The Clustering of the SDSS Main Galaxy Sample II: Mock galaxy catalogues and a measurement of the growth of structure from Redshift Space Distortions at $z=0.15$

TL;DR

This work measures Redshift-Space Distortions in SDSS DR7 MGS at $z\approx0.15$ by constructing 1000 realistic mock catalogues with PICOLA, populating halos via HOD, and validating a CLPT-based RSD model. It jointly fits monopole and quadrupole moments of the correlation function, accounting for AP distortions and binning effects, to extract $f\sigma_{8}$ and bias parameters, obtaining $f\sigma_{8}$ around $0.49$–$0.53$ and constraining the growth index $\gamma$ when combined with Planck and CMASS data. The analyses show strong consistency with General Relativity while highlighting the importance of allowing AP parameters, particularly $\alpha$, to vary in growth measurements. The methodology provides robust covariance handling, systematic tests, and a framework for future low-redshift RSD studies with large-scale surveys.

Abstract

We measure Redshift-Space Distortions (RSD) in the two-point correlation function of a sample of $63,163$ spectroscopically identified galaxies with $z < 0.2$, an epoch where there are currently only limited measurements, from the Sloan Digital Sky Survey (SDSS) Data Release 7 Main Galaxy Sample. Our sample, which we denote MGS, covers 6,813 deg$^2$ with an effective redshift $z_{eff}=0.15$ and is described in our companion paper (Paper I), which concentrates on BAO measurements. In order to validate the fitting methods used in both papers, and derive errors, we create and analyse 1000 mock catalogues using a new algorithm called PICOLA to generate accurate dark matter fields. Haloes are then selected using a friends-of-friends algorithm, and populated with galaxies using a Halo-Occupation Distribution fitted to the data. Using errors derived from these mocks, we fit a model to the monopole and quadrupole moments of the MGS correlation function. If we assume no Alcock-Paczynski (AP) effect (valid at $z=0.15$ for any smooth model of the expansion history), we measure the amplitude of the velocity field, $fσ_{8}$, at $z=0.15$ to be $0.49_{-0.14}^{+0.15}$. We also measure $fσ_{8}$ including the AP effect. This latter measurement can be freely combined with recent Cosmic Microwave Background results to constrain the growth index of fluctuations, $γ$. Assuming a background $Λ$CDM cosmology and combining with current Baryon Acoustic Oscillation data we find $γ= 0.64 \pm 0.09$, which is consistent with the prediction of General Relativity ($γ\approx 0.55$), though with a slight preference for higher $γ$ and hence models with weaker gravitational interactions.

Figures (24)

• Figure 1: The blue area shows a flat, all-sky projection of the footprint of our MGS sample, which occupies 6,813 deg$^2$. The red area shows the same geometry, after a 180$^{\rm o}$ rotation. This illustrates how we produce two mock galaxy samples from every full-sky dark matter halo catalog.
• Figure 2: The number density as a function of redshift for our galaxy sample compared to the mean of the mocks after subsampling. The error bars come from the standard deviation of our 1000 mock realisations
• Figure 3: The power spectrum of the dark matter field in a cubic box from the picola and gadget-2 runs described in the text. We can see good agreement between the two even into the non-linear regime.
• Figure 4: A comparison of the halo mass function from our gadget-2 and picola simulations run from the same initial conditions. We see a lack of halos on small scales due to the finite mesh resolution, but this is easily compensated for with the HOD fitting described later.
• Figure 5: The normalised number of constituent dark matter particles found within a halo as a function of their separation from the halo centre of mass, in units of the virial radius, for a given halo mass range. We see that the halos from picola are generally more dispersed than those from gadget-2, where the particles have not collapsed sufficiently for the FoF algorithm to group them. This in turn leads to a slight lack of low mass halos overall, which we are able to correct for in our HOD fitting method.