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Register a new userThe Galaxy and Mass N-Point Correlation Functions: a Blast from the Past
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P. J. E. Peebles
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Correlation functions and related statistics have been favorite measures of the distributions of extragalactic objects ever since people started analyzing the clustering of the galaxies in the 1930s. I review the evolving reasons for this choice, and comment on some of the present issues in the application and interpretation of these statistics, with particular attention to the question of how closely galaxies trace mass.
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We derive analytic covariance matrices for the $N$-Point Correlation Functions (NPCFs) of galaxies in the Gaussian limit. Our results are given for arbitrary $N$ and projected onto the isotropic basis functions of Cahn & Slepian (2020), recently shown to facilitate efficient NPCF estimation. A numerical implementation of the 4PCF covariance is compared to the sample covariance obtained from a set of lognormal simulations, Quijote dark matter halo catalogues, and MultiDark-Patchy galaxy mocks, with the latter including realistic survey geometry. The analytic formalism gives reasonable predictions for the covariances estimated from mock simulations with a periodic-box geometry. Furthermore, fitting for an effective volume and number density by maximizing a likelihood based on Kullback-Leibler divergence is shown to partially compensate for the effects of a non-uniform window function.
We present here a new algorithm for the fast computation of N-point correlation functions in large astronomical data sets. The algorithm is based on kdtrees which are decorated with cached sufficient statistics thus allowing for orders of magnitude speed-ups over the naive non-tree-based implementation of correlation functions. We further discuss the use of controlled approximations within the computation which allows for further acceleration. In summary, our algorithm now makes it possible to compute exact, all-pairs, measurements of the 2, 3 and 4-point correlation functions for cosmological data sets like the Sloan Digital Sky Survey (SDSS; York et al. 2000) and the next generation of Cosmic Microwave Background experiments (see Szapudi et al. 2000).
We compute covariance matrices for many observed estimates of the stellar mass function of galaxies from $z=0$ to $zapprox 4$, and for one estimate of the projected correlation function of galaxies split by stellar mass at $zlesssim 0.5$. All covariance matrices include contributions due to large scale structure, the preference for galaxies to be found in groups and clusters, and for shot noise. These covariance matrices are made available for use in constraining models of galaxy formation and the galaxy-halo connection.
We present an analysis of large-scale structure from the Spitzer Wide-area Infrared Extragalactic legacy survey, SWIRE. The two-point angular correlation functions were computed for galaxies detected in the 3.6-micron IRAC band, on angular scales up to a degree. Significant evolution in the clustering amplitude was detected, as the median redshift of the samples increases from z=0.2 to 0.6. The galaxy clustering in the GALICS semi-analytic models was compared with the observed correlation functions and found to disagree with the data at faint flux limits.
We present the measurements of the luminosity-dependent redshift-space three-point correlation functions (3PCFs) for the Sloan Digital Sky Survey (SDSS) DR7 Main galaxy sample. We compare the 3PCF measurements to the predictions from three different halo and subhalo models. One is the halo occupation distribution (HOD) model and the other two are extensions of the subhalo abundance matching (SHAM) model by allowing the central and satellite galaxies to have different occupation distributions in the host halos and subhalos. Parameters in all the models are chosen to best describe the projected and redshift-space two-point correlation functions (2PCFs) of the same set of galaxies. All three model predictions agree well with the 3PCF measurements for the most luminous galaxy sample, while the HOD model better performs in matching the 3PCFs of fainter samples (with luminosity threshold below $L^*$), which is similar in trend to the case of fitting the 2PCFs. The decomposition of the model 3PCFs into contributions from different types of galaxy triplets shows that on small scales the dependence of the 3PCFs on triangle shape is driven by nonlinear redshift-space distortion (and not by the intrinsic halo shape) while on large scales it reflects the filamentary structure. The decomposition also reveals more detailed differences in the three models, which are related to the radial distribution, the mean occupation function, and the velocity distribution of satellite galaxies inside halos. The results suggest that galaxy 3PCFs can further help constrain the above galaxy-halo relation and test theoretical models.
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