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Wei XUE Mcgill University based on work with A. Vincent and J. Cline Phys.Rev. D81 (2010) 083512 Phys.Rev. D82 (2010) 123519 COSMIC RAY ANOMALIES, GAMMA RAY CONSTRAINTS AND SUBHALOS IN MODELS OF DARK MATER ANNIHILATION Wei XUE McGill University 1 OUTLINE Cosmic Anomaly Dark Matter Subhalos outside Dark Matter subhalos inside Particle Physics realization 2 Cosmic Ray Anomaly Charged Cosmic Particles Positron fraction(>10Gev) PAMELA Electron+Positron Peaking around 500Gev Fermi 3 Dark Matter The Phenomena have no known astrophysics origin (Could be pulsar?) Attractive explanation: 1 Tev WIMP DM + DM → messengers fields φ (on shell) → SM particles. mφ<2mproton Sommerfeld enhancement to cross section <σv>=BF × 3×10-26cm3s-1 Two issues: Gamma Ray? substructure? 4 FromPhysics N-body System Simulation ★Via Lactea II 1 DM main halo in the centre 100 inside the visible galaxy Correlated 20,047 System resolved DM subhalos Liouville’s conservation law(too much information) ★Extend as far out as 4,000 kpc Our Visible galaxy is 40 kpc aross 5 Subhalos contributions Positive contribution Large Number 20,000 subhalos High density small dispersion velocity sub-substructure Negative contribution long distance to the milky way 6 GALPROP+Via Lactea II GALPROP Numerically solve diffusion equation of electrons and positrons d ∂ ψe (x, p,t)=Qe (x,E)+ (D(E) ψe (x, p,t)) + [b(x,E)ψ (x, p,t)] dt ± ± ∇ · ∇ ± ∂E ± Source 2 r α 3 Main halo: ρEin(r)=ρsexp 1 −α rs − the annihilation rate of diffuse DM particles of the host subhalo i halo. " ! Subhalos:For a given subhalo i at a distance !i from the edge of i the diffusion zone of the galaxy, the flux of e+ or e− on thissimilar boundary takes density the form profile, i ∞ 2 2 8 kpc dΦi dN r ρi diffusion zone = BSH!σv" (!i) 2 2 dr (3) dE dE !0 !i MDM 20 kpc where BSH is an average boost factor for the subhalos due to Sommerfeld enhancement for example, and ρ (r) is the Change the boundary conditioni FIG. of 1: GALPROP Geometry of a subhalo shining by leptons on the bound- mass density profile of the subhalo. The unboosted cross ary of diffusion zone of the galaxy. section is assumed to be !σv" =3× 10−26 cm3 s−1 in usingaccordance the with subhalos the standard assumption data that from the DM Via Lactea II abundance was determined by freeze-out starting from a ity dispersion is at a maximum, through the relation thermal density. In a more exact treatment, the boost ∼ rs = rvmax /2.212, while the prefactor scales with the factor would be velocity dependent [25, 26] and appear ∼ 2 2 7 within the average over DM velocities indicated by the maximum velocity vmax as ρs = vmax/(0.897 · 4πrs G). brackets in !σv". Moreover each subhalo in general has a To incorporate the contribution (3) to the lepton flux different boost factor since the velocity dispersions that from the subhalos in GALPROP, we add delta func- tion source terms to q(r, z, p) for the cylindrical surface determine BSH depend on the size of the subhalo [13]. For this preliminary study, we simply parametrize the effect bounding the diffusion zone, as illustrated in fig. 1: by an average boost factor, where the averaging includes dΦi the sum over all subhalos as well as the integration over qdisk =2δ(z ± h/2) cos θi dE velocities. &i The energy spectrum dN/dE of electrons from the DM dΦi qband =2δ(r − R) sin θi (5) annihilations is taken for simplicity to be a step function dE −1 &i at the interaction point, dN/dE = MDMΘ(MDM − E0), where E0 is the energy immediately following the an- where h and R are respectively the height and radius of nihilation. We are interested in models where the DM the cylinder. The factor of 2 corrects for the fact that particles initially annihilate into two hidden sector gauge sources in GALPROP have no directionality, whereas the or Higgs bosons, each of which subsequently decays into flux impinging on the surface is inward. The sum is over + − e e [3]. The four-body phase space would thus be a the 20,048 resolved subhalos in the Via Lactea II simu- more exact expression for dN/dE, but the step function lation. In addition, the sources were averaged over the has the correct qualitative shape and is simpler to imple- azimuthal angle φ because GALPROP assumes cylindri- ment in GALPROP. cal symmetry in its 2D mode (and the 3D mode runs too The energy of the electron at the edge of the galaxy is slowly for our purposes). Finally, the distance !i must reduced from its initial value E0 by scattering with CMB be corrected for subhalos that are close to the diffusion photons before reaching the galaxy (starlight, infrared zone; rather than the distance to the center of the galaxy, radiation and synchrotron radiation are only important it should be the distance to the cylindrical boundary. On in the inner galaxy [27]), according to the loss equation average, this is a reduction by 17 kpc compared to the 2 2 dE/d! = −κE [9] where κ =(4σT /3me) uCMB =6.31 × distance to the galactic center. −7 −1 8π ! 2 10 kpc GeV , σT = 3 (αEM /mec) is the Thomson Although most subhalos were located outside of the 3 cross-section and uCMB =0.062 eV/cm is the present diffusion zone, there are 143 lying inside, whose contri- energy density of the CMB. It is convenient to write the bution required special treatment. Assuming approxi- −1 + − solution in the inverted form: E0 =(−κ! +1/E(!)) mate isotropy, we took their entire flux of e + e to be for substitution into dN/dE. Numerically, we find that pumped into the diffusion zone from the boundary rather the losses outside the diffusion zone make a small correc- than from their individual positions. Treating them in tion, and that the distinction between E0 and E(!) is not this manner allowed us to group their contribution with important here. that of the other subhalos and thus consider a single av- Each subhalo is characterized by a density profile that erage boost factor for all subhalos. This approximation has been fit to the Einasto form would break down if one subhalo happened to be very close to our position in the galaxy, but treating such a α 2 r case would anyway require going beyond the standard ρi = ρs,i exp − − 1 (4) " α ## rs,i $ $% cylindrical symmetry (2D) mode of GALPROP and us- ing the much slower 3D mode. We believe this treatment with α =0.17 [15]. The scale radius is found to be is conservative in the sense that it should only underes- proportional to the radius rvmax at which the veloc- timate the contributions of the nearby subhalos. Mainhalo+Subhalo better fit to PAMELA and Fermi with 2.2 Tev WIMP when subhalos are included(BFSH=3744,BFMH=92) Larger mass is because of larger propagation distance. The energy loss is due to Inverse Compton Scattering with CMB, IR and Starlight 5 3 10 Subhalo and main halo annihilation ) Main halo only 1 − 2 sr 1 10 − s 2 − m 2 2 2 ! 10 1 Total Flux 10 Subhalo Contribution dN/dE (GeV Main Halo Contribution 3 E Astrophysical Background Fermi Data 1 2 3 10 10 10 0.5 1 1.5 2 2.5 3 3.5 4 Energy (GeV) DM mass (TeV) FIG. 3: Same as fig. 2, but now including subhalo contribu- FIG. 6: Combined χ2 for the Fermi and PAMELA data as tions to the lepton fluxes. afunctionofthedarkmattermass,fortheunconstrained background. Dashed (blue) line: main halo DM annihilation 8 only. Solid (red) line: subhalo and main halo contributions combined. 3 10 −1 Subhalo and main halo annihilation 10 Main halo only 2 10 positron fraction −2 positron fraction 2 ! 10 background PAMELA data 1 10 1 2 3 10 10 10 Energy (GeV) FIG. 4: PAMELA data and predicted positron fraction of the 0 best main-halo-only fit to Fermi and PAMELA data, with an 10 unconstrained background. 0.5 1 1.5 2 2.5 3 3.5 4 DM mass (TeV) 2 + − FIG. 7: χ versus MDM for the Fermi e + e data using the GALPROP constrained background. Dashed (blue) line: main halo only. Solid (red) line: subhalos plus main halo. −1 10 ) − 4.2. Constrained background + e + /(e + We performed a second analysis by taking the elec- e −2 tron and positron backgrounds to be those predicted by 10 GALPROP. In this case, although there is no good simul- positron fraction taneous fit to the combined PAMELA and Fermi data, background PAMELA data we nevertheless find that SH contributions improve the fit. In rough agreement with ref. [6], we find that the 1 2 3 10 10 10 PAMELA data require a boost factor several times higher Energy (GeV) than that needed to fit the Fermi data. 2 The plots of χ versus MDM, for both the MH-only and FIG. 5: Same as fig. 4, but now including subhalo contribu- MH+SH models, are shown respectively for the Fermi tions to the lepton fluxes. and PAMELA data in figures 7 and 8. It is striking that Gamma Ray Best DM annihilation models predict much larger gamma ray fluxes near the galactic center(GC) from Final state radiation (Bresstrahlung) and Inverse Compton Scattering(ICS) Most Constrints come from ICS here We used the first year of Fermi LAT difuse gamma ray(Aug 8 2008 to Aug 25 2009) data available from NASA to constrain the allowable DM annhihilaiton 9 AddingNumerical subhalos and still explaining Result PAMELA and Fermi only slightly reduce the gamma ray constraints Density of DM main halo in the GC is still high DM profile and final state(4e,4μ,π,e) has some impact on it, but not enough 10 What about local subhalo? 100(s) subhalos inside the galaxy from Via Lactrea small velocity, high density and close to us PAMELA and Fermi excess can come from the close subhalo We are within 3 kpc of subhalo centre, but further away than 20pc.
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