arXiv subjects

Joel R. Primack

Publications and source records attributed to Joel R. Primack.

At least 37 records · Page 2Linked to original sources

arXiv2022

Galaxy Correlation Function and Local Density from Photometric Redshifts Using the Stochastic Order Redshift Technique (SORT)

The stochastic order redshift technique (SORT) is a simple, efficient, and robust method to improve cosmological redshift measurements. The method relies upon having a small ($\sim$10 per cent) reference sample of high-quality redshifts. Within pencil-beam-like sub-volumes surrounding each galaxy, we use the precise dN/d$z$ distribution of the reference sample to recover new redshifts and assign them one-to-one to galaxies such that the original rank order of redshifts is preserved. Preserving the rank order is motivated by the fact that random variables drawn from Gaussian probability density functions with different means but equal standard deviations satisfy stochastic ordering. The process is repeated for sub-volumes surrounding each galaxy in the survey. This results in every galaxy with an uncertain redshift being assigned multiple "recovered" redshifts from which a new redshift estimate can be determined. An earlier paper applied SORT to a mock Sloan Digital Sky Survey at $z \lesssim$ 0.2 and accurately recovered the two-point correlation function on scales $\gtrsim$4 $h^{-1}$Mpc. In this paper, we test the performance of SORT in surveys spanning the redshift range 0.75$<z<$2.25. We used two mock surveys extracted from the Small MultiDark-Planck and Bolshoi-Planck N-body simulations with dark matter haloes that were populated by the Santa Cruz semi-analytic model. We find that SORT is able to improve redshift estimates and recover distinctive large-scale features of the cosmic web. Further, it provides unbiased estimates of the redshift-space two-point correlation function $ξ(s)$ on scales $\gtrsim$2.5 $h^{-1}$Mpc, as well as local densities in regions of average or higher density. This may allow improved understanding of how galaxy properties relate to their local environments.

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arXiv2021

An observational determination of the evolving extragalactic background light from the multiwavelength HST/CANDELS survey in the Fermi and CTA era

The diffuse extragalactic background light (EBL) is formed by ultraviolet (UV), optical, and infrared (IR) photons mainly produced by star formation processes over the history of the Universe, and contains essential information about galaxy evolution and cosmology. Here, we present a new determination of the evolving EBL spectral energy distribution using a novel approach purely based on galaxy data aiming to reduce current uncertainties on the higher redshifts and IR intensities. Our calculations use multiwavelength observations from the UV to the far-IR of a sample of approximately 150,000 galaxies detected up to $z\sim 6$ in the five fields of the Cosmic Assembly Near-Infrared Deep Extragalactic Legacy Survey (CANDELS) from the Hubble Space Telescope. This is one of the most comprehensive and deepest multi-wavelength galaxy datasets ever obtained. These unprecedented resources allow us to derive the overall EBL evolution up to $z\sim 6$ and its uncertainties. Our results agree with cosmic observables estimated from galaxy surveys and $γ$-ray attenuation such as monochromatic luminosity densities, including those in the far-IR, and star formation rate densities, also at the highest redshits. Optical depths from our EBL approximation, which will be robust at high redshifts and for $γ$ rays up to tens of TeV, will be reported in a companion paper.

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arXiv2021

The AGORA High-resolution Galaxy Simulations Comparison Project. III: Cosmological zoom-in simulation of a Milky Way-mass halo

We present a suite of high-resolution cosmological zoom-in simulations to $z=4$ of a $10^{12}\,{\rm M}_{\odot}$ halo at $z=0$, obtained using seven contemporary astrophysical simulation codes widely used in the numerical galaxy formation community. Physics prescriptions for gas cooling, heating, and star formation, are similar to the ones used in our previous {\it AGORA} disk comparison but now account for the effects of cosmological processes. In this work, we introduce the most careful comparison yet of galaxy formation simulations run by different code groups, together with a series of four calibration steps each of which is designed to reduce the number of tunable simulation parameters adopted in the final run. After all the participating code groups successfully completed the calibration steps, we reach a suite of cosmological simulations with similar mass assembly histories down to $z=4$. With numerical accuracy that resolves the internal structure of a target halo, we find that the codes overall agree well with one another in e.g., gas and stellar properties, but also show differences in e.g., circumgalactic medium properties. We argue that, if adequately tested in accordance with our proposed calibration steps and common parameters, the results of high-resolution cosmological zoom-in simulations can be robust and reproducible. New code groups are invited to join this comparison by generating equivalent models by adopting the common initial conditions, the common easy-to-implement physics package, and the proposed calibration steps. Further analyses of the simulations presented here will be in forthcoming reports from our Collaboration.

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arXiv2021

A Deep Learning Approach for Characterizing Major Galaxy Mergers

Fine-grained estimation of galaxy merger stages from observations is a key problem useful for validation of our current theoretical understanding of galaxy formation. To this end, we demonstrate a CNN-based regression model that is able to predict, for the first time, using a single image, the merger stage relative to the first perigee passage with a median error of 38.3 million years (Myrs) over a period of 400 Myrs. This model uses no specific dynamical modeling and learns only from simulated merger events. We show that our model provides reasonable estimates on real observations, approximately matching prior estimates provided by detailed dynamical modeling. We provide a preliminary interpretability analysis of our models, and demonstrate first steps toward calibrated uncertainty estimation.

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arXiv2021

Mock Lightcones and Theory Friendly Catalogs for the CANDELS Survey

We present mock catalogs created to support the interpretation of the CANDELS survey. We extract halos along past lightcones from the Bolshoi Planck dissipationless N-body simulations and populate these halos with galaxies using two different independently developed semi-analytic models of galaxy formation and the empirical model UniverseMachine. Our mock catalogs have geometries that encompass the footprints of observations associated with the five CANDELS fields. In order to allow field-to-field variance to be explored, we have created eight realizations of each field. In this paper, we present comparisons with observable global galaxy properties, including counts in observed frame bands, luminosity functions, color-magnitude distributions and color-color distributions. We additionally present comparisons with physical galaxy parameters derived from SED fitting for the CANDELS observations, such as stellar masses and star formation rates. We find relatively good agreement between the model predictions and CANDELS observations for luminosity and stellar mass functions. We find poorer agreement for colors and star formation rate distributions. All of the mock lightcones as well as curated "theory friendly" versions of the observational CANDELS catalogs are made available through a web-based data hub.

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arXiv2020

The star-forming main sequence and the contribution of dust-obscured star formation since $z\sim4$ from the FUV+IR luminosity functions

An analytical approach is proposed to study the evolution of the star-forming galaxy (SFG) main sequence (MS) and the fraction of dust-obscured SF up to $z\sim4$. Far-ultraviolet (FUV) and infrared (IR) star formation rates, SFRs, are described as conditional probability functions of $M_{\ast}$. We convolve them with the galaxy stellar mass function (GSMF) of SFGs to derive the FUV and IR LFs. The 2 SF modes formalism is used to describe starburst galaxies. By fitting observed FUV and IR LFs, the parametrization of SFR$_{\rm FUV}-M_{\ast}$ and SFR$_{\rm IR}-M_{\ast}$ are constrained. Our derived SFR$_{\rm FUV+IR}-M_{\ast}$ reproduces the evolution of the MS as compared to other observational inferences. At any redshift, we find that the sSFR$_{\rm FUV+IR}-M_{\ast}$ relation for MS SFGs approaches to a power law at the high-mass end. At lower masses, it bends and eventually the slope sign changes from negative to positive at very low masses. At $z\sim0$, this change of sign is at $M_{\ast}\sim5\times10^{8}{\rm M}_{\odot}$ close to dust-obscured SF regime, $M_{\ast}\sim6\times10^{8}{\rm M}_{\odot}$. The slope sign change is related to the knee of the FUV LF. Our derived dust-obscured fractions agree with previous determinations at $0\leq z\leq2.5$. Dust-obscured fractions depend strongly on mass with almost no dependence with redshift at $z\gtrsim1.2$. At $z\lesssim0.75$ high-mass galaxies become more "transparent" compared to their high redshift counterparts. On the opposite, low- and intermediate-mass galaxies have become more obscured by dust. The joint evolution of the GSMF and the FUV and IR LFs is a promising approach to study mass growth and dust formation/destruction mechanisms.

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arXiv2020

CANDELS Meets GSWLC: Evolution of the Relationship Between Morphology and Star Formation Since z = 2

Galaxy morphology and its evolution over the cosmic epoch hold important clues for understanding the regulation of star formation (SF). However, studying the relationship between morphology and SF has been hindered by the availability of consistent data at different redshifts. Our sample, combining CANDELS (0.8 < z < 2.5) and the GALEX-SDSS-WISE Legacy Catalog (GSWLC; z ~ 0), has physical parameters derived using consistent SED fitting with flexible dust attenuation laws. We adopt visual classifications from Kartaltepe et al. 2015 and expand them to z ~ 0 using SDSS images matching the physical resolution of CANDELS rest-frame optical images and deep FUV GALEX images matching the physical resolution of the CANDELS rest-frame FUV images. Our main finding is that disks with SF clumps at z ~ 0 make a similar fraction (~15%) of star-forming galaxies as at z ~ 2. The clumpy disk contribution to the SF budget peaks at z ~ 1, rather than z ~ 2, suggesting that the principal epoch of disk assembly continues to lower redshifts. Star-forming spheroids ("blue nuggets"), though less centrally concentrated than quenched spheroids, contribute significantly (~15%) to the SF budget at z ~ 1-2, suggesting that compaction precedes quenching. Among green valley and quiescent galaxies, the pure spheroid fraction drops since z ~ 1, whereas spheroids with disks (S0-like) become dominant. Mergers at or nearing coalescence are enhanced in SFR relative to the main sequence at all redshifts by a factor of ~2, but contribute $\lesssim$5% to the SF budget, with their contribution remaining small above the main sequence.

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arXiv2020

The SFR-radius connection: data and implications for wind strength and halo concentration

This paper is one in a series that explores the importance of radius as a second parameter in galaxy evolution. The topic investigated here is the relationship between star formation rate (SFR) and galaxy radius ($R_{\rm e}$) for main-sequence star-forming galaxies. The key observational result is that, over a wide range of stellar mass and redshift in both CANDELS and SDSS, there is little trend between SFR and $R_{\rm e}$ at fixed stellar mass. The Kennicutt-Schmidt law, or any similar density-related star formation law, then implies that smaller galaxies must have lower gas fractions than larger galaxies (at fixed $M_{\ast}$), and this is supported by observations of local star-forming galaxies. We investigate the implication by adopting the equilibrium "bathtub" model: the ISM gas mass is assumed to be constant over time and the net star formation rate is the difference between the accretion rate of gas onto the galaxy from the halo and the outflow rate due to winds. To match the observed null correlation between SFR and radius, the bathtub model requires that smaller galaxies at fixed mass have weaker galactic winds. Our hypothesis is that galaxies are a 2-dimensional family whose properties are set mainly by halo mass and concentration. Galaxy radius and accretion rate plausibly both depend on halo concentration, which predicts how wind strength should vary with $R_{\rm e}$ and SFR.

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arXiv2020

Quenching as a Contest between Galaxy Halos and their Central Black Holes

Existing models of galaxy formation have not yet explained striking correlations between structure and star-formation activity in galaxies, notably the sloped and moving boundaries that divide star-forming from quenched galaxies in key structural diagrams. This paper uses these and other relations to ``reverse-engineer'' the quenching process for central galaxies. The basic idea is that star-forming galaxies with larger radii (at a given stellar mass) have lower black-hole masses due to lower central densities. Galaxies cross into the green valley when the cumulative effective energy radiated by their black hole equals $\sim4\times$ their halo-gas binding energy. Since larger-radii galaxies have smaller black holes, one finds they must evolve to higher stellar masses in order to meet this halo-energy criterion, which explains the sloping boundaries. A possible cause of radii differences among star-forming galaxies is halo concentration. The evolutionary tracks of star-forming galaxies are nearly parallel to the green-valley boundaries, and it is mainly the sideways motions of these boundaries with cosmic time that cause galaxies to quench. BH-scaling laws for star-forming, quenched, and green-valley galaxies are different, and most BH mass growth takes place in the green valley. Implications include: the radii of star-forming galaxies are an important second parameter in shaping their black holes; black holes are connected to their halos but in different ways for star-forming, quenched, and green-valley galaxies; and the same BH-halo quenching mechanism has been in place since $z \sim 3$. We conclude with a discussion of black hole-galaxy co-evolution, the origin and interpretation of BH scaling laws.

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arXiv2020

Structural and Stellar Population Properties vs. Bulge Types in Sloan Digital Sky Survey Central Galaxies

This paper studies pseudo-bulges (P-bulges) and classical bulges (C-bulges) in Sloan Digital Sky Survey central galaxies using the new bulge indicator $ΔΣ_1$, which measures relative central stellar-mass surface density within 1 kpc. We compare $ΔΣ_1$ to the established bulge-type indicator $Δ\langleμ_e\rangle$ from Gadotti (2009) and show that classifying by $ΔΣ_1$ agrees well with $Δ\langleμ_e\rangle$. $ΔΣ_1$ requires no bulge-disk decomposition and can be measured on SDSS images out to $z = 0.07$. Bulge types using it are mapped onto twenty different structural and stellar-population properties for 12,000 SDSS central galaxies with masses 10.0 < log $M_*$/$M_{\odot}$ < 10.4. New trends emerge from this large sample. Structural parameters show fairly linear log-log relations vs. $ΔΣ_1$ and $Δ\langleμ_e\rangle$ with only moderate scatter, while stellar-population parameters show a highly non-linear "elbow" in which specific star-formation rate remains roughly flat with increasing central density and then falls rapidly at the elbow, where galaxies begin to quench. P-bulges occupy the low-density end of the horizontal arm of the elbow and are universally star-forming, while C-bulges occupy the elbow and the vertical branch and exhibit a wide range of star-formation rates at fixed density. The non-linear relation between central density and star-formation rate has been seen before, but this mapping onto bulge class is new. The wide range of star-formation rates in C-bulges helps to explain why bulge classifications using different parameters have sometimes disagreed in the past. The elbow-shaped relation between density and stellar indices suggests that central structure and stellar-populations evolve at different rates as galaxies begin to quench.

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arXiv2020

The AGORA high-resolution galaxy simulations comparison project: Public data release

As part of the AGORA High-resolution Galaxy Simulations Comparison Project (Kim et al. 2014, 2016) we have generated a suite of isolated Milky Way-mass galaxy simulations using 9 state-of-the-art gravito-hydrodynamics codes widely used in the numerical galaxy formation community. In these simulations we adopted identical galactic disk initial conditions, and common physics models (e.g., radiative cooling and ultraviolet background by a standardized package). Subgrid physics models such as Jeans pressure floor, star formation, supernova feedback energy, and metal production were carefully constrained. Here we release the simulation data to be freely used by the community. In this release we include the disk snapshots at 0 and 500Myr of evolution per each code as used in Kim et al. (2016), from simulations with and without star formation and feedback. We encourage any member of the numerical galaxy formation community to make use of these resources for their research - for example, compare their own simulations with the AGORA galaxies, with the common analysis yt scripts used to obtain the plots shown in our papers, also available in this release.

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arXiv2019

The Activation of Galactic Nuclei and Their Accretion Rates are Linked to the Star Formation Rates and Bulge-types of Their Host Galaxies

We use bulge-type classifications of 809 representative SDSS galaxies by Gadotti (2009) to classify a large sample of galaxies into real bulges (classical or elliptical) and pseudobulges using Random Forest. We use structural and stellar population predictors that can easily be measured without image decomposition. Multiple parameters such as the central mass density with 1 kpc, concentration index, Sérsic index and velocity dispersion do result in accurate bulge classifications when combined together. We classify $\sim 44,500$ face-on galaxies above stellar mass of 10$^{10}$ M$_\odot$ and redshift $ 0.02 < z < 0.07$ into real bulges or pseudobulges with $93 \pm 2$\% accuracy. We show that $\sim 75 - 90\%$ of AGNs identified by the optical line ratio diagnostic are hosted by real bulges. The pseudobulge fraction significantly decreases with AGN signature as the line ratios change from indicating pure star formation ($\sim 54 \pm 4$ \%), to composite of star formation and AGN ($\sim 18 \pm 3$\%), and to AGN-dominated galaxies ($\sim 5 \pm 3$\%). Using the dust-corrected [\ion{O}{3}] luminosity as an AGN accretion indicator, and the stellar mass and radius as proxies for a black hole mass, we find that AGNs in real bulges have lower Eddington ratios than AGNs in pseudobulges. Real bulges have a wide range of AGN and star formation activities, although most of them are weak AGNs. For both bulge-types, their Eddington ratios are correlated with specific star formation rates (SSFR). Real bulges have lower specific accretion rate but higher AGN fraction than pseudobulges do at similar SSFRs.

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arXiv2019

High-redshift Galaxy Formation with Self-consistently Modeled Stars and Massive Black Holes: Stellar Feedback and Quasar Growth

As computational resolution of modern cosmological simulations reach ever so close to resolving individual star-forming clumps in a galaxy, a need for "resolution-appropriate" physics for a galaxy-scale simulation has never been greater. To this end, we introduce a self-consistent numerical framework that includes explicit treatments of feedback from star-forming molecular clouds (SFMCs) and massive black holes (MBHs). In addition to the thermal supernovae feedback from SFMC particles, photoionizing radiation from both SFMCs and MBHs is tracked through full 3-dimensional ray tracing. A mechanical feedback channel from MBHs is also considered. Using our framework, we perform a state-of-the-art cosmological simulation of a quasar-host galaxy at z~7.5 for ~25 Myrs with all relevant galactic components such as dark matter, gas, SFMCs, and an embedded MBH seed of ~> 1e6 Ms. We find that feedback from SFMCs and an accreting MBH suppresses runaway star formation locally in the galactic core region. Newly included radiation feedback from SFMCs, combined with feedback from the MBH, helps the MBH grow faster by retaining gas that eventually accretes on to the MBH. Our experiment demonstrates that previously undiscussed types of interplay between gas, SFMCs, and a MBH may hold important clues about the growth and feedback of quasars and their host galaxies in the high-redshift Universe.

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arXiv2019

Studying the Physical Properties of Tidal Features I. Extracting Morphological Substructure in CANDELS Observations and VELA Simulations

The role of major mergers in galaxy evolution remains a key open question. Existing empirical merger identification methods use non-parametric and subjective visual classifications which can pose systematic challenges to constraining merger histories. As a first step towards overcoming these challenges, we develop and share publicly a new Python-based software tool that identifies and extracts the flux-wise and area-wise significant contiguous regions from the model-subtracted "residual" images produced by popular parametric light-profile fitting tools (e.g., GALFIT). Using Hubble Space Telescope ($HST$) $H$-band single-Sérsic residual images of $17$ CANDELS galaxies, we demonstrate the tool's ability to measure the surface brightness and improve the qualitative identification of a variety of common residual features (disk structures, spiral substructures, plausible tidal features, and strong gravitational arcs). We test our method on synthetic $HST$ observations of a $z\sim 1.5$ major merger from the VELA hydrodynamic simulations. We extract $H$-band residual features corresponding to the birth, growth, and fading of tidal features during different stages and viewing orientations at CANDELS depths and resolution. We find that the extracted features at shallow depths have noisy visual appearance and are susceptible to viewing angle effects. For a VELA $z\sim 3$ major merger, we find that James Webb Space Telescope NIRCam observations can probe high-redshift tidal features with considerable advantage over existing $HST$ capabilities. Further quantitative analysis of plausible tidal features extracted with our new software hold promise for the robust identification of hallmark merger signatures and corresponding improvements to merger rate constraints.

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arXiv2019

The Global Star-Formation Law by Supernova Feedback

We address a simple model where the Kennicutt-Schmidt (KS) relation between the macroscopic densities of star-formation rate (SFR, $ρ_{\rm sfr}$) and gas ($n$) in galactic discs emerges from self-regulation of the SFR via supernova feedback. It arises from the physics of supernova bubbles, insensitive to the microscopic SFR recipe and not explicitly dependent on gravity. The key is that the filling factor of SFR-suppressed supernova bubbles self-regulates to a constant, $f\sim 0.5$. Expressing the bubble fading radius and time in terms of $n$, the filling factor is $f \propto S\,n^{-s}$ with $s\sim 1.5$, where $S$ is the supernova rate density. A constant $f$ thus refers to $ρ_{\rm sfr} \propto n^{1.5}$, with a density-independent SFR efficiency per free-fall time $\sim 0.01$. The self-regulation to $f \sim 0.5$ and the convergence to a KS relation independent of the local SFR recipe are demonstrated in cosmological and isolated-galaxy simulations using different codes and recipes. In parallel, the spherical analysis of bubble evolution is generalized to clustered supernovae, analytically and via simulations, yielding $s \simeq 1.5 \pm 0.5$. An analysis of photo-ionized bubbles about pre-supernova stars yields a range of KS slopes but the KS relation is dominated by the supernova bubbles. Superbubble blowouts may lead to an alternative self-regulation by outflows and recycling. While the model is over-simplified, its simplicity and validity in the simulations may argue that it captures the origin of the KS relation.

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arXiv2019

Distinguishing Mergers and Disks in High Redshift Observations of Galaxy Kinematics

The majority of massive star-forming galaxies at $z\sim2$ have velocity gradients suggestive of rotation, in addition to large amounts of disordered motions. In this paper, we demonstrate that it is challenging to distinguish the regular rotation of a disk galaxy from the orbital motions of merging galaxies with seeing-limited data. However, the merger fractions at $z\sim2$ are likely too low for this to have a large effect on measurements of disk fractions. To determine how often mergers pass for disks, we look to galaxy formation simulations. We analyze $\sim$24000 synthetic images and kinematic maps of 31 high-resolution simulations of isolated galaxies and mergers at $z\sim2$. We determine if the synthetic observations pass criteria commonly used to identify disk galaxies, and whether the results are consistent with their intrinsic dynamical states. Galaxies that are intrinsically mergers pass the disk criteria for anywhere from 0 to 100$\%$ of sightlines. The exact percentage depends strongly on the specific disk criteria adopted, and weakly on the separation of the merging galaxies. Therefore, one cannot tell with certainty whether observations of an individual galaxy indicate a merger or a disk. To estimate the fraction of mergers passing as disks in current kinematics samples, we combine the probability that a merger will pass as a disk with theoretical merger fractions from a cosmological simulation. Taking the latter at face-value, the observed disk fractions are overestimated by small amounts: at most by $5\%$ at high stellar mass ($10^{10-11}$ M$_{\odot}$) and $15\%$ at low stellar mass ($10^{9-10}$ M$_{\odot}$).

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arXiv2018

The evolution of galaxy shapes in CANDELS: from prolate to oblate

We model the projected b/a-log a distributions of CANDELS main sequence star-forming galaxies, where a (b) is the semi-major (semi-minor) axis of the galaxy images. We find that smaller-a galaxies are rounder at all stellar masses M and redshifts, so we include a when analyzing b/a distributions. Approximating intrinsic shapes of the galaxies as triaxial ellipsoids and assuming a multivariate normal distribution of galaxy size and two shape parameters, we construct their intrinsic shape and size distributions to obtain the fractions of prolate, oblate and spheroidal galaxies in each redshift and mass bin. We find that galaxies tend to be prolate at low m and high redshifts, and oblate at high M and low redshifts, qualitatively consistent with van der Wel et al. (2014), implying that galaxies tend to evolve from prolate to oblate. These results are consistent with the predictions from simulations (Ceverino et al. 2015, Tomassetti et al. 2016) that the transition from prolate to oblate is caused by a compaction event at a characteristic mass range, making the galaxy center baryon dominated. We give probabilities of a galaxy's being prolate, oblate or spheroidal as a function of its M, redshift, projected b/a and a, which can facilitate target selections of galaxies with specific shapes at hight redshifts. We also give predicted optical depths of galaxies, which are qualitatively consistent with the expected correlation that AV should be higher for edge-on disk galaxies in each log a slice at low redshift and high mass bins.

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arXiv2018

Is the dark-matter halo spin a predictor of galaxy spin and size?

The similarity between the distributions of spins for galaxies ($λ_{\rm g}$) and for dark-matter haloes ($λ_{\rm h}$), indicated both by simulations and observations, is naively interpreted as a one-to-one correlation between the spins of a galaxy and its host halo. This is used to predict galaxy sizes in semi-analytic models via $R_{\rm e}\simeqλ_{\rm h} R_{\rm v}$, with $R_{\rm e}$ the half-mass radius of the galaxy and $R_{\rm v}$ the halo radius. Utilizing two different suites of zoom-in cosmological simulations, we find that $λ_{\rm g}$ and $λ_{\rm h}$ are in fact only barely correlated, especially at $z\geq 1$. A general smearing of this correlation is expected based on the different spin histories, where the more recently accreted baryons through streams gain and then lose significant angular momentum compared to the gradually accumulated dark matter. Expecting the spins of baryons and dark matter to be correlated at accretion into $R_{\rm v}$, the null correlation at the end reflects an anti-correlation between $λ_{\rm g}/λ_{\rm h}$ and $λ_{\rm h}$, which can partly arise from mergers and a compact star-forming phase that many galaxies undergo. On the other hand, the halo and galaxy spin vectors tend to be aligned, with a median $\cosθ=0.6$-0.7 between galaxy and halo, consistent with instreaming within a preferred plane. The galaxy spin is better correlated with the spin of the inner halo, but this largely reflects the effect of the baryons on the halo. Following the null spin correlation, $λ_{\rm h}$ is not a useful proxy for $R_{\rm e}$. While our simulations reproduce a general relation of the sort $R_{\rm e}=AR_{\rm vir}$, in agreement with observational estimates, the relation becomes tighter with $A=0.02(c/10)^{-0.7}$, where $c$ is the halo concentration, which in turn introduces a dependence on mass and redshift.

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