Non-Separable Halo Bias from High-Redshift Galaxy Clustering

TL;DR

The study tests the long-standing separability assumption of halo bias in the halo model on quasi-linear scales by leveraging large-volume Abacus simulations and high-redshift galaxy data from HSC-SSP. By defining and measuring the separability function s(M1,M2,r,z) from halo cross- and auto-correlations, the authors find substantial non-separability on ~1–5 Mpc scales that grows with redshift and halo mass, with s as low as ~0.45 at z~3 for massive, widely separated mass pairs. Observational measurements using z~3.6 LBGs yield strong evidence for non-separability, consistent with simulation predictions, and the effect persists even after accounting for satellites via a simple HOD. These results imply that non-separable, scale-dependent halo bias must be modeled to accurately interpret high-z clustering and that cross-correlation measurements offer a powerful avenue to improve the galaxy–halo connection in upcoming surveys.

Abstract

The halo model provides a powerful framework for interpreting galaxy clustering by linking the spatial distribution of dark matter haloes to the underlying matter distribution. A key assumption within the halo bias approximation of the halo model is that, on sufficiently large scales, the halo bias between two halo populations is a separable function of the mass of each population. In this work, we test the validity of this approximation on quasi-linear scales using both simulations and observational data across a broad range of halo masses and redshifts. In particular, we define a separability function based on halo or galaxy cross-correlations to quantify deviations from halo bias separability, and measure it from N-body simulations. We find significant departures from separability on quasi-linear scales (\(\sim 1\text{--}5\,\mathrm{Mpc}\)) at high redshifts (\(z \geq 3\)), leading to a suppression in the scale-dependent halo bias and hence in halo cross-correlations by up to a factor of 2 -- or even higher. In contrast, deviations at low redshifts remain modest. Additionally, using high-redshift (\(z \sim 3.6\)) galaxy samples, we detect deviations from bias separability that closely align with simulation predictions. The breakdown of the separable bias approximation on quasi-linear scales at high redshifts underscore the importance to account for non-separability in models of the galaxy-halo connection in this regime. Furthermore, these results highlight the potential of high-redshift galaxy cross-correlations as a probe for improving the galaxy-halo connection from upcoming large-scale surveys.

Figures (6)

• Figure 1: Top panel: Halo masses corresponding to various values of $\nu$ as a function of redshift. Bottom panel: The total number of dark matter haloes in unit logarithmic mass interval in the sky, per unit redshift interval, with a given $\nu$, as a function of redshift.
• Figure 2: Normalized redshift distribution of g-dropouts with $20<\rm m_{\rm UV}<24.5$ from HSC-SSP wide survey.
• Figure 3: The halo bias separability function as a function of the halo separation at the redshifts 0 (red diamonds), 1 (green squares) and 3 (blue circles), for halo samples in different mass bins, as indicated in the legend. The measurements in upper and lower panels are respectively from the base and the huge simulations.
• Figure 4: The dependence of $s(r)$ on effective mass of bin pairs, $M^{\rm av}$, and logarithmic mass separation between bins, $\Delta \log M^{\rm av}$. Left panel:$s(r)$ measured for two halo pairs with the same $\Delta \log M^{\rm av} \simeq 0.36$ but different $M^{\rm av}$. Red circles correspond to mass bins $3.0\times10^{12} < M_1/M_\odot < 4.55\times10^{12}$ and $6.89\times10^{12} < M_2/M_\odot < 1.04\times10^{13}$, while blue squares correspond to $6.89\times10^{12} < M_1/M_\odot < 1.04\times10^{13}$ and $1.58\times10^{13} < M_2/M_\odot < 2.40\times10^{13}$. The $M^{\rm av}$ of bin pairs are $5.59\times10^{12}\,M_\odot$ (red squares) and $1.28\times10^{13}\,M_\odot$ (blue squares). Right panel:$s(r)$ measured for two halo pairs with the same $M^{\rm av} \simeq 10^{13}\,M_\odot$ but different $\Delta \log M^{\rm av}$. Red circles corresponds to $5.21\times10^{12} < M_1/M_\odot < 7.50\times10^{12}$ and $1.33\times10^{13} < M_2/M_\odot < 1.92\times10^{13}$, while blue squares correspond to $3.26\times10^{12} < M_1/M_\odot < 4.69\times10^{12}$ and $2.13\times10^{13} < M_2/M_\odot < 3.07\times10^{13}$. Here $\Delta \log M^{\rm av} =0.407$ for the red circles and $\Delta \log M^{\rm av} = 0.815$ for the blue squares.
• Figure 5: The bias separability function derived using HSC-SSP galaxy samples at $z \sim 3.6$ (red squares) and Abacus Simulation halo catalogues at $z \sim 3$ (blue circles) using base simulation.