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Sadegh Khochfar

Publications and source records attributed to Sadegh Khochfar.

At least 73 records · Page 4Linked to original sources

The impact of reionization on the formation of supermassive black hole seeds

Direct collapse black holes (DCBHs) formed from the collapse of atomically-cooled primordial gas in the early Universe are strong candidates for the seeds of supermassive BHs. DCBHs are thought to form in atomic cooling haloes in the presence of a strong molecule-dissociating, Lyman-Werner (LW) radiation field. Given that star forming galaxies are likely to be the source of the LW radiation in this scenario, ionizing radiation from these galaxies may accompany the LW radiation. We present cosmological simulations resolving the collapse of primordial gas into an atomic cooling halo, including the effects of both LW and ionizing radiation. We find that in cases where the gas is not self-shielded from the ionizing radiation, the collapse can be delayed by ~ 25 Myr. When the ionized gas does collapse, the free electrons that are present catalyze H2 formation. In turn, H2 cooling becomes efficient in the center of the halo, and DCBH formation is prevented. We emphasize, however, that in many cases the gas collapsing into atomic cooling haloes at high redshift is self-shielding to ionizing radiation. Therefore, it is only in a fraction of such haloes in which DCBH formation is prevented due to reionization.

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The First Population II Stars Formed in Externally Enriched Mini-halos

We present a simulation of the formation of the earliest Population II stars, starting from cosmological initial conditions and ending when metals created in the first supernovae are incorporated into a collapsing gas-cloud. This occurs after a supernova blast-wave collides with a nearby mini-halo, inducing further turbulence that efficiently mixes metals into the dense gas in the center of the halo. The gas that first collapses has been enriched to a metallicity of Z ~ 2e-5 Zsun. Due to the extremely low metallicity, collapse proceeds similarly to metal-free gas until dust cooling becomes efficient at high densities, causing the cloud to fragment into a large number of low mass objects. This external enrichment mechanism provides a plausible origin for the most metal-poor stars observed, such as SMSS J031300.36-670839.3, that appear to have formed out of gas enriched by a single supernova. This mechanism operates on shorter timescales than the time for low-mass mini-halos (M < 5e5 Msun) to recover their gas after experiencing a supernova. As such, metal-enriched stars will likely form first via this channel if the conditions are right for it to occur. We identify a number of other externally enriched halos that may form stars in this manner. These halos have metallicities as high as 0.01 Zsun, suggesting that some members of the first generation of metal-enriched stars may be hiding in plain sight in current stellar surveys.

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The First Billion Years Project: The escape fraction of ionizing photons in the epoch of reionization

Proto-galaxies forming in low-mass dark matter haloes are thought to provide the majority of ionizing photons needed to reionize the Universe, due to their high escape fractions of ionizing photons. We study how the escape fraction in high-redshift galaxies relates to the physical properties of the halo in which the galaxies form, by computing escape fractions in more than 75000 haloes between redshifts 27 and 6 that were extracted from the First Billion Years project, high-resolution cosmological hydrodynamics simulations of galaxy formation. We find that the main constraint on the escape fraction is the gas column density in a radius of 10 pc around the stellar populations, causing a strong mass dependence of the escape fraction. The lower potential well in haloes with virial mass below 1e8 solar mass results in low column densities that can be penetrated by radiation from young stars (age < 5 Myr). In haloes with virial mass above 1e8 solar mass supernova feedback is important, but only 30% of the haloes in this mass range have an escape fraction higher than 1%. We find a large range of escape fractions in haloes with similar properties, caused by different distributions of the dense gas in the halo. This makes it very hard to predict the escape fraction on the basis of halo properties and results in a highly anisotropic escape fraction. The strong mass dependence, the large spread and the large anisotropy of the escape fraction may strongly affect the topology of reionization and is something current models of cosmic reionization should strive to take into account.

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The Atlas3D Project - XXX. Star formation histories and stellar population scaling relations of early-type galaxies

We present the stellar population content of early-type galaxies from the Atlas3D survey. Using spectra integrated within apertures covering up to one effective radius, we apply two methods: one based on measuring line-strength indices and applying single stellar population (SSP) models to derive SSP-equivalent values of stellar age, metallicity, and alpha enhancement; and one based on spectral fitting to derive non-parametric star-formation histories, mass-weighted average values of age, metallicity, and half-mass formation timescales. Using homogeneously derived effective radii and dynamically-determined galaxy masses, we present the distribution of stellar population parameters on the Mass Plane (M_JAM, Sigma_e, R_maj), showing that at fixed mass, compact early-type galaxies are on average older, more metal-rich, and more alpha-enhanced than their larger counterparts. From non-parametric star-formation histories, we find that the duration of star formation is systematically more extended in lower mass objects. Assuming that our sample represents most of the stellar content of today's local Universe, approximately 50% of all stars formed within the first 2 Gyr following the big bang. Most of these stars reside today in the most massive galaxies (>10^10.5 M_sun), which themselves formed 90% of their stars by z~2. The lower-mass objects, in contrast, have formed barely half their stars in this time interval. Stellar population properties are independent of environment over two orders of magnitude in local density, varying only with galaxy mass. In the highest-density regions of our volume (dominated by the Virgo cluster), galaxies are older, alpha-enhanced and have shorter star-formation histories with respect to lower density regions.

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Can the 21 cm signal probe Population III and II star formation?

Using varying models for the star formation rate (SFR) of Population (Pop) III and II stars at z>6 we derive the expected redshift history of the global 21 cm signal from the inter-galactic medium (IGM). To recover the observed Thomson scattering optical depth of the cosmic microwave background (CMB) requires SFRs at the level of ~ 10^-3 Msun/yr/Mpc^3 at z ~ 15 from Pop III stars, or ~ 10^-1Msun/yr/Mpc^3 at z ~ 7 from Pop II stars. In the case the SFR is dominated by Pop III stars, the IGM quickly heats above the CMB at z > 12 due to heating from supernovae. In addition, Lyman-alpha photons from haloes hosting Pop III stars couple the spin temperature to that of the gas, resulting in a deep absorption signal. If the SFR is dominated by Pop II stars, the IGM slowly heats and exceeds the CMB temperature at z ~ 10. However, the larger and varying fraction of Pop III stars is able to break this degeneracy. We find that the impact of the initial mass function (IMF) of Pop III stars on the 21 cm signal results in an earlier change to a positive signal if the IMF slope is ~ -1.2. Measuring the 21 cm signal at z > 10 with next generation radio telescopes such as the Square Kilometre Array will be able to investigate the contribution from Pop III and Pop II stars to the global star formation rate.

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The Atlas3D project -- XXIX. The new look of early-type galaxies and surrounding fields disclosed by extremely deep optical images

Galactic archeology based on star counts is instrumental to reconstruct the past mass assembly of Local Group galaxies. The development of new observing techniques and data-reduction, coupled with the use of sensitive large field of view cameras, now allows us to pursue this technique in more distant galaxies exploiting their diffuse low surface brightness (LSB) light. As part of the Atlas3D project, we have obtained with the MegaCam camera at the Canada-France Hawaii Telescope extremely deep, multi--band, images of nearby early-type galaxies. We present here a catalog of 92 galaxies from the Atlas3D sample, that are located in low to medium density environments. The observing strategy and data reduction pipeline, that achieve a gain of several magnitudes in the limiting surface brightness with respect to classical imaging surveys, are presented. The size and depth of the survey is compared to other recent deep imaging projects. The paper highlights the capability of LSB--optimized surveys at detecting new prominent structures that change the apparent morphology of galaxies. The intrinsic limitations of deep imaging observations are also discussed, among those, the contamination of the stellar halos of galaxies by extended ghost reflections, and the cirrus emission from Galactic dust. The detection and systematic census of fine structures that trace the present and past mass assembly of ETGs is one of the prime goals of the project. We provide specific examples of each type of observed structures -- tidal tails, stellar streams and shells --, and explain how they were identified and classified. We give an overview of the initial results. The detailed statistical analysis will be presented in future papers.

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Connection between dynamically derived IMF normalisation and stellar population parameters

We report on empirical trends between the dynamically determined stellar initial mass function (IMF) and stellar population properties for a complete, volume-limited sample of 260 early-type galaxies from the Atlas3D project. We study trends between our dynamically-derived IMF normalisation and absorption line strengths, and interpret these via single stellar population- (SSP-) equivalent ages, abundance ratios (measured as [alpha/Fe]), and total metallicity, [Z/H]. We find that old and alpha-enhanced galaxies tend to have on average heavier (Salpeter-like) mass normalisation of the IMF, but stellar population does not appear to be a good predictor of the IMF, with a large range of normalisation at a given population parameter. As a result, we find weak IMF-[alpha/Fe] and IMF-age correlations, and no significant IMF-[Z/H] correlation. The observed trends appear significantly weaker than those reported in studies that measure the IMF normalisation via low-mass star demographics inferred through stellar spectral analysis.

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The Atlas3D project - XXIV. The intrinsic shape distribution of early-type galaxies

We use the Atlas3D sample to perform a study of the intrinsic shapes of early-type galaxies, taking advantage of the available combined photometric and kinematic data. Based on our ellipticity measurements from the Sloan Digital Sky Survey Data Release 7, and additional imaging from the Isaac Newton Telescope, we first invert the shape distribution of fast and slow rotators under the assumption of axisymmetry. The so-obtained intrinsic shape distribution for the fast rotators can be described with a Gaussian with a mean flattening of q=0.25 and standard deviation sigma_q = 0.14, and an additional tail towards rounder shapes. The slow rotators are much rounder, and are well described with a Gaussian with mean q = 0.63 and sigma_q =0.09. We then checked that our results were consistent when applying a different and independent method to obtain intrinsic shape distributions, by fitting the observed ellipticity distributions directly using Gaussian parametrisations for the intrinsic axis ratios. Although both fast and slow rotators are identified as early-type galaxies in morphological studies, and in many previous shape studies are therefore grouped together, their shape distributions are significantly different, hinting at different formation scenarios. The intrinsic shape distribution of the fast rotators shows similarities with the spiral galaxy population. Including the observed kinematic misalignment in our intrinsic shape study shows that the fast rotators are predominantly axisymmetric, with only very little room for triaxiality. For the slow rotators though there are very strong indications that they are (mildly) triaxial.

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The First Billion Years project: dark matter haloes going from contraction to expansion and back again

We study the effect of baryons on the inner dark matter profile of the first galaxies using the First Billion Years simulation between z=16-6 before secular evolution sets in. Using a large statistical sample from two simulations of the same volume and cosmological initial conditions, one with and one without baryons, we are able to directly compare haloes with their baryon-free counterparts, allowing a detailed study of the modifications to the dark matter density profile due to the presence of baryons during the first billion years of galaxy formation. For each of the ~ 5000 haloes in our sample we quantify the impact of the baryons using eta, defined as the ratio of dark matter mass enclosed in 100 pc in the baryonic run to its counterpart without baryons. During this epoch of rapid growth of galaxies, we find that many haloes of these first galaxies show an enhancement of dark matter in the halo centre compared to the baryon-free simulation, while many others show a deficit. We find that the mean value of eta is close to unity, but there is a large dispersion, with a standard deviation of 0.677. The enhancement is cyclical in time and tracks the star formation cycle of the galaxy; as gas falls to the centre and forms stars, the dark matter moves in as well. Supernova feedback then removes the gas, and the dark matter again responds to the changing potential. We study three physical models relating the motion of baryons to that of the dark matter: adiabatic contraction, dynamical friction, and rapid outflows. Abridged, see text for full abstract

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Revised rate coefficients for H$_2$ and H$^-$ destruction by realistic stellar spectra

Understanding the processes that can destroy H$_2$ and H$^-$ species is quintessential in governing the formation of the first stars, black holes and galaxies. In this study we compute the reaction rate coefficients for H$_2$ photo--dissociation by Lyman--Werner photons ($11.2 - 13.6$ eV), and H$^-$ photo--detachment by 0.76 eV photons emanating from self-consistent stellar populations that we model using publicly available stellar synthesis codes. So far studies that include chemical networks for the formation of molecular hydrogen take these processes into account by assuming that the source spectra can be approximated by a power-law dependency or a black-body spectrum at 10$^4$ or $10^5$ K. We show that using spectra generated from realistic stellar population models can alter the reaction rates for photo-dissociation, $\rm k_{\rm{di}}$, and photo-detachment, $\rm k_{\rm{de}}$, significantly. In particular, $\rm k_{\rm{de}}$ can be up to $\sim 2-4$ orders of magnitude lower in the case of realistic stellar spectra suggesting that previous calculations have over-estimated the impact that radiation has on lowering H$_2$ abundances. In contrast to burst modes of star formation, we find that models with continuous star formation predict increasing $\rm k_{\rm{de}}$ and $\rm k_{\rm{di}}$, which makes it necessary to include the star formation history of sources to derive self-consistent reaction rates, and that it is not enough to just calculate J$_{21}$ for the background. For models with constant star formation rate the change in shape of the spectral energy distribution leads to a non-negligible late-time contribution to $\rm k_{\rm{de}}$ and $\rm k_{\rm{di}}$, and we present self-consistently derived cosmological reaction rates based on star formation rates consistent with observations of the high redshift Universe.

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The HST/ACS Coma Cluster Survey - VII. Structure and Assembly of Massive Galaxies in the Center of the Coma Cluster

We constrain the assembly history of galaxies in the projected central 0.5 Mpc of the Coma cluster by performing structural decomposition on 69 massive (M_star >= 10^9 M_sun) galaxies using high-resolution F814W images from the HST Treasury Survey of Coma. Each galaxy is modeled with up to three Sersic components having a free Sersic index n. After excluding the two cDs in the projected central 0.5 Mpc of Coma, 57% of the galactic stellar mass in the projected central 0.5 Mpc of Coma resides in classical bulges/ellipticals while 43% resides in cold disk-dominated structures. Most of the stellar mass in Coma may have been assembled through major (and possibly minor) mergers. Hubble types are assigned based on the decompositions, and we find a strong morphology-density relation; the ratio of (E+S0):spirals is (91.0%):9.0%. In agreement with earlier work, the size of outer disks in Coma S0s/spirals is smaller compared with lower-density environments captured with SDSS (Data Release 2). Among similar-mass clusters from a hierarchical semi-analytic model, no single cluster can simultaneously match all the global properties of the Coma cluster. The model strongly overpredicts the mass of cold gas and underpredicts the mean fraction of stellar mass locked in hot components over a wide range of galaxy masses. We suggest that these disagreements with the model result from missing cluster physics (e.g., ram-pressure stripping), and certain bulge assembly modes (e.g., mergers of clumps). Overall, our study of Coma underscores that galaxy evolution is not solely a function of stellar mass, but also of environment.

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The ATLAS3D Project - XXVIII. Dynamically-driven star formation suppression in early-type galaxies

We present measurements of the star formation rate (SFR) in the early-type galaxies (ETGs) of the ATLAS3D sample, based on Wide-field Infrared Survey Explorer (WISE) 22um and Galaxy Evolution Explorer (GALEX) far-ultraviolet emission. We combine these with gas masses estimated from 12CO and HI data in order to investigate the star formation efficiency (SFE) in a larger sample of ETGs than previously available. We first recalibrate (based on WISE data) the relation between old stellar populations (traced at Ks-band) and 22um luminosity, allowing us to remove the contribution of 22um emission from circumstellar dust. We then go on to investigate the position of ETGs on the Kennicutt-Schmidt (KS) relation. Molecular gas-rich ETGs have comparable star formation surface densities to normal spiral galaxy centres, but they lie systematically offset from the KS relation, having lower star formation efficiencies by a factor of ~2.5 (in agreement with other authors). This effect is driven by galaxies where a substantial fraction of the molecular material is in the rising part of the rotation curve, and shear is high. We show here for the first time that although the number of stars formed per unit gas mass per unit time is lower in ETGs, it seems that the amount of stars formed per free-fall time is approximately constant. The scatter around this dynamical relation still correlates with galaxy properties such as the shape of the potential in the inner regions. This leads us to suggest that dynamical properties (such as shear or the global stability of the gas) may be important second parameters that regulate star formation and cause much of the scatter around star-formation relations.

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Angular momentum loss of primordial gas in Lyman-alpha radiation field

We present results on the radiation drag exerted by an isotropic and homogenous background of Lya photons on neutral gas clouds orbiting within HII regions around Population III stars of different masses. The Doppler shift causes a frequency difference between photons moving in the direction of the cloud and opposite to it resulting in a net momentum loss of the cloud in the direction of motion. We find that half of the angular momentum of gas with v_theta <~ 20 km/s near (r <~ 3 kpc) a Population III star of 120 Msun at z=20 is lost within ~ 10^6 yr. The radiation drag is a strong function of cloud velocity that peaks at v ~ 20 km/s reflecting the frequency dependence of the photon cross section. Clouds moving with velocities larger than ~ 100 km/s loose their angular momentum on time scales of ~ 10^8 yr. At lower redshifts radiation drag becomes inefficient as the Lya photon density in HII regions decreases by a factor (1+z)^3 and angular momentum is lost on time scales > 10^8 yr even for low velocity clouds. Our results suggest that a sweet spot exists for the loss of angular momentum by radiation drag for gas clouds at z > 10 and with v ~ 20 km/s. Comparison to dynamical friction forces acting on typical gas clouds suggest that radiation drag is the dominant effect impacting the orbit. We propose that this effect can suppress the formation of extended gas discs in the first galaxies and help gas accretion near galactic centres and central black holes.

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The Atlas3D project - XXVI. HI discs in real and simulated fast and slow rotators

One quarter of all nearby early-type galaxies (ETGs) outside Virgo host a disc/ring of HI with size from a few to tens of kpc and mass up to ~1e+9 solar masses. Here we investigate whether this HI is related to the presence of a stellar disc within the host making use of the classification of ETGs in fast and slow rotators (FR/SR). We find a large diversity of HI masses and morphologies within both families. Surprisingly, SRs are detected as often, host as much HI and have a similar rate of HI discs/rings as FRs. Accretion of HI is therefore not always linked to the growth of an inner stellar disc. The weak relation between HI and stellar disc is confirmed by their frequent kinematical misalignment in FRs, including cases of polar and counterrotating gas. In SRs the HI is usually polar. This complex picture highlights a diversity of ETG formation histories which may be lost in the relative simplicity of their inner structure and emerges when studying their outer regions. We find that LCDM hydrodynamical simulations have difficulties reproducing the HI properties of ETGs. The gas discs formed in simulations are either too massive or too small depending on the star formation feedback implementation. Kinematical misalignments match the observations only qualitatively. The main point of conflict is that nearly all simulated FRs and a large fraction of all simulated SRs host corotating HI. This establishes the HI properties of ETGs as a novel challenge to simulations.

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NGC1266 as a Local Candidate for Rapid Cessation of Star Formation

We present new Spectrographic Areal Unit for Research on Optical Nebulae (SAURON) integral-field spectroscopy and Swift Ultraviolet Optical Telescope (UVOT) observations of molecular outflow host galaxy NGC 1266 that indicate NGC 1266 has experienced a rapid cessation of star formation. Both the SAURON maps of stellar population age and the Swift UVOT observations demonstrate the presence of young ($< 1$ Gyr) stellar populations within the central 1 kpc, while existing Combined Array for Research in Millimeter-wave Astronomy (CARMA) CO(1--0) maps indicate that the sites of current star formation are constrained to the inner few hundred parsecs of the galaxy only. The optical spectrum of NGC 1266 from Moustakas & Kennicutt (2006) reveal a characteristic post-starburst (K+A) stellar population and Davis et al. (2012) confirm that ionized gas emission in the system originate from a shock. Galaxies with K+A spectra and shock-like ionized gas line ratios may comprise an important, overlooked segment of the post-starburst population, containing exactly those objects in which the AGN is actively expelling the star-forming material. While AGN activity is not the likely driver of the post-starburst event that occurred 500 Myr ago, the faint spiral structure seen in the Hubble Space Telescope (HST) Wide-field Camera 3 (WFC3) Y-, J- and H-band imaging seems to point to the possibility of gravitational torques being the culprit. If the molecular gas were driven into the center at the same time as the larger scale galaxy disk underwent quenching, the AGN might be able to sustain the presence of molecular gas for $\gtrsim 1$ Gyr by cyclically injecting turbulent kinetic energy into the dense molecular gas via a radio jet, inhibiting star formation.

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The ATLAS3D Project -- XXIII. Angular momentum and nuclear surface brightness profiles

[Abridged and Edited] We investigate nuclear light profiles in 135 ATLAS3D galaxies for which the Hubble Space Telescope (HST) imaging is available and compare them to the large scale kinematics obtained with the SAURON integral-field spectrograph. Specific angular momentum, lambda_R, correlates with the shape of nuclear light profiles, where cores are typically found in slow rotators and core-less galaxies are fast rotators. Cores are found only in massive galaxies and only in systems with the stellar mass M>8x10^10 Msun. Based on our sample, we, however, see no evidence for a bimodal distribution of nuclear slopes. The best predictor for finding a core is based on the stellar velocity dispersion within an effective radius, sigma_e, and specific angular momentum, where cores are found for lambda_R<0.25 and sigma_e>160 km/s. We estimate that only about 10% of nearby early-type galaxies contain cores. Furthermore, we show that there is a genuine population of fast rotators with cores. We also show that core fast rotators are morphologically, kinematically and dynamically different from core slow rotators. The cores of fast rotators could harbour black holes of similar masses to those in core slow rotators, but typically more massive than those found in core-less fast rotators. Core-less galaxies, and especially core-less fast rotators, are under-luminous in the diffuse X-ray emission, but the presence of a core does not imply high X-ray luminosities. We postulate a possible population of core-less galaxies among slow rotators, which can not be explained as face-on discs, but comprise a genuine sub-population of slow rotators. These galaxies are typically less massive and flatter than core slow rotators, and show evidence for dynamical cold structures and exponential photometric components. We discuss possible processes for formation of cores and their subsequent preservation.

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Unravelling obese black holes in the first galaxies

We predict the existence and observational signatures of a new class of objects that assembled early, during the first billion years of cosmic time: Obese Black-hole Galaxies (OBGs). OBGs are objects in which the mass of the central black hole initially exceeds that of the stellar component of the host galaxy, and the luminosity from black-hole accretion dominates the starlight. From a cosmological simulation, we demonstrate that there are sites where star formation is initially inhibited and direct-collapse black holes (DCBHs) form due to the photo-dissociating effect of Lyman-Werner radiation on molecular hydrogen. We show that the formation of OBGs is inevitable, because the probability of finding the required extra-galactic environment and the right physical conditions in a halo conducive to DCBH formation is quite high in the early universe. We estimate an OBG number density of 0.009/Mpc^3 at z~8 and 0.03/Mpc^3 at z~6. Extrapolating from our simulation volume, we infer that the most luminous quasars detected at z~6 likely transited through an earlier OBG phase. We find that these primordial galaxies start off with an over-massive BH and acquire their stellar component from subsequent merging as well as in-situ star formation. In doing so, they inevitably go through an OBG phase dominated by the accretion luminosity at the Eddington rate or below, released from the growing BH. The OBG phase is characterised by an ultra-violet (UV) spectrum with slope of beta ~ -2.3 and the absence of a Balmer Break. OBGs should also be spatially unresolved, and are expected to be brighter than the majority of known high-redshift galaxies. OBGs could potentially be revealed via HST follow-up imaging of samples of brighter Lyman-break galaxies provided by wide-area ground-based surveys such as UltraVISTA, and should be easily uncovered and studied with instruments aboard JWST...(abridged)

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The Atlas3D project - XX. Mass-size and mass-sigma distributions of early-type galaxies: bulge fraction drives kinematics, mass-to-light ratio, molecular gas fraction and stellar initial mass function

We study the (M,sigma) and (M,Re) projections of the thin Mass Plane (MP) (M,sigma,Re) which describes the distribution of the galaxy population. The distribution of galaxy properties on the MP is characterized by: (i) a zone of exclusion described by two power-laws joined by a break at M 3e10 Msun. This results in a break in the mean M-sigma relation with Msigma^2.3 and M sigma^4.7 at small and large sigma respectively; (ii) a mass M 2e11 Msun which separates a population dominated by flat fast rotator with disks and spiral galaxies at lower masses, from one dominated by quite round slow rotators at larger masses; (iii) below that mass the distribution of ETGs properties tends to be constant along lines of constant sigma; (iv) it forms a parallel sequence with the distribution of spiral galaxies; (v) at even lower masses, the distribution of fast rotator ETGs and late spirals naturally extends to that of dwarf ETGs (Sph) and dwarf irregulars (Im) respectively. We show via dynamical models that sigma traces the bulge fraction, which drives the observed trends in M/L, Hbeta, colour, IMF and molecular gas fraction. We interpret this as due to a combination of two main effects: (i) an increase of the bulge fraction which increases sigma and greatly enhances the likelihood for a galaxy to have its star formation quenched, and (ii) dry merging, increasing galaxy mass along lines of nearly constant sigma, while leaving the population unchanged. [Abriged]

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