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Michael R. Blanton

Publications and source records attributed to Michael R. Blanton.

At least 55 records · Page 3Linked to original sources

The Time-Domain Spectroscopic Survey: Target Selection for Repeat Spectroscopy

As astronomers increasingly exploit the information available in the time domain, spectroscopic variability in particular opens broad new channels of investigation. Here we describe the selection algorithms for all targets intended for repeat spectroscopy in the Time Domain Spectroscopic Survey (TDSS), part of the extended Baryon Oscillation Spectroscopic Survey within the Sloan Digital Sky Survey-IV. Also discussed are the scientific rationale and technical constraints leading to these target selections. The TDSS includes a large "Repeat Quasar Spectroscopy" (RQS) program delivering ~13,000 repeat spectra of confirmed SDSS quasars, and several smaller "Few-Epoch Spectroscopy" (FES) programs targeting specific classes of quasars as well as stars. The RQS program aims to provide a large and diverse quasar data set for studying variations in quasar spectra on timescales of years, a comparison sample for the FES quasar programs, and opportunity for discovering rare, serendipitous events. The FES programs cover a wide variety of phenomena in both quasars and stars. Quasar FES programs target broad absorption line quasars, high signal-to-noise ratio normal broad line quasars, quasars with double-peaked or very asymmetric broad emission line profiles, binary supermassive black hole candidates, and the most photometrically variable quasars. Strongly variable stars are also targeted for repeat spectroscopy, encompassing many types of eclipsing binary systems, and classical pulsators like RR Lyrae. Other stellar FES programs allow spectroscopic variability studies of active ultracool dwarf stars, dwarf carbon stars, and white dwarf/M dwarf spectroscopic binaries. We present example TDSS spectra and describe anticipated sample sizes and results.

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SDSS-V: Pioneering Panoptic Spectroscopy

SDSS-V will be an all-sky, multi-epoch spectroscopic survey of over six million objects. It is designed to decode the history of the Milky Way, trace the emergence of the chemical elements, reveal the inner workings of stars, and investigate the origin of planets. It will also create an integral-field spectroscopic map of the gas in the Galaxy and the Local Group that is 1,000x larger than the current state of the art and at high enough spatial resolution to reveal the self-regulation mechanisms of galactic ecosystems. SDSS-V will pioneer systematic, spectroscopic monitoring across the whole sky, revealing changes on timescales from 20 minutes to 20 years. The survey will thus track the flickers, flares, and radical transformations of the most luminous persistent objects in the universe: massive black holes growing at the centers of galaxies. The scope and flexibility of SDSS-V will be unique among extant and future spectroscopic surveys: it is all-sky, with matched survey infrastructures in both hemispheres; it provides near-IR and optical multi-object fiber spectroscopy that is rapidly reconfigurable to serve high target densities, targets of opportunity, and time-domain monitoring; and it provides optical, ultra-wide-field integral field spectroscopy. SDSS-V, with its programs anticipated to start in 2020, will be well-timed to multiply the scientific output from major space missions (e.g., TESS, Gaia, eROSITA) and ground-based projects. SDSS-V builds on the 25-year heritage of SDSS's advances in data analysis, collaboration infrastructure, and product deliverables. The project is now refining its science scope, optimizing the survey strategies, and developing new hardware that builds on the SDSS-IV infrastructure. We present here an overview of the current state of these developments as we seek to build our worldwide consortium of institutional and individual members.

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The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: First measurement of Baryon Acoustic Oscillations between redshift 0.8 and 2.2

We present measurements of the Baryon Acoustic Oscillation (BAO) scale in redshift-space using the clustering of quasars. We consider a sample of 147,000 quasars from the extended Baryon Oscillation Spectroscopic Survey (eBOSS) distributed over 2044 square degrees with redshifts $0.8 < z < 2.2$ and measure their spherically-averaged clustering in both configuration and Fourier space. Our observational dataset and the 1400 simulated realizations of the dataset allow us to detect a preference for BAO that is greater than 2.8$σ$. We determine the spherically averaged BAO distance to $z = 1.52$ to 3.8 per cent precision: $D_V(z=1.52)=3843\pm147 \left(r_{\rm d}/r_{\rm d, fid}\right)\ $Mpc. This is the first time the location of the BAO feature has been measured between redshifts 1 and 2. Our result is fully consistent with the prediction obtained by extrapolating the Planck flat $Λ$CDM best-fit cosmology. All of our results are consistent with basic large-scale structure (LSS) theory, confirming quasars to be a reliable tracer of LSS, and provide a starting point for numerous cosmological tests to be performed with eBOSS quasar samples. We combine our result with previous, independent, BAO distance measurements to construct an updated BAO distance-ladder. Using these BAO data alone and marginalizing over the length of the standard ruler, we find $Ω_Λ > 0$ at 6.6$σ$ significance when testing a $Λ$CDM model with free curvature.

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The clustering of luminous red galaxies at z $\sim$ 0.7 from eBOSS and BOSS data

We present the first scientific results from the luminous red galaxy sample (LRG) of the extended Baryon Oscillation Spectroscopic Survey (eBOSS). We measure the small and intermediate scale clustering from a sample of more than 61,000 galaxies in the redshift range $0.6 < z < 0.9$. We interpret these measurements in the framework of the Halo Occupation Distribution. The bias of eBOSS LRGs is $2.30 \pm 0.03$, with a satellite fraction of $13\pm3$\% and a mean halo mass of $2.5\times10^{13}h^{-1}M_{\odot}$. These results are consistent with expectations, demonstrating that eBOSS galaxies will be reliable tracers of large scale structure at $z\sim 0.7$. The eBOSS galaxy bias implies a scatter of luminosity at fixed halo mass, $σ_{\log L}$, of 0.19 dex. Using the clustering of massive galaxies from BOSS-CMASS, BOSS-LOWZ, and SDSS, we find that $σ_{\log L}=0.19$ is consistent with observations over the full redshift range that these samples cover. The addition of eBOSS to previous surveys allows investigation of the evolution of massive galaxies over the past $\sim 7$ Gyr.

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The SDSS-IV MaNGA Sample: Design, Optimization, and Usage Considerations

We describe the sample design for the SDSS-IV MaNGA survey and present the final properties of the main samples along with important considerations for using these samples for science. Our target selection criteria were developed while simultaneously optimizing the size distribution of the MaNGA integral field units (IFUs), the IFU allocation strategy, and the target density to produce a survey defined in terms of maximizing S/N, spatial resolution, and sample size. Our selection strategy makes use of redshift limits that only depend on i-band absolute magnitude ($M_i$), or, for a small subset of our sample, $M_i$ and color (NUV-i). Such a strategy ensures that all galaxies span the same range in angular size irrespective of luminosity and are therefore covered evenly by the adopted range of IFU sizes. We define three samples: the Primary and Secondary samples are selected to have a flat number density with respect to $M_i$ and are targeted to have spectroscopic coverage to 1.5 and 2.5 effective radii (Re), respectively. The Color-Enhanced supplement increases the number of galaxies in the low-density regions of color-magnitude space by extending the redshift limits of the Primary sample in the appropriate color bins. The samples cover the stellar mass range $5\times10^8 \leq M_* \leq 3\times10^{11} M_{\odot}$ and are sampled at median physical resolutions of 1.37 kpc and 2.5 kpc for the Primary and Secondary samples respectively. We provide weights that will statistically correct for our luminosity and color-dependent selection function and IFU allocation strategy, thus correcting the observed sample to a volume limited sample.

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Sloan Digital Sky Survey IV: Mapping the Milky Way, Nearby Galaxies, and the Distant Universe

We describe the Sloan Digital Sky Survey IV (SDSS-IV), a project encompassing three major spectroscopic programs. The Apache Point Observatory Galactic Evolution Experiment 2 (APOGEE-2) is observing hundreds of thousands of Milky Way stars at high resolution and high signal-to-noise ratio in the near-infrared. The Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey is obtaining spatially-resolved spectroscopy for thousands of nearby galaxies (median redshift of z = 0.03). The extended Baryon Oscillation Spectroscopic Survey (eBOSS) is mapping the galaxy, quasar, and neutral gas distributions between redshifts z = 0.6 and 3.5 to constrain cosmology using baryon acoustic oscillations, redshift space distortions, and the shape of the power spectrum. Within eBOSS, we are conducting two major subprograms: the SPectroscopic IDentification of eROSITA Sources (SPIDERS), investigating X-ray AGN and galaxies in X-ray clusters, and the Time Domain Spectroscopic Survey (TDSS), obtaining spectra of variable sources. All programs use the 2.5-meter Sloan Foundation Telescope at Apache Point Observatory; observations there began in Summer 2014. APOGEE-2 also operates a second near-infrared spectrograph at the 2.5-meter du Pont Telescope at Las Campanas Observatory, with observations beginning in early 2017. Observations at both facilities are scheduled to continue through 2020. In keeping with previous SDSS policy, SDSS-IV provides regularly scheduled public data releases; the first one, Data Release 13, was made available in July 2016.

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The Effect of Fiber Collisions on the Galaxy Power Spectrum Multipole

Fiber-fed multi-object spectroscopic surveys, with their ability to collect an unprecedented number of redshifts, currently dominate large-scale structure studies. However, physical constraints limit these surveys from successfully collecting redshifts from galaxies too close to each other on the focal plane. This ultimately leads to significant systematic effects on galaxy clustering measurements. Using simulated mock catalogs, we demonstrate that fiber collisions have a significant impact on the power spectrum, $P(k)$, monopole and quadrupole that exceeds sample variance at scales smaller than $k\sim0.1~h/Mpc$. We present two methods to account for fiber collisions in the power spectrum. The first, statistically reconstructs the clustering of fiber collided galaxy pairs by modeling the distribution of the line-of-sight displacements between them. It also properly accounts for fiber collisions in the shot-noise correction term of the $P(k)$ estimator. Using this method, we recover the true $P(k)$ monopole of the mock catalogs with residuals of $<0.5\%$ at $k=0.3~h/Mpc$ and $<4\%$ at $k=0.83~h/Mpc$ -- a significant improvement over existing correction methods. The quadrupole, however, does not improve significantly. The second method models the effect of fiber collisions on the power spectrum as a convolution with a configuration space top-hat function that depends on the physical scale of fiber collisions. It directly computes theoretical predictions of the fiber-collided $P(k)$ multipoles and reduces the influence of smaller scales to a set of nuisance parameters. Using this method, we reliably model the effect of fiber collisions on the monopole and quadrupole down to the scale limits of theoretical predictions. The methods we present in this paper will allow us to robustly analyze galaxy power spectrum multipole measurements to much smaller scales than previously possible.

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The Data Reduction Pipeline for the SDSS-IV MaNGA IFU Galaxy Survey

Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) is an optical fiber-bundle integral-field unit (IFU) spectroscopic survey that is one of three core programs in the fourth-generation Sloan Digital Sky Survey (SDSS-IV). With a spectral coverage of 3622 - 10,354 Angstroms and an average footprint of ~ 500 arcsec^2 per IFU the scientific data products derived from MaNGA will permit exploration of the internal structure of a statistically large sample of 10,000 low redshift galaxies in unprecedented detail. Comprising 174 individually pluggable science and calibration IFUs with a near-constant data stream, MaNGA is expected to obtain ~ 100 million raw-frame spectra and ~ 10 million reduced galaxy spectra over the six-year lifetime of the survey. In this contribution, we describe the MaNGA Data Reduction Pipeline (DRP) algorithms and centralized metadata framework that produces sky-subtracted, spectrophotometrically calibrated spectra and rectified 3-D data cubes that combine individual dithered observations. For the 1390 galaxy data cubes released in Summer 2016 as part of SDSS-IV Data Release 13 (DR13), we demonstrate that the MaNGA data have nearly Poisson-limited sky subtraction shortward of ~ 8500 Angstroms and reach a typical 10-sigma limiting continuum surface brightness mu = 23.5 AB/arcsec^2 in a five arcsec diameter aperture in the g band. The wavelength calibration of the MaNGA data is accurate to 5 km/s rms, with a median spatial resolution of 2.54 arcsec FWHM (1.8 kpc at the median redshift of 0.037) and a median spectral resolution of sigma = 72 km/s.

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SDSS-IV MaNGA IFS Galaxy Survey --- Survey Design, Execution, and Initial Data Quality

The MaNGA Survey (Mapping Nearby Galaxies at Apache Point Observatory) is one of three core programs in the Sloan Digital Sky Survey IV. It is obtaining integral field spectroscopy (IFS) for 10K nearby galaxies at a spectral resolution of R~2000 from 3,622-10,354A. The design of the survey is driven by a set of science requirements on the precision of estimates of the following properties: star formation rate surface density, gas metallicity, stellar population age, metallicity, and abundance ratio, and their gradients; stellar and gas kinematics; and enclosed gravitational mass as a function of radius. We describe how these science requirements set the depth of the observations and dictate sample selection. The majority of targeted galaxies are selected to ensure uniform spatial coverage in units of effective radius (Re) while maximizing spatial resolution. About 2/3 of the sample is covered out to 1.5Re (Primary sample), and 1/3 of the sample is covered to 2.5Re (Secondary sample). We describe the survey execution with details that would be useful in the design of similar future surveys. We also present statistics on the achieved data quality, specifically, the point spread function, sampling uniformity, spectral resolution, sky subtraction, and flux calibration. For our Primary sample, the median r-band signal-to-noise ratio is ~73 per 1.4A pixel for spectra stacked between 1-1.5 Re. Measurements of various galaxy properties from the first year data show that we are meeting or exceeding the defined requirements for the majority of our science goals.

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Towards an Understanding of Changing-Look Quasars: An Archival Spectroscopic Search in SDSS

The uncertain origin of the recently-discovered `changing-looking' quasar phenomenon -- in which a luminous quasar dims significantly to a quiescent state in repeat spectroscopy over ~10 year timescales -- may present unexpected challenges to our understanding of quasar accretion. To better understand this phenomenon, we take a first step to building a sample of changing-look quasars with a systematic but simple archival search for these objects in the Sloan Digital Sky Survey Data Release 12. By leveraging the >10 year baselines for objects with repeat spectroscopy, we uncover two new changing-look quasars, and a third discovered previously. Decomposition of the multi-epoch spectra and analysis of the broad emission lines suggest that the quasar accretion disk emission dims due to rapidly decreasing accretion rates (by factors of >2.5), while disfavoring changes in intrinsic dust extinction for the two objects where these analyses are possible. Broad emission line energetics also support intrinsic dimming of quasar emission as the origin for this phenomenon rather than transient tidal disruption events or supernovae. Although our search criteria included quasars at all redshifts and transitions from either quasar-like to galaxy-like states or the reverse, all of the clear cases of changing-look quasars discovered were at relatively low-redshift (z ~ 0.2 - 0.3) and only exhibit quasar-like to galaxy-like transitions.

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PRIMUS + DEEP2: Clustering of X-ray, Radio and IR-AGN at z~0.7

We measure the clustering of X-ray, radio, and mid-IR-selected active galactic nuclei (AGN) at 0.2 < z < 1.2 using multi-wavelength imaging and spectroscopic redshifts from the PRIMUS and DEEP2 redshift surveys, covering 7 separate fields spanning ~10 square degrees. Using the cross-correlation of AGN with dense galaxy samples, we measure the clustering scale length and slope, as well as the bias, of AGN selected at different wavelengths. Similar to previous studies, we find that X-ray and radio AGN are more clustered than mid-IR-selected AGN. We further compare the clustering of each AGN sample with matched galaxy samples designed to have the same stellar mass, star formation rate, and redshift distributions as the AGN host galaxies and find no significant differences between their clustering properties. The observed differences in the clustering of AGN selected at different wavelengths can therefore be explained by the clustering differences of their host populations, which have different distributions in both stellar mass and star formation rate. Selection biases inherent in AGN selection, therefore, determine the clustering of observed AGN samples. We further find no significant difference between the clustering of obscured and unobscured AGN, using IRAC or WISE colors or X-ray hardness ratio.

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The SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Overview and Early Data

The Extended Baryon Oscillation Spectroscopic Survey (eBOSS) will conduct novel cosmological observations using the BOSS spectrograph at Apache Point Observatory. Observations will be simultaneous with the Time Domain Spectroscopic Survey (TDSS) designed for variability studies and the Spectroscopic Identification of eROSITA Sources (SPIDERS) program designed for studies of X-ray sources. eBOSS will use four different tracers to measure the distance-redshift relation with baryon acoustic oscillations (BAO). Using more than 250,000 new, spectroscopically confirmed luminous red galaxies at a median redshift z=0.72, we project that eBOSS will yield measurements of $d_A(z)$ to an accuracy of 1.2% and measurements of H(z) to 2.1% when combined with the z>0.6 sample of BOSS galaxies. With ~195,000 new emission line galaxy redshifts, we expect BAO measurements of $d_A(z)$ to an accuracy of 3.1% and H(z) to 4.7% at an effective redshift of z= 0.87. A sample of more than 500,000 spectroscopically-confirmed quasars will provide the first BAO distance measurements over the redshift range 0.9 2.1; these new data will enhance the precision of $d_A(z)$ and H(z) by a factor of 1.44 relative to BOSS. Furthermore, eBOSS will provide improved tests of General Relativity on cosmological scales through redshift-space distortion measurements, improved tests for non-Gaussianity in the primordial density field, and new constraints on the summed mass of all neutrino species. Here, we provide an overview of the cosmological goals, spectroscopic target sample, demonstration of spectral quality from early data, and projected cosmological constraints from eBOSS.

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SDSS-IV/MaNGA: Spectrophotometric Calibration Technique

Mapping Nearby Galaxies at Apache Point Observatory (MaNGA), one of three core programs in the Sloan Digital Sky Survey-IV (SDSS-IV), is an integral-field spectroscopic (IFS) survey of roughly 10,000 nearby galaxies. It employs dithered observations using 17 hexagonal bundles of 2 arcsec fibers to obtain resolved spectroscopy over a wide wavelength range of 3,600-10,300A. To map the internal variations within each galaxy, we need to perform accurate {\it spectral surface photometry}, which is to calibrate the specific intensity at every spatial location sampled by each individual aperture element of the integral field unit. The calibration must correct only for the flux loss due to atmospheric throughput and the instrument response, but not for losses due to the finite geometry of the fiber aperture. This requires the use of standard star measurements to strictly separate these two flux loss factors (throughput versus geometry), a difficult challenge with standard single-fiber spectroscopy techniques due to various practical limitations. Therefore, we developed a technique for spectral surface photometry using multiple small fiber-bundles targeting standard stars simultaneously with galaxy observations. We discuss the principles of our approach and how they compare to previous efforts, and we demonstrate the precision and accuracy achieved. MaNGA's relative calibration between the wavelengths of H$α$ and H$β$ has a root-mean-square (RMS) of 1.7%, while that between [NII] $λ$6583A and [OII] $λ$3727A has an RMS of 4.7%. Using extinction-corrected star formation rates and gas-phase metallicities as an illustration, this level of precision guarantees that flux calibration errors will be sub-dominant when estimating these quantities. The absolute calibration is better than 5% for more than 89% of MaNGA's wavelength range.

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PRIMUS: The Effect of Physical Scale on the Luminosity-Dependence of Galaxy Clustering via Cross-Correlations

We report small-scale clustering measurements from the PRIMUS spectroscopic redshift survey as a function of color and luminosity. We measure the real-space cross-correlations between 62,106 primary galaxies with PRIMUS redshifts and a tracer population of 545,000 photometric galaxies over redshifts from z=0.2 to z=1. We separately fit a power-law model in redshift and luminosity to each of three independent color-selected samples of galaxies. We report clustering amplitudes at fiducial values of z=0.5 and L=1.5 L*. The clustering of the red galaxies is ~3 times as strong as that of the blue galaxies and ~1.5 as strong as that of the green galaxies. We also find that the luminosity dependence of the clustering is strongly dependent on physical scale, with greater luminosity dependence being found between r=0.0625 Mpc/h and r=0.25 Mpc/h, compared to the r=0.5 Mpc/h to r=2 Mpc/h range. Moreover, over a range of two orders of magnitude in luminosity, a single power-law fit to the luminosity dependence is not sufficient to explain the increase in clustering at both the bright and faint ends at the smaller scales. We argue that luminosity-dependent clustering at small scales is a necessary component of galaxy-halo occupation models for blue, star-forming galaxies as well as for red, quenched galaxies.

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The Apache Point Observatory Galactic Evolution Experiment (APOGEE)

The Apache Point Observatory Galactic Evolution Experiment (APOGEE), one of the programs in the Sloan Digital Sky Survey III (SDSS-III), has now completed its systematic, homogeneous spectroscopic survey sampling all major populations of the Milky Way. After a three year observing campaign on the Sloan 2.5-m Telescope, APOGEE has collected a half million high resolution (R~22,500), high S/N (>100), infrared (1.51-1.70 microns) spectra for 146,000 stars, with time series information via repeat visits to most of these stars. This paper describes the motivations for the survey and its overall design---hardware, field placement, target selection, operations---and gives an overview of these aspects as well as the data reduction, analysis and products. An index is also given to the complement of technical papers that describe various critical survey components in detail. Finally, we discuss the achieved survey performance and illustrate the variety of potential uses of the data products by way of a number of science demonstrations, which span from time series analysis of stellar spectral variations and radial velocity variations from stellar companions, to spatial maps of kinematics, metallicity and abundance patterns across the Galaxy and as a function of age, to new views of the interstellar medium, the chemistry of star clusters, and the discovery of rare stellar species. As part of SDSS-III Data Release 12, all of the APOGEE data products are now publicly available.

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The SDSS-IV extended Baryonic Oscillation Spectroscopic Survey: Luminous Red Galaxy Target Selection

We describe the algorithm used to select the Luminous Red Galaxy (LRG) sample for the extended Baryon Oscillation Spectroscopic Survey (eBOSS) of the Sloan Digital Sky Survey IV (SDSS-IV) using photometric data from both the SDSS and the Wide-Field Infrared Survey Explorer (WISE). LRG targets are required to meet a set of color selection criteria and have z-band and i-band MODEL magnitudes z < 19.95 and 19.9 < i < 21.8, respectively. Our algorithm selects roughly 50 LRG targets per square degree, the great majority of which lie in the redshift range 0.6 < z < 1.0 (median redshift 0.71). We demonstrate that our methods are highly effective at eliminating stellar contamination and lower-redshift galaxies. We perform a number of tests using spectroscopic data from SDSS-III/BOSS to determine the redshift reliability of our target selection and its ability to meet the science requirements of eBOSS. The SDSS spectra are of high enough signal-to-noise ratio that at least 89% of the target sample yields secure redshift measurements. We also present tests of the uniformity and homogeneity of the sample, demonstrating that it should be clean enough for studies of the large-scale structure of the universe at higher redshifts than SDSS-III/BOSS LRGs reached.

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Dark Matter Halo Models of Stellar Mass-Dependent Galaxy Clustering in PRIMUS+DEEP2 at 0.2<z<1.2

We utilize $Λ$CDM halo occupation models of galaxy clustering to investigate the evolving stellar mass dependent clustering of galaxies in the PRIsm MUlti-object Survey (PRIMUS) and DEEP2 Redshift Survey over the past eight billion years of cosmic time, between $0.2<z<1.2$. These clustering measurements provide new constraints on the connections between dark matter halo properties and galaxy properties in the context of the evolving large-scale structure of the universe. Using both an analytic model and a set of mock galaxy catalogs, we find a strong correlation between central galaxy stellar mass and dark matter halo mass over the range $M_\mathrm{halo}\sim10^{11}$-$10^{13}~h^{-1}M_\odot$, approximately consistent with previous observations and theoretical predictions. However, the stellar-to-halo mass relation (SHMR) and the mass scale where star formation efficiency reaches a maximum appear to evolve more strongly than predicted by other models, including models based primarily on abundance-matching constraints. We find that the fraction of satellite galaxies in haloes of a given mass decreases significantly from $z\sim0.5$ to $z\sim0.9$, partly due to the fact that haloes at fixed mass are rarer at higher redshift and have lower abundances. We also find that the $M_1/M_\mathrm{min}$ ratio, a model parameter that quantifies the critical mass above which haloes host at least one satellite, decreases from $\approx20$ at $z\sim0$ to $\approx13$ at $z\sim0.9$. Considering the evolution of the subhalo mass function vis-à-vis satellite abundances, this trend has implications for relations between satellite galaxies and halo substructures and for intracluster mass, which we argue has grown due to stripped and disrupted satellites between $z\sim0.9$ and $z\sim0.5$.

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Stellar Metallicity Gradients in SDSS galaxies

We infer stellar metallicity and abundance ratio gradients for a sample of red galaxies in the Sloan Digital Sky Survey (SDSS) Main galaxy sample. Because this sample does not have multiple spectra at various radii in a single galaxy, we measure these gradients statistically. We separate galaxies into stellar mass bins, stack their spectra in redshift bins, and calculate the measured absorption line indices in projected annuli by differencing spectra in neighboring redshift bins. After determining the line indices, we use stellar population modeling from the EZ\_Ages software to calculate ages, metallicities, and abundance ratios within each annulus. Our data covers the central regions of these galaxies, out to slightly higher than $1 R_{e}$. We find detectable gradients in metallicity and relatively shallow gradients in abundance ratios, similar to results found for direct measurements of individual galaxies. The gradients are only weakly dependent on stellar mass, and this dependence is well-correlated with the change of $R_e$ with mass. Based on this data, we report mean equivalent widths, metallicities, and abundance ratios as a function of mass and velocity dispersion for SDSS early-type galaxies, for fixed apertures of 2.5 kpc and of 0.5 $R_e$.

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