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Marijn Franx

Publications and source records attributed to Marijn Franx.

At least 37 records · Page 2Linked to original sources
arXiv2024

Medium Bands, Mega Science: a JWST/NIRCam Medium-Band Imaging Survey of Abell 2744

In this paper, we describe the "Medium Bands, Mega Science" JWST Cycle 2 survey (JWST-GO-4111) and demonstrate the power of these data to reveal both the spatially-integrated and spatially-resolved properties of galaxies from the local universe to the era of cosmic dawn. Executed in November 2023, MegaScience obtained ~30 arcmin^2 of deep multiband NIRCam imaging centered on the z~0.3 Abell 2744 cluster, including eleven medium-band filters and the two shortest-wavelength broad-band filters, F070W and F090W. Together, MegaScience and the UNCOVER Cycle 1 treasury program provide a complete set of deep (~28-30 mag) images in all NIRCam medium- and broad-band filters. This unique dataset allows us to precisely constrain photometric redshifts, map stellar populations and dust attenuation for large samples of distant galaxies, and examine the connection between galaxy structures and formation histories. MegaScience also includes ~17 arcmin^2 of NIRISS parallel imaging in two broad-band and four medium-band filters from 0.9-4.8um, expanding the footprint where robust spectral energy distribution (SED) fitting is possible. We provide example SEDs and multi-band cutouts at a variety of redshifts, and use a catalog of JWST spectroscopic redshifts to show that MegaScience improves both the scatter and catastrophic outlier rate of photometric redshifts by factors of 2-3. Additionally, we demonstrate the spatially-resolved science enabled by MegaScience by presenting maps of the [OIII] line emission and continuum emission in three spectroscopically-confirmed z>6 galaxies. We show that line emission in reionization-era galaxies can be clumpy, extended, and spatially offset from continuum emission, implying that galaxy assembly histories are complex even at these early epochs. We publicly release fully reduced mosaics and photometric catalogs for both the NIRCam primary and NIRISS parallel fields.

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arXiv2024

The UNCOVER Survey: A First-look HST+JWST Catalog of Galaxy Redshifts and Stellar Population Properties Spanning $0.2 \lesssim z \lesssim 15$

The recent UNCOVER survey with the James Webb Space Telescope (JWST) exploits the nearby cluster Abell 2744 to create the deepest view of our universe to date by leveraging strong gravitational lensing. In this work, we perform photometric fitting of more than 50,000 robustly detected sources out to $z \sim 15$. We show the redshift evolution of stellar ages, star formation rates, and rest-frame colors across the full range of $0.2 \lesssim z \lesssim 15$. The galaxy properties are inferred using the Prospector Bayesian inference framework using informative Prospector-$β$ priors on masses and star formation histories to produce joint redshift and stellar population posteriors, and additionally lensing magnification is performed on-the-fly to ensure consistency with the scale-dependent priors. We show that this approach produces excellent photometric redshifts with $σ_{\rm NMAD} \sim 0.03$, of a similar quality to the established photometric redshift code EAzY. In line with the open-source scientific objective of the Treasury survey, we publicly release the stellar population catalog with this paper, derived from the photometric catalog adapting aperture sizes based on source profiles. This release includes posterior moments, maximum-likelihood spectra, star-formation histories, and full posterior distributions, offering a rich data set to explore the processes governing galaxy formation and evolution over a parameter space now accessible by JWST.

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arXiv2023

Ionised gas kinematics and dynamical masses of $z\gtrsim6$ galaxies from JADES/NIRSpec high-resolution spectroscopy

We explore the kinematic gas properties of six $5.5 1$ thus far. The cold gas masses implied by the observed star formation rates are $\sim 10\times$ larger than the stellar masses. We find that their ionised gas is spatially resolved by JWST, with evidence for broadened lines and spatial velocity gradients. Using a simple thin-disc model, we fit these data with a novel forward modelling software that accounts for the complex geometry, point spread function, and pixellation of the NIRSpec instrument. We find the sample to include both rotation- and dispersion-dominated structures, as we detect velocity gradients of $v(r_{\rm e})\approx100-150\,{\rm km\,s^{-1}}$, and find velocity dispersions of $σ_0\approx 30-70\,{\rm km\,s^{-1}}$ that are comparable to those at cosmic noon. The dynamical masses implied by these models ($M_{\rm dyn}\sim10^{9-10}\,{\rm M_\odot}$) are larger than the stellar masses by up to a factor 40, and larger than the total baryonic mass (gas + stars) by a factor of $\sim 3$. Qualitatively, this result is robust even if the observed velocity gradients reflect ongoing mergers rather than rotating discs. Unless the observed emission line kinematics is dominated by outflows, this implies that the centres of these galaxies are dark-matter dominated or that star formation is $3\times$ less efficient, leading to higher inferred gas masses.

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arXiv2023

A census of star formation histories of massive galaxies at 0.6 < z < 1 from spectro-photometric modeling using Bagpipes and Prospector

We present individual star-formation histories of $\sim3000$ massive galaxies (log($\mathrm{M_*/M_{\odot}}$) > 10.5) from the Large Early Galaxy Astrophysics Census (LEGA-C) spectroscopic survey at a lookback time of $\sim$7 billion years and quantify the population trends leveraging 20hr-deep integrated spectra of these $\sim$ 1800 star-forming and $\sim$ 1200 quiescent galaxies at 0.6 < $z$ < 1.0. Essentially all galaxies at this epoch contain stars of age < 3 Gyr, in contrast with older massive galaxies today, facilitating better recovery of previous generations of star formation at cosmic noon and earlier. We conduct spectro-photometric analysis using parametric and non-parametric Bayesian SPS modeling tools - Bagpipes and Prospector to constrain the median star-formation histories of this mass-complete sample and characterize population trends. A consistent picture arises for the late-time stellar mass growth when quantified as $t_{50}$ and $t_{90}$, corresponding to the age of the universe when galaxies formed 50\% and 90\% of their total stellar mass, although the two sets of models disagree at the earliest formation times (e.g. $t_{10}$). Our results reveal trends in both stellar mass and stellar velocity dispersion as in the local universe - low-mass galaxies with shallower potential wells grow their stellar masses later in cosmic history compared to high-mass galaxies. Unlike local quiescent galaxies, the median duration of late-time star-formation ($τ_{SF,late}$ = $t_{90}$ - $t_{50}$) does not consistently depend on the stellar mass. This census sets a benchmark for future deep spectro-photometric studies of the more distant universe.

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arXiv2023

The UNCOVER Survey: A first-look HST+JWST catalog of 60,000 galaxies near Abell 2744 and beyond

In November 2022, the James Webb Space Telescope (JWST) returned deep near-infrared images of Abell 2744 -- a powerful lensing cluster capable of magnifying distant, incipient galaxies beyond it. Together with the existing Hubble Space Telescope (HST) imaging, this publicly available dataset opens a fundamentally new discovery space to understand the remaining mysteries of the formation and evolution of galaxies across cosmic time. In this work, we detect and measure some 60,000 objects across the 49 arcmin$^2$ JWST footprint down to a $5\,σ$ limiting magnitude of $\sim$30 mag in 0.32" apertures. Photometry is performed using circular apertures on images matched to the point spread function of the reddest NIRCam broad band, F444W, and cleaned of bright cluster galaxies and the related intra-cluster light. To give an impression of the photometric performance, we measure photometric redshifts and achieve a $σ_{\rm NMAD}\approx0.03$ based on known, but relatively small, spectroscopic samples. With this paper, we publicly release our HST and JWST PSF-matched photometric catalog with optimally assigned aperture sizes for easy use, along with single aperture catalogs, photometric redshifts, rest-frame colors, and individual magnification estimates. These catalogs will set the stage for efficient and deep spectroscopic follow-up of some of the first JWST-selected samples in Summer 2023.

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arXiv2023

JWST/NIRSpec Measurements of Extremely Low Metallicities in High Equivalent Width Lyman-$α$ Emitters

Deep VLT/MUSE optical integral field spectroscopy has recently revealed an abundant population of ultra-faint galaxies ($M_{UV} \approx -15$; 0.01 $L_{\star}$) at $z=$2.9$-$6.7 due to their strong Lyman-$α$ emission with no detectable continuum. The implied Lyman-$α$ equivalent widths can be in excess of 100-200 Angstrom, challenging existing models of normal star formation and indicating extremely young ages, small stellar masses, and a very low amount of metal enrichment. We use JWST/NIRSpec's microshutter array to follow-up 45 of these galaxies (11h in G235M/F170LP and 7h in G395M/F290LP), as well as 45 lower-equivalent width Lyman-$α$ emitters. Our spectroscopy covers the range 1.7$-$5.1 micron in order to target strong optical emission lines: H$α$, [N II], [O III], and H$β$. Individual measurements as well as stacks reveal line ratios consistent with a metal poor nature (2$-$40% $Z_{\odot}$, depending on the calibration). The galaxies with the highest equivalent widths of Lyman-$α$, in excess of 90 Angstrom, have lower [N II]/H$α$ (1.9-$σ$) and [O III]/H$β$ (2.2-$σ$) ratios than those with lower equivalent widths, implying lower gas-phase metallicities at a combined significance of 2.4-$σ$. This implies a selection based on Lyman-$α$ equivalent width is an efficient technique for identifying younger, less chemically enriched systems.

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arXiv2023

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

We examine the wavelength dependence of radial light profiles based on Sérsic index $n$ measurements of 1067 galaxies with M$_*\geq$ 10$^{9.5}$M$_\odot$ and in the redshift range $0.5 < z < 3$. The sample and rest-frame optical light profiles are drawn from CANDELS$+$3D-HST; rest-frame near-infrared light profiles are inferred from CEERS JWST/NIRCam imaging. $n$ shows only weak dependence on wavelength, regardless of redshift, galaxy mass and type: on average, star-forming galaxies have $n = 1-1.5$ and quiescent galaxies have $n = 3-4$ in the rest-frame optical and near-infrared. The strong correlation at all wavelengths between $n$ and star-formation activity implies a physical connection between the radial stellar mass profile and star-formation activity. The main caveat is that the current sample is too small to discern trends for the most massive galaxies (M$_* > 10^{11}M_\odot$).

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arXiv2023

Stellar Half-Mass Radii of $0.5<z<2.3$ Galaxies: Comparison with JWST/NIRCam Half-Light Radii

We use CEERS JWST/NIRCam imaging to measure rest-frame near-IR light profiles of $>$500 $M_\star>10^{10}~M_\odot$ galaxies in the redshift range $0.5 10^{11}~M_\odot$) quiescent galaxies between $z=0.5$ and $z=2.3$, again comparing $R_{\rm{opt}}$, \rmass~and \rmassd. We conclude that the main tenets of the size evolution narrative established over the past 20 years, based on rest-frame optical light profile analysis, still hold in the era of JWST/NIRCam observations in the rest-frame near-IR.

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arXiv2023

UNCOVER: Candidate Red Active Galactic Nuclei at 3<z<7 with JWST and ALMA

The James Webb Space Telescope (JWST) is revolutionizing our knowledge of $z>5$ galaxies and their actively accreting black holes. Using the JWST Cycle 1 Treasury program Ultradeep NIRSpec and NIRCam ObserVations before the Epoch of Reionization (UNCOVER) in the lensing field Abell 2744, we report the identification of a sample of little red dots at $3 < z_{\rm{phot}} < 7$ that likely contain highly-reddened accreting supermassive black holes. Using a NIRCam-only selection to F444W$<27.7$ mag, we find 26 sources over the $\sim45$ arcmin$^{2}$ field that are blue in F115W$-$F200W$\sim0$ (or $β_{\rm UV}\sim-2.0$ for $f_λ \propto λ^β$), red in F200W$-$F444W = $1-4$ ($β_{\rm opt} \sim +2.0$), and are dominated by a point-source like central component. Of the 20 sources with deep ALMA 1.2-mm coverage, none are detected individually or in a stack. For the majority of the sample, SED fits to the JWST+ALMA observations prefer models with hot dust rather than obscured star-formation to reproduce the red NIRCam colors and ALMA 1.2-mm non-detections. While compact dusty star formation can not be ruled out, the combination of extremely small sizes ($\langle r_e \rangle\approx50$ pc after correction for magnification), red rest-frame optical slopes, and hot dust can by explained by reddened broad-line active galactic nuclei (AGNs). Our targets have faint $M_{\rm 1450} \approx -14\ \, {\rm to} -18$ mag but inferred bolometric luminosities of $L_{\rm bol} = 10^{43}-10^{46}$ erg/s, reflecting their obscured nature. If the candidates are confirmed as AGNs with upcoming UNCOVER spectroscopy, then we have found an abundant population of reddened luminous AGN that are at least ten times more numerous than UV-luminous AGN at the same intrinsic bolometric luminosity.

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arXiv2023

JWST UNCOVER: Extremely red and compact object at$z_{\mathrm{phot}}\simeq7.6$ triply imaged by Abell 2744

Recent JWST/NIRCam imaging taken for the ultra-deep UNCOVER program reveals a very red dropout object at $z_{\mathrm{phot}}\simeq7.6$, triply imaged by the galaxy cluster Abell 2744 ($z_{\mathrm{d}}=0.308$). All three images are very compact, i.e. unresolved, with a de-lensed size upper-limit of $r_{e}\lesssim35$ pc. The images have apparent magnitudes of $m_{\mathrm{F444W}}\sim25-26$ AB, and the magnification-corrected absolute UV magnitude of the source is $M_{\mathrm{UV},1450}=-16.81\pm0.09$. From the sum of observed fluxes and from a spectral energy distribution (SED) analysis, we obtain estimates of the bolometric luminosities of the source of $L_{\mathrm{bol}}\gtrsim10^{43} \frac{\mathrm{erg}}{\mathrm{s}}$ and $L_{\mathrm{bol}}\sim10^{44}-10^{46} \frac{\mathrm{erg}}{\mathrm{s}}$, respectively. Based on its compact, point-like appearance, its position in color-color space and the SED analysis, we tentatively conclude that this object is a UV-faint dust-obscured quasar-like object, i.e. an active galactic nucleus (AGN) at high redshift. We also discuss other alternative origins for the object's emission features, including a massive star cluster, Population III, supermassive, or dark stars, or a direct-collapse black hole. Although populations of red galaxies at similar photometric redshifts have been detected with JWST, this object is unique in that its high-redshift nature is corroborated geometrically by lensing, that it is unresolved despite being magnified -- and thus intrinsically even more compact -- and that it occupies notably distinct regions in both size-luminosity and color-color space. Planned UNCOVER JWST/NIRSpec observations, scheduled in Cycle 1, will enable a more detailed analysis of this object.

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arXiv2023

UNCOVERing the extended strong lensing structures of Abell 2744 with the deepest JWST imaging

We present a new parametric lens model for the massive galaxy cluster Abell~2744 based on the new ultra-deep JWST imaging taken in the framework of the UNCOVER program. These observations constitute the deepest JWST images of a lensing cluster to date, adding to the existing deep Hubble Space Telescope (HST) images and the recent JWST ERS and DDT data taken for this field. The wide field-of-view of UNCOVER ($\sim45$ arcmin$^2$) extends beyond the cluster's well-studied central core and reveals a spectacular wealth of prominent lensed features around two massive cluster sub-structures in the north and north-west, where no multiple images were previously known. The 75 newly uncovered multiple images and candidates of 16 sources allow us, for the first time, to constrain the lensing properties and total mass distribution around these extended cluster structures using strong lensing (SL). Our model yields an effective Einstein radius of $θ_{E,\mathrm{main}}\simeq23''$ for the main cluster core (for $z_{\mathrm{s}}=2$), enclosing a mass of $M(θ<θ_{E,\mathrm{main}})\simeq7.7\times10^{13}$ M$_{\odot}$, and $θ_{E,\mathrm{NW}}\simeq13''$ for the newly discovered north-western SL structure enclosing $M(θ<θ_{E,\mathrm{NW}})\simeq2.2\times10^{13}$ M$_{\odot}$. The northern clump is somewhat less massive with $θ_{E,\mathrm{N}}\simeq7''$ enclosing $M(θ<θ_{E,\mathrm{N}})\simeq8\times10^{12}$ M$_{\odot}$. We find the northern sub-structures of Abell~2744 to broadly agree with the findings from weak lensing (WL) and align with the filamentary structure found by these previous studies. Our model in particular reveals a large area of high magnifications between the various cluster structures, which will be paramount for lensed galaxy studies in the UNCOVER field. The model is made publicly available to accompany the first UNCOVER data release.

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arXiv2023

The Gas-Phase Mass--Metallicity Relation for Massive Galaxies at $z\sim0.7$ with the LEGA-C Survey

The massive end of the gas-phase mass--metallicity relation (MZR) is a sensitive probe of active galactic nuclei (AGN) feedback that is a crucial but highly uncertain component of galaxy evolution models. In this paper, we extend the $z\sim0.7$ MZR by $\sim$0.5 dex up to log$(M_\star/\textrm{M}_\odot)\sim11.1$. We use extremely deep VLT VIMOS spectra from the Large Early Galaxy Astrophysics Census (LEGA-C) survey to measure metallicities for 145 galaxies. The LEGA-C MZR matches the normalization of the $z\sim0.8$ DEEP2 MZR where they overlap, so we combine the two to create an MZR spanning from 9.3 to 11.1 log$(M_\star/\textrm{M}_\odot)$. The LEGA-C+DEEP2 MZR at $z\sim0.7$ is offset to slightly lower metallicities (0.05-0.13 dex) than the $z\sim0$ MZR, but it otherwise mirrors the established power law rise at low/intermediate stellar masses and asymptotic flattening at high stellar masses. We compare the LEGA-C+DEEP2 MZR to the MZR from two cosmological simulations (IllustrisTNG and SIMBA), which predict qualitatively different metallicity trends for high-mass galaxies. This comparison highlights that our extended MZR provides a crucial observational constraint for galaxy evolution models in a mass regime where the MZR is very sensitive to choices about the implementation of AGN feedback.

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arXiv2023

From Carbon to Cobalt: Chemical compositions and ages of $z\sim0.7$ quiescent galaxies

We present elemental abundance patterns (C, N, Mg, Si, Ca, Ti, V, Cr, Fe, Co, and Ni) for a population of 135 massive quiescent galaxies at $z\sim0.7$ with ultra-deep rest-frame optical spectroscopy drawn from the LEGA-C survey. We derive average ages and elemental abundances in four bins of stellar velocity dispersion ($σ_v$) ranging from 150$~$km$\,$s$^{-1}$ to 250$~$km$\,$s$^{-1}$ using a full-spectrum hierarchical Bayesian model. The resulting elemental abundance measurements are precise to 0.05$\,$dex. The majority of elements, as well as the total metallicity and stellar age, show a positive correlation with $σ_v$. Thus, the highest dispersion galaxies formed the earliest and are the most metal-rich. We find only mild or non-significant trends between [X/Fe] and $σ_v$, suggesting that the average star-formation timescale does not strongly depend on velocity dispersion. To first order, the abundance patterns of the $z\sim0.7$ quiescent galaxies are strikingly similar to those at $z\sim0$. However, at the lowest velocity dispersions the $z\sim0.7$ galaxies have slightly enhanced N, Mg, Ti, and Ni abundance ratios and earlier formation redshifts than their $z\sim0$ counterparts. Thus, while the higher-mass quiescent galaxy population shows little evolution, the low-mass quiescent galaxies population has grown significantly over the past six billion years. Finally, the abundance patterns of both $z\sim0$ and $z\sim0.7$ quiescent galaxies differ considerably from theoretical prediction based on a chemical evolution model, indicating that our understanding of the enrichment histories of these galaxies is still very limited.

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arXiv2023

Spectroscopic confirmation of four metal-poor galaxies at z=10.3-13.2

Finding and characterising the first galaxies that illuminated the early Universe at cosmic dawn is pivotal to understand the physical conditions and the processes that led to the formation of the first stars. In the first few months of operations, imaging from the James Webb Space Telescope (JWST) have been used to identify tens of candidates of galaxies at redshift (z) greater than 10, less than 450 million years after the Big Bang. However, none of these candidates has yet been confirmed spectroscopically, leaving open the possibility that they are actually low-redshift interlopers. Here we present spectroscopic confirmation and analysis of four galaxies unambiguously detected at redshift 10.3<z<13.2, previously selected from NIRCam imaging. The spectra reveal that these primeval galaxies are extremely metal poor, have masses between 10^7 and a few times 10^8 solar masses, and young ages. The damping wings that shape the continuum close to the Lyman edge are consistent with a fully neutral intergalactic medium at this epoch. These findings demonstrate the rapid emergence of the first generations of galaxies at cosmic dawn.

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arXiv2023

JEMS: A deep medium-band imaging survey in the Hubble Ultra-Deep Field with JWST NIRCam & NIRISS

We present JEMS (JWST Extragalactic Medium-band Survey), the first public medium-band imaging survey carried out using JWST/NIRCam and NIRISS. These observations use $\sim2μ$m and $\sim4μ$m medium-band filters (NIRCam F182M, F210M, F430M, F460M, F480M; and NIRISS F430M & F480M in parallel) over 15.6 square arcminutes in the Hubble Ultra Deep Field (UDF), thereby building on the deepest multi-wavelength public datasets available anywhere on the sky. We describe our science goals, survey design, NIRCam and NIRISS image reduction methods, and describe our first data release of the science-ready mosaics. Our chosen filters create a JWST imaging survey in the UDF that enables novel analysis of a range of spectral features potentially across the redshift range of $0.3 1$ magnitude) across redshifts $1.5<z<9.3$, most prominently H$α$+[NII] and [OIII]+H$β$. We present our first data release including science-ready mosaics of each medium-band image available to the community, adding to the legacy value of past and future surveys in the UDF. We also describe future data releases. This survey demonstrates the power of medium-band imaging with JWST, informing future extragalactic survey strategies using JWST observations.

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arXiv2022

A common origin for the Fundamental Plane of quiescent and star-forming galaxies in the EAGLE simulations

We use the EAGLE cosmological simulations to perform a comprehensive and systematic analysis of the $z=0.1$ Fundamental Plane (FP), the tight relation between galaxy size, mass and velocity dispersion. We first measure the total mass and velocity dispersion (including both random and rotational motions) within the effective radius to show that simulated galaxies obey a total mass FP that is very close to the virial relation ($<10\%$ deviation), indicating that the effects of non-homology are weak. When we instead use the stellar mass, we find a strong deviation from the virial plane, which is driven by variations in the dark matter content. The dark matter fraction is a smooth function of the size and stellar mass, and thereby sets the coefficients of the stellar mass FP without substantially increasing the scatter. Hence, both star-forming and quiescent galaxies obey the same FP, with equally low scatter (0.02 dex). We employ simulations with a variable stellar initial mass function (IMF) to show that IMF variations have a modest additional effect on this FP. Moreover, when we use luminosity-weighted mock observations of the size and spatially-integrated velocity dispersion, the inferred FP changes only slightly. However, the scatter increases significantly, due to the luminosity-weighting and line-of-sight projection of the velocity dispersions, and measurement uncertainties on the half-light radii. Importantly, we find significant differences between the simulated FP and observations, which likely reflects a systematic difference in the stellar mass distributions. Therefore, we suggest the stellar mass FP offers a simple test for cosmological simulations, requiring minimal post-processing of simulation data.

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arXiv2022

The Velocity Dispersion Function for Massive Quiescent and Star-Forming Galaxies at 0.6 $<$ z $\leq$ 1.0

We present the first direct spectroscopic measurement of the stellar velocity dispersion function (VDF) for massive quiescent and star-forming galaxies at $0.6 < z \leq 1.0$. For this analysis we use individual measurements of stellar velocity dispersion from high-S/N spectra from the public Large Early Galaxy Astrophysics Census (LEGA-C) survey. We report a remarkable stability of the VDF for both quiescent and star-forming galaxies within this redshift range, though we note the presence of weak evolution in the number densities of star-forming galaxies. We compare both VDFs with previous direct and inferred measurements at local and intermediate redshifts, with the caveat that previous measurements of the VDF for star-forming galaxies are poorly constrained at all epochs. We emphasize that this work is the first to directly push to low-stellar velocity dispersion ($σ_\star > 100$ km s$^{-1}$) and extend to star-forming galaxies. We are largely consistent with the high-sigma tail measured from BOSS, and we find that the VDF remains constant from the median redshift of LEGA-C, $z\sim0.8$, to the present day.

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arXiv2022

The Mass Scale of High-Redshift Galaxies: Virial Mass Estimates Calibrated with Stellar Dynamical Models from LEGA-C

Dynamical models for $673$ galaxies at $z=0.6-1.0$ with spatially resolved (long-slit) stellar kinematic data from LEGA-C are used to calibrate virial mass estimates defined as $M_{\rm{vir}}=K σ'^2_{\star,\rm{int}} R$, with $K$ a scaling factor, $σ'_{\star,\rm{int}}$ the spatially-integrated stellar velocity second moment from the LEGA-C survey and $R$ the effective radius measured from a Sérsic profile fit to HST imaging. The sample is representative for $M_{\star}>3\times10^{10}~M_{\odot}$ and includes all types of galaxies, irrespective of morphology and color. We demonstrate that using $R=R_{\rm{sma}}$~(the semi-major axis length of the ellipse that encloses 50\% of the light) in combination with an inclination correction on $σ'_{\star,\rm{int}}$~produces an unbiased $M_{\rm{vir}}$. We confirm the importance of projection effects on $σ'_{\star,\rm{int}}$ by showing the existence of a similar residual trend between virial mass estimates and inclination for the nearby early-type galaxies in the ATLAS$^{\rm{3D}}$~survey. Also, as previously shown, when using a Sérsic profile-based $R$ estimate, then a Sérsic index-dependent correction to account for non-homology in the radial profiles is required. With respect to analogous dynamical models for low-redshift galaxies from the ATLAS$^{\rm{3D}}$~survey we find a systematic offset of 0.1 dex in the calibrated virial constant for LEGA-C, which may be due to physical differences between the galaxy samples or an unknown systematic error. Either way, with our work we establish a common mass scale for galaxies across 8 Gyr of cosmic time with a systematic uncertainty of at most 0.1 dex.

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