WMAP7 and future CMB constraints on annihilating dark matter: implications for GeV-scale WIMPs

TL;DR

The paper assesses CMB constraints on annihilating dark matter in the GeV-scale, focusing on $m_{{\rm DM}}=5-100$ GeV. It shows that the CMB signal from annihilations is largely independent of structure formation details and can be described by a single particle-physics parameter, the neutrino-energy fraction $f_{{\nu}}$, enabling a simple, model-independent bound on the annihilation cross section via a fitting formula. Using WMAP7 with a six-parameter $\Lambda$CDM baseline extended by $(m_{{\rm DM}}, \langle\sigma_A\upsilon\rangle/m_{{\rm DM}})$, they derive Eq. (1): $(1-f_{{\nu}})\frac{\langle\sigma_A\upsilon\rangle\,[3\times10^{-26}\,{\rm cm^3\,s^{-1}}]}{m_{{\rm DM}}\,[{\rm GeV}]}< r$, and provide 1- and 2-sigma bounds for WMAP7, Planck, and CVL, showing Planck will decisively test all light-DM channels. They find that the CoGeNT/DAMA-favored region around $m_{{\rm DM}}\sim 6-8$ GeV is compatible with a standard thermal cross section only for channels with many neutrinos, while other channels are constrained; the Fermi/WMAP haze explanation based on large annihilation boosts is strongly disfavored. Overall, the work offers a practical, broadly applicable method to constrain light WIMPs with current and future CMB data, highlighting the pivotal role of energy deposition efficiency and Planck-era measurements in testing light DM scenarios.

Abstract

(Context) We calculate constraints from current and future cosmic microwave background (CMB) measurements on annihilating dark matter (DM) with masses below the electroweak scale: m_{DM}=5-100 GeV. In particular, we focus our attention on the lower end of this mass range, as DM particles with masses m_{DM} ~ 10 GeV have been recently claimed to be consistent with the CoGeNT and DAMA/LIBRA results, while also providing viable DM candidates to explain the measurements of Fermi and WMAP haze. (Aims) We study the model (in)dependence of CMB spectrum on particle physics DM models, large scale structure formation and cosmological uncertainties. We attempt to find a simple and practical recipe for estimating current and future CMB bounds on a broad class of DM annihilation models. (Results) We show that in the studied DM mass range the CMB signal of DM annihilations is independent of the details of large scale structure formation, distribution and profile of DM halos and other cosmological uncertainties. All particle physics models of DM annihilation can be described with only one parameter, the fraction of energy carried away by neutrinos in DM annihilation. As the main result we provide a simple and rather generic fitting formula for calculating CMB constraints on the annihilation cross section of light WIMPs. We show that thermal relic DM in the CoGeNT, DAMA favoured mass range is in a serious conflict with present CMB data for the annihilation channels with few neutrinos, and will definitely be tested by the Planck mission for all possible DM annihilation channels. Also, our findings strongly disfavor the claim that thermal relic DM annihilations with m_{DM} ~ 10 GeV and $<sigma_av> ~ 9x10^{-25} cm^{3}s^{-1} could be a cause for Fermi and WMAP haze.

Figures (5)

• Figure 1: The redshift $z^{'}$ where the optical depth for photons reaches unity (i.e., $\tau(z,z^{'})=1$) for several 'observer's redshifts': $z=0,10,500,1000$. Here the energy plotted is the photon energy at redshift $z$. The light gray region corresponds to the DM mass interval considered in this paper.
• Figure 2: Lefthand column from top to bottom: (i)$f$-parameters for the $\mu$-channel assuming $m_{{\rm DM}}=10$ GeV (dark solid lines) and $m_{{\rm DM}}=100$ GeV (light solid lines). In both cases, the lowest curve out of the triple of lines corresponds to only the smooth background, the middle one includes halos with a lower mass cutoff of $10^{-6}M_{\odot}$, while the top one has $10^{-9}M_{\odot}$. The dotted lines represent high-redshift fits (valid for $z\gtrsim 170$) as given by 2009PhRvD..80d3526S. The dashed line shows the CMB visibility function. Here $zg(z){\rm d}\ln z$ gives the probability that the CMB photon last scattered in the logarithmic redshift interval ${\rm d}\ln z$ centered on redshift $z$. (ii) Fraction of free electrons as a function of redshift for $m_{{\rm DM}}=10$ GeV and $100$ GeV, along with two values for $\langle\sigma_A\upsilon\rangle/(\langle\sigma_A\upsilon\rangle_{{\rm std}}m_{{\rm DM}}[{\rm GeV}])$: 1 and 10. Here $\langle\sigma_A\upsilon\rangle_{{\rm std}}=3\times10^{-26}$ cm$^{3}$s$^{-1}$ is the standard thermal cross section. For the meaning of each line, see the description given in the legend. The lowest dotted line represents the standard $\Lambda$CDM case with no additional energy input from the annihilating DM. (iii) Matter temperature as a function of redshift. The models shown are exactly the same as in the panel above. The long dashed line compares the temperature of CMB. (iv) The CMB visibility function $g(z)$ times redshift $z$ for the same models as shown in the above two panels. Righthand column from top to bottom: (i) Angular power spectra of CMB temperature fluctuations for the same models as already given above. (ii) Temperature and E-mode polarization cross-spectra. (iii) E-mode polarization spectra. In all of the righthand panels the points with errorbars show the 7-year measurements by the WMAP space mission.
• Figure 3: The WMAP7 parameter constraints for the $\mu$ annihilation channel. Along with two annihilation parameters $\log_{10}(m_{{\rm DM}})$ and $\langle\sigma_A\upsilon\rangle/m_{{\rm DM}}$, we also show the constraints on the other 6-parameter $\Lambda$CDM background model: $\Omega_{\rm B}h^2$, $\Omega_{\rm DM}h^2$, $H_0$, $\tau$, $n_{\rm S}$, $\log_{10}(A_{\rm S})$. From the inside out the colored 2D areas show the $1$-sigma and $2$-sigma regions after marginalization over the other parameters, and the dashed lines show the same regions for the basic 6-parameter $\Lambda$CDM without annihilating DM. The topmost panels in each column plot the marginalized 1D probability distributions for all of the parameters.
• Figure 4: Upper panel:$f$-parameters for all of the channels considered in this work and for several DM particle masses in the interval $m_{{\rm DM}}=5-100$ GeV. For all of the cases, the asymptotic high-redshift $f$-parameter values have been renormalized to be equal to one. Lower panel: The same as above, after dividing with a 'typical shape', $(f_{\max}(z)+f_{\min}(z))/2$, of the $f$-parameter curve.
• Figure 5: WMAP, Planck, and CVL 1-sigma constraints on the $\langle\sigma_A\upsilon\rangle-m_{{\rm DM}}$ plane for $\mu$ (upper panel) and $e$ (lower panel) annihilation channels. The solid lines show the upper bounds on annihilation cross section as determined directly through full MCMC calculations. The shaded regions around solid lines show the results from the simple recipe of Eq. (\ref{['eq1']}) with values of $r$ taken from Table \ref{['tab1']}. The vertical gray stripe shows the range of WIMP masses ($m_{{\rm DM}}=6-8$ GeV) that provide a good fit to CoGeNT and DAMA/LIBRA data 2010PhRvD..82l3509H. The vertical dotted line marks the lowest DM particle mass $5$ GeV available for PYTHIA simulations. Extrapolations are shown below that value.