The immitigable nature of assembly  bias: the impact of halo definition on assembly bias

Abstract

Dark matter halo clustering depends not only on halo mass, but also on other properties such as concentration and shape. This phenomenon is known broadly as assembly bias. We explore the dependence of assembly bias on halo definition, parametrized by spherical overdensity parameter, ∆. We summarize the strength of concentration-, shape-, and spin-dependent halo clustering as a function of halo mass and halo definition. Concentration-dependent clustering depends strongly on mass at all ∆. For conventional halo definitions (∆ ∼ 200m − 600m), concentration-dependent clustering at low mass is driven by a population of haloes that is altered through interactions with neighbouring haloes. Concentration-dependent clustering can be greatly reduced through a mass-dependent halo definition with ∆ ∼ 20m − 40m for haloes with M 200m 10 12 h −1 M . Smaller ∆ implies larger radii and mitigates assembly bias at low mass by subsuming altered, so-called backsplash haloes into now larger host haloes. At higher masses (M 200m 10 13 h −1 M ) larger overdensities, ∆ 600m, are necessary. Shapeand spin-dependent clustering are significant for all halo definitions that we explore and exhibit a relatively weaker mass dependence. Generally, both the strength and the sense of assembly bias depend on halo definition, varying significantly even among common definitions. We identify no halo definition that mitigates all manifestations of assembly bias. A halo definition that mitigates assembly bias based on one halo property (e.g., concentration) must be mass dependent. The halo definitions that best mitigate concentration-dependent halo clustering do not coincide with the expected average splashback radii at fixed halo mass.

The three causes of low-mass assembly bias

“…However, as discussed in section 2.8.1, any approach that relies on measuring the connection between a proxy and formation time has serious issues. Instead, in this paper, we follow an approach similar to that of Villarreal et al (2017). We determine the strength of the connection between assembly bias and a proxy X by finding the percentage of haloes ranked by X that need to be removed from the sample to eliminate the assembly bias signal.…”

“…Our work uses an approach similar to that of Villarreal et al (2017), so we have performed an in-depth comparison with their results. We find broad qualitative agreement between our D vir results and the results of Villarreal et al (2017), but find that quantitatively the ∆ values they report imply D vir values smaller than our findings by ≈ 25%.…”

On the Assembly Bias of Cool Core Clusters Traced by Hα Nebulae

“…The assembly bias effect was first recognized in Nbody simulations, whereby e.g., massive (> 10 14 M ) halos that formed earlier showed lower clustering at fixed halo mass (Gao et al 2005;Wechsler et al 2006;Wang et al 2007). Parameters other than halo age were also found to correlate with clustering, such as concentration (Wechsler et al 2006;Faltenbacher & White 2010;Villarreal et al 2017), spin Lacerna & Padilla 2012;Lazeyras et al 2017), halo shape (Lazeyras et al 2017;Villarreal et al 2017), and the level of halo substructure (Wechsler et al 2006;. Most of these secondary properties correlate strongly with assembly history, thus the effect was named assembly bias.…”

PRIMUS: Clustering of Star-forming and Quiescent Central Galaxies at 0.2 < z < 0.9

“…This assumption has proven to be remarkably powerful. Subsequent refinements of these models, such as the Halo Occupation Distribution (HOD), the Conditional Luminosity Function (CLF), and abundance matching have shown that a wide variety of large-scale structure measurements are consistent with the existence of a tight scaling relation between central galaxy stellar mass (or luminosity) and host halo mass (Tinker et al 2005;Zehavi et al 2005;Yang et al 2003;Coil et al 2006;Cacciato et al 2013;Kravtsov et al 2004;Conroy et al 2006;Wake et al 2011;Reddick et al 2013;Leauthaud et al 2012). Moreover, in the HOD and CLF, the total number of satellite galaxies brighter than some threshold scales simply as a power law with halo mass.…”

“…As models of the relationship between galaxies and their halos continue to be refined, a natural question is whether, and to what extent, various galaxy properties depend on properties of halos besides mass. This question first arose after the discovery of so-called "halo assembly bias": at fixed halo mass, the clustering of simulated halos shows strong dependence on halo formation time 2 Berti et al (Gao et al 2005), halo concentration, and other properties Dalal et al 2008;Villarreal et al 2017;Mao et al 2018;Salcedo et al 2018;Johnson et al 2018;Mansfield & Kravtsov 2019). Thus if the true statistical connection between galaxies and halos has additional dependence on halo assembly, then the standard "halo mass only" assumption of the HOD can lead to misinterpretation of galaxy clustering measurements, a phenomenon referred to as "galaxy assembly bias" (Zentner et al 2016;Wechsler & Tinker 2018).…”