New Dark Matter Physics: Clues from Halo Structure

TL;DR

This paper addresses the small-scale tensions of cold, collisionless dark matter by proposing a finite primordial phase density $Q$ that both filters small-scale perturbations and imposes a phase-space limit on halo cores. It develops a framework linking microphysical properties of relics (mass, spin, and possible self-interactions) to observable halo structures, predicting core radii that scale with $Q$ and halo velocity, and a scale-dependent filtering of the power spectrum through the wavenumber $k_X$. The authors explore both collisionless warm dark matter (thermal or degenerate relics) and collisional dark matter, employing isothermal and Lane-Emden polytrope models to assess core stability and the impact of heat conduction, finding that conduction generally disfavors moderately collisional regimes. By comparing with rotation curves of dwarfs and clusters, they derive constraints on particle masses (e.g., $m_X$ in the few hundred eV to ~keV range) and highlight the need for simulations with warm distribution functions to determine whether primordial $Q$ is preserved in halo centers, ultimately connecting particle physics to galactic structure observations.

Abstract

We examine the effect of primordial dark matter velocity dispersion and/or particle self-interactions on the structure and stability of galaxy halos, especially with respect to the formation of substructure and central density cusps. Primordial velocity dispersion is characterised by a ``phase density'' $Q\equiv ρ/<v^2>^{3/2}$, which for relativistically-decoupled relics is determined by particle mass and spin and is insensitive to cosmological parameters. Finite $Q$ leads to small-scale filtering of the primordial power spectrum, which reduces substructure, and limits the maximum central density of halos, which eliminates central cusps. The relationship between $Q$ and halo observables is estimated. The primordial $Q$ may be preserved in the cores of halos and if so leads to a predicted relation, closely analogous to that in degenerate dwarf stars, between the central density and velocity dispersion. Classical polytrope solutions are used to model the structure of halos of collisional dark matter, and to show that self-interactions in halos today are probably not significant because they destabilize halo cores via heat conduction. Constraints on masses and self-interactions of dark matter particles are estimated from halo stability and other considerations.

Figures (2)

• Figure 1: Characteristic masses and velocities as a function of inverse scale factor $(1+z)$, for a cosmological model with $\Omega_X=0.3$, $\Lambda=0.7$. Mass and velocity are plotted in units with $H_0=\bar{\rho}=c=1$, or $M=0.3\rho_{crit} c^3H_0^{-3}=1.56\times 10^{21}h_{70}M_\odot$. The total rest mass of dark matter in a volume $H^{-3}$ is denoted by $Hx$; total mass-energy of all forms in the same volume is denoted by $H$. Characteristic rms velocities and streaming masses (rest mass of $X$ in a volume $k_X^{-3}$) are also shown, for dark matter with three different phase densities. The cases plotted correspond to relativistically-decoupled thermal relics decoupling at three different effective degrees of freedom, corresponding to 1, 8, and 80 times that for a single standard massive neutrino--- "hot", "warm", and "cool". (For $h=0.7$, the corresponding masses are 13, 108, and 1076 eV respectively, and the rms velocities at the present epoch are $1.3\times 10^{-5}$, $7.9\times 10^{-7}$, and$3.6\times 10^{-8}$, respectively). Note the long flat period with nearly constant comoving $k_X$ for the cool particles, during the period when the universe is radiation-dominated but $X$ is nonrelativistic. The difference between streaming and collisional behavior during this period has a significant effect on the scale of filtering in the transfer function, with a sharper cutoff and a smaller scale (for fixed $k_X$) in the collisional Jeans limit.
• Figure 2: A sketch of the principal constraints from halo structure arguments on the masses of collisional dark matter particle $X$ and particle mediating its self-interactions, $Y$. This plot assumes a coupling constant $e=0.1$. The rightmost region is indistinguishable from standard collisionless CDM. The region labled "Jeans" is essentially collisionless today, but collisional before $t_{eq}$ and consistent with other constraints; in this regime the particles are no longer free-streaming, and the filtering scale and the shape of the transfer function are significantly modified by self-interactions. Somewhat stronger interactions lead to a conductive instability in halos; the "unstable cores" constraint is ruled out if we require stability down to halo velocities of 30 ${\rm km \ s^{-1}}$. The leftmost region ("fluid") produces halos which are so collisional they are stable against conduction for a Hubble time, but is probably ruled out by the unusual fluid-dynamical behavior this would cause in the trajectories of satellite galaxies and galaxies in clusters. The upper constraint comes from suppression of the annihilation channel (by the inability to radiate $Y$); if this does not apply (that is, if there there no $\bar{X}$ around) then parallel, somewhat higher constraints come from suppressing dissipation by $Y$ radiation, or from the prohibition against bound $X$ atoms. The bottom constraint corresponds to a phase-packing limit for giant galaxies; this last constraint on mass applies for relativistically-decoupled light relics only, and is ten times higher if we use the limit from dwarf spheroidals.