Analyzing Baryon Acoustic Oscillations in Sparse Spectroscopic Samples via Cross-Correlation with Dense Photometry

We develop a formalism for measuring the cosmological distance scale from baryon acoustic oscillations (BAO) using the cross-correlation of a sparse redshift survey with a denser photometric sample. This reduces the shot noise that would otherwise affect the auto-correlation of the sparse spectroscopic map. As a proof of principle, we make the first on-sky application of this method to a sparse sample defined as the z>0.6 tail of the Sloan Digital Sky Survey's (SDSS) BOSS/CMASS sample of galaxies and a dense photometric sample from SDSS DR9. We find a 2.8sigma preference for the BAO peak in the cross-correlation at an effective z=0.64, from which we measure the angular diameter distance D_M(z=0.64) = (2418 +/- 73 Mpc) (r_s/r_{s,fid}). Accordingly, we expect that using this method to combine sparse spectroscopy with the deep, high quality imaging that is just now becoming available will enable higher precision BAO measurements than possible with the spectroscopy alone.Comment: 14 pages, 4 figures; updated reference

A Practical Computational Method for the Anisotropic Redshift-Space 3-Point Correlation Function

We present an algorithm enabling computation of the anisotropic redshift-space galaxy 3-point correlation function (3PCF) scaling as $N^2$, with $N$ the number of galaxies. Our previous work showed how to compute the isotropic 3PCF with this scaling by expanding the radially-binned density field around each galaxy in the survey into spherical harmonics and combining these coefficients to form multipole moments. The $N^2$ scaling occurred because this approach never explicitly required the relative angle between a galaxy pair about the primary galaxy. Here we generalize this work, demonstrating that in the presence of azimuthally-symmetric anisotropy produced by redshift-space distortions (RSD) the 3PCF can be described by two triangle side lengths, two independent total angular momenta, and a spin. This basis for the anisotropic 3PCF allows its computation with negligible additional work over the isotropic 3PCF. We also present the covariance matrix of the anisotropic 3PCF measured in this basis. Our algorithm tracks the full 5-D redshift-space 3PCF, uses an accurate line of sight to each triplet, is exact in angle, and easily handles edge correction. It will enable use of the anisotropic large-scale 3PCF as a probe of RSD in current and upcoming large-scale redshift surveys.Comment: 17 pages, 2 figures, MNRAS submitte

An Analytical Model for the Triaxial Collapse of Cosmological Perturbations

We present an analytical model for the non-spherical collapse of overdense regions out of a Gaussian random field of initial cosmological perturbations. The collapsing region is treated as an ellipsoid of constant density, acted upon by the quadrupole tidal shear from the surrounding matter. The dynamics of the ellipsoid is set by the ellipsoid self-gravity and the external quadrupole shear. Both forces are linear in the coordinates and therefore maintain homogeneity of the ellipsoid at all times. The amplitude of the external shear is evolved into the non-linear regime in thin spherical shells that are allowed to move only radially according to the mass interior to them. We describe how the initial conditions can be drawn in the appropriate correlated way from a random field of initial density perturbations. By considering many random realizations of the initial conditions, we calculate the distribution of shapes and angular momenta acquired by objects through the coupling of their quadrupole moment to the tidal shear. The average value of the spin parameter, 0.04, is found to be only weakly dependent on the system mass, the mean cosmological density, or the initial power spectrum of perturbations, in agreement with N-body simulations. For the cold dark matter power spectrum, most objects evolve from a quasi-spherical initial state to a pancake or filament and then to complete virialization. Low-spin objects tend to be more spherical. The evolution history of shapes is primarily induced by the external shear and not by the initial triaxiality of the objects. The statistical distribution of the triaxial shapes of collapsing regions can be used to test cosmological models against galaxy surveys on large scales.Comment: 42 pages, Tex, followed by 10 uuencoded figure

Modeling the large-scale redshift-space 3-point correlation function of galaxies

We present a configuration-space model of the large-scale galaxy 3-point correlation function (3PCF) based on leading-order perturbation theory and including redshift space distortions (RSD). This model should be useful in extracting distance-scale information from the 3PCF via the Baryon Acoustic Oscillation (BAO) method. We include the first redshift-space treatment of biasing by the baryon-dark matter relative velocity. Overall, on large scales the effect of RSD is primarily a renormalization of the 3PCF that is roughly independent of both physical scale and triangle opening angle; for our adopted $\Omega_{\rm m}$ and bias values, the rescaling is a factor of $\sim 1.8$. We also present an efficient scheme for computing 3PCF predictions from our model, important for allowing fast exploration of the space of cosmological parameters in future analyses.Comment: 23 pages, 11 figures, submitted MNRA