Physical properties of galaxies at z>7 are of interest for understanding both the early phases of star formation and the process of cosmic reionization. Chemical abundance measurements offer valuable information on the integrated star formation history, and hence ionizing photon production, as well as the rapid gas accretion expected at such high redshifts. We use reported measurements of [O III] 88$μ$m emission and star formation rate to estimate gas-phase oxygen abundances in five galaxies at z=7.1-9.1 using the direct T_e method. We find typical abundances 12+log(O/H) = 7.9 ($\sim$0.2 times the solar value) and an evolution of 0.9$\pm$0.5 dex in oxygen abundance at fixed stellar mass from z$\simeq$8 to 0. These results are compatible with theoretical predictions, albeit with large (conservative) uncertainties in both mass and metallicity. We assess both statistical and systematic uncertainties to identify promising means of improvement with the Atacama Large Millimeter Array (ALMA) and the James Webb Space Telescope (JWST). In particular we highlight [O III] 52$μ$m as a valuable feature for robust metallicity measurements. Precision of 0.1-0.2 dex in T_e-based O/H abundance can be reasonably achieved for galaxies at z$\approx$5-8 by combining [O III] 52$μ$m with rest-frame optical strong lines. It will also be possible to probe gas mixing and mergers via resolved T_e-based abundances on kpc scales. With ALMA and JWST, direct metallicity measurements will thus be remarkably accessible in the reionization epoch.
We report J-band MOSFIRE spectroscopy of a low-mass (log$(M_*/M_\odot)=8.62^{+0.10}_{-0.06}$) star-forming galaxy at $z=0.997$ showing the detection of [NII] and [SII] alongside a strong H$α$ line. We derive a gas-phase metallicity of log$(\text{O}/\text{H})=7.99^{+0.13}_{-0.23}$, placing this object in a region of $M_* - Z$ space that is sparsely populated at this redshift. Furthermore, many existing metallicity measurements in this $M_* - z$ regime are derived from only [NII]/H$α$ (N2), a diagnostic widely used in high-redshift metallicity studies despite the known strong degeneracy with the…
We introduce ProSpect, a generative galaxy spectral energy distribution (SED) package that encapsulates the best practices for SED methodologies in a number of astrophysical domains. ProSpect comes with two popular families of stellar population libraries (BC03 and EMILES), and a large variety of methods to construct star formation and metallicity histories. It models dust through the use of a Charlot & Fall attenuation model, with re-emission using Dale far-infrared templates. It also has the ability to model AGN through the inclusion of a simple AGN and hot torus model. Finally, it makes use…
We analyse the metallicity histories of ~4,500 galaxies from the GAMA survey at z<0.06 modelled by the SED-fitting code ProSpect using an evolving metallicity implementation. These metallicity histories, in combination with the associated star formation histories, allow us to analyse the inferred gas-phase mass--metallicity relation. Furthermore, we extract the mass--metallicity relation at a sequence of epochs in cosmic history, to track the evolving mass--metallicity relation with time. Through comparison with observations of gas-phase metallicity over a large range of redshifts, we show tha…
The [OIII] 88 $μ$m fine structure emission line has been detected into the Epoch of Reionization (EoR) from star-forming galaxies at redshifts $6 < z \lesssim 9$ with ALMA. These measurements provide valuable information regarding the properties of the interstellar medium (ISM) in the highest redshift galaxies discovered thus far. The [OIII] 88 $μ$m line observations leave, however, a degeneracy between the gas density and metallicity in these systems. Here we quantify the prospects for breaking this degeneracy using future ALMA observations of the [\oiii] 52 $μ$m line. Among the current set o…
The metallicity spread, or the metallicity trend along the evolutionary sequence of a globular cluster, is a rich source of information to help understand the cluster physics (e.g. multiple populations) and stellar physics (e.g. atomic diffusion). Low-resolution integral-field-unit spectroscopy in the optical with the MUSE is an attractive prospect if it can provide these diagnostics because it allows us to extract spectra of a large fraction of the cluster stars. We investigate the possibilities of full-spectrum fitting to derive stellar parameters and chemical abundances at low spectral reso…
Gas-phase metallicities of galaxies are typically measured through auroral or nebular emission lines, but metallicity also leaves an imprint on the overall spectral energy distribution (SED) of a galaxy and can be estimated through SED fitting. We use the ProSpect SED fitting code with a flexible parametric star formation history and an evolving metallicity history to self-consistently measure metallicities, stellar mass, and other galaxy properties for $\sim90\,000$ galaxies from the Deep Extragalactic VIsible Legacy Survey (DEVILS) and Galaxy and Mass Assembly (GAMA) survey. We use these to …
The prospects for using the present-day data on metallicity of globular clusters (GCs) of the Galaxy to put constraints on the distance to the Galactic center, $R_0$, are considered. We have found that the GCs of the metal-rich and metal-poor subsystems separately form a bar-like structure in metallicity maps whose parameters are very close to those for the Galactic bar. The results indicate the existence of a bar component within both the metal-rich and metal-poor subsystems of GCs. The bar GCs could have formed within the already existing Galactic bar or could have later been locked in reson…
We investigate how HII region temperature structure assumptions affect "direct-method" spatially-resolved metallicity observations using multispecies auroral lines in a galaxy from the SAMI Galaxy Survey. SAMI609396B, at redshift $z=0.018$, is a low-mass galaxy in a minor merger with intense star formation, analogous to conditions at high redshifts. We use three methods to derive direct metallicities and compare with strong-line diagnostics. The spatial metallicity trends show significant differences among the three direct methods. Our first method is based on the commonly used electron temper…
We study the direct gas-phase oxygen abundance using the well-detected auroral [OIII]4363 line in the stacked spectra of a sample of local analogs of high-redshift galaxies. These local analogs share the same location as $z\sim2$ star-forming galaxies on the Baldwin-Phillips-Terlevich diagram. This type of analog has the same ionized interstellar medium (ISM) properties as high-redshift galaxies. We establish empirical metallicity calibrations between the direct gas-phase oxygen abundances ($7.8<12+\log(\rm{O/H})<8.4$) and the N2/O3N2 indices in our local analogs. We find significant systemati…
A promising supermassive black hole seed formation channel is that of direct collapse from primordial gas clouds. We perform a suite of 3D hydrodynamics simulations of an isolated turbulent gas cloud to investigate conditions conducive to forming massive black hole seeds via direct collapse, probing the impact of cloud metallicity, gas temperature floor and cooling physics on cloud fragmentation. We find there is no threshold in metallicity which produces a sharp drop in fragmentation. When molecular cooling is not present, metallicity has little effect on fragmentation. When molecular cooling…
We present a direct determination of the stellar metallicity in the close pair galaxy NGC~4038 (D = 20 Mpc) based on the quantitative analysis of moderate resolution KMOS/VLT spectra of three super star clusters (SSCs). The method adopted in our analysis has been developed and optimised to measure accurate metallicities from atomic lines in the $J$-band of single red supergiant (RSG) or RSG-dominated star clusters. Hence, our metallicity measurements are not affected by the biases and poorly understood systematics inherent to strong line HII methods which are routinely applied to massive data …
We present electron temperature ($T_e$) maps for the edge-on system Mrk 1486, affording "direct-method" gas-phase metallicity measurements across $5.\!\!^{\prime\prime}8$ (4.1 kpc) along the minor axis and $9.\!\!^{\prime\prime}9$ (6.9 kpc) along the major axis. These maps, enabled by strong detections of the [OIII]$λ$4363 auroral emission line across a large spatial extent of Mrk 1486, reveal a clear negative minor axis $T_e$ gradient in which temperature decreases with increasing distance from the disk plane. We find that the lowest metallicity spaxels lie near the extremes of the major axis…
We present the first direct determination of a stellar metallicity in the spiral galaxy NGC4258 (D=7.6 Mpc) based on the quantitative analysis of a low-resolution (~5 AE) Keck LRIS spectrum of a blue supergiant star located in its disk. A determination of stellar metallicity in this galaxy is important for the absolute calibration of the Cepheid Period-Luminosity relation as an anchor for the extragalactic distance scale and for a better characterization of its dependence as a function of abundance. We find a value 0.2 dex lower than solar metallicity at a galactocentric distance of 8.7 kpc, i…
We apply the spectral energy distribution (SED) fitting code ProSpect to multiwavelength imaging for $\sim$7,000 galaxies from the GAMA survey at $z<0.06$, in order to extract their star formation histories. We combine a parametric description of the star formation history with a closed-box evolution of metallicity where the present-day gas-phase metallicity of the galaxy is a free parameter. We show with this approach that we are able to recover the observationally determined cosmic star formation history (CSFH), an indication that stars are being formed in the correct epoch of the Universe, …
A galaxy's metallicity provides a record of star formation, gas accretion, and gas outflow, and is therefore one of the most informative measurements that can be made at high redshift. It is also one of the most difficult. I review methods of determining chemical abundances in distant star-forming galaxies, and summarize results for galaxies at 1<z<3. I then focus on the mass-metallicity relation, its evolution with redshift, and its uses in constraining inflows and outflows of gas, and conclude with a brief discussion of future prospects for metallicity measurements at high redshift.
Cold accretion is a primary growth mechanism of simulated galaxies, yet observational evidence of "cold flows" at redshifts where they should be most efficient ($z=2$-4) is scarce. In simulations, cold streams manifest as Lyman-limit absorption systems (LLSs) with low heavy-element abundances similar to those of the diffuse IGM. Here we report on an abundance survey of 17 H I-selected LLSs at $z=3.2$-4.4 which exhibit no metal absorption in SDSS spectra. Using medium-resolution spectra obtained at Magellan, we derive ionization-corrected metallicities (or limits) with a Markov-Chain Monte Carl…
We examine the metallicity distribution of the Galactic thick disk using F, G, and K dwarf stars selected from the Sloan Digital Sky Survey, Data Release 8. Using the large sample of dwarf stars with proper motions and spectroscopically determined stellar parameters, metallicity gradients in the radial direction for various heights above the Galactic plane and in the vertical direction for various radial distances from the Galaxy center have been found. In particular, we find a vertical metallicity gradient of -0.113 +/- 0.010 (-0.125 +/- 0.008) dex/kpc using an isochrone (photometric) distanc…
From our recent catalog based on the first Gaia data release (TGAS), we select wide binaries in which both stars have been observed by the Radial Velocity Experiment (RAVE) or the Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST). Using RAVE and LAMOST metallicities and RAVE Mg, Al, Si, Ti, and Fe abundances, we find that the differences in the metallicities and elemental abundances of components of wide binaries are consistent with being due to observational uncertainties, in agreement with previous results for smaller and more restricted samples. The metallicity and elementa…
We present the first direct calibration of strong-line metallicity diagnostics at significant cosmological distances using a sample at z=0.8 drawn from the DEEP2 Galaxy Redshift Survey. Oxygen and neon abundances are derived from measurements of electron temperature and density. We directly compare various commonly used relations between gas-phase metallicity and strong line ratios of O, Ne, and H at z=0.8 and z=0. There is no evolution with redshift at high precision ($Δ\log{\mathrm{O/H}} = -0.01\pm0.03$, $Δ\log{\mathrm{Ne/O}} = 0.01 \pm 0.01$). O, Ne, and H line ratios follow the same locus …
(Abridged) Combining the deepest Herschel extragalactic surveys (PEP, GOODS-H, HerMES), and Monte Carlo mock catalogs, we explore the robustness of dust mass estimates based on modeling of broad band spectral energy distributions (SEDs) with two popular approaches: Draine & Li (2007, DL07) and a modified black body (MBB). As long as the observed SED extends to at least 160-200 micron in the rest frame, M(dust) can be recovered with a >3 sigma significance and without the occurrence of systematics. An average offset of a factor ~1.5 exists between DL07- and MBB-based dust masses, based on consi…
Two recent empirical developments in the study of extragalactic globular cluster (GC) populations are the color-magnitude relation of the blue GCs (the "blue tilt") and the nonlinearity of the dependence of optical GC colors on metallicity. The color-magnitude relation, interpreted as a mass-metallicity relation, is thought to be a consequence of self-enrichment. Nonlinear color-metallicity relations have been shown to produce bimodal color distributions from unimodal metallicity distributions. We simulate GC populations including both a mass-metallicity scaling relation and nonlinear color-me…
We analyse the chemical properties of three z~8 galaxies behind the galaxy cluster SMACS J0723.3-7327, observed as part of the Early Release Observations programme of the James Webb Space Telescope (JWST). Exploiting [O III]4363 auroral line detections in NIRSpec spectra, we robustly apply the direct Te method for the very first time at such high redshift, measuring metallicities ranging from extremely metal poor (12+log(O/H)~7) to about one-third solar. We also discuss the excitation properties of these sources, and compare them with local strong-line metallicity calibrations. We find that no…
In this study we focus on the $z\sim6.6$ Lyman-$α$ CR7 consisting of clump A that is host to a potential direct collapse black hole (DCBH), and two metal enriched star forming clumps B and C. In contrast to claims that signatures of metals rule out the existence of DCBHs, we show that metal pollution of A from star forming clumps clumps B and C is inevitable, and that A can form a DCBH well before its metallicity exceeds the critical threshold of $10^{-5}-10^{-6}\ \rm Z_{\odot}$. Assuming metal mixing happens instantaneously, we derive the metallicity of A based on the star formation history o…
The gas metallicity of galaxies is often estimated using strong emission lines such as the optical lines of [OIII] and [OII]. The most common measure is "R23", defined as ([OII]$λ$$λ$3726, 3729 + [OIII]$λ$$λ$4959,5007)/H$β$. Most calibrations for these strong-line metallicity indicators are for continuum selected galaxies. We report a new empirical calibration of R23 for extreme emission-line galaxies using a large sample of about 800 star-forming green pea galaxies with reliable T$_e$-based gas-phase metallicity measurements. This sample is assembled from Sloan Digital Sky Survey (SDSS) Data …
We review the present methodology for the use of Sulfur as global metallicity tracer in galaxies, which allows performing a complete abundance analysis using mainly the red to near infrared spectral region, and extending the range of directly derived abundances up to 5 times the S solar photospheric value. The empirical calibration of Sulfur via the S23 parameter is also reviewed.
We have constructed a catalog containing best available astrometric, photometric, radial velocity and astrophysical data for mainly F-type and G-type stars (called the Astrometric catalog associated with Astrophysical Data, ACAD), which contains 27,553 records, and is used for the purpose of analyzing the stellar kinematics in the Solar neighborhood. Using the Lindblad-Oort Model and compiled ACAD, we calculated the Solar motion and Oort constants in different age/metallicity bins. The evolution of kinematical parameters with stellar age and metallicity were investigated directly. The results …
We investigate archaeologically how the metallicity in both stellar and gaseous components of spiral galaxies of differing masses evolve with time, using data from the SDSS-IV MaNGA survey. For the stellar component, we can measure this evolution directly by decomposing the galaxy absorption-line spectra into populations of different ages and determining their metallicities. For the gaseous component, we can only measure the present-day metallicity directly from emission lines. However, there is a well-established relationship between gas metallicity, stellar mass and star formation rate which…
We present spectra of 14 A-type supergiants in the metal-rich spiral galaxy M83. We derive stellar parameters and metallicities, and measure a spectroscopic distance modulus m-M = 28.47 +\- 0.10 (4.9 +\- 0.2 Mpc), in agreement with other methods. We use the stellar characteristic metallicity of M83 and other systems to discuss a version of the galaxy mass-metallicity relation that is independent of the analysis of nebular emission lines and the associated systematic uncertainties. We reproduce the radial metallicity gradient of M83, which flattens at large radii, with a chemical evolution mode…
A Glimpse of the Low-Mass End of the Direct Mass-Metallicity Relation at $z\sim6-8$
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Institut d’Astrophysique de Paris, CNRS, Sorbonne Université（巴黎天体物理研究所，法国国家科学研究中心，索邦大学）；MIT Kavli Institute for Astrophysics and Space Research（麻省理工学院卡弗里天体物理与空间研究所）；University of Toronto（多伦多大学）
The ubiquity of substructure in the stellar halo has already been demonstrated by the SDSS and 2MASS and future surveys promise to explore the halo in ever more detail. This paper examines what can be learnt from current and future photometric-databases using group-finding techniques. We compare groups recovered from a sample of M-giants from 2MASS with those found in synthetic surveys of simulated $Λ$CDM stellar halos and demonstrate broad consistency. We also find that these recovered groups are likely to represent the majority of high-luminosity ($\log(L/L_{Sun})>6.67$) satellites accreted …
We use integral field spectroscopic (IFS) observations from the Gemini North Multi-Object Spectrograph (GMOS-N) to study the central H II region in a nearby blue compact dwarf (BCD) galaxy NGC 4449. The IFS data enable us to explore the variation of physical and chemical conditions of the star-forming region and the surrounding gas on spatial scales as small as 5.5 pc. Our kinematical analysis shows possible signatures of shock ionisation and shell structures in the surroundings of the star-forming region. The metallicity maps of the region, created using direct T$_e$ and indirect strong line …
The relative abundances of the Fe-peak elements (Ti-Zn) at the lowest metallicities are intimately linked to the physics of core-collapse supernova explosions. With a sample of 25 very metal-poor damped Lyman-alpha systems, we investigate the trends of the Fe-peak element ratios with metallicity. For nine of the 25 DLAs, a direct measurement (or useful upper limit) of one or more of the Ti,Cr,Co,Ni,Zn/Fe abundance ratios could be determined from detected absorption lines. For the remaining systems (without detections), we devised a new form of spectral stacking to estimate the typical Fe-peak …
DIISC-VII: Linking Radial Gas Motions to Anomalously Low Metallicity Star-forming Regions in the XUV Disk of NGC 3344
Arizona State University（亚利桑那州立大学）；Università di Firenze（佛罗伦萨大学）；INAF - Osservatorio Astrofisico di Arcetri（意大利国家天体物理研究所阿切特里天文台）；Inter-University Centre for Astronomy and Astrophysics（大学间天文与天体物理中心）；University of California, San Diego（加州大学圣地亚哥分校）；Eureka Scientific Inc.（尤里卡科学公司）；National Radio Astronomy Observatory（美国国家射电天文台）
Galaxy metallicity scaling relations provide a powerful tool for understanding galaxy evolution, but obtaining unbiased global galaxy gas-phase oxygen abundances requires proper treatment of the various line-emitting sources within spectroscopic apertures. We present a model framework that treats galaxies as ensembles of HII and diffuse ionized gas (DIG) regions of varying metallicities. These models are based upon empirical relations between line ratios and electron temperature for HII regions, and DIG strong-line ratio relations from SDSS-IV MaNGA IFU data. Flux-weighting effects and DIG con…
Unveiling the Cosmic Chemistry II: "Direct" $T_e$-based metallicity of galaxies at 3 $< z <$ 10 with JWST/NIRSpec
Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology（麻省理工学院卡弗里天体物理学与空间研究研究所）；University of Kentucky（肯塔基大学）；University of Virginia（弗吉尼亚大学）
Direct T_e-based Metallicities of z=2-9 Galaxies with JWST/NIRSpec: Empirical Metallicity Calibrations Applicable from Reionization to Cosmic Noon
University of Kentucky（肯塔基大学）；University of California, Davis（加州大学戴维斯分校）；University of California, Los Angeles（加州大学洛杉矶分校）；University of Arizona（亚利桑那大学）；University of California, Riverside（加州大学河滨分校）；Cosmic Dawn Center (DAWN)（宇宙黎明中心）；Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所）
We report a method of identifying candidate low-metallicity blue compact dwarf galaxies (BCDs) from the Sloan Digital Sky Survey (SDSS) imaging data and present 3-m Lick Observatory and 10-m W.M. Keck Observatory optical spectroscopic observations of 94 new systems that have been discovered with this method. The candidate BCDs are selected from Data Release 12 (DR12) of SDSS based on their photometric colors and morphologies. Using the Kast spectrometer on the 3-m telescope, we confirm that the candidate low-metallicity BCDs are emission-line galaxies and we make metallicity estimates using th…
We present an abundance analysis of seven super-star clusters in the disk of M83. The near-infrared spectra of these clusters are dominated by Red Supergiants, and the spectral similarity in the J-band of such stars at uniform metallicity means that the integrated light from the clusters may be analysed using the same tools as those applied to single stars. Using data from VLT/KMOS we estimate metallicities for each cluster in the sample. We find that the abundance gradient in the inner regions of M83 is flat, with a central metallicity of [Z] = 0.21$\pm$0.11 relative to a Solar value of $Z_\o…
Hydroxyl ($\rm OH$) is known to form efficiently in cold gas ($T\sim 100$K) along with the molecule $\rm H_2$ and can be used as an efficient tracer of the diffuse molecular gas in the interstellar medium (ISM). Using a simple formalism describing the $\rm H\,I/H_2$ transition and a reduced network of major chemical reactions, we present a semi-analytical prescription to estimate the abundances of O-bearing molecules in the diffuse ISM. We show that predictions based on our prescription are in good agreement with the estimates obtained using the MEUDON PDR code which utilizes the full reaction…
Our research on the age-metallicity and mass-metallicity relations of galaxies is presented and compared to the most recent investigations in the field. We have been able to measure oxygen abundances using the direct method for objects spanning four orders of magnitude in mass, and probing the last 4 Gyr of galaxy evolution. We have found preliminary evidence that the metallicity evolution is consistent with expectations based on age-metallicity relations obtained with low resolution stellar spectra of resolved Local Group galaxies.
The origin of the blue supergiant (BSG) progenitor of Supernova (SN) 1987A has long been debated, along with the role that its sub-solar metallicity played. We now have a sample of 1987A-like SNe that arise from the core collapse (CC) of BSGs. The metallicity of the explosion sites of the known BSG SNe is investigated, as well as their association to star-forming regions. Both indirect and direct metallicity measurements of 13 BSG SN host galaxies are presented, and compared to those of other CC SN types. Indirect measurements are based on the known luminosity-metallicity relation and on publi…
Low metallicity stars give rise to unique spectacular transients and are of immense interest for understanding stellar evolution. Their importance has only grown further with the recent detections of mergers of stellar mass black holes that likely originate mainly from low metallicity progenitor systems. Moreover, the formation of low metallicity stars is intricately linked to galaxy evolution, in particular to early enrichment and to later accretion and mixing of lower metallicity gas. Because low metallicity stars are difficult to observe directly, cosmological simulations are crucial for un…
We investigate the upper stellar mass limit set by radiative feedback by the forming star with various accretion rates and metallicities. To this end, we numerically solve the structures of both a protostar and its surrounding accretion envelope assuming a spherical symmetric and steady flow. The optical depth of the dust cocoon, a dusty part of the accretion envelope, differs among the direct light from the stellar photosphere and the diffuse light re-emitted as dust thermal emission. As a result, varying the metallicity qualitatively changes the way that the radiative feedback suppresses the…
There is now strong evidence that Long-duration Gamma-Ray Bursts (LGRBs) are preferentially formed in low-metallicity environments. However, the magnitude of this effect, and its functional dependence on metallicity have not been well characterized. In our previous paper, Graham & Fruchter (2013), we compared the metallicity distribution of LGRB host galaxies to the that of star forming galaxies in the local universe. Here we build upon this work by in effect dividing one distribution by the other, and thus directly determine the relative rate of LGRB formation as a function of metallicity in …
Size differences of approx. 20% between red (metal-rich) and blue (metal-poor) sub-populations of globular clusters have been observed, generating an ongoing debate as to weather these originate from projection effects or the difference in metallicity. We present direct N-body simulations of metal-rich and metal-poor stellar populations evolved to study the effects of metallicity on cluster evolution. The models start with N = 100000 stars and include primordial binaries. We also take metallicity dependent stellar evolution and an external tidal field into account. We find no significant diffe…
The rate of long-duration gamma ray bursts (GRBs) has been identified as a potential proxy for the star formation rate (SFR) across redshift, but the exact relationship depends on GRB progenitor models (single versus binary). The single-progenitor collapsar model accounts for the preference towards low-metallicity GRB progenitors, but is in apparent tension with some high-metallicity GRB host galaxy measurements. As a possible solution, we consider the scenario where high-metallicity GRB hosts harbour low metallicity regions in which GRB progenitors form. For this, we use the IllustrisTNG cosm…
The late assembly of massive galaxies is thought to be dominated by stellar accretion in their outskirts (beyond 2 effective radii Re) due to dry, minor galaxy mergers. We use observations of 1010 passive early-type galaxies (ETGs) within z<0.15 from SDSS IV MaNGA to search for evidence of this accretion. The outputs from the stellar population fitting codes FIREFLY, pPXF, and Prospector are compared to control for systematic errors in stellar metallicity (Z) estimation. We find that the average radial logZ/Zsun profiles of ETGs in various stellar mass (M) bins are not linear. As a result, the…
