Distribution of annihilation luminosities in dark matter substructure

Savvas M. Koushiappas, Andrew R. Zentner, and Andrey V. Kravtsov

Phys. Rev. D 82, 083504 – Published 6 October 2010

Abstract

We calculate the probability distribution function (PDF) of the expected annihilation luminosities of dark matter subhalos as a function of subhalo mass and distance from the Galactic center using a semianalytical model of halo evolution. We find that the PDF of luminosities is relatively broad, exhibiting a spread of as much as an order of magnitude at fixed subhalo mass and halo-centric distance. The luminosity PDF allows for simple construction of mock samples of $γ$ -ray luminous subhalos and assessment of the variance in the predicted $γ$ -ray signals from dark matter annihilation. Other applications include quantifying the variance among the expected luminosities of dwarf spheroidal galaxies, assessing the level at which dark matter annihilation can be a contaminant in the expected $γ$ -ray signal from other astrophysical sources, as well as estimating the level at which nearby subhalos can contribute to the antimatter flux.

Received 14 June 2010

DOI:https://doi.org/10.1103/PhysRevD.82.083504

Authors & Affiliations

Savvas M. Koushiappas^1,*, Andrew R. Zentner^2,†, and Andrey V. Kravtsov^3,4,5,‡

¹Department of Physics, Brown University, 182 Hope Street, Providence, Rhode Island 02912, USA
²Department of Physics & Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
³Kavli Institute for Cosmological Physics, The University of Chicago, Chicago, Illinois 60637, USA
⁴Enrico Fermi Institute, The University of Chicago, Chicago, Illinois 60637, USA
⁵Department of Astronomy & Astrophysics, The University of Chicago, Chicago, Illinois 60605, USA

^*koushiappas@brown.edu
^†zentner@pitt.edu
^‡andrey@oddjob.uchicago.edu

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Issue

Vol. 82, Iss. 8 — 15 October 2010

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Images

Figure 1
Left panel: The mean contribution to the annihilation flux from all subhalos in a logarithmic interval of subhalo mass (horizontal axis) and line-of-sight distance (vertical axis), with ${\tilde{F}}_{M, ℓ}$ defined in Eq. (1) in units of ${cm}^{- 2} s^{- 1} {sr}^{- 1}$ . This panel shows the mean contributions along a line of sight 90° away from the Galactic center. The color at each position designates the value of ${\tilde{F}}_{M, ℓ}$ , where lighter colors indicate larger values as shown in the color bar. The contribution along the line of sight peaks at $\sim 10 kpc$ at all masses. Right panel: The mean number of subhalos per logarithmic interval of subhalo mass and logarithmic line-of-sight interval. Lighter colors designate larger numbers of subhalos according to the color bar. Smaller objects dominate the number density at all radii [see Eq. (2)].Reuse & Permissions
Figure 2
The cumulative velocity function of subhalos. The solid black line shows the average velocity function over all 200 realizations of the formation of a Milky Way-size halo. The short-dashed red line shows the velocity function derived for Galactic halos which have a concentration $c > 13.4$ , while the long-dashed blue line shows the velocity function for Galactic halos with $c < 6.7$ . The dotted line shows the behavior of an $N (> V_{\max }) \propto V_{\max }^{- 3}$ power law, which describes the subhalo velocity function in cosmological simulations.Reuse & Permissions
Figure 3
Example probability distribution functions of the $γ$ -ray luminosity for three sample mass and radial bins. The solid curve depicts a histogram of the distribution of luminosities in each bin. The dashed curve shows the fitting function of Eq. (5).Reuse & Permissions
Figure 4
Probability distribution functions of the $γ$ -ray luminosity of a $10^{6} M_{⊙}$ subhalo at three different radial distances from the Galactic center [Eq. (5) and parameters from Table ]. The solid curve depicts a histogram of the distribution of luminosities in host halos with a concentration in the 68 percentile about the mean of the sample of 200 realizations ( $C_{0}$ ). The short-dashed curve shows the subhalo luminosity PDF for host halos with a concentration in the upper 16% ( $C_{+}$ ), while the long-dashed curve shows the subhalo luminosity PDF for host halos with a concentration in the lower 16% ( $C_{-}$ ).Reuse & Permissions
Figure 5
The flux probability distribution function derived using Eq. (5) and the $C_{0}$ parameters of Table . The solid blue lines are the flux PDF along a line of sight at 20° relative to the Galactic center, while the dashed red lines are along 180°. Thick lines correspond to a minimum subhalo mass of $10^{4} M_{⊙}$ , while thin lines correspond to a minimum subhalo mass of $10^{5} M_{⊙}$ . The black dotted line depicts the single halo flux PDF derived under the assumption of a delta function luminosity PDF.Reuse & Permissions

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