The detailed gaseous structure and the onset of galaxy formation in low-mass dark matter halos
Alejandro Benitez-Llambay, 18 May 2020
The Λ-cold dark matter (ΛCDM) cosmological model makes specific and robust predictions for the growth, structure and abundance of dark matter haloes, the sites where galaxies form. These are: (i) dark matter haloes grow hierarchically: small haloes form first and larger haloes form subsequently by mergers of smaller haloes; (ii) the internal structure of dark matter haloes is self-similar; (iii) the number density of haloes per unit mass rises steeply towards low masses, implying that a large fraction of low-mass haloes must fail to form a galaxy and remain dark at redshift z=0 if ΛCDM is to be reconciled with the relatively flat faint end of the observed galaxy stellar mass function.
In ΛCDM a cutoff in the mass of dark matter haloes that can host galaxies is expected on general grounds and due to the impact of cosmic reionization, which heated the gas in the Universe to a temperature \(\sim 10^{4} K\), preveting it from accretting onto small haloes. The exact value of the critical halo mass for galaxies form is, however, uncertain.
Research project
In this research project we explored whether the predictions of ΛCDM actually imply a minimum halo mass at z=0 below which galaxies cannot form, and if so, we studied how does this depend on the characteristic scales of cosmic reionization. To this end we developed an analytic model to constrain the value of the critical halo mass for galaxies to form and contrasted our results with high-resolution numerical simulations.
Impact of cosmic reionization on galaxy formation
We illustrate the need to know the value of the critical halo mass for galaxies to form in Figure 1, in which we assume that prior to reionization galaxy formation can only take place in haloes in which atomic hydrogen can cool. The corresponding critical mass is approximately,
\begin{equation} M_H^z \sim (4 \times 10^{7} \ M_{\odot} ) \left ( \frac{1+z}{11} \right)^{-3/2}. \end{equation}
We follow the evolution of a halo of present-day mass, \(M_{\rm cr}^0 = 5 \times 10^{9} \ M_{\odot}\), which, for illustration purposes, we take to be the critical mass above which all dark matter haloes host a luminous galaxy at z=0. The red solid line shows the average mass growth of a CDM halo of that mass. The halo mass required for galaxy formation to proceed is shown by the black dashed line. At the redshift of reionization this jumps from \(M_{H}^{z}\) to \(M_{\rm cr}^z\). The blue dashed line shows the evolution of \(M_{\rm cr}^z\), assumed to be the mass of a halo of virial temperature \(T_{\rm b} = 2\times 10^4 \ K\).
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| Figure 1. Redshift evolution of the critical halo mass above which atomic hydrogen cooling becomes efficient (orange dashed line), the critical mass corresponding to a fixed virial temperature, \(T_{200} = T_{\rm b} = 2 \times 10^4 \ K\) (blue dashed line), and the mean mass assembly history of a ΛCDM halo of present-day mass, \(M_{200} \sim 5 \times 10^{9} \ M_{\odot} h^{-1}\) (red solid line). The effective critical mass for gas to collapse is shown by the dot-dashed black line. For this particular example, the value of the present-day critical mass constrains both, the redshift of reionization and the temperature of the intergalactic medium. The brown thin solid lines show two particular mass assembly histories of dark matter haloes of present-day mass, \(M_{200} \sim 3 \times 10^{9} M_{\odot}\), i.e., of mass, \(M_{200} < M_{\rm cr}^0\). One halo never exceeds \(M_{\rm cr}^z\) and is expected to remain dark at z=0. The other was more massive than the critical mass prior to reionization and is expected to host a luminous galaxy at z=0. |
In this example, all haloes of \(M_{200} \ge M_{\rm cr}^0\) will host a luminous galaxy at z=0. Some haloes of \(M_{200} \leq M_{\rm cr}^0\) will be dark but others will also host a luminous galaxy, depending on their previous history. The thin brown lines in illustrate two different mass accretions histories that lead to the same halo mass at z=0, \(M_{200} < M_{\rm cr}^0\). One of them never crosses the critical mass required for gas to collapse, whereas the other, although below the critical mass at z=0, exceeded \(M_{H}^{z}\) before cosmic reionization. Of the two, only the later is expected to host a luminous galaxy today. This example illustrates the origin of the stochastic nature of galaxy formation in dark matter haloes of mass close to the critical value. None of the dark matter haloes of mass \(M_{200} \leq M_{H,0}\) at z=0 can host a luminous galaxy, as CDM haloes can only grow in mass unless they become a satellite of a more massive system, after which they may be subject to mass loss from tidal stripping.
The present-day value of the critical mass, \(M_{\rm cr}^0\), that separates haloes that were able to form a galaxy from those that were not is a direct probe of the epoch and characteristic scales of reionization. This quantity must be calculated self-consistently from observational constrains and theoretical considerations.
Result
The outcome of this research project is that the redshift-dependent value of the critical mass for galaxies to form can be accurately derived using simple analytical considerations, and that the Halo ocupation fraction (HOF) -i.e., the fraction of dark matter halos that can host a galaxy at a given halo mass- can be accurately predicted. We show this in Figure 2, where we compare the z=0 HOF as derived from high-resolution numerical simulations (blue curve), from simulated ΛCDM mass accretion histories (orange) and theoretical mass accretion histories (green). The agreement between the curves is remarkable and demonstrates that the physics behind the onset of galaxy formation is understood in detail. Figure 2 also shows that a cutoff galaxy formation below a halo mass \(M_{200} 3 \times 10^8 M_{\odot}\) is expected in ΛCDM. Finding an isolated galaxy inhabiting a halo below this mass scale would constitute a challenge to ΛCDM.
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| Figure 2. Comparison of the $z=0$ halo occupation fraction (HOF) measured in simulations and derived from analytical considerations. |