TeV Particle Astrophysics II Madison (Aug. 29, 2006)
Comic Gamma-Ray Background from Dark Matter Annihilation Shin’ichiro Ando (California Institute of Technology) S. Ando & E. Komatsu, Phys. Rev. D 73, 023521 (2006) S. Ando, E. Komatsu, T. Narumoto & T. Totani, to be submitted
1. Introduction
Cosmic gamma-ray background (CGB) Extragalactic Diffuse γ-ray Background
100.0 HEAO A2,A4(LED)
E2 dJ/dE (keV2/(cm2-s-keV-sr)
ASCA
HEAO-A4 (MED)
10.0
COMPTEL
EGRET
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v 0.1 10-1
http://cossc.gsfc.nasa.gov/docs/cgro/egret/
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Strong et al. 2004
Fig. 3.— Extragalactic X-ray and γ-ray spectrum. Data compilation from Sreekumar et al. (1998) except for (Weidenspointner et al. 2000) and EGRET 30 MeV – 20 GeV (this work).
(1998). Fig. 3 shows the extragalactic X- and ground, using the compilation by Sreekumar e but using our new EGRET values, and al COMPTEL results (Weidenspointner et al. 2
Discovered with EGRET at GeV region Same photon intensity coming from all the directions Table 3. EGRB intensity.
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106
Eγ , MeV
Intensity, cm−2 sr−1 s−1 MeV−1
Total error
30–50 50–70 70–100 100–150 150–300 300–500 500–1000 1000–2000 2000–4000
8.40 × 10−7 5.30 × 10−7 2.22 × 10−7 8.96 × 10−8 2.61 × 10−8 6.00 × 10−9 1.52 × 10−9 3.20 × 10−10 1.20 × 10−10
2.54 × 10−7 0.80 × 10−7 0.22 × 10−7 0.91 × 10−8 0.26 × 10−8 0.63 × 10−9 0.17 × 10−9 0.44 × 10−10 0.16 × 10−10
4. FURTHER CHECKS FOR SYSTEMATICS MODEL
In order to check the robustness of our mates, we compare estimates based on data hemispheres and four quarter spheres (Tab tests for the presence of apparent anisotro EGRB values, and thus gives an independe
Origin of CGB at GeV region: Candidates 1. Blazars • AGN population beaming towards Earth • ~50 detected as point sources by EGRET
2. Galaxy clusters • Either pp collisions or electron inverse-Compton
3. Dark matter annihilation • Good candidate motivated by particle physics (e.g., supersymmetric neutralino) • Energy spectrum is characteristic
Blazar contribution ✦
Luminosity function constructed with the detected EGRET blazar properties
he 68%, 95% and 99% C.L. regions for the PLE model parameters [the faint-end slope index γ1 and the mean gamma-ray 0 (Lγ /Lr )"]. The best-fit values, (!p",γ1 ) = (3.28,0.69), are shown by the cross. The dashed contours correspond to .33 , respectively, where η is the ratio of the normalizations of the gamma-ray to radio luminosity functions.
GAMMA-RAY LUMINOSITY FUNCTION OF BLAZARS
Narumoto & Totani 2006 1.6
dN/d(log10z)
1.2
LDDE model PLE model SS96 model EGRET blazars
LDDE model PLE model SS96 model EGRET blazars
0.6 0.5 dN/d(log10L!)
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F IG . data. 6.— The Luminosity of the blazars. Thefor line are the same as Figure 5. The luminosity is νL EGRET blazars. The histogram is the EGRET solid anddistribution dashed curves areEGRET the best-fit models themarkings LDDE and 1σ Poisson error. elihood analysis. The dotted curve is obtained from the blazar GLF model of SS96. The error bars are 1σ Poisson error.
Luminosity-dependent density evolution (LDDE) model is more prefered
Blazar contribution ✦
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✦
Best LDDE model explains only ~25% of the CGB above 100 MeV Most CGB still can only be explained, although such a model is disfavored at ~2σ level Still, the excess around 3 GeV cannot be attributed to blazars
[32]. The blazar model also would imply ∼ 1000 sources with a > 300 GeV flux of the order of a typical Whipplesource, whereas the steeper power law alone corresponds to ∼ 40 sources. The first number seems worryingly large in view of the ∼ 10 confirmed sources, in spite of excessive observation campaigns on candidate sources from
Dark matter annihilation? ✦
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Annihilation into gamma rays in all the observable dark halos Is the excess due to this signal? Constraint by the Galactic center (Ando 2005, PRL 94, 171303) can be avoided by ✦
✦
Elsässer & Mannheim 2005
FIG. 2: Extragalactic gamma-ray background: spectrum as determined from EGRET data by Strong et al. (data points);
substructure (Oda, Totani & Nagashima 2005), or minispikes around IMBH (Horiuchi & Ando 2006; see also, Bertone, Zentner & Silk 2005)
Quick summary on CGB ✦
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EGRET confirmed the existence of diffuse extragalactic gamma-ray emission (CGB) The CGB would contributed by either ✦
astrophysical sources such as blazars, or
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annihilating dark matter
GLAST could pinpoint the origin ✦
Better understanding of blazars
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Potentially a smoking gun of dark matter annihilation
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Spectrum might not be sufficient for such a strong claim
2. Anisotropy as a Smoking Gun
Anisotropy from dark matter annihilation ✦
Rate of annihilation depends on density squared ✦
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A characteristic very different from ordinary astrophysical objects
The CGB anisotropy should also be quite different This could provide more stringent evidence of particle dark matter
Angular power spectrum Dark matter halo
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✦
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θ (= π / l)
Projected along the line of sight is the CGB intensity Angular power spectrum, Cl, is related to the spatial power spectrum via Limber’s equation 3D correlation can be modeled, using ✦
halo mass function, and
✦
density profile in each halo
2 annihilation is proportional to the density squared, ρ χ, 2 2 wherethef CGB =δ − "δ # and the energy thesolid function# intensity (number per unitindex area, in time, ˆ canformulaand energy toward the n be W isangle, suppressed forrange) simplicity. To direction clarify our as quantity f˜k as the Fourier transtion, generally we here expressed define the w
A few equations..., if you want
Gamma-ray intensity: vi formation of f (r), and ! its power spectrum Pf (k) by the 2(3) 3 # + z]Eγ , r), (Ntio ˜ ˜ ˆ ˆ I ( n, E ) = dr δ (r, nr)W ([1 (1) γ γ ! relation "fk fk # = (2π) δ (k + k )Pf (k), where δ ) th represents the N -dimensional delta function. We note sc Spherical expansion: where Eγcomoving is the gamma-ray energy, z since the redshift, that k is aharmonic wavenumber, it is ar the Fourier ! ˆ δI ( n) ˆ distance comoving distance, δ the overdensity at nr compared to The γ variable corresponding to the comoving r. 2 ˆ = alm Ylm (n) " Clfunction = !|alm the!Iuniversal average, and W is some of |gamma" γ goal of the present paper is to evaluate the angular power lm ray energy and r that 1 2 is given below. Note that we label spectrum C ≡ "|a | #, which is shown to be given by l lm time by r (or redshift z used interchangeably), and space Limber’s equation: ˆ" We first derive the concrete form by r = nr. # of the $ dr general formula for the2intensity is given l function W . The 2 "Iγ # Cl = {W ([1 + z]Eγ , r)} Pf k = ; r , 2 r r (8) 2 2 − "δ # f = δ where the detailed derivation is summarized in Ap-
3D power spectrum (z=0) ∆2f (k)
k 3 Pf (k) = 2π 2 !δ 2 "2
Ando & Komatsu, PRD 73, 023521 (2006)
Angular power spectrum ✦
✦
✦
Ando & Komatsu, PRD 73, 023521 (2006)
Mmin is the lower mass cutoff, below which no dark halos are formed Mmin = 10−6 Msun is set by the free-streaming of the neutralino Mmin = 106 Msun is set by the Jeans mass of the baryon, below which halos might be tidally disrupted
3. Detectability
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Detector background !
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tional model (44-500180) for the sky regions described in Table 2: top row H–A–B, middle row ents are: π 0in -decay red), (dashes,middle green),row bremsstrahlung (dash-dot, cyan), EGRB (thin described Table(dots, 2: top rowICH–A–B,
Detectability: Pure dark matter case Ando & Komatsu, PRD 73, 023521 (2006) ✦
Adopted GLAST parameters:
Aeff
104 cm2
Ωfov
2.4 sr
θres
0.115°
T
1 yr
Detectability: Lower Cutoff
Ando & Komatsu, PRD 73, 023521 (2006)
Mixed case with blazars Mmin = 106 Msun
Mmin = 10−6 Msun
Ando et al., to be submitted
4. Conclusions
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The CGB anisotropy would be a key to revealing the origin of CGB, and potentially be a smoking gun of annihilating dark matter ✦
✦ ✦
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The resulting angular spectrum would be very different from the case of other sources
We developed a new formalism for that calculation We showed that if the annihilating dark matter is a main CGB constituent, GLAST can detect anisotropy in a few years This is also true even with the existence of other sources like blazars, if the current dark matter contribution exceeds 30% at 10 GeV
