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.Comment: 13 pages, 6 figures, 5 tables; published in ApJ (revised to match published version

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

We utilize $\Lambda$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-\`{a}-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 $z\sim0.5$.Comment: 17 pages, 9 figures and 4 tables; Astrophysical Journal, publishe

Galaxies Probing Galaxies at High Resolution: Co-Rotating Gas Associated with a Milky Way Analog at z=0.4

We present results on gas flows in the halo of a Milky Way-like galaxy at z=0.413 based on high-resolution spectroscopy of a background galaxy. This is the first study of circumgalactic gas at high spectral resolution towards an extended background source (i.e., a galaxy rather than a quasar). Using longslit spectroscopy of the foreground galaxy, we observe spatially extended H alpha emission with circular rotation velocity v=270 km/s. Using echelle spectroscopy of the background galaxy, we detect Mg II and Fe II absorption lines at impact parameter rho=27 kpc that are blueshifted from systemic in the sense of the foreground galaxy's rotation. The strongest absorber EW(2796) = 0.90 A has an estimated column density (N_H>10^19 cm-2) and line-of-sight velocity dispersion (sigma=17 km/s) that are consistent with the observed properties of extended H I disks in the local universe. Our analysis of the rotation curve also suggests that this r=30 kpc gaseous disk is warped with respect to the stellar disk. In addition, we detect two weak Mg II absorbers in the halo with small velocity dispersions (sigma<10 km/s). While the exact geometry is unclear, one component is consistent with an extraplanar gas cloud near the disk-halo interface that is co-rotating with the disk, and the other is consistent with a tidal feature similar to the Magellanic Stream. We can place lower limits on the cloud sizes (l>0.4 kpc) for these absorbers given the extended nature of the background source. We discuss the implications of these results for models of the geometry and kinematics of gas in the circumgalactic medium.Comment: 14 pages, 6 figures, submitted to ApJ, comments welcom

Missing Data and Multiple Imputation: An Unbiased Approach

The default method of dealing with missing data in statistical analyses is to only use the complete observations (complete case analysis), which can lead to unexpected bias when data do not meet the assumption of missing completely at random (MCAR). For the assumption of MCAR to be met, missingness cannot be related to either the observed or unobserved variables. A less stringent assumption, missing at random (MAR), requires that missingness not be associated with the value of the missing variable itself, but can be associated with the other observed variables. When data are truly MAR as opposed to MCAR, the default complete case analysis method can lead to biased results. There are statistical options available to adjust for data that are MAR, including multiple imputation (MI) which is consistent and efficient at estimating effects. Multiple imputation uses informing variables to determine statistical distributions for each piece of missing data. Then multiple datasets are created by randomly drawing on the distributions for each piece of missing data. Since MI is efficient, only a limited number, usually less than 20, of imputed datasets are required to get stable estimates. Each imputed dataset is analyzed using standard statistical techniques, and then results are combined to get overall estimates of effect. A simulation study will be demonstrated to show the results of using the default complete case analysis, and MI in a linear regression of MCAR and MAR simulated data. Further, MI was successfully applied to the association study of CO2 levels and headaches when initial analysis showed there may be an underlying association between missing CO2 levels and reported headaches. Through MI, we were able to show that there is a strong association between average CO2 levels and the risk of headaches. Each unit increase in CO2 (mmHg) resulted in a doubling in the odds of reported headaches