Halo mass functions at high redshift

TL;DR

This paper assesses whether halo mass function (HMF) uncertainties could underlie apparent tensions between JWST observations of $z>10$ galaxies and $\Lambda$CDM predictions. By performing dark-matter-only N-body simulations with Enzo and SWIFT and pairing them with multiple (semi-)analytic HMF fits (PS, SMT, Reed07, WatsonFoF, WatsonSO), the authors quantify the discrepancy between direct N-body results and analytic forms across $z \sim 10$–$20$. They find that, in the mass range accessible to JWST, differences between N-body and analytic fits are typically within a factor of $\lesssim 2$ at $z\sim10$ and remain subdominant relative to other uncertainties, though larger deviations appear at higher redshifts and high masses. The results support the use of analytic HMFs for interpreting high-$z$ galaxy abundances, while highlighting the importance of resolution and astrophysical uncertainties beyond halo counting in driving the observed tensions.

Abstract

Recent JWST observations of very early galaxies, at $\rm{z \gtrsim 10}$, have led to claims that tension exists between the sizes and luminosities of high-redshift galaxies and what is predicted by standard $Λ$CDM models. Here we use the adaptive mesh refinement code $\texttt{Enzo}$ and the N-body smoothed particle hydrodynamics code $\texttt{SWIFT}$ to compare (semi-)analytic halo mass functions against the results of direct N-body models at high redshift. In particular, our goal is to investigate the variance between standard halo mass functions derived from (semi-)analytic formulations and N-body calculations and to determine what role any discrepancy may play in driving tensions between observations and theory. We find that the difference between direct N-body calculations and (semi-) analytic halo mass function fits is less than a factor of 2 (at $\rm{z \sim 10}$) within the mass range of galaxies currently being observed by JWST, and is therefore not a dominant source of error when comparing theory and observation at high redshift.

Figures (9)

• Figure 1: Comparing the FOF and HOP halo number densities derived from Enzo and SWIFT simulation data (with halo masses on a logarithmic scale). We show how the ratio of the HOP number density to the FOF number density varies with halo mass. The HOP number density is within a factor of 2 of its FOF counterpart - particularly at the z = 10 outputs. Some larger deviations at higher z are seen as expected.
• Figure 1: Comparing the Enzo and SWIFT halo number densities contrasted with 5 halo number densities derived from fits at $z=20.0$ (upper panel), $z=15.0$ (centre panel) and $z=10.0$ (bottom panel) using the HOP halo finder (with halo masses and number densities on a logarithmic scale).
• Figure 2: Comparing the Enzo and SWIFT halo number densities with five halo number densities derived from fits (see Table \ref{['tab:HMFs']}) at $z=20.0$ (upper panel), $z=15.0$ (centre panel) and $z=10.0$ (lower panel) using the FOF halo finder (with halo masses and number densities on a logarithmic scale). The black rectangles indicate the regions for more detailed analysis as seen in Figure \ref{['fig:FOFZoom']}. The yellow shaded regions represent the approximate range of halo masses detected by JWST at $z \geq 10.0$. Over the halo mass range selected at $z=10.0$, all but the PS fit agree with numerical results within a factor of 2.
• Figure 2: High-mass sections of Figure \ref{['fig:HOP']} (centre and bottom panels) shown in more detail.
• Figure 3: A zoom-in onto the black rectangles identified in Figure \ref{['fig:FOF']} (with halo masses and number densities on a logarithmic scale). These mass ranges represent the most massive halos accessible via numerical simulation at these redshifts. At this higher level of detail we see some discrepancy between the numerical halo mass functions of Enzo and SWIFT and their (semi-)analytical counterparts, particularly at $z=15.0$. The residuals for each of the lines are shown in Figure \ref{['fig:EnzoVFOF']} and Figure \ref{['fig:SWIFTVFOF']}.