Evaluating the origins of the secondary bias based on the correlation of halo properties with the linear density field

¹ Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy, University of Science and Technology of China, Hefei, Anhui 230026, PR China
e-mail: wambyybz@mail.ustc.edu.cn; whywang@ustc.edu.cn
² School of Astronomy and Space Science, University of Science and Technology of China, Hefei 230026, PR China
³ Department of Astronomy, University of Massachusetts, Amherst, MA 01003-9305, USA
⁴ Institute for the Physics and Mathematics of the Universe (Kavli IPMU, WPI), UTIAS, Tokyo Institutes for Advanced Study, University of Tokyo, Chiba 277-8583, Japan
⁵ Department of Astronomy, and IFSA Collaborative Innovation Center, Shanghai Jiao Tong University, Shanghai 200240, PR China

Received: 14 April 2021
Accepted: 30 July 2021

Abstract

Using two sets of large N-body simulations, we studied the origins of the correlations between halo assembly time (z_f), concentration (v_max/v₂₀₀), and spin (λ) with the large-scale evolved density field at given halo mass, namely, the secondary bias. We find that the secondary bias is a secondary effect resulting from the correlations of halo properties with the linear density estimated at the same comoving scale. Using the linear density on different scales, we find two types of correlations. The internal correlation, which reflects the correlation of halo properties with the mean linear over-density, δ_L, within the halo Lagrangian radius, R_L, is positive for both z_f and v_max/v₂₀₀, and negative for λ. The external correlation, which describes the correlation of halo properties with linear overdensity at R > R_L for a given δ_L, shows trends that are contrary to the internal correlation. Both of the external and internal correlations depend only weakly on halo mass, indicating a similar origin for halos of different masses. Our findings offer a transparent perspective on the origins of the secondary bias, which can be largely explained by the competition between the external and internal correlations with the correlation of the linear density field on different scales. The combination of these two types of correlations has the potential to establish the complex halo-mass dependence of the secondary bias observed in the simulations.