Galaxy Clustering in the Completed SDSS Redshift Survey: The Dependence on Color and Luminosity (1005.2413v2)

Abstract: We measure the luminosity and color dependence of galaxy clustering in the SDSS DR7 main galaxy sample, focusing on the projected correlation function w_p(r_p) of volume-limited samples. We interpret our measurements using halo occupation distribution (HOD) modeling assuming a Lambda-CDM cosmology. The amplitude of w_p(r_p) grows slowly with luminosity for L < L_* and increases sharply at higher luminosities, with bias factor b(>L)=1.06+0.23(L/L_)^{1.12}. At fixed luminosity, redder galaxies have a stronger and steeper w_p(r_p), a trend that runs steadily from the bluest galaxies to the reddest galaxies. The individual luminosity trends for the red and blue galaxy populations are strikingly different. Blue galaxies show a slow but steady increase of w_p(r_p) with luminosity, at all scales. The large-scale clustering of red galaxies shows little luminosity dependence until a sharp increase at L > 4L_, but the lowest luminosity red galaxies (0.04-0.25 L_*) show very strong clustering on scales r_p < 2 Mpc/h. Most of the observed trends can be naturally understood within the LCDM+HOD framework. The growth of w_p(r_p) with luminosity reflects an overall shift in the halo mass scale, in particular an increase in the minimum host halo mass Mmin. The mass at which a halo has, on average, one satellite galaxy brighter than L is M_1 ~ 17 Mmin(L) over most of the luminosity range. The growth and steepening of w_p(r_p) for redder galaxies reflects the increasing fraction of galaxies that are satellite systems in high mass halos instead of central systems in low mass halos, a trend that is especially marked at low luminosities. Our extensive measurements, provided in tabular form, will allow detailed tests of theoretical models of galaxy formation, a firm grounding of semi-empirical models of the galaxy population, and new cosmological tests.

• The paper identifies a clear luminosity dependence in clustering, with a steep increase in bias for galaxies brighter than L_*.
• The paper reveals that red galaxies cluster significantly more strongly than blue ones, emphasizing their residence in massive halos.
• The paper employs HOD modeling within a ΛCDM framework to uncover detailed halo occupation trends and cross-correlation effects.

Analyzing Galaxy Clustering with SDSS DR7

The paper by Zehavi et al. provides a comprehensive analysis of galaxy clustering using data from the Sloan Digital Sky Survey (SDSS) Seventh Data Release. With approximately 700,000 galaxies over 8000 square degrees, this dataset presents an unprecedented opportunity to understand the large-scale structure of the universe through galaxy clustering, focusing on dependencies related to luminosity and color. The paper applies the Halo Occupation Distribution (HOD) model within a $\Lambda$CDM cosmological framework to interpret the measurements, thereby elucidating the connection between galaxies and the underlying dark matter halos they inhabit.

Luminosity Dependence

The clustering of galaxies was measured for both luminosity bins and threshold samples, revealing a nuanced luminosity dependence. For galaxies with luminosities below $L_*$, clustering amplitude grows slowly, while for $L > L_*$, the growth is sharper. This behavior is reflected in the large-scale bias, parameterized as $b_g(>L) = 1.06 + 0.21(L/L_*)^{1.12}$. The inferred halo mass scales ($M_{\rm min}$ for central galaxies and $M_1$ for additional satellite galaxies) increase with galaxy brightness. As per HOD interpretations, galaxies in more massive halos show stronger clustering, particularly at higher luminosities where a steeper relation between halo mass and galaxy occupation is evident.

Color Dependence

Besides luminosity, color is a critical factor in galaxy clustering, influenced by star formation histories. Red galaxies exhibit significantly stronger clustering than blue ones, with differences also visible in velocity space. These tendencies are understandable within the framework where red galaxies reside in more massive halos with larger velocity dispersions. The paper finds a monotonic trend of increasing clustering amplitude with redder color in both color-defined and luminosity-bin samples, further emphasizing the complexity of galaxy-halo interactions.

Cross-Correlation Insights

The exploration of cross-correlation functions between red and blue galaxies yields additional insight into their distribution. On large scales, cross-correlations align with the geometric mean of their respective auto-correlations, while at smaller scales, subtle deviations suggest mild segregation, indicative of differential halo occupation or pairwise galaxy interaction effects.

Implications and Future Directions

This paper highlights the utility of HOD models in deciphering the intricate relationships between galaxy properties and their hosting dark matter halos. The work supports a picture where halo mass influences galaxy clustering trends significantly, mediated by galaxy luminosity and color. Interestingly, faint red galaxies exhibited unexpectedly strong small-scale clustering, posing a challenge that invites further inquiry into environmental dependencies or alternative modeling approaches that might better capture these complexities.

In a practical sense, these results reinforce our understanding of galaxy distribution as a biased tracer of the underlying dark matter framework and motivate ongoing refinements of theoretical models. They also provide robust constraints for future cosmological analyses leveraging both new galaxy surveys and cross-correlation techniques with complementary probes, such as lensing and redshift distortions, to further refine our knowledge of cosmic structure and evolution. The completeness and precision offered by SDSS DR7 ensure its analyses will remain a valuable benchmark for forthcoming high-redshift surveys aiming to probe the evolving universe’s intricate tapestry.