The mass and redshift dependence of halo star clustering

TL;DR

This study extends halo-star clustering analyses to a broad range of host halo masses ($11.25<\log_{10}M_{200c}/\mathrm{M}_\odot<15$) and redshifts ($0<z<1.5$) using IllustrisTNG simulations. It quantifies halo-star clustering with the 2PCF, computed via the Landy-Szalay estimator on ex-situ halo stars across different radii scaled by $R_{200c}$, and assesses its relationship to formation redshifts through Spearman's $\rho$ over multiple radii. The main findings show that the strength of the 2PCF correlates negatively with the formation redshift $z_{3/4}$, with stronger signals at higher $z$ and weaker correlations in more massive halos; this reflects the competing influences of phase mixing and ongoing accretion, plus larger radial anisotropy in satellites around massive hosts. The work reveals that late-time accretion in massive halos can mask formation-history signals, while low-mass halos exhibit clearer correlations, aided by more tangentially biased orbits and reduced recent accretion. Overall, halo-star clustering emerges as a statistically meaningful tracer of assembly history, modulated by mass assembly rate and orbital anisotropy, with implications for interpreting halo formation in both simulations and observations.

Abstract

We adopt the two point correlation function (2PCF) as a statistical tool to quantify the spatial clustering of halo stars, for galaxy systems spanning a wide range in host halo virial mass ($11.25<\log_{10}M_{200c}/\mathrm{M}_\odot<15$) and redshifts ($0<z<1.5$) from the IllustrisTNG simulations. Consistent with a previous study \cite[][Paper I]{2024ApJ...961..223Z}, we identify clear correlations between the strength of the 2PCF signals and galaxy formation redshifts, but over a much wider mass range. We find that such correlations are slightly stronger at higher redshifts, and get weakened with the increase of host halo mass. We demonstrate that the spatial clustering of halo stars is affected by two factors: 1) the clustering gets gradually weakened as time passes (phase mixing); 2) newly accreted stars at more recent times would increase the clustering. For more massive galaxy systems, they assemble late and the newly accreted stars would increase the clustering. The late assembly of massive systems may also help to explain the weaker correlations between the 2PCF signals and the galaxy formation redshifts in massive halos, as their 2PCFs are affected more by recently accreted stars, while formation redshift characterizes mass accretion on a much longer timescale. We find that the orbits of satellite galaxies in more massive halos maintain larger radial anisotropy, reflecting the more active accretion state of their hosts while also contributing to their stronger mass loss rates.

Figures (7)

• Figure 1: This Figure, together with Figure \ref{['fig:TNGcorr_b']} below, shows the median 2PCF signals for halo stars in galaxies with different halo mass, redshift and formation redshift from TNG50, TNG100 or TNG300. For panels in the same row, they refer to galaxies with the same host halo mass, and the number in brackets of the left panel in each row corresponds to the log halo mass range. The leftmost panels also indicate the source of the results, specifying whether they come from the TNG50, TNG100 or TNG300 simulation. For panels in the same column, they are 2PCF signals at the same redshift, as indicated by the text on top of each column. In each panel, galaxies are divided into three different ranges according to their formation redshifts ($z_{3/4}$, see the legend), and their median 2PCFs are plotted in different colors and symbols. Here $z_{3/4}$ is defined as the redshift at which one galaxy has accreted three-fourths of its total ex-situ stellar mass at the corresponding redshift. $r$ in the $x$-axis is the galactocentric distance. When calculating the 2PCFs, we choose a fixed pair separation of $\Delta x=2.5-5$ kpc. The error bars are based on the 1-$\sigma$ scatters of 100 bootstrapped sub samples.
• Figure 2: A continuation of Figure \ref{['fig:TNGcorr']} above.
• Figure 3: The Spearman correlation coefficients ($\rho$) between the 2PCF signals and the galaxy formation redshifts defined in different ways and at different galactocentric distances. Following Figure \ref{['fig:TNGcorr']}, we adopt TNG50, TNG100 and TNG300 to continuously cover the full mass range, with the name of the simulation and the mass range of $\log_{10}M_{200c}/\mathrm{M}_\odot$ indicated by texts of each panel. We only show the results at redshift $z=0$. In each panel, dotted blue, dash-dotted orange and dashed green curves refer to the Spearman correlation coefficients with $z_{1/4}$, $z_{1/2}$ and $z_{3/4}$. Here $z_{1/4}$, $z_{1/2}$ and $z_{3/4}$ are defined as the redshifts at which the galaxies have accreted one-fourth, half and three-fourths of their total ex-situ stellar mass at redshift $z=0$. Negative correlation coefficients mean the clustering strength revealed by the 2PCF signals and the galaxy formation redshifts are anti-correlated, i.e., the clustering decreases with the increase in the formation redshifts.
• Figure 4: The 2PCF signals as a function of galactocentric distances, $r$, scaled by $R_{200c}$. This figure is based on TNG50. We plot in each panel 2PCF measurements at the same redshift/snapshot. Different symbols connected by lines with varying colors in the same panel refer to the median 2PCFs for galaxies in four mass bins of $M_{200c}$ (see the legend). Galaxies are no longer divided into bins according to their formation redshifts.
• Figure 5: The ex-situ stellar mass accretion histories of galaxy systems in four different halo mass ($M_{200c}$) bins, as indicated by the legend. The curves are medians taken over the assembly histories of galaxies in the same mass bin, and are normalized to be unity at redshift $z=0$. The gray dashed vertical lines mark the positions of redshifts $z=0.5$, $1.0$ and $1.5$. The plot is based on TNG50.