The mass function and average mass-loss rate of dark matter subhaloes

By F. V. D. Bosch, G. Tormen, Carlo Giocoli. 2004

183 citations recorded by the source corpus.

We present a simple, semi-analytical model to compute the mass functions of dark matter subhaloes. The masses of subhaloes at their time of accretion are obtained from a standard merger tree. During the subsequent evolution, the subhaloes experience mass loss due to the combined effect of dynamical friction, tidal stripping, and tidal heating. Rather than integrating these effects along individual subhalo orbits, we consider the average mass-loss rate, where the average is taken over all possible orbital configurations. Under the Ansatz that the average distribution of orbits is independent of parent halo mass, this allows us to write the average mass-loss rate as a simple function that depends only on redshift and on the instantaneous mass ratio of subhalo and parent halo. After calibrating this model by matching the subhalo mass function (SHMF) of cluster-sized dark matter haloes obtained from high-resolution, numerical simulations, we investigate the predicted mass and redshift dependence of the SHMF. We find that, contrary to previous claims, the subhalo mass function is not universal. Instead, both the slope and the normalization depend on the ratio of the parent halo mass, M, and the characteristic non-linear mass M ∗ . This simply reflects a halo formation time dependence; more massive parent haloes form later, thus allowing less time for mass loss to operate. We predict that galaxy-sized haloes, with a present-day mass of M � 10 12 h −1 M� ,h av ea n average mass fraction of dark matter subhaloes that is a factor of 3 lower than for massive clusters with M � 10 15 h −1 M� .W ealso analyse the halo-to-halo scatter in SHMFs, and show that the subhalo mass fraction of individual haloes depends most strongly on their accretion history in the last ∼1 Gyr. Finally we provide a simple fitting function for the average SHMF of a parent halo of any mass at any redshift and for any cosmology, and briefly discuss several implications of our findings. Ke yw ords: methods: statistical ‐ galaxies: haloes ‐ cosmology: theory ‐ dark matter.

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Citations in the corpus

A Cosmological Framework for the Co-Evolution of Quasars, Supermassive Black Holes, and Elliptical Galaxies. II. Formation of Red Ellipticals (2007, methodology): “At lower masses, major mergers are rare; this is true of both halo-halo major mergers (e.g., van den Bosch et al. 2005) and galaxy-galaxy mergers (which are further suppressed at these masses because of the relative scalings of orbital velocities and internal galaxy velocities, i.e., two such…”
The Dependence of Halo Clustering on Halo Formation History, Concentration, and Occupation (2005, background): “We confirm and update earlier results (e.g., Gao et al. 2004; Zentner et al. 2005; van den Bosch et al. 2005; Taylor & Babul 2005) that the occupation number of satellite halos is strongly correlated with both concentration and formation time.”
Galaxy assembly bias: a significant source of systematic error in the galaxy–halo relationship (2013, background): “Halo concentration correlates with formation time so the sense of this effect is intuitive: more highly concentrated halos assembled their masses earlier, thereby leaving more time for processes such as dynamical friction to deplete their subhalo populations (see also van den Bosch et al. 2005).”
A Cosmological Framework for the Co-Evolution of Quasars, Supermassive Black Holes, and Elliptical Galaxies. I. Galaxy Mergers and Quasar Activity (2007, methodology): “Alternatively, we have adopted it directly from Gao et al. (2004) and Nurmi et al. (2008) or calculated it following van den Bosch et al. (2005) and Vale & Ostriker (2006) and obtain similar results.”
Mapping stellar content to dark matter haloes using galaxy clustering and galaxy–galaxy lensing in the SDSS DR7 (2015, background): “…masses of their subhalos were reduced due to the combined effect of tidal stripping and dynamical friction, whereas their stellar masses in the centre of those subhalos were much less affected and are thus more closely tied to the infall masses (Reddick et al. 2013; van den Bosch et al. 2005).”
Shredded Galaxies as the Source of Diffuse Intrahalo Light on Varying Scales (2007, methodology): “Here we provide a brief overview of the technique and refer the reader to Zentner et al. (2005) and the similar models of Taylor & Babul (2004), Peñarrubia & Benson (2005), Faltenbacher & Mathews (2005), and van den Bosch et al. (2005) for more detail.”
MERGERS IN ΛCDM: UNCERTAINTIES IN THEORETICAL PREDICTIONS AND INTERPRETATIONS OF THE MERGER RATE (2010, methodology): “We also compare these simulation results with an analytic approximation: using the methodology in van den Bosch et al. (2005) to predict the merger rate analytically from a modified extended Press-Schechter formalism (note that these authors consider only the main branch mergers; because we are…”
Ahf: AMIGA'S HALO FINDER (2009, background): “It has been found before (e.g. Ghigna et al. 2000; Helmi et al. 2002; De Lucia et al. 2004; Gao et al. 2004; van den Bosch et al. 2005; Diemand et al. 2007; Giocoli et al. 2008; Springel et al. 2008) that the subhalo mass function can be described with a functional form Nsub(> M) ∝ M −α, with α =…”
The Milky Way’s bright satellites as an apparent failure of ΛCDM (2011, background): “…radii of dark matter halos is essentially self-similar when measured in terms of Vmax/Vvir (e.g., Gao et al. 2004; De Lucia et al. 2004; van den Bosch et al. 2005; Gao et al. 2011), and the cumulative abundance of dark matter subhalos in a given halo scales as N(>Vmax) ∝ V −3max (Springel et…”
Redefining the Missing Satellites Problem (2007, background): “The scatter in the subhalo mass function increases at the very high mass end, which reflects the fact that these most massive subhalos are those that are accreted most recently (Zentner & Bullock 2003; van den Bosch et al. 2005).”
Cosmological constraints from a combination of galaxy clustering and lensing – I. Theoretical framework (2012, unknown): “…distribution of satellite galaxies in clusters and groups seem to suggest that us(r|M) is in reasonable agreement with an NFW profile, for which γ = 1 (e.g., Beers & Tonry 1986; Carlberg, Yee & Ellingson 1997a; van der Marel et al. 2000; Lin, Mohr & Stanford 2004; van den Bosch et al. 2005a).”
The Most Dark-Matter-dominated Galaxies: Predicted Gamma-Ray Signals from the Faintest Milky Way Dwarfs (2007, result): “This is a similar result to those obtained in semianalytic models of many realizations of the subhalo population (Zentner & Bullock 2003; van den Bosch et al. 2005).”
Properties of galaxy groups in the Sloan Digital Sky Survey – I. The dependence of colour, star formation and morphology on halo mass (2005, methodology): “…the two-point correlation function of groups (Yang et al. 2005b), the galaxy occupation statistics of dark matter haloes (Yang et al. 2005c), the phase-space parameters of brightest halo galaxies (van den Bosch et al. 2005b) and the crosscorrelation between galaxies and groups (Yang et al. 2005d).”
The population of dark matter subhaloes: mass functions and average mass-loss rates (2007, methodology): “To perform the self-consistency check mentioned above, we therefore use the same Monte Carlo method as van den Bosch et al. (2005), but we randomly remove satellite branches from the merger tree with a probability Preject = nsim(mv/M0) nEPS(mv/M0) , (11) where nsim and nEPS are the unevolved…”