Bounds on Cross-sections and Lifetimes for Dark Matter Annihilation and Decay into Charged Leptons from Gamma-ray Observations of Dwarf Galaxies

TL;DR

This paper derives conservative gamma-ray bounds on dark matter annihilation and decay into charged leptons using FSR from four Milky Way dwarf spheroidal galaxies observed by ACTs. It formulates the flux in terms of LOS integrals $\mathcal{L}_{\rm ann}$ and $\mathcal{L}_{\rm dec}$ and computes them by marginalizing over flexible DM density profiles constrained by stellar kinematics, then translates ACT flux limits into upper bounds on $\langle \sigma v \rangle$ and lower bounds on $\tau$ for six leptonic channels, including intermediate-$φ$ scenarios and $\tau$ channels. The study finds that, absent additional boosts, these bounds do not rule out DM explanations of the PAMELA/ATIC excesses, though Willman 1 and, to lesser extents, Draco constrain some channels; Sommerfeld enhancement in dwarf environments could bring some cross-sections close to current bounds. It further predicts that Fermi could detect gamma-rays from Segue 1 for a sizable portion of the PAMELA/ATIC-favored parameter space within a year, highlighting Segue 1 as a compelling target for both Fermi and ACTs to probe leptonic DM scenarios.

Abstract

We provide conservative bounds on the dark matter cross-section and lifetime from final state radiation produced by annihilation or decay into charged leptons, either directly or via an intermediate particle $φ$. Our analysis utilizes the experimental gamma-ray flux upper limits from four Milky Way dwarf satellites: HESS observations of Sagittarius and VERITAS observations of Draco, Ursa Minor, and Willman 1. Using 90% confidence level lower limits on the integrals over the dark matter distributions, we find that these constraints are largely unable to rule out dark matter annihilations or decays as an explanation of the PAMELA and ATIC/PPB-BETS excesses. However, if there is an additional Sommerfeld enhancement in dwarfs, which have a velocity dispersion ~10 to 20 times lower than that of the local Galactic halo, then the cross-sections for dark matter annihilating through $φ$'s required to explain the excesses are very close to the cross-section upper bounds from Willman 1. Dark matter annihilation directly into $τ$'s is also marginally ruled out by Willman 1 as an explanation of the excesses, and the required cross-section is only a factor of a few below the upper bound from Draco. Finally, we make predictions for the gamma-ray flux expected from the dwarf galaxy Segue 1 for the Fermi Gamma-ray Space Telescope. We find that for a sizeable fraction of the parameter space in which dark matter annihilation into charged leptons explains the PAMELA excess, Fermi has good prospects for detecting a gamma-ray signal from Segue 1 after one year of observation.

Figures (4)

• Figure 1: Annihilation cross-section upper bounds as a function of dark matter mass obtained from gamma-ray observations of the four Milky Way dwarf galaxies: Willman 1, Sagittarius, Ursa Minor, and Draco. These bounds were calculated using the $90\%$ confidence level lower limit on each $\mathcal{L}_{\rm{ann}}$ value given in Table \ref{['tab:dwarfs']}. The bounds given are for six different channels, which are from top curve to bottom curve: $\chi\chi \to \phi\phi \to \mu^{+}\mu^{-}\mu^{+}\mu^{-}$ for $m_{\phi}=250$ MeV, $\chi\chi \to \phi\phi \to e^{+}e^{-}e^{+}e^{-}$ for $m_{\phi}=100$ MeV, $\chi\chi \to \mu^{+}\mu^{-}$, $\chi\chi \to e^{+}e^{-}$, $\chi\chi \to \phi\phi$ for the case where $\phi$ decays directly to $\gamma\gamma$ with a branching ratio of $10\%$ and to $e^+e^-$ with a branching ratio of $90\%$, and $\chi\chi \to \tau^{+}\tau^{-}$. Here $\phi$ is a new mediator particle as discussed in e.g. Cholis2008Arkani-Hamed2008.
• Figure 2: Decay lifetime lower bounds as a function of dark matter mass obtained from gamma-ray observations of the four Milky Way dwarf galaxies: Willman 1, Sagittarius, Ursa Minor, and Draco. These bounds were calculated using the $90\%$ confidence level lower limit on each $\mathcal{L}_{\rm{dec}}$ value given in Table \ref{['tab:dwarfs']}. The bounds given are for six different channels, which are from bottom curve to top curve: $\chi \to \phi\phi \to \mu^{+}\mu^{-}\mu^{+}\mu^{-}$ for $m_{\phi}=250$ MeV, $\chi \to \phi\phi \to e^{+}e^{-}e^{+}e^{-}$ for $m_{\phi}=100$ MeV, $\chi \to \mu^{+}\mu^{-}$, $\chi \to e^{+}e^{-}$, $\chi \to \phi\phi \to e^{+}e^{-}$ for the case where $\phi$ decays directly to $\gamma\gamma$ with a branching ratio of $10\%$ and to $e^+e^-$ with a branching ratio of $90\%$, and $\chi \to \tau^{+}\tau^{-}$.
• Figure 3: Predicted flux levels (solid black lines) for the Fermi satellite from the dwarf galaxy Segue 1, as a function of dark matter mass and annihilation cross-section, for four different annihilation channels: $\chi\chi \to e^{+}e^{-}$, $\chi\chi \to \mu^{+}\mu^{-}$, $\chi\chi \to \phi\phi \to e^{+}e^{-}e^{+}e^{-}$ for $m_{\phi}=5$ MeV, and $\chi\chi \to \phi\phi \to \mu^{+}\mu^{-}\mu^{+}\mu^{-}$ for $m_{\phi}=250$ MeV. Here we assume $E_{th}=100$ MeV in eq. (\ref{['equ:flux']}), and with this $E_{th}$, after one year of observing, Fermi can detect sources above a flux level of $2.4\times 10^{-9}$ cm$^{-2}$s$^{-1}$ with $3\sigma$ significance (dashed line). The fluxes were calculated assuming the mean expected value of $\cal{L}_{\rm ann}$. For all four channels, the dotted lines indicate the approximate values for the annihilation cross-section and mass suggested by the PAMELA data (the ATIC preferred region is, very roughly, a subset of this line). For the channels with an intermediate $\phi$, the dot-dashed line is the PAMELA suggested region assuming an additional maximum Sommerfeld enhancement to the cross-section in Segue 1. The expected fluxes for the other dwarf galaxies may be estimated by a simple rescaling with appropriate ratios of $\cal{L}_{\rm ann}$.
• Figure 4: Predicted flux levels (solid black lines) for the Fermi satellite from the dwarf galaxy Segue 1, as a function of dark matter mass and annihilation cross-section, for the four annihilation channels listed in Figure \ref{['fig:FermiSegue_100MeV']}. Here we assume $E_{th}=5$ GeV in eq. (\ref{['equ:flux']}), and with this $E_{th}$, after one year of observing, Fermi can detect sources above a flux level of $1.2\times 10^{-10}$ cm$^{-2}$s$^{-1}$ with $3\sigma$ significance (dashed line). The fluxes were calculated assuming the mean expected value of $\cal{L}_{\rm ann}$. The dotted and dot-dashed lines are the same as in Figure \ref{['fig:FermiSegue_100MeV']}.