individual galaxies, exemplified by the two simulation tracks shown in Figure 8. Under the assumption of weak feedback, galaxies evolve according to secular processes, and their radial gradients flatten over time (Pilkington et al. 2012). Given the mass assembly downsizing, more massive galaxies are in a later phase of disk growth than less massive ones (Brinchmann et al. 2004). Collectively, a positive mass dependence of radial gradients manifests. However, when feedback is enhanced, feedback-driven gas flows can efficiently mix stellar nucleosynthesis yields and prevent any metal inhomogeneity from emerging (Ma et al. 2017). This effect is more pronounced in lower-mass galaxies living in smaller dark matter halos with shallower gravitational potentials. As a result, a generally negative mass dependence (flat/inverted gradients at the low-mass end and negative gradients at the high-mass end) can be anticipated.

Figure 9 also shows the 2σ spread of the mass dependence from the FIRE simulations (Ma et al. 2017). Given the relatively strong feedback scheme implemented in FIRE, we expect a negative mass dependence, which is indeed seen. Remarkably, the predictions of the FIRE simulations match very well the linear regression fit based on the combined high-z metallicity gradient sample. Our result is thus in better agreement with enhanced feedback—rather than secular processes—playing a significant role in shaping the chemical enrichment and structural evolution during the disk mass assembly (Hopkins et al. 2014; Vogelsberger et al. 2014).

To verify that the observed trends are robust, we subdivide the gradient measurements into three mass bins and perform a separate linear regression analysis to each bin. The results are given in Table 2. We see that the intercept value becomes more negative as ${M}_{* }$ increases, with the slopes all consistent with zero, confirming the negative mass dependence of metallicity gradients over the entire mass range. More importantly, we observe an increase in the intrinsic scatter of metallicity gradients with ${M}_{* }$ from high- to low-mass regimes, consistent with the findings in local spiral galaxies by Bresolin (2019). This increase in scatter can also be found if separating the galaxies based on their sSFR.²⁰ For galaxies in the combined sample with $\mathrm{sSFR}\gtrsim 5\,{\mathrm{Gyr}}^{-1}$, the scatter is constrained to be $\sigma ={0.082}_{-0.011}^{+0.012}$ (case IVa in Table 2), whereas for galaxies with sSFR ≲ 5 Gyr⁻¹, the scatter is instead $\sigma ={0.046}_{-0.006}^{+0.007}$ (case IVb in Table 2).

The increase of sSFR in low-mass systems can be ascribed to the accretion of low-metallicity gas from the cosmic filaments (i.e., cold-mode gas accretion; Dekel et al. 2009) or gravitational interaction events amplifying the star formation efficiency (i.e., merger-induced starbursts; Stott et al. 2013). Both of them can bring about large dispersions in the radial chemical profiles. To investigate which of the two effects is more dominant in boosting the chemostructural diversity in low-mass high-sSFR galaxies, we turn to the global MZR of our sample, presented in Section 3.6 (see Figure 5). We rely on the WISP measurements as the control sample because of the similar source selection criteria, mass coverage, redshift range, and consistent techniques in estimating SFR (based on Balmer line fluxes) and metallicity (assuming the Maiolino et al. 2008 calibrations).

We find that in the medium-mass bin (${M}_{* }/{M}_{\odot }\,\in [{10}^{9},{10}^{10}]$), the galaxies in our sample with a higher SFR than that of the WISP stacks are more metal-poor by 0.15 dex than the WISP metallicities in the corresponding mass range. This is supportive of the cold-mode accretion diluting the global metallicity of our galaxies, stimulating star formation and increasing the intrinsic scatter of metallicity gradients. However, in the low-mass bin (${M}_{* }/{M}_{\odot }\in [{10}^{8},{10}^{9}]$), our galaxies with a higher SFR than WISP show significant metal enrichment, i.e., higher by 0.27 dex than the corresponding WISP metallicities. We hence argue that in the dwarf mass regime of ${M}_{* }\lesssim {10}^{9}\,{M}_{\odot }$, merger-driven starbursts play a more predominant role than the cold-mode accretion does to boost the chemostructural diversity. Our result is consistent with the sharp increase of the merger fraction—from 10% to over 50% for galaxies at ${M}_{* }\sim {10}^{10}$–10^8.5 at z ∼ 1.5—found by the HiZELS survey (Stott et al. 2013, 2014). For the part of our dwarf galaxies on which we have mapped their gas kinematics using Keck OSIRIS, we also found that the velocity field becomes more turbulent (i.e., with lower ratios of rotational speed versus velocity dispersion) for galaxies with higher sSFR (Hirtenstein et al. 2019). This kinematic evidence further reinforces the scenario that mergers boost the star formation efficiency, random motions, and chemostructural diversity in dwarf galaxies at cosmic noon.

Lastly, the combined high-z metallicity gradient sample reveals that inverted gradients are almost exclusively found in the low-mass range, i.e., ${M}_{* }\lesssim 3\times {10}^{9}$ (see also Carton et al. 2018). This feature is also seen in the local universe; only the lowest ${M}_{* }$ bin (at $\sim {10}^{9}\,{M}_{\odot }$) from the MaNGA survey shows a positive gradient slope (Belfiore et al. 2017). The reason for inverted gradients in isolated systems is still under debate, with possible causes ranging from centrally directed cold-mode accretion (Cresci et al. 2010) to metal-loaded outflows triggered by galactic winds (Wang et al. 2019). In any case, these processes should be more pronounced in low-mass systems, suggested by the occurrence rate of this inverted-gradient phenomenon.

To summarize, we have presented an unprecedentedly large sample of sub-kpc resolution metallicity radial gradients in 76 gravitationally lensed star-forming galaxies at 1.2 ≲ z ≲ 2.3 using HST near-infrared slitless spectroscopy. We performed state-of-the-art reduction of grism data, careful stellar continuum SED fitting after subtracting nebular emission from broadband photometry, and Bayesian inferences of metallicity and SFR based on emission line fluxes. Our sample spans an ${M}_{* }$ range of [10⁷, 10¹⁰] ${M}_{\odot }$, an instantaneous SFR range of [1, 100] ${M}_{\odot }$ yr⁻¹, and a global metallicity range of 7.6 ≲ $12\,+\mathrm{log}({\rm{O}}/{\rm{H}})$ ≲ 9.0, i.e., $[\tfrac{1}{12}$, 2] solar. At a 2σ confidence level, we secured 15 and seven galaxies that show negative and inverted gradients, respectively. Collecting all high-resolution gradient measurements at high redshifts currently existing (where the results presented in this work constitute 2/3 of all measurements), we measure a weak negative mass dependence over 4 orders of magnitude in ${M}_{* }$: Δlog(O/H)/${\rm{\Delta }}r\,[\mathrm{dex}\,{\mathrm{kpc}}^{-1}]$ = (−0.020 ± 0.007) + (−0.016 ± 0.008) $\mathrm{log}({M}_{* }/{10}^{9.4}\,{M}_{\odot })$, with σ = 0.060 ± 0.006 being the intrinsic scatter. This supports enhanced feedback as the main driver of the chemostructural evolution of star-forming galaxies at cosmic noon. Moreover, we also find that the intrinsic scatter of metallicity gradients increases with decreasing ${M}_{* }$ and increasing sSFR. Combined with the global metallicity measurements, our result is consistent with the hypothesis that the combined effect of cold-mode gas accretion and merger-induced starbursts strongly boosts the chemostructural diversity of low-mass star-forming galaxies at cosmic noon, with mergers playing a much more predominant role in the dwarf mass regime of ${M}_{* }\lesssim {10}^{9}\,{M}_{\odot }$. This work demonstrates that by accurately mapping the radial chemical profiles of star-forming galaxies at high redshifts, we can cast strong constraints on the role that feedback, gas flows, and mergers play in the early phase of disk mass assembly. The observed trends between metallicity and galaxy properties, while weak, are nonetheless very well measured over a wide dynamic range of mass. This census offers a stringent test for theoretical models and cosmological simulations, as the resulting trends are highly sensitive to baryon cycling processes at the peak of cosmic star formation (1.2 ≲ z ≲ 2.3). Using the Near-Infrared Imager and Slitless Spectrograph (NIRISS) on board the soon-to-be-launched James Webb Space Telescope (JWST), the GLASS-JWST ERS program (PI: Treu; ID 1324) and the CAnadian NIRISS Unbiased Cluster Survey (CANUCS) GTO program (PI: Willott) will conduct K-band slitless spectroscopy on several galaxy cluster center fields. The data acquired by these programs will enable sub-kpc resolution measurements of metallicity gradients to z ≲ 3.5 and thus extend the test for theoretical predictions to even higher redshifts.

We thank the anonymous referee for careful reading and constructive comments that improved the quality of our paper. This work is supported by NASA through HST grant HST-GO-13459. X.W. acknowledges support by UCLA through a dissertation year fellowship. X.W. is greatly indebted to his family, i.e., Dr. Xiaolei Meng, SX Wang, and ST Wang, for their tremendous love, care, and support during the COVID-19 pandemic, without which this work could not have been completed.

Software: APLpy (Robitaille & Bressert 2012), AstroDrizzle (Gonzaga 2012), Astropy (Price-Whelan et al. 2018), Emcee (Foreman-Mackey et al. 2013), FAST (Kriek et al. 2009), Grizli (G. Brammer et al. 2020, in preparation), SExtractor (Bertin & Arnouts 1996), VorBin (Cappellari & Copin 2003).

As explained in Section 3.6, we use Voronoi tessellation to divide the spatial extent of our sample galaxies into subregions, where we measure metallicities individually to estimate their radial gradients. This tessellation process is by default performed in the image plane, since the noise properties of the observed emission line fluxes are well defined in the image plane. Furthermore, the majority of our sample galaxies have magnifications less than 4, and the sample median value is μ = 2.69 (see the results presented in Table A1), which indicates that the highly anisotropic lensing phenomenon is relatively rare in our sample.

Table A1.  Measured Quantities of Our Sample Galaxies

Cluster	ID	R.A.	Decl.	${z}_{\mathrm{spec}}$	${\rm{\Delta }}\mathrm{log}({\rm{O}}/{\rm{H}})/{\rm{\Delta }}r$	F140Wa	${r}_{{\rm{F}}140{\rm{W}}}$ b	Observed Integrated Emission Line Fluxes $({10}^{-17}$ $\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$)						μc	Stellar Continuum SED Fitting			[N ii]/Hαd	Nebular Emission Diagnostics
		(deg)	(deg)		(dex kpc−1)	(AB mag)
								${f}_{[{\rm{O}}{\rm\small{II}}]}$	${f}_{{\rm{H}}\gamma }$	${f}_{{\rm{H}}\beta }$	${f}_{[{\rm{O}}{\rm\small{III}}]}$	${f}_{{\rm{H}}\alpha }$	${f}_{[{\rm{S}}{\rm\small{II}}]}$		log (${M}_{* }$ e/${M}_{\odot }$)	SFRSe(${M}_{\odot }$ yr−1)	${A}_{{\rm{V}}}^{{\rm{S}}}$		$12+\mathrm{log}({\rm{O}}/{\rm{H}})$	${A}_{{\rm{V}}}^{{\rm{N}}}$	SFRNe (${M}_{\odot }$ yr−1)
A370	01513	39.958904	−1.565269	1.27	−0.230 ± 0.026	21.17	0.95	20.05 ± 2.47	1.36 ± 1.06	8.53 ± 0.80	28.99 ± 0.88	37.55 ± 1.07	5.20 ± 1.10	${2.80}_{-0.03}^{+0.02}$	${9.72}_{-0.03}^{+0.23}$	${1.30}_{-1.26}^{+58.61}$	${0.90}_{-0.38}^{+0.50}$	${0.19}_{-0.01}^{+0.08}$	${8.36}_{-0.13}^{+0.10}$	${1.02}_{-0.42}^{+0.45}$	${10.70}_{-3.43}^{+5.11}$
A370	01590	39.965663	−1.566864	1.96	0.115 ± 0.056	23.85	0.57	4.61 ± 0.79	4.60 ± 2.74	2.89 ± 2.48	19.48 ± 1.05	⋯	⋯	${17.76}_{-7.58}^{+10.14}$	${7.48}_{-0.35}^{+0.32}$	${0.28}_{-0.18}^{+0.55}$	${0.00}_{-0.00}^{+0.21}$	${0.04}_{-0.00}^{+0.00}$	${8.07}_{-0.35}^{+0.21}$	<1.06	${2.73}_{-2.00}^{+13.54}$
A370	02056	39.959425	−1.573309	1.27	0.023 ± 0.009	23.30	0.91	13.75 ± 2.00	4.74 ± 0.92	3.25 ± 0.70	32.83 ± 0.83	10.15 ± 1.14	⋯	${3.55}_{-0.10}^{+0.08}$	${8.50}_{-0.09}^{+0.10}$	${5.01}_{-4.27}^{+2.97}$	${1.00}_{-0.33}^{+0.19}$	${0.05}_{-0.00}^{+0.01}$	${7.98}_{-0.20}^{+0.18}$	$\lt 0.73$	${4.03}_{-1.74}^{+5.14}$
A370	02546	39.961942	−1.577895	1.27	0.029 ± 0.108	24.24	0.90	6.56 ± 1.60	0.58 ± 0.72	1.23 ± 0.66	6.98 ± 0.66	3.81 ± 0.68	0.98 ± 0.68	${3.41}_{-0.08}^{+0.05}$	${8.25}_{-0.22}^{+0.13}$	${0.61}_{-0.52}^{+0.58}$	${0.20}_{-0.20}^{+0.32}$	${0.05}_{-0.00}^{+0.00}$	${8.10}_{-0.35}^{+0.25}$	$\lt 0.64$	${0.92}_{-0.35}^{+1.12}$
A370	03097	39.959500	−1.584013	1.55	−0.016 ± 0.054	22.56	0.94	11.81 ± 0.97	5.65 ± 0.63	4.03 ± 1.31	6.41 ± 1.14	34.27 ± 1.60	⋯	${2.55}_{-0.08}^{+0.06}$	${9.28}_{-0.06}^{+0.21}$	${0.73}_{-0.73}^{+8.55}$	${0.30}_{-0.30}^{+0.52}$	${0.11}_{-0.01}^{+0.01}$	${8.78}_{-0.12}^{+0.09}$	${1.55}_{-0.30}^{+0.29}$	${26.80}_{-6.63}^{+8.71}$
A370	03751	39.977361	−1.591636	1.97	0.122 ± 0.008	21.55	0.70	29.57 ± 0.51	7.21 ± 0.67	17.68 ± 0.68	111.41 ± 0.84	⋯	⋯	${6.35}_{-0.58}^{+0.40}$	${9.05}_{-0.06}^{+0.05}$	${32.91}_{-10.50}^{+3.28}$	${0.80}_{-0.11}^{+0.01}$	${0.07}_{-0.00}^{+0.00}$	${8.08}_{-0.12}^{+0.11}$	${0.85}_{-0.14}^{+0.21}$	${26.23}_{-2.34}^{+3.19}$
A370	03834	39.979759	−1.591402	1.25	0.017 ± 0.011	23.56	0.91	2.51 ± 2.71	3.71 ± 0.74	2.56 ± 0.60	15.80 ± 0.79	7.02 ± 0.70	0.78 ± 0.69	${3.18}_{-0.12}^{+0.11}$	${8.58}_{-0.08}^{+0.27}$	${0.33}_{-0.24}^{+8.25}$	${0.90}_{-0.26}^{+0.60}$	${0.06}_{-0.01}^{+0.01}$	${7.88}_{-0.22}^{+0.22}$	$\lt 0.32$	${1.43}_{-0.35}^{+0.77}$
A2744	00144	3.606322	−30.380061	1.34	0.020 ± 0.085	22.76	0.92	7.45 ± 2.39	2.28 ± 1.12	3.71 ± 3.10	6.38 ± 1.45	14.13 ± 1.17	1.08 ± 1.19	${1.43}_{-0.01}^{+0.01}$	${9.56}_{-0.21}^{+0.17}$	${15.30}_{-14.67}^{+22.41}$	${1.10}_{-0.50}^{+0.42}$	${0.15}_{-0.04}^{+0.04}$	${8.55}_{-0.22}^{+0.13}$	${0.77}_{-0.45}^{+0.57}$	${7.66}_{-2.45}^{+4.52}$
A2744	00161	3.588863	−30.380291	1.36	0.027 ± 0.063	23.55	0.93	4.50 ± 1.30	1.95 ± 0.65	2.71 ± 1.86	12.51 ± 1.21	6.31 ± 0.70	0.25 ± 0.71	${2.12}_{-0.01}^{+0.02}$	${8.53}_{-0.09}^{+0.18}$	${2.72}_{-2.41}^{+5.94}$	${0.40}_{-0.38}^{+0.32}$	${0.05}_{-0.00}^{+0.01}$	${8.00}_{-0.25}^{+0.21}$	$\lt 0.27$	${1.88}_{-0.31}^{+0.65}$
A2744	00169	3.571780	−30.380437	1.68	−0.147 ± 0.079	23.83	0.58	4.45 ± 0.59	3.94 ± 1.00	3.07 ± 0.70	18.64 ± 0.74	⋯	⋯	${2.76}_{-0.02}^{+0.02}$	${8.17}_{-0.05}^{+0.02}$	${4.36}_{-1.30}^{+0.03}$	${0.40}_{-0.14}^{+0.01}$	${0.05}_{-0.00}^{+0.00}$	${8.06}_{-0.25}^{+0.19}$	$\lt 1.06$	$\lt 14.87$
A2744	00188	3.573408	−30.380770	1.76	0.033 ± 0.030	21.77	0.95	16.97 ± 0.82	3.00 ± 1.43	5.48 ± 1.02	13.56 ± 1.09	⋯	⋯	${2.79}_{-0.02}^{+0.03}$	${9.93}_{-0.07}^{+0.12}$	${1.39}_{-1.39}^{+20.38}$	${0.90}_{-0.34}^{+0.30}$	${0.20}_{-0.02}^{+0.04}$	${8.55}_{-0.10}^{+0.09}$	$\lt 0.68$	${12.86}_{-5.74}^{+16.11}$
A2744	00263	3.591110	−30.381705	1.89	0.018 ± 0.014	23.02	0.65	6.68 ± 0.55	3.19 ± 0.84	4.14 ± 0.68	34.01 ± 0.75	⋯	⋯	${2.21}_{-0.02}^{+0.02}$	${8.58}_{-0.01}^{+0.12}$	${10.39}_{-4.87}^{+2.19}$	${0.20}_{-0.14}^{+0.10}$	${0.05}_{-0.00}^{+0.00}$	${8.02}_{-0.17}^{+0.14}$	${0.90}_{-0.62}^{+0.88}$	${21.64}_{-10.71}^{+34.81}$
A2744	00892	3.599948	−30.393554	1.34	0.044 ± 0.041	23.21	0.74	14.74 ± 0.98	3.14 ± 0.48	6.97 ± 0.45	37.56 ± 1.01	26.46 ± 0.54	5.58 ± 0.53	${1.90}_{-0.02}^{+0.02}$	${8.63}_{-0.04}^{+0.03}$	${9.16}_{-3.56}^{+3.59}$	${0.90}_{-0.13}^{+0.10}$	${0.06}_{-0.00}^{+0.00}$	${8.25}_{-0.10}^{+0.09}$	${0.39}_{-0.24}^{+0.31}$	${8.67}_{-1.60}^{+2.53}$
A2744	00893	3.600091	−30.393759	1.34	−0.066 ± 0.085	22.58	0.90	15.59 ± 1.46	1.02 ± 0.75	3.97 ± 0.67	17.64 ± 1.43	17.00 ± 0.79	4.91 ± 0.79	${1.90}_{-0.02}^{+0.02}$	${9.24}_{-0.12}^{+0.15}$	${25.81}_{-24.47}^{+17.37}$	${1.20}_{-0.52}^{+0.21}$	${0.10}_{-0.01}^{+0.02}$	${8.39}_{-0.12}^{+0.10}$	$\lt 0.38$	${5.33}_{-1.03}^{+1.83}$
A2744	00895	3.576755	−30.393627	1.37	0.139 ± 0.079	22.91	0.87	14.76 ± 1.07	0.05 ± 0.64	6.59 ± 0.91	22.15 ± 1.11	18.12 ± 0.64	2.56 ± 0.64	${3.29}_{-0.04}^{+0.05}$	${8.66}_{-0.06}^{+0.15}$	${3.11}_{-2.07}^{+9.15}$	${0.70}_{-0.26}^{+0.30}$	${0.06}_{-0.00}^{+0.01}$	${8.29}_{-0.09}^{+0.09}$	${1.41}_{-0.29}^{+0.31}$	${7.81}_{-1.86}^{+2.54}$
A2744	01057	3.575089	−30.399687	1.74	−0.033 ± 0.049	21.88	0.90	10.73 ± 0.79	⋯	4.28 ± 0.93	26.52 ± 1.05	⋯	⋯	${2.64}_{-0.03}^{+0.03}$	${9.52}_{-0.15}^{+0.10}$	${24.44}_{-22.43}^{+17.59}$	${0.50}_{-0.37}^{+0.29}$	${0.13}_{-0.02}^{+0.01}$	${8.21}_{-0.13}^{+0.12}$	$\lt 0.61$	${10.51}_{-4.19}^{+13.74}$
A2744	01279	3.576955	−30.400863	1.34	−0.051 ± 0.014	23.67	0.83	8.63 ± 1.34	1.23 ± 0.68	5.94 ± 0.60	29.19 ± 1.27	12.51 ± 0.70	1.54 ± 0.69	${2.71}_{-0.04}^{+0.03}$	${8.12}_{-0.03}^{+0.04}$	${2.80}_{-1.10}^{+1.12}$	${0.40}_{-0.17}^{+0.11}$	${0.05}_{-0.00}^{+0.00}$	${8.00}_{-0.15}^{+0.13}$	$\lt 0.22$	${2.83}_{-0.44}^{+0.79}$
A2744	01649	3.578893	−30.409998	1.26	0.026 ± 0.011	22.67	0.95	8.27 ± 4.96	1.07 ± 1.39	1.67 ± 1.58	23.97 ± 1.50	10.04 ± 1.54	⋯	${2.46}_{-0.03}^{+0.02}$	${9.10}_{-0.17}^{+0.21}$	${4.35}_{-4.30}^{+13.14}$	${0.60}_{-0.42}^{+0.52}$	${0.10}_{-0.02}^{+0.02}$	${7.95}_{-0.24}^{+0.21}$	${1.33}_{-0.86}^{+1.02}$	${8.35}_{-5.01}^{+15.09}$
A2744	01773	3.576699	−30.410185	1.66	0.129 ± 0.079	22.95	0.88	8.68 ± 0.72	2.46 ± 1.06	2.74 ± 0.81	10.98 ± 0.85	⋯	⋯	${2.00}_{-0.02}^{+0.02}$	${9.32}_{-0.19}^{+0.10}$	${8.31}_{-8.24}^{+8.41}$	${0.50}_{-0.50}^{+0.33}$	${0.11}_{-0.02}^{+0.01}$	${8.46}_{-0.12}^{+0.12}$	$\lt 1.01$	${14.68}_{-8.68}^{+32.79}$
A2744	01897	3.574584	−30.412278	1.37	−0.159 ± 0.076	22.87	0.90	15.77 ± 1.74	2.18 ± 0.89	2.23 ± 1.10	7.95 ± 1.19	13.62 ± 1.02	3.68 ± 0.98	${1.68}_{-0.01}^{+0.01}$	${9.39}_{-0.20}^{+0.12}$	${10.56}_{-10.47}^{+10.17}$	${0.90}_{-0.44}^{+0.38}$	${0.12}_{-0.03}^{+0.02}$	${8.56}_{-0.11}^{+0.09}$	$\lt 0.51$	${5.17}_{-1.39}^{+2.87}$
M0416	00094	64.033092	−24.056326	1.36	−0.010 ± 0.126	22.25	0.93	8.52 ± 1.42	1.83 ± 1.04	0.16 ± 0.98	7.33 ± 1.37	17.85 ± 0.85	3.32 ± 0.85	${1.47}_{-0.01}^{+0.02}$	${9.72}_{-0.15}^{+0.08}$	${10.27}_{-10.06}^{+15.13}$	${0.90}_{-0.36}^{+0.27}$	${0.18}_{-0.03}^{+0.02}$	${8.57}_{-0.14}^{+0.15}$	${1.50}_{-0.51}^{+0.59}$	${14.78}_{-5.48}^{+9.31}$
M0416	00519	64.032451	−24.068482	2.09	−0.037 ± 0.025	21.52	0.89	10.61 ± 1.08	⋯	4.81 ± 0.94	45.24 ± 1.11	⋯	⋯	${4.74}_{-2.63}^{+11.66}$	${9.85}_{-0.54}^{+0.35}$	${210.95}_{-149.96}^{+263.50}$	${1.80}_{-0.00}^{+0.00}$	${0.16}_{-0.07}^{+0.08}$	${8.03}_{-0.12}^{+0.10}$	$\lt 0.65$	${11.13}_{-9.16}^{+44.59}$
M0416	00572	64.047481	−24.068851	1.90	0.045 ± 0.047	22.94	0.72	9.32 ± 0.78	5.94 ± 4.44	7.47 ± 1.05	26.96 ± 1.13	⋯	⋯	${3.31}_{-0.08}^{+0.09}$	${8.72}_{-0.03}^{+0.06}$	${14.45}_{-2.19}^{+3.35}$	${0.80}_{-0.03}^{+0.10}$	${0.05}_{-0.00}^{+0.00}$	${8.25}_{-0.22}^{+0.15}$	$\lt 1.22$	${21.50}_{-12.22}^{+36.41}$
M0416	00889	64.026197	−24.074377	1.63	0.054 ± 0.038	22.91	0.83	8.79 ± 0.42	2.39 ± 0.37	2.71 ± 0.48	18.55 ± 0.55	⋯	⋯	${3.22}_{-0.04}^{+0.03}$	${8.72}_{-0.10}^{+0.09}$	${7.45}_{-4.23}^{+2.96}$	${0.40}_{-0.20}^{+0.12}$	${0.06}_{-0.01}^{+0.00}$	${8.27}_{-0.12}^{+0.11}$	$\lt 0.55$	${5.50}_{-2.06}^{+6.52}$
M0416	00932	64.018102	−24.075620	2.18	−0.082 ± 0.073	22.16	0.92	13.67 ± 1.33	⋯	4.87 ± 0.95	17.30 ± 1.08	⋯	⋯	${1.86}_{-0.02}^{+0.02}$	${10.03}_{-0.15}^{+0.06}$	${74.38}_{-72.49}^{+31.79}$	${1.10}_{-0.52}^{+0.16}$	${0.19}_{-0.03}^{+0.02}$	${8.45}_{-0.13}^{+0.11}$	$\lt 0.94$	${43.12}_{-24.74}^{+88.65}$
M0416	00955	64.041852	−24.075813	1.99	−0.079 ± 0.014	23.12	0.36	7.32 ± 0.44	3.52 ± 1.09	6.88 ± 0.60	57.38 ± 0.71	⋯	⋯	${2.81}_{-0.05}^{+0.05}$	${8.15}_{-0.08}^{+0.01}$	${4.18}_{-0.84}^{+0.08}$	${0.10}_{-0.10}^{+0.01}$	${0.04}_{-0.00}^{+0.00}$	${7.95}_{-0.13}^{+0.12}$	${1.02}_{-0.66}^{+0.68}$	${32.07}_{-16.46}^{+36.99}$
M0416	01047	64.021434	−24.078456	2.22	−0.044 ± 0.040	22.88	0.96	4.64 ± 0.89	0.05 ± 0.65	1.80 ± 0.60	14.75 ± 0.72	⋯	⋯	${2.85}_{-0.03}^{+0.05}$	${9.38}_{-0.11}^{+0.08}$	${8.04}_{-1.90}^{+2.43}$	${0.20}_{-0.19}^{+0.14}$	${0.09}_{-0.01}^{+0.01}$	${7.97}_{-0.31}^{+0.28}$	${2.29}_{-1.47}^{+1.59}$	${55.56}_{-44.42}^{+242.09}$
M0416	01197	64.023302	−24.081517	2.23	−0.083 ± 0.027	22.45	0.94	9.61 ± 1.45	3.83 ± 1.08	5.02 ± 1.02	40.99 ± 1.17	⋯	⋯	${5.11}_{-0.12}^{+0.10}$	${9.17}_{-0.09}^{+0.04}$	${0.07}_{-0.00}^{+38.09}$	${0.00}_{-0.00}^{+1.00}$	${0.08}_{-0.00}^{+0.00}$	${7.97}_{-0.20}^{+0.18}$	$\lt 1.00$	$\lt 27.87$
M0416	01213	64.035828	−24.081321	1.63	−0.052 ± 0.048	22.65	0.77	11.39 ± 0.83	2.91 ± 0.91	4.24 ± 0.70	30.81 ± 0.77	⋯	⋯	${3.33}_{-0.06}^{+0.07}$	${8.74}_{-0.01}^{+0.08}$	${1.28}_{-0.75}^{+0.02}$	${0.10}_{-0.10}^{+0.07}$	${0.06}_{-0.00}^{+0.00}$	${8.17}_{-0.13}^{+0.12}$	$\lt 0.55$	${7.08}_{-2.67}^{+8.81}$
M0717	01007	109.388805	37.752159	1.85	−0.065 ± 0.034	22.23	0.84	8.01 ± 1.20	16.05 ± 2.03	3.81 ± 1.68	32.95 ± 1.70	⋯	⋯	${6.96}_{-0.55}^{+0.62}$	${9.00}_{-0.11}^{+0.11}$	${29.32}_{-12.33}^{+2.49}$	${1.30}_{-0.18}^{+0.02}$	${0.07}_{-0.01}^{+0.01}$	${7.96}_{-0.24}^{+0.21}$	$\lt 1.21$	${7.27}_{-4.10}^{+13.98}$
M0717	01131	109.381097	37.750440	1.85	−0.055 ± 0.028	22.07	0.75	27.83 ± 0.95	⋯	12.00 ± 1.43	53.78 ± 1.30	⋯	⋯	${7.86}_{-0.96}^{+1.04}$	${8.95}_{-0.15}^{+0.19}$	${6.23}_{-5.45}^{+17.82}$	${0.90}_{-0.30}^{+0.24}$	${0.07}_{-0.01}^{+0.02}$	${8.30}_{-0.11}^{+0.10}$	$\lt 0.53$	${9.07}_{-3.87}^{+11.67}$
M0717	01636	109.376338	37.744601	1.85	−0.059 ± 0.040	22.97	0.78	12.42 ± 0.57	1.12 ± 0.90	3.41 ± 0.71	22.03 ± 0.78	⋯	⋯	${3.52}_{-0.09}^{+0.13}$	${9.04}_{-0.18}^{+0.11}$	${13.91}_{-13.08}^{+10.92}$	${1.00}_{-0.42}^{+0.21}$	${0.08}_{-0.02}^{+0.01}$	${8.30}_{-0.11}^{+0.10}$	$\lt 0.47$	${7.29}_{-2.58}^{+8.48}$
M0717	02043	109.394456	37.739171	1.86	−0.200 ± 0.076	24.49	0.21	0.07 ± 0.59	1.16 ± 1.26	3.57 ± 0.93	19.27 ± 0.81	⋯	⋯	${14.96}_{-1.33}^{+1.25}$	${6.93}_{-0.03}^{+0.04}$	${0.25}_{-0.02}^{+0.02}$	${0.00}_{-0.00}^{+0.00}$	${0.05}_{-0.00}^{+0.00}$	${7.70}_{-0.24}^{+0.29}$	${2.94}_{-1.79}^{+1.63}$	${17.16}_{-14.80}^{+88.69}$
M0717	02064	109.413018	37.738458	2.08	0.044 ± 0.047	23.42	0.64	15.24 ± 1.29	⋯	3.92 ± 1.18	24.27 ± 1.20	⋯	⋯	${5.69}_{-0.39}^{+0.42}$	${8.23}_{-0.05}^{+0.15}$	${4.73}_{-3.37}^{+0.46}$	${0.60}_{-0.20}^{+0.07}$	${0.04}_{-0.00}^{+0.00}$	${8.31}_{-0.11}^{+0.10}$	$\lt 0.49$	${6.92}_{-2.65}^{+8.50}$
M0744	00920	116.212401	39.460342	1.28	−0.194 ± 0.077	20.81	0.95	13.04 ± 6.32	0.01 ± 1.30	6.74 ± 1.76	41.30 ± 1.25	42.86 ± 1.22	9.02 ± 1.21	${10.83}_{-0.76}^{+1.01}$	${9.33}_{-0.06}^{+0.15}$	${3.20}_{-1.83}^{+6.28}$	${0.80}_{-0.21}^{+0.27}$	${0.11}_{-0.01}^{+0.03}$	${7.99}_{-0.28}^{+0.22}$	${1.75}_{-0.86}^{+0.79}$	${5.76}_{-3.50}^{+7.20}$
M0744	01031	116.212064	39.459430	1.27	0.178 ± 0.242	20.94	0.93	24.57 ± 2.77	6.57 ± 1.25	20.09 ± 0.93	36.40 ± 1.09	48.45 ± 1.15	17.99 ± 1.13	${6.31}_{-0.31}^{+0.36}$	${9.58}_{-0.10}^{+0.15}$	${4.79}_{-1.80}^{+9.09}$	${0.70}_{-0.11}^{+0.32}$	${0.16}_{-0.02}^{+0.03}$	${8.52}_{-0.13}^{+0.11}$	${1.63}_{-0.97}^{+0.78}$	${22.33}_{-14.78}^{+32.02}$
M0744	01203	116.197585	39.456699	1.65	0.111 ± 0.017	21.68	0.64	34.00 ± 0.96	7.06 ± 1.00	17.46 ± 1.06	117.66 ± 1.17	⋯	⋯	${2.25}_{-0.03}^{+0.03}$	${9.41}_{-0.01}^{+0.01}$	${75.31}_{-1.11}^{+1.04}$	${1.00}_{-0.00}^{+0.00}$	${0.12}_{-0.00}^{+0.00}$	${8.10}_{-0.12}^{+0.10}$	${0.89}_{-0.20}^{+0.28}$	${47.74}_{-3.06}^{+5.28}$
M0744	01370	116.236950	39.454058	1.37	−0.116 ± 0.111	22.71	0.94	5.59 ± 1.52	⋯	2.22 ± 1.18	12.37 ± 1.39	10.19 ± 0.81	2.38 ± 0.80	${1.55}_{-0.02}^{+0.01}$	${9.56}_{-0.06}^{+0.16}$	${3.71}_{-3.69}^{+17.90}$	${1.10}_{-0.32}^{+0.34}$	${0.15}_{-0.01}^{+0.03}$	${8.29}_{-0.17}^{+0.13}$	${0.54}_{-0.37}^{+0.54}$	${4.57}_{-1.24}^{+2.63}$
M0744	01734	116.219106	39.449158	1.49	0.085 ± 0.034	22.62	0.77	16.67 ± 1.45	3.16 ± 0.92	7.48 ± 1.86	30.72 ± 1.53	19.46 ± 1.08	10.71 ± 2.31	${1.63}_{-0.01}^{+0.02}$	${9.17}_{-0.01}^{+0.14}$	${43.51}_{-43.43}^{+0.30}$	${1.10}_{-1.00}^{+0.05}$	${0.09}_{-0.00}^{+0.02}$	${8.25}_{-0.11}^{+0.09}$	$\lt 0.17$	${8.97}_{-1.31}^{+2.11}$
M0744	02341	116.212719	39.441062	1.28	0.031 ± 0.044	22.60	0.93	4.92 ± 1.55	0.69 ± 0.68	3.38 ± 0.78	11.49 ± 0.71	10.74 ± 0.65	3.20 ± 0.63	${1.13}_{-0.00}^{+0.00}$	${9.47}_{-0.07}^{+0.11}$	${3.01}_{-2.88}^{+19.34}$	${0.50}_{-0.30}^{+0.42}$	${0.14}_{-0.01}^{+0.02}$	${8.27}_{-0.25}^{+0.14}$	${0.63}_{-0.41}^{+0.55}$	${6.17}_{-1.86}^{+3.65}$
M1423	00410	215.941735	24.088841	1.79	0.104 ± 0.054	23.19	0.77	7.50 ± 0.47	3.10 ± 0.71	3.08 ± 0.54	18.78 ± 0.64	⋯	⋯	${1.46}_{-0.01}^{+0.02}$	${9.03}_{-0.07}^{+0.11}$	${20.72}_{-18.14}^{+6.12}$	${0.60}_{-0.33}^{+0.11}$	${0.08}_{-0.01}^{+0.01}$	${8.24}_{-0.14}^{+0.12}$	$\lt 0.59$	${15.47}_{-6.11}^{+25.95}$
M1423	00433	215.954478	24.088107	1.63	−0.095 ± 0.046	23.00	0.80	7.83 ± 0.85	0.47 ± 0.61	4.28 ± 1.70	18.45 ± 1.03	⋯	⋯	${3.64}_{-0.13}^{+0.06}$	${8.94}_{-0.16}^{+0.15}$	${10.22}_{-10.03}^{+8.63}$	${1.00}_{-0.63}^{+0.28}$	${0.08}_{-0.01}^{+0.01}$	${8.27}_{-0.21}^{+0.15}$	$\lt 1.03$	${8.97}_{-5.32}^{+20.72}$
M1423	00493	215.952044	24.083337	1.78	−0.028 ± 0.089	21.75	0.93	13.40 ± 2.17	3.05 ± 3.47	19.79 ± 2.00	18.92 ± 2.61	⋯	⋯	${5.14}_{-0.20}^{+0.42}$	${9.66}_{-0.24}^{+0.24}$	${6.60}_{-6.60}^{+9.50}$	${0.60}_{-0.44}^{+0.40}$	${0.14}_{-0.03}^{+0.05}$	${8.52}_{-0.15}^{+0.13}$	${1.67}_{-0.80}^{+0.39}$	$\gt 26.26$
M1423	00908	215.957460	24.079767	1.31	−0.233 ± 0.104	21.91	0.96	12.88 ± 4.10	⋯	4.07 ± 2.50	8.01 ± 3.07	17.25 ± 1.47	⋯	${2.12}_{-0.01}^{+0.03}$	${9.54}_{-0.12}^{+0.34}$	${12.11}_{-11.30}^{+78.23}$	${1.20}_{-0.70}^{+0.51}$	${0.15}_{-0.02}^{+0.09}$	${8.60}_{-0.20}^{+0.17}$	${0.75}_{-0.49}^{+0.75}$	${5.81}_{-2.14}^{+4.91}$
M1423	00909	215.957063	24.079622	1.32	−0.260 ± 0.085	23.08	0.86	16.21 ± 1.76	3.73 ± 0.82	3.47 ± 1.24	12.18 ± 1.48	14.55 ± 0.78	4.38 ± 0.78	${2.21}_{-0.02}^{+0.04}$	${8.72}_{-0.12}^{+0.15}$	${6.09}_{-5.65}^{+6.44}$	${0.60}_{-0.43}^{+0.26}$	${0.06}_{-0.01}^{+0.01}$	${8.51}_{-0.09}^{+0.08}$	$\lt 0.28$	${3.66}_{-0.64}^{+1.09}$
M1423	00976	215.938230	24.078815	1.24	−0.023 ± 0.059	22.85	0.89	9.56 ± 1.47	1.96 ± 0.60	4.02 ± 0.46	17.47 ± 0.53	15.17 ± 0.57	2.78 ± 0.55	${1.45}_{-0.01}^{+0.01}$	${9.00}_{-0.11}^{+0.17}$	${3.54}_{-2.72}^{+22.83}$	${0.50}_{-0.25}^{+0.50}$	${0.09}_{-0.01}^{+0.01}$	${8.30}_{-0.11}^{+0.09}$	${0.44}_{-0.26}^{+0.29}$	${5.49}_{-1.14}^{+1.61}$
M1423	01564	215.943001	24.069814	1.41	0.207 ± 0.104	23.84	0.79	5.95 ± 0.77	1.94 ± 0.43	2.27 ± 1.21	9.01 ± 0.76	5.97 ± 0.48	1.67 ± 0.48	${2.85}_{-0.07}^{+0.04}$	${8.68}_{-0.07}^{+0.01}$	${0.02}_{-0.02}^{+0.24}$	${0.60}_{-0.25}^{+0.12}$	${0.06}_{-0.00}^{+0.00}$	${8.33}_{-0.12}^{+0.10}$	$\lt 0.22$	${1.53}_{-0.28}^{+0.48}$
M1423	01682	215.959334	24.067604	1.32	−0.000 ± 0.038	23.80	0.90	8.07 ± 1.04	1.59 ± 0.47	4.30 ± 1.63	17.49 ± 0.89	6.85 ± 0.47	0.48 ± 0.47	${1.28}_{-0.00}^{+0.01}$	${8.62}_{-0.08}^{+0.10}$	${2.91}_{-1.95}^{+8.45}$	${0.50}_{-0.22}^{+0.31}$	${0.06}_{-0.00}^{+0.01}$	${8.09}_{-0.17}^{+0.13}$	$\lt 0.16$	${3.35}_{-0.47}^{+0.72}$
M1423	01808	215.960238	24.065007	2.02	0.035 ± 0.053	23.33	0.87	4.28 ± 0.36	0.90 ± 0.52	1.92 ± 0.79	8.75 ± 0.54	⋯	⋯	${1.28}_{-0.00}^{+0.01}$	${9.44}_{-0.13}^{+0.11}$	${14.51}_{-14.01}^{+12.61}$	${0.60}_{-0.48}^{+0.20}$	${0.11}_{-0.01}^{+0.01}$	${8.33}_{-0.15}^{+0.13}$	${1.04}_{-0.73}^{+1.08}$	${21.46}_{-12.51}^{+56.60}$
M2129	00340	322.352173	−7.679022	2.09	−0.021 ± 0.018	23.73	0.81	1.95 ± 0.89	1.08 ± 0.64	0.64 ± 0.57	10.54 ± 0.65	⋯	⋯	${1.46}_{-0.01}^{+0.02}$	${8.94}_{-0.04}^{+0.17}$	${20.70}_{-13.92}^{+6.83}$	${0.80}_{-0.28}^{+0.10}$	${0.07}_{-0.00}^{+0.01}$	${7.84}_{-0.38}^{+0.40}$	${1.75}_{-1.16}^{+1.18}$	${43.84}_{-31.85}^{+112.18}$
M2129	00380	322.364762	−7.679957	1.81	−0.074 ± 0.036	24.55	0.67	1.50 ± 0.39	2.06 ± 0.58	2.22 ± 0.77	6.94 ± 0.54	⋯	⋯	${1.56}_{-0.01}^{+0.02}$	${8.23}_{-0.07}^{+0.17}$	${3.94}_{-3.46}^{+1.05}$	${0.40}_{-0.31}^{+0.11}$	${0.05}_{-0.00}^{+0.00}$	${7.89}_{-0.52}^{+0.41}$	${1.47}_{-0.94}^{+1.36}$	${16.98}_{-10.93}^{+56.16}$
M2129	00440	322.366118	−7.681231	1.36	0.034 ± 0.050	22.16	0.88	8.43 ± 1.81	⋯	6.34 ± 2.65	8.86 ± 1.97	33.17 ± 1.40	6.90 ± 1.34	${1.53}_{-0.01}^{+0.02}$	${9.63}_{-0.11}^{+0.13}$	${59.57}_{-56.40}^{+42.05}$	${1.50}_{-0.53}^{+0.22}$	${0.16}_{-0.02}^{+0.03}$	${8.63}_{-0.12}^{+0.14}$	${2.05}_{-0.42}^{+0.41}$	${44.89}_{-13.01}^{+17.40}$
M2129	00465	322.367391	−7.681865	1.36	0.036 ± 0.027	22.34	0.88	7.06 ± 1.23	1.81 ± 0.62	3.08 ± 0.85	1.27 ± 1.15	27.21 ± 0.70	5.59 ± 0.68	${1.57}_{-0.01}^{+0.02}$	${9.71}_{-0.08}^{+0.08}$	${2.92}_{-2.70}^{+99.02}$	${1.20}_{-0.25}^{+0.80}$	${0.18}_{-0.02}^{+0.02}$	${8.90}_{-0.15}^{+0.13}$	${2.26}_{-0.55}^{+0.58}$	${42.01}_{-14.75}^{+24.05}$
M2129	00565	322.364752	−7.683770	1.37	0.064 ± 0.064	22.34	0.92	10.16 ± 2.04	1.77 ± 1.00	12.87 ± 2.50	15.41 ± 1.84	17.05 ± 1.14	5.64 ± 1.14	${2.00}_{-0.02}^{+0.02}$	${9.46}_{-0.16}^{+0.26}$	${1.65}_{-1.64}^{+41.19}$	${0.70}_{-0.36}^{+0.77}$	${0.13}_{-0.02}^{+0.05}$	${8.33}_{-0.39}^{+0.15}$	$\lt 0.42$	${5.60}_{-1.34}^{+2.83}$
M2129	00690	322.346464	−7.685883	1.88	0.049 ± 0.043	23.08	0.78	9.45 ± 0.59	0.70 ± 0.95	4.85 ± 0.76	18.93 ± 0.82	⋯	⋯	${2.73}_{-0.07}^{+0.02}$	${8.85}_{-0.05}^{+0.10}$	${15.65}_{-10.14}^{+6.52}$	${0.80}_{-0.20}^{+0.10}$	${0.06}_{-0.00}^{+0.01}$	${8.33}_{-0.14}^{+0.11}$	$\lt 1.01$	${15.12}_{-7.66}^{+27.89}$
M2129	01408	322.369038	−7.700541	1.48	0.087 ± 0.125	23.65	0.83	4.86 ± 0.70	1.39 ± 0.45	2.27 ± 0.73	8.91 ± 0.79	8.43 ± 0.57	4.23 ± 0.76	${1.49}_{-0.02}^{+0.02}$	${8.98}_{-0.09}^{+0.16}$	${16.52}_{-16.29}^{+9.96}$	${1.20}_{-0.73}^{+0.21}$	${0.08}_{-0.00}^{+0.01}$	${8.32}_{-0.17}^{+0.15}$	$\lt 0.48$	${4.81}_{-1.27}^{+2.41}$
M2129	01539	322.363350	−7.703212	1.64	0.021 ± 0.027	22.08	0.94	13.52 ± 0.95	0.45 ± 1.21	6.47 ± 1.12	9.61 ± 1.12	⋯	⋯	${1.39}_{-0.01}^{+0.01}$	${9.93}_{-0.12}^{+0.08}$	${45.29}_{-44.93}^{+59.20}$	${1.00}_{-0.50}^{+0.30}$	${0.21}_{-0.03}^{+0.03}$	${8.63}_{-0.12}^{+0.13}$	${1.09}_{-0.72}^{+0.75}$	${31.57}_{-19.34}^{+55.80}$
M2129	01665	322.358149	−7.706707	1.56	−0.028 ± 0.030	23.26	0.79	6.84 ± 0.68	1.91 ± 0.47	3.74 ± 0.78	15.71 ± 0.85	4.35 ± 1.29	⋯	${1.40}_{-0.01}^{+0.01}$	${9.31}_{-0.21}^{+0.11}$	${6.99}_{-6.93}^{+7.03}$	${0.50}_{-0.43}^{+0.36}$	${0.11}_{-0.03}^{+0.01}$	${8.18}_{-0.16}^{+0.13}$	$\lt 0.28$	${6.23}_{-1.41}^{+2.77}$
M2129	01833	322.362724	−7.709921	2.30	0.034 ± 0.011	22.45	0.91	20.08 ± 1.32	3.42 ± 0.92	8.64 ± 0.96	47.71 ± 1.15	⋯	⋯	${1.27}_{-0.01}^{+0.01}$	${9.76}_{-0.03}^{+0.05}$	${150.11}_{-16.90}^{+39.63}$	${1.00}_{-0.01}^{+0.10}$	${0.14}_{-0.00}^{+0.01}$	${8.24}_{-0.13}^{+0.11}$	$\lt 0.65$	${87.00}_{-36.79}^{+109.28}$
RX J1347	00664	206.904786	−11.750602	1.69	−0.090 ± 0.040	23.01	0.48	12.64 ± 0.65	4.88 ± 1.09	5.93 ± 0.79	51.74 ± 0.95	⋯	⋯	${1.40}_{-0.07}^{+0.11}$	${8.81}_{-0.03}^{+0.02}$	${1.52}_{-0.11}^{+0.09}$	${0.00}_{-0.00}^{+0.00}$	${0.06}_{-0.00}^{+0.00}$	${8.08}_{-0.15}^{+0.14}$	$\lt 0.85$	${34.43}_{-16.28}^{+54.74}$
RX J1347	01443	206.882540	−11.764358	1.77	−0.028 ± 0.038	21.75	0.93	21.20 ± 0.96	⋯	6.34 ± 1.21	18.50 ± 1.30	⋯	⋯	${3.36}_{-0.39}^{+0.70}$	${9.49}_{-0.09}^{+0.19}$	${0.77}_{-0.64}^{+46.86}$	${0.30}_{-0.24}^{+0.62}$	${0.12}_{-0.01}^{+0.03}$	${8.53}_{-0.11}^{+0.10}$	$\lt 0.63$	${12.80}_{-6.71}^{+20.97}$
RX J2248	00206	342.175906	−44.516503	1.43	−0.020 ± 0.104	21.53	0.97	14.31 ± 1.82	0.36 ± 1.05	7.84 ± 1.80	7.13 ± 1.72	12.87 ± 1.05	⋯	${1.83}_{-0.02}^{+0.01}$	${9.87}_{-0.03}^{+0.04}$	${0.05}_{-0.05}^{+3.05}$	${0.50}_{-0.20}^{+0.25}$	${0.22}_{-0.01}^{+0.01}$	${8.60}_{-0.11}^{+0.10}$	$\lt 0.23$	${4.09}_{-0.73}^{+1.27}$
RX J2248	00331	342.169955	−44.518922	1.93	0.004 ± 0.029	23.29	0.79	9.03 ± 0.65	2.54 ± 0.99	2.96 ± 1.29	15.17 ± 0.90	⋯	⋯	${1.86}_{-0.02}^{+0.02}$	${9.01}_{-0.04}^{+0.20}$	${0.58}_{-0.35}^{+9.53}$	${0.00}_{-0.00}^{+0.58}$	${0.07}_{-0.00}^{+0.02}$	${8.36}_{-0.13}^{+0.11}$	$\lt 0.72$	${16.56}_{-7.66}^{+27.33}$
RX J2248	00428	342.186462	−44.521187	1.23	0.052 ± 0.036	22.19	0.96	8.61 ± 5.13	0.95 ± 1.51	10.12 ± 1.11	24.10 ± 1.15	11.30 ± 1.33	⋯	${4.97}_{-0.09}^{+0.08}$	${9.13}_{-0.10}^{+0.05}$	${1.92}_{-0.42}^{+0.54}$	${0.20}_{-0.15}^{+0.11}$	${0.10}_{-0.01}^{+0.00}$	${8.05}_{-0.24}^{+0.17}$	$\lt 0.19$	${1.31}_{-0.22}^{+0.36}$
RX J2248	00786	342.169402	−44.527222	1.84	−0.135 ± 0.070	23.81	0.46	7.24 ± 0.67	2.04 ± 0.97	2.77 ± 0.76	25.73 ± 0.86	⋯	⋯	${3.38}_{-0.06}^{+0.07}$	${7.96}_{-0.01}^{+0.03}$	${2.70}_{-0.17}^{+0.05}$	${0.30}_{-0.01}^{+0.00}$	${0.05}_{-0.00}^{+0.00}$	${8.12}_{-0.15}^{+0.13}$	$\lt 0.73$	${9.32}_{-4.22}^{+15.70}$
RX J2248	01250	342.192946	−44.536578	1.40	−0.068 ± 0.094	22.52	0.88	8.96 ± 2.06	⋯	0.25 ± 2.06	15.49 ± 1.92	17.06 ± 1.11	4.18 ± 1.13	${3.14}_{-0.05}^{+0.04}$	${9.17}_{-0.06}^{+0.08}$	${0.16}_{-0.16}^{+1.02}$	${0.20}_{-0.20}^{+0.33}$	${0.09}_{-0.01}^{+0.01}$	${8.41}_{-0.12}^{+0.12}$	${1.14}_{-0.54}^{+0.62}$	${6.71}_{-2.47}^{+4.51}$
M1149	00270	177.385990	22.414074	1.27	−0.160 ± 0.030	22.55	0.71	10.28 ± 5.23	4.84 ± 8.65	24.87 ± 0.94	29.58 ± 0.72	13.33 ± 0.36	0.36 ± 0.35	${1.96}_{-0.03}^{+0.03}$	${9.00}_{-0.04}^{+0.12}$	${0.24}_{-0.20}^{+13.40}$	${0.20}_{-0.20}^{+0.60}$	${0.09}_{-0.00}^{+0.01}$	${7.91}_{-0.15}^{+0.14}$	$\lt 0.03$	${3.04}_{-0.13}^{+0.15}$
M1149	00593	177.406922	22.407499	1.48	−0.010 ± 0.020	22.40	0.81	23.44 ± 1.40	6.00 ± 0.85	5.72 ± 0.44	31.48 ± 0.45	29.90 ± 0.34	5.31 ± 0.41	${2.02}_{-0.03}^{+0.04}$	${9.13}_{-0.01}^{+0.09}$	${39.40}_{-39.32}^{+0.65}$	${1.00}_{-1.00}^{+0.03}$	${0.09}_{-0.00}^{+0.01}$	${8.38}_{-0.06}^{+0.06}$	${0.93}_{-0.14}^{+0.14}$	${17.50}_{-2.10}^{+2.32}$
M1149	00600	177.389220	22.407583	2.31	−0.180 ± 0.080	24.12	0.76	1.01 ± 0.38	1.33 ± 0.29	1.40 ± 0.27	8.31 ± 0.31	⋯	⋯	${6.87}_{-0.29}^{+0.33}$	${8.32}_{-0.03}^{+0.09}$	${0.90}_{-0.06}^{+0.04}$	${0.00}_{-0.00}^{+0.01}$	${0.04}_{-0.00}^{+0.00}$	${7.83}_{-0.23}^{+0.28}$	$\lt 0.85$	${3.10}_{-1.55}^{+6.36}$
M1149	00676	177.415126	22.406195	1.68	0.060 ± 0.050	23.31	0.78	7.48 ± 0.77	2.58 ± 0.29	2.57 ± 0.19	16.16 ± 0.22	⋯	⋯	${1.77}_{-0.04}^{+0.04}$	${8.93}_{-0.07}^{+0.16}$	${18.72}_{-17.88}^{+5.91}$	${0.90}_{-0.50}^{+0.10}$	${0.07}_{-0.01}^{+0.01}$	${8.19}_{-0.10}^{+0.09}$	$\lt 0.18$	${4.91}_{-0.69}^{+1.66}$
M1149	00683	177.397234	22.406181	1.68	−0.220 ± 0.050	24.41	0.10	3.80 ± 1.02	6.97 ± 0.48	6.05 ± 0.33	28.23 ± 0.33	⋯	⋯	${5.83}_{-0.26}^{+0.23}$	${6.90}_{-0.02}^{+0.02}$	${0.24}_{-0.01}^{+0.01}$	${0.00}_{-0.00}^{+0.00}$	${0.05}_{-0.00}^{+0.00}$	${7.58}_{-0.14}^{+0.34}$	$\lt 0.10$	${3.20}_{-0.37}^{+0.67}$
M1149	00862	177.403416	22.402433	1.49	−0.040 ± 0.020	21.41	0.97	19.22 ± 3.17	⋯	11.35 ± 1.08	5.96 ± 1.03	45.12 ± 0.70	⋯	${3.63}_{-0.06}^{+0.08}$	${9.79}_{-0.15}^{+0.10}$	${24.57}_{-20.09}^{+8.35}$	${1.00}_{-0.31}^{+0.16}$	${0.19}_{-0.04}^{+0.03}$	${8.96}_{-0.08}^{+0.06}$	${0.72}_{-0.29}^{+0.29}$	${11.96}_{-2.56}^{+3.23}$
M1149	01058	177.391848	22.400105	1.25	−0.030 ± 0.030	22.61	0.33	21.25 ± 2.59	16.58 ± 1.09	13.49 ± 0.69	94.78 ± 0.56	40.66 ± 0.29	2.06 ± 0.28	${3.83}_{-0.06}^{+0.07}$	${8.10}_{-0.08}^{+0.01}$	${3.69}_{-0.60}^{+0.06}$	${0.10}_{-0.10}^{+0.02}$	${0.05}_{-0.00}^{+0.00}$	${7.96}_{-0.10}^{+0.10}$	$\lt 0.02$	${4.31}_{-0.13}^{+0.19}$
M1149	01322	177.392541	22.394921	1.49	−0.010 ± 0.020	23.33	0.78	0.20 ± 1.68	5.35 ± 0.96	0.82 ± 0.61	16.73 ± 0.62	7.14 ± 0.41	8.37 ± 0.80	${2.88}_{-0.04}^{+0.06}$	${8.84}_{-0.01}^{+0.02}$	${20.93}_{-0.87}^{+0.30}$	${1.60}_{-0.01}^{+0.00}$	${0.07}_{-0.00}^{+0.00}$	${8.21}_{-0.08}^{+0.07}$	$\lt 0.18$	${1.78}_{-0.21}^{+0.40}$
M1149	01468	177.406546	22.392860	1.89	−0.070 ± 0.040	23.54	0.37	2.71 ± 0.80	3.29 ± 0.39	2.58 ± 0.30	39.69 ± 0.31	⋯	⋯	${56.29}_{-6.27}^{+8.89}$	${6.22}_{-0.06}^{+0.05}$	${0.05}_{-0.01}^{+0.01}$	${0.00}_{-0.00}^{+0.00}$	${0.05}_{-0.00}^{+0.00}$	${7.92}_{-0.08}^{+0.08}$	$\lt 0.69$	${0.49}_{-0.24}^{+0.72}$
M1149	01704	177.398643	22.387499	2.28	0.020 ± 0.080	24.97	0.52	3.30 ± 0.30	0.83 ± 0.22	0.87 ± 0.21	7.86 ± 0.26	⋯	⋯	${2.66}_{-0.10}^{+0.07}$	${7.71}_{-0.08}^{+0.11}$	${1.11}_{-0.14}^{+0.24}$	${0.00}_{-0.00}^{+0.05}$	${0.04}_{-0.00}^{+0.00}$	${8.18}_{-0.10}^{+0.10}$	$\lt 0.36$	${3.86}_{-1.04}^{+3.49}$

Notes.

^aThe observed ${{JH}}_{140}$-band magnitude before accounting for lensing magnification. ^bThe reduction factor of ${{JH}}_{140}$-band flux after subtracting the nebular emission that falls within the corresponding wavelength window. ^cThe lensing magnification estimated from various mass models of galaxy clusters. For all HFF clusters, we use the Sharon & Johnson version 4corr models (Johnson et al. 2014). For all CLASH-only clusters, except RX J1347, we use the Zitrin PIEMD+eNFW version 2 models (Zitrin et al. 2015). For RX J1347, we use our own model built closely following the approach in Johnson et al. (2014). ^dThe flux ratio of $[{\rm{N}}\,{\rm\small{II}}]$ and Hα, estimated from the prescription of Faisst et al. (2018). This value is used to correct for the blended Hα–$[{\rm{N}}\,{\rm\small{II}}]$ fluxes in grism spectra, if necessary. ^eValues presented here are corrected for lensing magnification.

A machine-readable version of the table is available.

Download table as:  DataTypeset images: 1 2

Nevertheless, there indeed exist some galaxies in our sample that are highly anisotropically magnified. It is thus important to verify that the highly anisotropic lensing effect does not introduce significant systematic offset into their radial gradients measured in the image plane. For that purpose, we measure their radial gradients in the source plane using similar methods to those outlined in Section 3.6. Figure A1 shows such an analysis of one exemplary source in our sample, i.e., MACS 0717–ID 01131 at z = 1.85 with μ = 5.88. The image-plane morphology, shown in Figure B1, indicates that one of the two spatial directions is preferentially magnified. Here, unlike the procedures given in Figure B1, we first transform the observed 2D emission line maps of this galaxy into its source plane by ray-tracing each pixel to its source-plane position according to the lensing deflection fields given by the adopted macroscopic lens model. Then the weighted Voronoi tessellation technique (Cappellari & Copin 2003; Diehl & Statler 2006) is again adopted to divide the source-plane surface into spatial bins with a constant S/N of 5 on $[{\rm{O}}\,{\rm\small{III}}]$, the same as used in the gradient measurement in the image plane. Our forward-modeling Bayesian method of metallicity inference is conducted in each individual source-plane Voronoi bin to yield metallicity maps in the source plane.

Zoom In Zoom Out Reset image size

For the galactocentric distance scale of each individual source-plane Voronoi bin, we again rely on the 2D elliptical Gaussian function fit to the source-plane stellar mass surface density map of this galaxy²¹ (see the second panel in Figure A1). This fitting procedure yields the best-fit inclination, axis ratio, and major-axis orientation of the galaxy so that we not only take out the effect of lensing distortion but also take into account the projection effect when determining the source intrinsic morphology. At last, the radial gradient can be given by a linear regression to the metallicity estimates in all source-plane Voronoi bins.

For our exemplary differentially magnified source MACS 0717–ID 01131, the metallicity gradient measured in its source plane is ${\rm{\Delta }}\mathrm{log}({\rm{O}}/{\rm{H}})/{\rm{\Delta }}r=-0.031\pm 0.023\,[\mathrm{dex}\,{\mathrm{kpc}}^{-1}]$, in agreement at a 1σ confidence level with the gradient measured in the image plane, i.e., ${\rm{\Delta }}\mathrm{log}({\rm{O}}/{\rm{H}})/{\rm{\Delta }}r=-0.055\,\pm 0.028[\mathrm{dex}\,{\mathrm{kpc}}^{-1}]$ (shown in Figure B1 and given in Table A1). We verified that this difference (≲0.03 $\mathrm{dex}\,{\mathrm{kpc}}^{-1}$, compatible within 1σ) is typical for the few highly anisotropically magnified galaxies in our sample. In fact, the metallicity radial gradient measurement in this galaxy was presented in our previous work (Jones et al. 2015). Using half of the grism data (two orbits of G141 and five orbits of G102) available at that time, Jones et al. (2015) estimated the radial metallicity gradient of this galaxy to be $-0.03\pm 0.03\,\mathrm{dex}\,{\mathrm{kpc}}^{-1}$ from metallicities measured in individual spatial pixels and $-0.05\pm 0.05\,\mathrm{dex}\,{\mathrm{kpc}}^{-1}$ from metallicities derived in radial annuli. We see that our updated results derived in both the image and source planes presented in this work are compatible with previous measurements within the measurement uncertainties.

In Figure B1 and its online figure set, we present the source 1D/2D grism spectra, color-composite image, stellar surface density stamp, and emission line maps, as well as the metallicity map and radial metallicity gradient measurements for the entire sample. Following the conventions adopted in Figures 2 and 7, we first show the 1D and 2D G102–G141 spectra at two separate PAs. Note that due to grism defects and/or falling outside the WFC3 FoV, some sources (i.e., A2744–ID 00144, A2744–ID 01897, and RX J1347–ID 00664) only have coverage from one of the orients. Beneath the spectra, we show the source 2D stamps. For sources at z ≲ 1.6, we display their Hα map, whereas for sources at higher redshifts, the Hγ map is shown instead, since Hα has already redshifted out of the wavelength coverage of HST grisms. The bottom panels show the metallicity map and radial gradient measurements.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

View figure set (65 panels)

Tarball of figure set images