The discovery of Ultra-Faint Dwarf (UFD) galaxies in the halo of the Milky Way extends the faint end of the galaxy luminosity function to a few hundred solar luminosities. This extremely low luminosity regime poses a significant challenge for the pho
tometric characterization of these systems. We present a suite of simulations aimed at understanding how different observational choices related to the properties of a low luminosity system impact our ability to determine its true structural parameters such as half-light radius and central surface brightness. We focus on estimating half-light radii (on which mass estimates depend linearly) and find that these numbers can have up to 100% uncertainties when relatively shallow photometric surveys, such as SDSS, are used. Our simulations suggest that to recover structural parameters within 10% or better of their true values: (a) the ratio of the field-of-view to the half-light radius of the satellite must be greater than three, (b) the total number of stars, including background objects should be larger than 1000, and (c) the central to background stellar density ratio must be higher than 20. If one or more of these criteria are not met, the accuracy of the resulting structural parameters can be significantly compromised. In the context of future surveys such as LSST, the latter condition will be closely tied to our ability to remove unresolved background galaxies. Assessing the reliability of measured structural parameters will become increasingly critical as the next generation of deep wide-field surveys detects UFDs beyond the reach of current spectroscopic limits.
We introduce a new statistic omega_l for measuring and analyzing large-scale structure and particularly the baryon acoustic oscillations. omega_l is a band-filtered, configuration space statistic that is easily implemented and has advantages over the
traditional power spectrum and correlation function estimators. Unlike these estimators, omega_l can localize most of the acoustic information into a single dip at the acoustic scale while also avoiding sensitivity to the poorly constrained large scale power (i.e., the integral constraint) through the use of a localized and compensated filter. It is also sensitive to anisotropic clustering through pair counting and does not require any binning. We measure the shift in the acoustic peak due to nonlinear effects using the monopole omega_0 derived from subsampled dark matter catalogues as well as from mock galaxy catalogues created via halo occupation distribution (HOD) modeling. All of these are drawn from 44 realizations of 1024^3 particle dark matter simulations in a 1h^{-1}Gpc box at z=1. We compare these shifts with those obtained from the power spectrum and conclude that the results agree. This indicates that any distance measurements obtained from omega_0 and P(k) will be consistent with each other. We also show that it is possible to extract the same amount of acoustic information using either omega_0 or P(k) from equal volume surveys.
We measure the clustering of a sample of photometrically selected luminous red galaxies around a low redshift (0.2<z<0.6) sample of quasars selected from the Sloan Digital Sky Survey Data Release 5. We make use of a new statistical estimator to obtai
n precise measurements of the LRG auto-correlations and constrain halo occupation distributions for them. These are used to generate mock catalogs which aid in interpreting our quasar-LRG cross correlation measurements. The cross correlation is well described by a power law with slope 1.8pm0.1 and r_0=6pm0.5 h^{-1} Mpc, consistent with observed galaxy correlation functions. We find no evidence for `excess clustering on 0.1 Mpc scales and demonstrate that this is consistent with the results of Serber et al (2006) and Strand et al (2007), when one accounts for several subtleties in the interpretation of their measurements. Combining the quasar-LRG cross correlation with the LRG auto-correlations, we determine a large-scale quasar bias b_QSO = 1.09pm0.15 at a median redshift of 0.43, with no observed redshift or luminosity evolution. This corresponds to a mean halo mass <M>~ 10^{12} h^{-1} M_sun, Eddington ratios from 0.01 to 1 and lifetimes less than 10^{7} yr. Using simple models of halo occupation, these correspond to a number density of quasar hosts greater than 10^{-3} h^{3} Mpc^{-3} and stellar masses less than 10^{11} h^{-1} M_sun. The small-scale clustering signal can be interpreted with the aid of our mock LRG catalogs, and depends on the manner in which quasars inhabit halos. We find that our small scale measurements are inconsistent with quasar positions being randomly subsampled from halo centers above a mass threshold, requiring a satellite fraction > 25 per cent.
