Constraints on Dark Matter annihilations from reionization and heating of the intergalactic gas

TL;DR

The paper addresses constraints on annihilating dark matter by energy deposition into the early Universe's intergalactic medium, using measurements of the optical depth $\tau$ and the IGM temperature $T_{\rm igm}$. The authors compute ionization and heating histories by solving coupled equations for the ionized fraction $x_{\rmion}(z)$ and $T_{\rm igm}(z)$, incorporating both prompt and inverse-Compton photons from DM annihilation and a halo-boosted annihilation rate $A(z)$ informed by structure formation and DM density profiles. They find the $\tau$-bound is the strongest, largely independent of the structure-formation history, while the $T_{\rm igm}$ bound can be competitive for small $m_\chi$ or hadronic channels and depends on halo modeling. Consequently, large portions of the parameter space motivated by cosmic-ray data (PAMELA, FERMI, HESS) are excluded, and low-mass DM is disfavored, highlighting reionization-era energy injection as a powerful probe of DM properties.

Abstract

Dark Matter annihilations after recombination and during the epoch of structure formation deposit energy in the primordial intergalactic medium, producing reionization and heating. We investigate the constraints that are imposed by the observed optical depth of the Universe and the measured temperature of the intergalactic gas. We find that the bounds are significant, and have the power to rule out large portions of the `DM mass/cross section' parameter space. The optical depth bound is generally stronger and does not depend significantly on the history of structure formation. The temperature bound can be competitive in some cases for small masses or the hadronic annihilation channels (and is affected somewhat by the details of structure formation). We find in particular that DM particles with a large annihilation cross section into leptons and a few TeV mass, such as those needed to explain the PAMELA and FERMI+HESS cosmic ray excesses in terms of Dark Matter, are ruled out as they produce too many free electrons. We also find that low mass particles (<~ 10 GeV) tend to heat too much the gas and are therefore disfavored.

Figures (5)

• Figure 1: The evolution of the effective DM density $\rho^{\rm eff}_{\rm DM}$ as a function of redshift. Blue, magenta and orange lines refer to $M_{\rm min}$=10$^{-9}$M$_\odot$/10$^{-6}$M$_\odot$/10$^{-3}$M$_\odot$, respectively (from top to bottom). The different panels assume different halo profiles.
• Figure 2: The effects produced by DM annihilations on the observables connected to reionization and heating, for the case of annihilations into $\tau^+\tau^-$. Left panel: the ionized fraction $x_{\rm ion}$ as function of redshift for $m_\chi = 2$ TeV and for increasing annihilation cross sections $\langle \sigma v \rangle$ = (0.4, 1.4, 5.1) $\cdot$ 10$^{-23}$ cm$^3$/sec (bottom to top). The thick red line individuates the value of the cross section for which the integrated optical depth exceeds the constraints. Central panel: the integrated optical depth $\delta \tau$ contributed by DM annihilations as a function of the annihilation cross section $\langle \sigma v \rangle$. We plot lines corresponding to $m_\chi$ = (10, 70, 170, 800, 2000, 10000) GeV, left to right. For a given mass, values of the cross sections larger than those where the horizontal line of the residual optical depth $\delta \tau = 0.062$ is crossed are excluded. Right panel: The temperature $T_{\rm igm}$ of the IGM as a function of redshift $z$, for different annihilation cross sections (increasing from bottom to top, the lower blue lines correspond to (0.2, 3.1) $\cdot$ 10$^{-24}$ cm$^3$/sec). The lowermost dotted line shows the adiabatic cooling in absence of DM annihilations. The data points reproduce the measurements of Schaye et al (2000) TigmObs2. In this example, any annihilation cross section larger than $7.9 \cdot 10^{-22} {\rm cm^3}/{\rm sec}$ (the uppermost red solid line) would lead to excessive heating of the IGM and is therefore excluded. The red dashed line corresponds to the cross section that already exceeds the $\delta \tau$ bound, which is therefore much more constraining for this example.
• Figure 3: As in figure \ref{['fig:results']}, but for annihilations into $e^+e^-$ and focussing on a small DM mass. Left panel: the ionized fraction $x_{\rm ion}$ as function of redshift for $m_\chi = 10$ GeV ($\langle \sigma v \rangle$ = (0.2, 0.7, 3.0) $\cdot$ 10$^{-26}$ cm$^3$/sec, bottom to top). Central panel: the integrated optical depth $\delta \tau$. Right panel: The temperature $T_{\rm igm}$ of the IGM as a function of redshift $z$. In this example, the maximum annihilation cross section (2.4 $\cdot$ 10$^{-26}$ cm$^3$/sec, the uppermost red solid line) leads to very significant heating of the IGM. The red dashed line corresponds to the cross section that exceeds the $\delta \tau$ bound, which is therefore a bit less constraining for this example.
• Figure 4: The regions on the parameter space 'DM mass' -- 'Annihilation cross section' that are excluded by the reionization and heating bounds. The first column of panels refers to DM annihilations into $e^+e^-$, the second into $\mu^+\mu^-$ and the third into $\tau^+\tau^-$; the three rows assume respectively an NFW, an Einasto and a Burkert profile. Each panel shows the exclusion contour due to exceeding the optical depth (blue short dashed line) and the exclusion contour imposed by excessive heating of the intergalactic gas (red long dashed line). We also report the regions that allow to fit the PAMELA positron data (green and yellow bands, 95 % and 99.999 % C.L. regions) and the PAMELA positron + FERMI and HESS data (red and orange blobs, 95 % and 99.999 % C.L. regions). The horizontal orange band indicates the typically preferred value for the thermal annihilation cross section.
• Figure 5: As in fig.\ref{['fig:exclusion1']}, but for $W^+W^-$, $b \bar{b}$ and $t \bar{t}$ annihilation channels. Since a DM particle fitting the PAMELA data has to be multi-TeV for these channels, the green/yellow bands are confined to large masses. There is no possibility to fit the FERMI and HESS data in these channels. The vertical cut indicates the kinematic threshold for the production of the primary annihilation particles.