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Constraining Dark Matter candidates from structure formation

C. Boehm, P. Fayet, R. Schaeffer

TL;DR

Böehm, Fayet, and Schaeffer present a model-independent framework to constrain Dark Matter candidates using structure formation by quantifying collisional damping of adiabatic fluctuations. They derive a total damping length $l_{cd}^{2}=l_{sd}^{2}+\sum_{i\neq dm}l_{id}^{2}$, where $l_{sd}$ and $l_{id}$ are computed from transport coefficients and interaction rates, and classify DM into six regions based on the epochs $a_{nr}$, $a_{dec}$ and $a_{eq}$. By requiring $l_{cd}$ to be smaller than the observable structure scale $l_{struct}\sim 100$ kpc, they obtain stringent bounds on DM–photon and DM–neutrino cross-sections at decoupling: $<\sigma v>_{\gamma-dm}\lesssim 7\times10^{-24}$ cm$^{3}$/s (≈$10^{-33}$ cm$^{2}$) and $<\sigma v>_{\nu-dm}\lesssim 1\times10^{-27}$ cm$^{3}$/s (≈$10^{-37}$ cm$^{2}$). The analysis further maps HDM/CDM/WDM/SDM regions in the mass–interaction plane and discusses how induced-damping can modify viable windows, highlighting that damping constraints complement relic-density requirements in shaping Dark Matter models.

Abstract

We show that collisional damping of adiabatic primordial fluctuations yields constraints on the possible range of mass and interaction rates of Dark Matter particles. Our analysis relies on a general classification of Dark Matter candidates, that we establish independently of any specific particle theory or model. From a relation between the collisional damping scale and the Dark Matter interaction rate, we find that Dark Matter candidates must have cross-sections at decoupling smaller than $ 10^{-33} \frac{m_{dm}}{1 MeV} cm^2$ with photons and $10^{-37} \frac{m_{dm}}{1 MeV} cm^2$ with neutrinos, to explain the observed primordial structures of $10^9$ Solar mass. These damping constraints are particularly relevant for Warm Dark Matter candidates. They also leave open less known regions of parameter space corresponding to particles having rather high interaction rates with other species than neutrinos and photons.

Constraining Dark Matter candidates from structure formation

TL;DR

Böehm, Fayet, and Schaeffer present a model-independent framework to constrain Dark Matter candidates using structure formation by quantifying collisional damping of adiabatic fluctuations. They derive a total damping length , where and are computed from transport coefficients and interaction rates, and classify DM into six regions based on the epochs , and . By requiring to be smaller than the observable structure scale kpc, they obtain stringent bounds on DM–photon and DM–neutrino cross-sections at decoupling: cm/s (≈ cm) and cm/s (≈ cm). The analysis further maps HDM/CDM/WDM/SDM regions in the mass–interaction plane and discusses how induced-damping can modify viable windows, highlighting that damping constraints complement relic-density requirements in shaping Dark Matter models.

Abstract

We show that collisional damping of adiabatic primordial fluctuations yields constraints on the possible range of mass and interaction rates of Dark Matter particles. Our analysis relies on a general classification of Dark Matter candidates, that we establish independently of any specific particle theory or model. From a relation between the collisional damping scale and the Dark Matter interaction rate, we find that Dark Matter candidates must have cross-sections at decoupling smaller than with photons and with neutrinos, to explain the observed primordial structures of Solar mass. These damping constraints are particularly relevant for Warm Dark Matter candidates. They also leave open less known regions of parameter space corresponding to particles having rather high interaction rates with other species than neutrinos and photons.

Paper Structure

This paper contains 8 sections, 8 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Collisional damping effects.
  3. Constraints from self-damping and free-streaming.
  4. Constraints from induced-damping.
  5. Dark Matter scenarios.
  6. HDM.
  7. CDM.
  8. WDM.

Figures (1)

  • Figure 1: The different Dark Matter scenarios (HDM, CDM, WDM and SDM) may be classified according to the particle mass (more precisely the product $\,m_{dm}\,\kappa_{dm} = 3 \,T_0/a_{nr}$ where the scale-factor $a_{nr}$ characterizes the epoch at which Dark Matter particles become non-relativistic), as well as the Dark Matter interaction rate $\Gamma_{dm} \,a^3$. This rate is evaluated at the epoch of Dark Matter decoupling or at the onset of structure formation, whichever occurs first. The two resulting regimes are separated by the horizontal dotted line corresponding to $\Gamma_{dm} \, a^3 \simeq 7 \ 10^{-20} \hbox{s}^{-1}$. The arrow on the right corresponds to the value of $\Gamma_{dm}\, a^3$ implied by the Spergel-Steinhardt spergel scenario. The dark hatched regions are excluded by collisional damping or free-streaming when we require fluctuations of scale above $100 \ \hbox{kpc}$, corresponding to $10^9M_{\odot}$, to survive. The light hatched regions are those excluded by the relic density requirement for particles which do not annihilate after becoming non-relativistic and do not decouple before or during inflation. The new additional constraints due to induced-damping are not represented here. We nevertheless indicate by the label "(WDM)" particles which, due to induced-damping, are only marginally allowed.