Precise constraints on the dark matter content of Milky Way dwarf galaxies for gamma-ray experiments

Louis E. Strigari, Savvas M. Koushiappas, James S. Bullock, and Manoj Kaplinghat

Phys. Rev. D 75, 083526 – Published 30 April 2007

Abstract

We examine the prospects for detecting $γ$ -rays from dark matter annihilation in the six most promising dwarf spheroidal (dSph) satellite galaxies of the Milky Way. We use recently measured velocity dispersion profiles to provide a systematic investigation of the dark matter mass distribution of each galaxy, and show that the uncertainty in the $γ$ -ray flux from mass modeling is less than a factor of $\sim 5$ for each dSph if we assume a smooth Navarro-Frenk-White (NFW) profile. We show that Ursa Minor and Draco are the most promising dSphs for $γ$ -ray detection with GLAST and other planned observatories. For each dSph, we investigate the flux enhancement resulting from halo substructure, and show that the enhancement factor relative to a smooth halo flux cannot be greater than about 100. This enhancement depends very weakly on the lower mass cutoff scale of the substructure mass function. While the amplitude of the expected flux from each dSph depends sensitively on the dark matter model, we show that the flux ratios between the six Sphs are known to within a factor of about 10. The flux ratios are also relatively insensitive to the current theoretical range of cold dark matter halo central slopes and substructure fractions.

Received 7 December 2006

DOI:https://doi.org/10.1103/PhysRevD.75.083526

Authors & Affiliations

Louis E. Strigari^1,*, Savvas M. Koushiappas^2,†, James S. Bullock^1,‡, and Manoj Kaplinghat^1,§

¹Center for Cosmology, Department of Physics and Astronomy, University of California, Irvine, California 92697, USA
²Theoretical Division and ISR Division, MS B227, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

^*Electronic address: lstrigar@uci.edu
^†Electronic address: smkoush@lanl.gov
^‡Electronic address: bullock@uci.edu
^§Electronic address: mkapling@uci.edu

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Vol. 75, Iss. 8 — 15 April 2007

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Images

Figure 1
The velocity dispersion profiles for Ursa Minor, with data from 61. The short-dashed curve shows a model with $ρ_{s} = 10^{8} M_{⊙} {kpc}^{- 3}$ and $r_{s} = 0.63 kpc$ , while the long-dashed curve depicts a model with $ρ_{s} = 10^{7} M_{⊙} {kpc}^{- 3}$ and $r_{s} = 3.1 kpc$ . Both curves have $β = 0.6$ .Reuse & Permissions
Figure 2
The allowed region in the $ρ_{s} − r_{s}$ plane for the six dSphs after marginalizing over the stellar velocity dispersion anisotropy parameter $β$ . Solid lines correspond to contours with $V_{\max }$ of 5, 10, 20, 40, 80, $150 km s^{- 1}$ . Long-dashed lines represent the $ρ_{s} − r_{s}$ relation as derived from the field halo relation, and the $2 − σ$ scatter above the median concentration vs mass relation. Dot-dashed lines represent the $ρ_{s} − r_{s}$ relation as derived from the tidally stripped halo relation, and the $2 − σ$ scatter below the median concentration vs mass relation.Reuse & Permissions
Figure 3
The allowed region in the $ρ_{s}^{2} r_{s}^{3} − ρ_{s}$ plane for each dSph after marginalizing over the stellar velocity dispersion anisotropy parameter $β$ filled region, and contour levels for the expected $γ$ -ray flux. Contours are shown for ${log }_{10} [d N_{γ} / d A d t] = - 13$ , $- 12$ , $- 11$ , and $- 10$ , where the flux is measured in photons ${cm}^{- 2} s^{- 1}$ . Solid contours depict the flux expected within a region of radius 2 degrees centered on the dwarf, while dot-dashed contours depict the same flux thresholds for a region of radius 0.1° centered on the dwarf. The hatched regions represent the preferred region from CDM theoretical modeling (see Fig. 2 and discussion in text).Reuse & Permissions
Figure 4
Examples of the flux spectrum of Ursa Minor for three cases where the quantities $({log }_{10} ρ_{s}, {log }_{10} r_{s}, M_{χ})$ take the values of (7.4, 0.033, 46) depicted with the long-dashed line, $(7.9, - 0.067, 46)$ shown as a short-dashed line, and $(7.9, - 0.067, 500)$ shown as the dot-dashed line. The value of $L$ that corresponds to these 3 cases is $[2.08 \times 10^{14}, 1.25 \times 10^{15}, 1.25 \times 10^{15}] GeV {cm}^{- 2} s^{- 1}$ , respectively. The units for $ρ_{s}$ are $M_{⊙} {kpc}^{- 3}$ , while $r_{s}$ is in kpc and $M_{χ}$ in GeV. No enhancement of flux from substructure is included; substructure could increase the flux by up to a factor of 100, increasing the prospects for detection. The calculated flux is integrated over an angular region of radius 0.1 degrees centered on the dSph, and the value of $P = P_{SUSY} \approx 10^{- 28} {cm}^{3} s^{- 1} {GeV}^{- 2}$ , which corresponds to the most optimistic scenario for supersymmetric dark matter (see Sec. 2). Open squares show the amplitude of the $γ$ -ray extragalactic emission [75], while filled circles correspond to the galactic emission of $γ$ -rays at high galactic latitudes [76].Reuse & Permissions
Figure 5
Left: The predicted substructure boost factors assuming a subhalo mass function scaling as $d N / d M \sim M^{- 1.9}$ . Right: The dependence of the overall substructure boost factor to the slope of the subhalo mass function for Ursa Minor. The assumed parameters are $M = 3.02 \times 10^{8} M_{⊙}$ , $ρ_{s} = 6.3 \times 10^{7} M_{⊙} {kpc}^{- 3}$ , and $r_{s} = 0.8 kpc$ .Reuse & Permissions

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