Angular Power Spectra with Finite Counts

Angular anisotropy techniques for cosmic diffuse radiation maps are powerful probes, even for quite small data sets. A popular observable is the angular power spectrum; we present a detailed study applicable to any unbinned source skymap S(n) from which N random, independent events are observed. Its exact variance, which is due to the finite statistics, depends only on S(n) and N; we also derive an unbiased estimator of the variance from the data. First-order effects agree with previous analytic estimates. Importantly, heretofore unidentified higher-order effects are found to contribute to the variance and may cause the uncertainty to be significantly larger than previous analytic estimates---potentially orders of magnitude larger. Neglect of these higher-order terms, when significant, may result in a spurious detection of the power spectrum. On the other hand, this would indicate the presence of higher-order spatial correlations, such as a large bispectrum, providing new clues about the sources. Numerical simulations are shown to support these conclusions. Applying the formalism to an ensemble of Gaussian-distributed skymaps, the noise-dominated part of the power spectrum uncertainty is significantly increased at high multipoles by the new, higher-order effects. This work is important for harmonic analyses of the distributions of diffuse high-energy gamma-rays, neutrinos, and charged cosmic rays, as well as for populations of sparse point sources such as active galactic nuclei.Comment: 27 pages, 8 figure

The Galactic Isotropic γ\gamma-ray Background and Implications for Dark Matter

We present an analysis of the radial angular profile of the galacto-isotropic (GI) $\gamma$-ray flux--the statistically uniform flux in circular annuli about the Galactic center. Two different approaches are used to measure the GI flux profile in 85 months of Fermi-LAT data: the BDS statistic method which identifies spatial correlations, and a new Poisson ordered-pixel method which identifies non-Poisson contributions. Both methods produce similar GI flux profiles. The GI flux profile is well-described by an existing model of bremsstrahlung, $\pi^0$ production, inverse Compton scattering, and the isotropic background. Discrepancies with data in our full-sky model are not present in the GI component, and are therefore due to mis-modeling of the non-GI emission. Dark matter annihilation constraints based solely on the observed GI profile are close to the thermal WIMP cross section below 100 GeV, for fixed models of the dark matter density profile and astrophysical $\gamma$-ray foregrounds. Refined measurements of the GI profile are expected to improve these constraints by a factor of a few.Comment: 20 pages, 15 figures, references adde

Dark matter indirect detection signals and the nature of neutrinos in the supersymmetric U(1)B−LU(1)_{B-L} extension of the standard model

In this paper, we study the prospects for determining the nature of neutrinos in the context of a supersymmetric $B-L$ extension of the standard model by using dark matter indirect detection signals and bounds on $N_{\text{eff}}$ from the cosmic microwave background data. The model contains two new dark matter candidates whose dominant annihilation channels produce more neutrinos than neutralino dark matter in the minimal supersymmetric standard model. The photon and neutrino counts may then be used to discriminate between the two models. If the dark matter comes from the B-L sector, its indirect signals and impact on the cosmic microwave background can shed light on the nature of the neutrinos. When the light neutrinos are of Majorana type, the indirect neutrino signal from the Sun and the galactic center may show a prompt neutrino box-feature, as well as an earlier cut-off in both neutrino and gamma ray energy spectra. When the light neutrinos are of Dirac type, their contribution to the effective number of neutrinos $N_{\text{eff}}$ is at a detectable level.Comment: 11 pages, 3 figures, 2 table

Improvements to the Calculation of Indirect Signals of Diffuse Gamma-rays and Neutrinos from Dark Matter Annihilation

A new formalism is presented for calculating the mean intensity spectrum and angular power spectrum of gamma-rays or neutrinos from extragalactic annihilating dark matter, taking into account the dependence of the relative motions of the annihilating particles on the annihilation cross section. To model the large scale dark matter distribution of mass and relative velocities, the halo distribution model is comprehensively summarized, and extended to include a universal radial profile of the particles' velocity variance, based on results from N-body computer simulations of dark matter halos. A velocity variance profile, associated with the NFW density profile, is proposed by enforcing a power-law profile of the pseudo phase-space density. This allows the large-scale velocity distribution to be described by virialized, gravitationally bound dark matter halos, as opposed to thermal motions used to describe the velocity distribution in the early Universe. The recent particle motion history of the Universe is presented for the described model. Sample extragalactic gamma-ray intensities from dark matter annihilation are shown for dark matter annihilating with p-wave, according to a relative-velocity-weighted annihilation cross section sigmav = a + bv^2, for constants a and b, with examples taken from supersymmetric models. For thermally produced dark matter, the p-wave suppresses the signal intensity. If b/a > 10^6, the p-wave hardens the intensity spectrum by an estimated factor of 1 + (6b/a)delta_I (E_gamma), and increases the angular power spectrum by a factor also depending on new coefficients (delta_Cl)^(1) (E_gamma ) and (delta_Cl)^(2) (E_gamma ). The energy-dependence of the new p-wave coefficients delta_I , (delta_Cl)^(1) (E_gamma ), and (delta_Cl)^(2) (E_gamma ) are shown for various annihilation spectra. Sample intensity spectra are also presented for Sommerfeld-enhanced annihilation. The intensity of neutrinos from dark matter annihilation is also considered. The variations between the dark matter annihilation signals for different particle phenomenologies suggest that particle physics constraints are possible from an observed indirect detection signal. Calculations of the annihilation signal from the galactic halo are also shown. The extragalactic signal's intensity is found to be consistent in magnitude with the galactic intensity?within the uncertainty of the models of the dark matter distribution?when looking out from the galactic plane. This suggests that the total cosmic signal may have significant contributions from both components

Effects of Velocity-Dependent Dark Matter Annihilation on the Energy Spectrum of the Extragalactic Gamma-ray Background

We calculate the effects of velocity-dependent dark matter annihilation cross sections on the intensity of the extragalactic gamma-ray background. Our formalism does not assume a locally thermal distribution of dark matter particles in phase space, and is valid for arbitrary velocity-dependent annihilation. As concrete examples, we calculate the effects of p-wave annihilation (with the $v$-weighted cross section of $\sigma v=a+bv^2$) on the mean intensity of extragalactic gamma rays produced in cosmological dark matter halos. This velocity variation makes the shape of the energy spectrum harder, but this change in the shape is too small to see unless b/a\agt 10^6. While we find no such models in the parameter space of the Minimal Supersymmetric Standard Model (MSSM), we show that it is possible to find b/a\agt 10^6 in the extension MSSM$\otimes U(1)_{B-L}$. However, we find that the most dominant effect of the p-wave annihilation is the suppression of the amplitude of the gamma-ray background. A non-zero $b$ at the dark matter freeze-out epoch requires a smaller value of $a$ in order for the relic density constraint to be satisfied, suppressing the amplitude by a factor as low as $10^{-6}$ for a thermal relic. Non-thermal relics will have weaker amplitude suppression. As another velocity-dependent effect, we calculate the spectrum for s-wave annihilation into fermions enhanced by the attractive Sommerfeld effect. Resonances associated with this effect result in significantly enhanced intensities, with a slightly softer energy spectrum.Comment: 18 pages, 10 figure