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Register a new userUpper Bound on the Dark Matter Total Annihilation Cross Section
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Authors
John F. Beacom
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We consider dark matter annihilation into Standard Model particles and show that the least detectable final states, namely neutrinos, define an upper bound on the total cross section. Calculating the cosmic diffuse neutrino signal, and comparing it to the measured terrestrial atmospheric neutrino background, we derive a strong and general bound. This can be evaded if the annihilation products are dominantly new and truly invisible particles. Our bound is much stronger than the unitarity bound at the most interesting masses, shows that dark matter halos cannot be significantly modified by annihilations, and can be improved by a factor of 10--100 with existing neutrino experiments.
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How large can the dark matter self-annihilation rate in the late universe be? This rate depends on (rho_DM/m_chi)^2 <sigma_A v>, where rho_DM/m_chi is the number density of dark matter, and the annihilation cross section is averaged over the velocity distribution. Since the clustering of dark matter is known, this amounts to asking how large the annihilation cross section can be. Kaplinghat, Knox, and Turner proposed that a very large annihilation cross section could turn a halo cusp into a core, improving agreement between simulations and observations; Hui showed that unitarity prohibits this for large dark matter masses. We show that if the annihilation products are Standard Model particles, even just neutrinos, the consequent fluxes are ruled out by orders of magnitude, even at small masses. Equivalently, to invoke such large annihilation cross sections, one must now require that essentially no Standard Model particles are produced.
We analyze 2.8-yr data of 1-100 GeV photons for clusters of galaxies, collected with the Large Area Telescope onboard the Fermi satellite. By analyzing 49 nearby massive clusters located at high Galactic latitudes, we find no excess gamma-ray emission towards directions of the galaxy clusters. Using flux upper limits, we show that the Fornax cluster provides the most stringent constraints on the dark matter annihilation cross section. Stacking a large sample of nearby clusters does not help improve the limit for most dark matter models. This suggests that a detailed modeling of the Fornax cluster is important for setting robust limits on the dark matter annihilation cross section based on clusters. We therefore perform the detailed mass modeling and predict the expected dark matter annihilation signals from the Fornax cluster, by taking into account effects of dark matter contraction and substructures. By modeling the mass distribution of baryons (stars and gas) around a central bright elliptical galaxy, NGC 1399, and using a modified contraction model motivated by numerical simulations, we show that the dark matter contraction boosts the annihilation signatures by a factor of 4. For dark matter masses around 10 GeV, the upper limit obtained on the annihilation cross section times relative velocity is <sigma v> <~ (2-3)x10^{-25} cm^3 s^{-1}, which is within a factor of 10 from the value required to explain the dark matter relic density. This effect is more robust than the annihilation boost due to substructure, and it is more important unless the mass of the smallest subhalos is much smaller than that of the Sun.
We study the effects of WIMP dark matter (DM) on the collapse and evolution of the first stars in the Universe. Using a stellar evolution code, we follow the pre-Main Sequence (MS) phase of a grid of metal-free stars with masses in the range 5-600 solar mass forming in the centre of a 1e6 solar mass halo at redhisft z=20. DM particles of the parent halo are accreted in the proto-stellar interior by adiabatic contraction and scattering/capture processes, reaching central densities of order 1e12 GeV/cm3 at radii of the order of 10 AU. Energy release from annihilation reactions can effectively counteract the gravitational collapse, in agreement with results from other groups. We find this stalling phase (known as dark star) is transients and lasts from 2.1e3 yr (M=600 solar mass) to 1.8e4 yr (M=9 solar mass). Later in the evolution, DM scattering/capture rate becomes high enough that energy deposition from annihilations significantly alters the pre-MS evolution of the star in a way that depends on DM (i) velocity dispersion, (ii) density, (iii) elastic scattering cross section with baryons. For our fiducial set of parameters (10 km/s, 1e11 GeV/cm3, 1e-38 cm2) we find that the evolution of stars of mass lower than 40 solar masses freezes on the HR diagram before reaching the ZAMS. Stars with bigger masses manage to ignite nuclear reactions; however, DM burning prolonges their lifetimes by a factor 2 (5) for a 600 (40) solar mass star.
Under the hypothesis of a Dark Matter composed by supersymmetric particles like neutralinos, we investigate the possibility that their annihilation in the haloes of nearby galaxies could produce detectable fluxes of $gamma$-photons. Expected fluxes depend on several, poorly known quantities such as the density profiles of Dark Matter haloes, the existence and prominence of central density cusps and the presence of a population of sub-haloes. We find that, for all reasonable choices of Dark Matter halo models, the intensity of the $gamma$-ray flux from some of the nearest extragalactic objects, like M31, is comparable or higher than the diffuse Galactic foreground. We show that next generation ground-based experiments could have the sensitivity to reveal such fluxes which could help us unveiling the nature of Dark Matter particles.
Critical probes of dark matter come from tests of its elastic scattering with nuclei. The results are typically assumed to be model-independent, meaning that the form of the potential need not be specified and that the cross sections on different nuclear targets can be simply related to the cross section on nucleons. For point-like spin-independent scattering, the assumed scaling relation is $sigma_{chi A} propto A^2 mu_A^2 sigma_{chi N}propto A^4 sigma_{chi N}$, where the $A^2$ comes from coherence and the $mu_A^2simeq A^2 m_N^2$ from kinematics for $m_chigg m_A$. Here we calculate where model independence ends, i.e., where the cross section becomes so large that it violates its defining assumptions. We show that the assumed scaling relations generically fail for dark matter-nucleus cross sections $sigma_{chi A} sim 10^{-32}-10^{-27};text{cm}^2$, significantly below the geometric sizes of nuclei, and well within the regime probed by underground detectors. Last, we show on theoretical grounds, and in light of existing limits on light mediators, that point-like dark matter cannot have $sigma_{chi N}gtrsim10^{-25};text{cm}^2$, above which many claimed constraints originate from cosmology and astrophysics. The most viable way to have such large cross sections is composite dark matter, which introduces significant additional model dependence through the choice of form factor. All prior limits on dark matter with cross sections $sigma_{chi N}>10^{-32};text{cm}^2$ with $m_chigtrsim 1;text{GeV}$ must therefore be re-evaluated and reinterpreted.
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