Fermi Gamma-ray Haze via Dark Matter and Millisecond Pulsars

A useful discrimination of various sources is their total power in the Milky Way halo. In order to estimate the power of the γ-ray haze, let us first calculate it in the γ-ray haze “window” used by Dobler et al. (2010) to find the spectrum of γ-rays in the haze. This region is -15 • < l < 15 • and -30 • < b < -10 • . The corresponding solid angle is Ω haze = (l 2 -l 1 )(sin b 2 -sin b 1 ) ≈ 0.17. Integrating the γ-ray spectrum in Figure 11 of Dobler et al. (2010), we find

where R ⊙ = 8.5 kpc is the distance from the GC to the Sun. The haze is observed within approximately θ = 45 • from the GC. The corresponding solid angle Ω tot = 2π(1-cos θ) ≈ 1.8. Therefore, the total luminosity of this γ-ray emission is

At first we will discuss possible astrophysical sources of the γ-ray haze. The current star formation rate in the halo of the Milky Way is very small. Thus the sources of the high energy particles should have a long lifetime. The two possibilities are type Ia supernovae (SNe) and millisecond pulsars (MSPs).

Let us estimate the output in the high energy electrons from the type Ia SNe. On average, SNe must produce ∼ 10 48 erg in relativistic electrons to account for the observed flux of cosmic-ray electrons (Kobayashi et al. 2004). The calculations for observed SNe predict similar or smaller power in electrons (Berezhko & Völk 2008;Zirakashvili & Aharonian 2010). The birth rate of Ia SNe per unit stellar mass in the Galactic halo can be estimated as (5.3 ± 1.1) × 10 -14 yr -1 M -1 ⊙ (Sullivan et al. 2006). In order to estimate the mass of the Milky Way stellar halo, we use the distribution of matter in the disk and in the halo given by Jurić et al. (2008) and, for the overall normalization, we use the local stellar density of the thin disk, 35 M ⊙ pc -2 (Kuijken & Gilmore 1989). Therefore, the inferred mass of the Milky Way stellar halo within 20 kpc of the GC is

with an uncertainty of at most a factor of 2. This gives a Ia SNe rate in the halo of about 5 × 10 -5 yr -1 or 2 × 10 -12 s -1 . Consequently, the electron output of the halo Ia SNe is

This is insufficient to account for the γ-ray haze already based on the total output energy (we need at least 10 38 erg s -1 ). Provided that the above estimations are good within an order of magnitude, we conclude that Ia SNe will not contribute a significant number of electrons and γ-rays in the haze region and we will not consider them in the following.

MSPs are known to emit pulsed γ-rays with a cutoff at a few GeV (Abdo et al. 2009a,b). Observations of X-ray nebula around some MSPs show a production of high energy electrons and positrons (Stappers et al. 2003;Kargaltsev et al. 2006), but the uncertainties in the particle spectrum are rather large. We will consider two possibilities for the total energy output in e + e -. In the first case, we assume that the electron emission from MSPs is similar to the electron emission from young radio pulsars, such as the Crab pulsar (Atoyan & Aharonian 1996). In particular, we assume that a large fraction of the spin-down energy of an MSP goes into electrons and positrons with a cut-off in the e + e -injection spectrum, E cut 100GeV. In this case, we demonstrate that the MSPs may be sufficient to explain γ-ray haze at all energies (although prompt γ-ray emission from DM annihilation may contribute significantly at E 100 GeV). In the second case, we assume that e + e -emission from MSPs is small, then the spectrum above 10 GeV requires an additional source, such as annihilating DM. At the moment both possibilities for e + e -emission are consistent with observations of MSP nebulae (Stappers et al. 2003). The average properties of pulsed γ-ray emission from MSPs for a sample of eight pulsars detected by Fermi (Abdo et al. 2009a) are presented in Table 1.

Index Γ Cutoff E cut (GeV) log 10 L (erg s -1 ) 1.5 ± 0.4 2.8 ± 1.9 33.9 ± 0.6

Table 1: Some average properties of eight MSPs observed by Fermi (Abdo et al. 2009a). Here we assume that

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