Modeling Luminosity-Dependent Galaxy Clustering Through Cosmic Time

TL;DR

This work addresses whether a one-to-one galaxy–halo correspondence can explain luminosity-dependent clustering over most of cosmic time. The authors adopt a non-parametric $L$-$V_{\rm max}$ relation, preserving the observed luminosity function, and assign luminosities using $V_{\rm max}^{\rm acc}$ for subhalos and $V_{\rm max}^{\rm now}$ for distinct halos. They demonstrate excellent agreement with observed clustering from $z\sim0$ to $z\sim5$ in SDSS, DEEP2, and LBG samples, including the small-scale upturn arising from the 1-halo term. The results imply a tight, time-stable connection between luminosity and halo velocity in dissipationless simulations, argue against substantial orphan populations, and provide a robust framework for interpreting galaxy clustering and the galaxy–mass relation across cosmic history.

Abstract

We employ high-resolution dissipationless simulations of the concordance LCDM cosmology to model the observed luminosity dependence and evolution of galaxy clustering through most of the age of the universe, from z~5 to z~0. We use a simple, non-parametric model which monotonically relates galaxy luminosities to the maximum circular velocity of dark matter halos (V_max) by preserving the observed galaxy luminosity function in order to match the halos in simulations with observed galaxies. The novel feature of the model is the use of the maximum circular velocity at the time of accretion, V_max,acc, for subhalos, the halos located within virial regions of larger halos. We argue that for subhalos in dissipationless simulations, V_max,acc reflects the luminosity and stellar mass of the associated galaxies better than the circular velocity at the epoch of observation, V_max,now. The simulations and our model L-V_max relation predict the shape, amplitude, and luminosity dependence of the two-point correlation function in excellent agreement with the observed galaxy clustering in the SDSS data at z~0 and in the DEEP2 samples at z~1 over the entire probed range of projected separations, 0.1<r_p/(Mpc/h)<10.0. In particular, the small-scale upturn of the correlation function from the power-law form in the SDSS and DEEP2 luminosity-selected samples is reproduced very well. At z~3-5, our predictions also match the observed shape and amplitude of the angular two-point correlation function of Lyman-break galaxies (LBGs) on both large and small scales, including the small-scale upturn.

Figures (11)

• Figure 1: Top panel: Cumulative velocity function for all halos identified in the L80 simulation at various redshifts, in units of $h^3$ Mpc$^{-3}$. Bottom panel: Fraction of subhalos as a function of redshift and maximum circular velocity at the time of accretion, $V_{\rm{max}}^{\rm{acc}}\,$. We truncate the curves where $N_{\rm{sub}}<10$ because in that regime poisson noise washes away any useful information. The arrow delimits our nominal completeness limit.
• Figure 2: Projected two-point correlation function at $z\sim0$ comparing the effects of selecting on $V_{\rm{max}}^{\rm{acc}}\,$ (solid lines) versus $V_{\rm{max}}^{\rm{now}}\,$ (dashed lines) at four different number density thresholds (labeled in the top right corner, in units of $h^3$ Mpc$^{-3}$). While there is a slight increase in the correlation function on large scales when using $V_{\rm{max}}^{\rm{acc}}\,$ rather than $V_{\rm{max}}^{\rm{now}}\,$, the difference is much stronger on small scales. The difference between $V_{\rm{max}}^{\rm{acc}}\,$ and $V_{\rm{max}}^{\rm{now}}\,$ is due to the tidal stripping of subhalos which have fallen into larger systems, hence correlation functions will be most strongly effected on small scales.
• Figure 3: Comparison of the galaxy-mass cross-correlation function for halos selected using $V_{\rm{max}}^{\rm{acc}}\,$ (solid lines) and $V_{\rm{max}}^{\rm{now}}\,$ (dashed lines) at two different circular velocity thresholds (labeled in the top right corner of each panel, in units of km s$^{-1}$).
• Figure 4: Comparison of the projected two-point correlation function for halos selected using $V_{\rm{max}}^{\rm{acc}}\,$ (solid lines) and $V_{\rm{max}}^{\rm{now}}\,$ (dashed lines) at four different redshifts, for a fixed number density, $n=1.5\times10^{-2} h^3$ Mpc$^{-3}$. This figure clearly shows that, while using $V_{\rm{max}}^{\rm{acc}}\,$ over $V_{\rm{max}}^{\rm{now}}\,$ results in a large difference at low redshift, it has very little impact at higher redshifts. The trend is similar for a wide range of number densities.
• Figure 5: Left: Comparison between the SDSS projected correlation function (points) and the correlation function derived from halos (solid lines) for various luminosity threshold samples. For comparison we include the correlation function of dark matter particles (dotted lines) at the median redshift of the sample. Right: The first moment of the halo occupation distribution (HOD) for the four halo samples. For all four samples, the gradual roll-off at small mass is due to scatter in the $V_{\rm{max}}\,$-mass relation. The fan (dotted lines) corresponds to slopes of 0.4, 0.7, and 1.0.