M. Lattanzi ICRA and Dip. di Fisica - Università di Roma La Sapienza In collaboration with L. Pieri (IAP, Paris) and J. Silk (Oxford) Based on ML, Silk, PRD 79, 083523 (2009) and Pieri, ML, Silk, MNRAS in press 12 th Marcel Grossmann Meeting Paris, 17 July 2009
!! On galactic scales:! Rotation curves of galaxies;! Weak gravitational lensing;! Velocity dispersion of dwarf spheroidal galaxies;! Velocity dispersion of spiral galaxy saltellites;!!on the scale of galaxy clusters:! Distribution of radial velocities;! Weak gravitational lensing;! X-ray emission;!! On cosmological scales:! CMB anisotropy spectrum;! Matter power spectrum.
... What is the Dark Matter made of? Supersymmetric particles, Kaluza Klein particles, sterile neutrinos, majorons, light dark matter, axions, x-citing DM, little Higgs, wimpzillas, Q-balls... How to detect Dark Matter? (and, even better, how to discriminate different candidates?)! Direct detection: look for the interaction of DM particles with the nucleons in the detector;! Indirect detection: observe the products of DM annihilations/ decays (gamma, neutrinos, positrons, antiprotons..):! Radio observations can probe the heating history of the IGM
Pamela measured an excess in the positron fraction in the cosmic rays at E>10GeV
ATIC FERMI HESS TEXT
The origin of the excess (excesses?) could well be astrophysical (e.g. a nearby pulsar), but it could also be due to dark matter annihilations. This interpretation however has to face several issues (Cirelli et al. 2008): "!The DM mass has to be ~ 1 TeV or more; "!Large cross sections (~10-22 cm 3 /s) are required (ann. flux ~ 1/m DM2 ); "!Final states should be mainly leptonic, to avoid over production of antiprotons; "!Annihilation suppressed in the inner galaxy (Bertone et al. 2009).
Can the excess be explained in terms of supersymmetric neutralinos? "! The inclusion of coannihilations opens the 1-10 TeV neutralino mass window to the WMAP5 dark matter density (Profumo 2006) "! The thermal cross section!v ~ 3x10-26 cm 3 /s is too low: a boost factor ~ 10 4 is required.! Clumpiness inside the galaxy could in principle provide some enhancement...!... however it has been shown that boosts larger than (few) x 10 are unlikely (Lavalle et al., 2008);! another possibility: Sommerfeld enhancement
The Sommerfeld enhancement is a non-relativistic, non-perturbative quantum correction to the annihilation cross section, arising when the particles interact through a potential. It is more effective at low velocities. The cross section in the early Universe is unchanged. (Profumo, 2005; Hisano et al, 2004; Hisano et al., 2005; Cirelli et al., 2007; March-Russel et al., 2008; Arkani-Hamed et al., 2009; Pospelov & Ritz, 2009; ML & Silk, 2009; March-Russel & West, 2009)
A classical analogy - Hard sphere collision:! = " r 2 #
A classical analogy Gravitational capture:! = " r 2 (1+v esc /v)#
In the language of Feynman diagrams, the Sommerfeld effect arises from the resummation of ladder diagrams where many gauge bosons are exchanged before the annihilation actually occurs: χ X...!v = S(",M) (!v) 0 # χ X This kind of diagrams arise naturally for a Wino-like or Higgsino-like neutralino; the particles that are exchanged are the SM gauge bosons.
10 6 10 5 10 5 10 4 S 10 4 1000 100 10 3 10 1 0.01 0.1 1 2 5 10 20 50 100 m DM TeV ML, Silk (2009)
4.5 TeV 10 4 ~1/v 2 S 1000 100 10 100 TeV 10 TeV 2 TeV ~1/v 1 10 5 10 4 0.001 0.01 0.1 Β ML, Silk (2009)
10 5 M sun 10 9 M sun 10 4 4.5 TeV halo 1000 100 TeV S 100 10 10 TeV 2 TeV 1 10 5 10 4 0.001 0.01 0.1 Β ML, Silk (2009)
In the galactic halo, "#10!3.$ However, the clumps in the halo can be much colder. For a clump of 10 5 M sun, "~10-5. From simulations, one can also infer that the velocity dispersion scales ~ M 0.25. This should continue down to the minimum halo mass, setted by the DM damping scale; for neutralinos this is ~ 10-6 M sun. On average, the signal is boosted up to a factor 10 4-10 5 in the cold clumps. Furthermore, assuming that the clump mass fraction f ~ t d = r/v r ~ r 3/2, one finds that the outer halo has a high survival fraction, while in the innermost galaxy all clumps are destroyed.
10-4 b E 2 d!/de [GeV cm -2 s -1 sr -1 ] 10-5 10-6 W Hyb2 Hyb1 " 10-7 0.1 1 10 100 1000 E [GeV] ML, Silk (2009)
10 18 10 20 CTA expected sensitivity, E 50 GeV CTA expected sensitivity, E 1 TeV Fermi expected sensitivity, E 3 GeV Sommerfeld Enhanced Cross Section Sagittarius W W Β 10 5 Σv cm 3 s 1 10 22 10 24 Β 10 3 Β 10 2 10 26 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Log M GeV Β 10 1 Pieri, ML, Silk (2009)
"!Detection of the DM particle is essential to establish its existence and constrain its properties; "!Indirect detection in multiple windows will be necessary to demonstrate its cosmological significance; "!Electron/positron data show hints of the presence of DM; "!However this interpretation has to face several issues; firstly, the boos factor problem; "!SUSY neutralinos can provide the necessary boost factor if nonperturbative corrections are taken into account; "!Most of the annihilation signal will come from cold substructures inside the galactic halo; "!To be solved: enhancement of the leptonic channels. "!To be done: propagation in the galactic magnetic field.
BACKUP SLIDES
10 9 10 10 Draco NFW Best Fit MAGIC upper limit 95 CL, E 140 GeV AH M 700 GeV, MV 100 MeV AH M 700 GeV, MV 1 GeV LS M 4.55 TeV, MV 80 GeV LS M 4.3 TeV, MV 80 GeV LS M 4.5 TeV, MV 80 GeV LS M 4.45 TeV, MV 80 GeV cm 2 s 1 10 11 10 12 10 13 10 14 10 15 0.0 0.2 0.4 0.6 0.8 1.0 deg Pieri, ML, Silk (2009)
Sagittarius NFW Best Fit 10 9 10 10 HESS upper limit 95 CL, E 250 GeV AH M 700 GeV, MV 100 MeV AH M 700 GeV, MV 1 GeV LS M 4.55 TeV, MV 80 GeV LS M 4.3 TeV, MV 80 GeV LS M 4.5 TeV, MV 80 GeV LS M 4.45 TeV, MV 80 GeV cm 2 s 1 10 11 10 12 10 13 10 14 10 15 0.0 0.2 0.4 0.6 0.8 1.0 deg Pieri, ML, Silk (2009)
Draco W W 10 18 CTA expected sensitivity, E 50 GeV CTA expected sensitivity, E 1 TeV Fermi expected sensitivity, E 3 GeV MAGIC 95 CL HESS GC 95 Σv cm 3 s 1 10 20 10 22 10 24 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Log M GeV Pieri, ML, Silk (2009)
Draco e e AH, M Φ 100 MeV 10 18 CTA expected sensitivity, E 50 GeV CTA expected sensitivity, E 1 TeV Fermi expected sensitivity, E 3 GeV MAGIC 95 CL HESS GC 95 Σv cm 3 s 1 10 20 10 22 10 24 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Log M GeV Pieri, ML, Silk (2009)
Since the neutralino is a majorana particle, its annihilation to fermions is suppressed by a factor (M/m f ) 2 due to helicity conservation. Thus the preferred annihilation channels are either gauge bosons or heavy quarks. However this can be circumvented if the annihilation proceeds through an intermediate state: χ 0 χ l W, Z... ν χ 0 χ + l +
Cirelli et al., arxiv:0809.2409
Cirelli et al., arxiv:0809.2409
Cirelli et al., arxiv:0809.2409
Cirelli et al., arxiv:0809.2409
Mass Luminosity (smooth) Luminosity (substructures) Springel et al., 2008