A 2.5% measurement of the growth rate from small-scale redshift space clustering of SDSS-III CMASS galaxies

TL;DR

This work delivers the most precise growth-rate constraint to date from small-scale redshift-space clustering by fitting a halo-occupation distribution (HOD) model to anisotropic CMASS DR10 data on scales from roughly 0.8 to 32 h^{-1} Mpc. By leveraging N-body–based halo catalogs and a carefully validated fiber-collision correction strategy, the authors jointly constrain the HOD and the velocity field, obtaining $f\sigma_8(z_{\rm eff}=0.57)=0.450\pm0.011$, in excellent agreement with Planck LCDM within ~1.9σ and representing a 2.5× improvement over the prior large-scale DR11 result. The analysis robustly demonstrates that a simple, velocity-rescaled halo model can reproduce the small-scale anisotropic clustering, while highlighting subtle systematics linked to central-velocity definitions and intra-halo motions. These results constrain modified gravity scenarios that alter pairwise infall and FOG dispersions on these scales and underscore the importance of precise galaxy–halo connections for cosmological inferences. The methodology and velocity-structure constraints established here set the stage for tighter tests of gravity and dark sector physics with forthcoming data sets.

Abstract

We perform the first fit to the anisotropic clustering of SDSS-III CMASS DR10 galaxies on scales of ~ 0.8 - 32 Mpc/h. A standard halo occupation distribution model evaluated near the best fit Planck LCDM cosmology provides a good fit to the observed anisotropic clustering, and implies a normalization for the peculiar velocity field of M ~ 2 x 10^13 Msun/h halos of f*sigma8(z=0.57) = 0.450 +/- 0.011. Since this constraint includes both quasi-linear and non-linear scales, it should severely constrain modified gravity models that enhance pairwise infall velocities on these scales. Though model dependent, our measurement represents a factor of 2.5 improvement in precision over the analysis of DR11 on large scales, f*sigma8(z=0.57) = 0.447 +/- 0.028, and is the tightest single constraint on the growth rate of cosmic structure to date. Our measurement is consistent with the Planck LCDM prediction of 0.480 +/- 0.010 at the ~1.9 sigma level. Assuming a halo mass function evaluated at the best fit Planck cosmology, we also find that 10% of CMASS galaxies are satellites in halos of mass M ~ 6 x 10^13 Msun/h. While none of our tests and model generalizations indicate systematic errors due to an insufficiently detailed model of the galaxy-halo connection, the precision of these first results warrant further investigation into the modeling uncertainties and degeneracies with cosmological parameters.

Figures (23)

• Figure 1: The two-dimensional correlation function $\xi(r_{\sigma}, r_{\pi})$ of SDSS-III CMASS galaxies. The perturbations of the observed redshifts about the Hubble flow due to peculiar velocities introduce anistropy in the correlation strength with respect to the line of sight (y-axis in the figure). In this plot fiber collisions have been corrected using the angular upweighting method. The dashed circle indicates the separation scale ($\sim 8$ h$^{-1}$ Mpc) at which the observed quadrupole transitions from positive (dominated by Finger-of-God velocities) to negative (dominated by large scale Kaiser infall velocities). Contours at $\xi = [2,1,0.5,0.25]$ are shown with solid black curves.
• Figure 2: The normalized redshift probability distribution for CMASS targets that were assigned fibers (blue) and fiber collided galaxies (green). For collided galaxies, we use the nearest neighbor redshifts as a proxy; since the galaxy in a fiber collision pair that receives the fiber is randomly chosen, this is an unbiased estimate of the redshift distribution for objects without a fiber due to a fiber collision.
• Figure 3: Two hundred bootstrap regions used to estimate the covariance matrix of observables from the survey. The individual subregions are squares (or a union of squares) in the coordinates $\Delta$dec, $cos({\rm dec}) \Delta$ra.
• Figure 4: The clustering of CMASS targets in the north and south as a function of angular separation $\theta$ in arcseconds. The top axis translates angular scales to comoving separations at the effective redshift of our sample, $z_{\rm eff} = 0.57$. The fiber collision scale, 62", is highlighted with the dashed vertical line in the upper panel. The dash-dot line shows the best fit power law. The lower panel highlights the $\sim 20\%$ deviation of the observed clustering from the best fit power law and also compares $w(\theta)$ measured in the northern and southern hemispheres to $w(\theta)$ for targets in tiled mock catalog (red). We show the diagonal elements of the bootstrap errors derived separately for the N and S, offset by $\pm 5$ per-cent in $\theta$ for clarity.
• Figure 5: The angular weights as a function of pair separation (solid) in the North (blue) and South (green). The upper panel compares the ${\rm w}_{\rm pair}$ below the fiber collision radius (dashed vertical line). The plate density in the south is slightly higher, so the angular weight is smaller on scales below the fiber collision radius. The red solid line is the angular weight derived from the tiled mock catalog. In the bottom panel, we show ${\rm w}_{\rm pair} - 1$ for the north (blue) and tiled mocks (red). The angular weight for the south is similar. For scales above the fiber collision radius, $|{\rm w}_{\rm pair} - 1|$ is smaller than 4% on all scales. To illustrate the level of correction to transform the full sample target clustering to the redshift cut subsample (i.e., $w_t$ entering Eq. \ref{['eq:angweight']}), we also show as dashed lines ${\rm w}_{\rm pair}$ corresponding to $w_s$ measured from all targets assigned fibers and $w_t$ measured from the full target catalog. In this case star targets and galaxies outside our redshift cuts are included. These two schemes produce nearly identical angular weights. The grey bands indicate the uncertainty in $w_t$ corresponding to the spectroscopic subsample that we propagate to our final estimates of $w_p$, $\hat{\xi}_{0,2}$, and $\xi_{0,2}$.