The Electron Injection Spectrum Determined By Anomalous Excesses in - PowerPoint PPT Presentation

Intro Model Method Spectra The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Data Tongyan Lin Harvard July 26, 2010 Based on Lin, Finkbeiner, and Dobler Phys. Rev. D 82, 023518 (2010) or 1004.0989 Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

Intro Model Method Spectra “Anomalies” in data → new source of GeV-TeV e ± ? PAMELA e + fraction Fermi cosmic ray ( e ± ) )) 0.4 - (e φ )+ 0.3 + (e 0.2 φ ) / ( + (e φ Positron fraction 0.1 Muller & Tang 1987 MASS 1989 TS93 HEAT94+95 CAPRICE94 AMS98 HEAT00 0.02 Clem & Evenson 2007 PAMELA 0.01 0.1 1 10 100 Energy (GeV) Fermi gamma ray “haze” WMAP “haze” 5 < E < 10 GeV residual (1 < E < 2 GeV) 23 GHz WMAP residual 1.60 0.3 20 20 Temperature [mK] [keV cm -2 s -1 sr -1 ] 10 10 0 0 -10 -10 -20 -20 -0.64 -0.1 40 20 0 -20 -40 40 20 0 -20 -40 Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

Intro Model Method Spectra Explanations of data Would like a consistent framework including new effects/sources without violating other CR signals (protons, antiprotons) Astrophysics that we don’t understand yet 1. Propagation, new effects in sources of CRs Poorly-understood new source injecting e ± 1. Annihilation of TeV-scale dark matter - Need boost factors, ¯ p problems 2. Decay of TeV-scale dark matter - τ ∼ 10 26 s 3. An astrophysical source such as pulsars - Morphology problems Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

Intro Model Method Spectra Procedure astrophysics or particle physics model ⇓ spectrum of particles produced by the source (e.g. Pythia) ⇓ propagation (e.g. GALPROP) ⇓ comparison with data Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

Intro Model Method Spectra Procedure astrophysics or particle physics model ⇑ ? spectrum of particles produced by the source (e.g. Pythia) ⇑ propagation (e.g. GALPROP) ⇑ comparison with data Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

Intro Model Method Spectra Outline Fit data to “backgrounds” plus new source: × dN x ) × τ − 1 Q ( E, � x ) ∼ n s ( � dE ( E ) (1) s x 0 ) of e ± which can best explain Fit for the injected spectrum Q ( E, � the “anomalous” signals for: 1. Annihilating Dark Matter 2. Decaying Dark Matter 3. Pulsars 4. Modification to “standard” electron injection 5. Combinations of the above without assuming a particle physics, pulsar, or SN model, except the spatial dependence. We use GALPROP. Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

Intro Model Method Spectra New sources: Include these source terms in Q ( E, � x ): � ρ χ ( � dE � σv � 0 BF � ρ 2 � 2 χ � annihilation: dN f E x ) → Q ( E, � x 0 ) m 2 2 ρ χ ( � x 0 ) χ � ρ χ ( � � decay: dN � ρ χ � x ) dE τ − 1 f E → Q ( E, � x 0 ) χ m χ ρ χ ( � x 0 ) � n p ( � � pulsars: dN x ) dE τ − 1 � n p � → Q ( E, � x 0 ) p n p ( � x 0 ) � n s ( � � SNe ( e − only) : dN x ) dE τ − 1 � n s � → Q ( E, � x 0 ) s n s ( � x 0 ) Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

Intro Model Method Spectra New sources: Include these source terms in Q ( E, � x ): � ρ χ ( � dE � σv � 0 BF � ρ 2 � 2 χ � annihilation: dN f E x ) → Q ( E, � x 0 ) m 2 2 ρ χ ( � x 0 ) χ � ρ χ ( � � decay: dN � ρ χ � x ) dE τ − 1 f E → Q ( E, � x 0 ) χ m χ ρ χ ( � x 0 ) � n p ( � � pulsars: dN x ) dE τ − 1 � n p � → Q ( E, � x 0 ) p n p ( � x 0 ) � n s ( � � SNe ( e − only) : dN x ) dE τ − 1 � n s � → Q ( E, � x 0 ) s n s ( � x 0 ) ◮ No prompt photons for DM annihilation, DM decay ◮ Ignore low-energy gamma rays from pulsars ◮ “Standard” spatial profiles: e.g., Einasto α = 0 . 12 , 0 . 17 , 0 . 22 Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

Intro Model Method Spectra Everything Else Primary e − : broken power law with varying index Secondary e ± : very sensitive to propagation parameters Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

Intro Model Method Spectra Everything Else Primary e − : broken power law with varying index Secondary e ± : very sensitive to propagation parameters Starlight model: we use the GALPROP default. Magnetic field model: we use r B = 4 . 5 , 6 . 5 , and 8 . 5kpc . � � � � − r − r ⊙ − z | B | = B 0 exp exp r B z B r B = 8 . 5kpc is actually the best: Haslam 408 MHz minus GALPROP r B = 4 . 5kpc, B 0 = 33 µG r B = 6 . 5kpc, B 0 = 18 µG r B = 8 . 5kpc, B 0 = 14 µG r B =4.5 kpc r B =6.5 kpc r B =8.5 kpc 90 300 300 90 300 300 90 300 300 200 200 200 200 200 200 45 45 45 10 -20 erg/Hz/s/cm 2 /sr 10 -20 erg/Hz/s/cm 2 /sr 10 -20 erg/Hz/s/cm 2 /sr 100 100 100 100 100 100 0 0 0 0 0 0 0 0 0 -100 -100 -100 -100 -100 -100 -45 -45 -45 -200 -200 -200 -200 -200 -200 -90 -300 -300 -90 -300 -300 -90 -300 -300 180 90 0 -90 -180 180 90 0 -90 -180 180 90 0 -90 -180 Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

Intro Model Method Spectra Method 1. Separate Q ( E, � x 0 ) spectrum into energy bins between 5-5000 GeV 2. Treat each bin as a delta-function injection (LINEAR problem) 3. Signals are obtained by taking a linear combination of signals from each delta function → Coefficients x , x i = Q ( E i , � x 0 ) 4. Matrix A maps x to predicted signals, A ij is the contribution to data point i for energy bin j 5. Fit to data minus background, b 6. Minimize χ 2 = ( A · x − b ) T C − 1 ( A · x − b ) using a non-negative fit. Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

Intro Model Method Spectra Summary of fit Linear fit parameters: ◮ Q ( E, � x 0 ) of new source in 17 log-spaced bins from 5-5000 GeV ◮ N ICS : normalization of background IC ◮ N s , N p , ∆ I wmap Nonlinear fit parameters: ◮ r B = 4 . 5 , 6 . 5 , and 8 . 5kpc ◮ γ e , Φ AMS , Φ + P AM , Φ − P AM , α = 0 . 12 , 0 . 17 , 0 . 22 350 data points: ◮ e + + e − flux: AMS, Fermi, HESS ◮ e + flux: PAMELA × e + + e − ◮ pion-subtracted Fermi gamma rays ◮ WMAP synchrotron at 23, 33, and 41 GHz ◮ Haslam 408 MHz Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

Intro Model Method Spectra Source Modification Best Fit Spectrum γ e = 2 . 65 0.100 0.0100 E 3 dN/dE [GeV 2 /cm 2 /s/sr] e + +e - flux E 3 dN/dE [GeV 2 /cm 2 /s/sr] Φ AMS = 0.52 e + flux e + fraction r B = 8 . 5kpc N p = 1.0, N s = 1.8 + = 0.08, N s = 1.8 + = 0.08, Φ PAM - = -0.01 Φ PAM Φ PAM φ e + /( φ e + + φ e - ) PAMELA data 0.10 0.010 0.0010 above 10 GeV and WMAP haze data 0.001 0.0001 0.01 1 10 100 1000 1 10 100 0.1 1.0 10.0 100.0 1000.0 E e [GeV] E e [GeV] E e [GeV] NOT included in fit. Intensity [10 -20 erg/Hz/s/cm 2 /sr] Intensity [10 -20 erg/Hz/s/cm 2 /sr] Intensity [10 -20 erg/Hz/s/cm 2 /sr] 15 15 15 WMAP synch WMAP synch WMAP synch 23 GHz 33 GHz 23 GHz, high l 10 ∆ S = 0.0 10 ∆ S = 0.0 10 ∆ S = 0.0 5 5 5 0 0 0 -40 -30 -20 -10 0 -40 -30 -20 -10 0 -40 -30 -20 -10 0 b (degrees) b (degrees) b (degrees) Local injection [10 -30 GeV/cm 3 /s] Intensity [10 -20 erg/Hz/s/cm 2 /sr] 2000 10 -2 250 Haslam 408 MHz E 2 dN/dE [MeV/cm 2 /sr/s] Fermi IC + brem Source injection N IC = 1.8 200 N h = 1.0 χ 2 =29.7 1500 10 -3 150 1000 100 10 -4 50 500 0 0 10 -5 -50 -40 -30 -20 -10 0 0.1 1.0 10.0 100.0 1000.0 10 100 1000 b (degrees) E γ [GeV] Injection energy [GeV] Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da