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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

SLIDE 2

Intro Model Method Spectra

“Anomalies” in data → new source of GeV-TeV e±?

PAMELA e+ fraction Fermi cosmic ray (e±)

Energy (GeV)

0.1 1 10 100

))

(e

φ )+

+

(e φ ) / (

+

(e φ Positron fraction

0.01 0.02 0.1 0.2 0.3 0.4 Muller & Tang 1987 MASS 1989 TS93 HEAT94+95 CAPRICE94 AMS98 HEAT00 Clem & Evenson 2007 PAMELA

Fermi gamma ray “haze” WMAP “haze”

0.64

1.60 [keV cm-2 s-1 sr-1]

5 < E < 10 GeV residual (1 < E < 2 GeV)

40 20

20
40
20
10

10 20

0.1

0.3 Temperature [mK]

23 GHz WMAP residual

40 20

20
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10

10 20 Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

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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 ∼ 1026s
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

SLIDE 4

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

SLIDE 5

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

SLIDE 6

Intro Model Method Spectra

Outline

Fit data to “backgrounds” plus new source: Q(E, x) ∼ ns( x) × τ −1

s

× dN dE (E) (1) Fit for the injected spectrum Q(E, x0) of e± which can best explain 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

SLIDE 7

Intro Model Method Spectra

New sources:

Include these source terms in Q(E, x): annihilation: dN dE σv0 BF ρ2

χ

m2

χ

fE 2 → Q(E, x0) ρχ( x) ρχ( x0) 2 decay: dN dE τ −1

χ

ρχ mχ fE → Q(E, x0) ρχ( x) ρχ( x0)

pulsars: dN

dE τ −1

p

np → Q(E, x0) np( x) np( x0)

SNe (e− only) : dN

dE τ −1

s

ns → Q(E, x0) ns( x) ns( x0)

Tongyan Lin

Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

SLIDE 8

Intro Model Method Spectra

New sources:

Include these source terms in Q(E, x): annihilation: dN dE σv0 BF ρ2

χ

m2

χ

fE 2 → Q(E, x0) ρχ( x) ρχ( x0) 2 decay: dN dE τ −1

χ

ρχ mχ fE → Q(E, x0) ρχ( x) ρχ( x0)

pulsars: dN

dE τ −1

p

np → Q(E, x0) np( x) np( x0)

SNe (e− only) : dN

dE τ −1

s

ns → Q(E, x0) ns( x) ns( x0)

◮ 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

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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

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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 rB = 4.5, 6.5, and 8.5kpc . |B| = B0 exp

−r − r⊙

rB

exp
− z

zB

rB = 8.5kpc is actually the best: Haslam 408 MHz minus GALPROP

rB = 4.5kpc, B0 = 33µG

rB=4.5 kpc

180 90

90
180
90
45

45 90

300
200
100

100 200 300

300
200
100

100 200 300 10-20erg/Hz/s/cm2/sr

rB = 6.5kpc, B0 = 18µG

rB=6.5 kpc

180 90

90
180
90
45

45 90

300
200
100

100 200 300

300
200
100

100 200 300 10-20erg/Hz/s/cm2/sr

rB = 8.5kpc, B0 = 14µG

rB=8.5 kpc

180 90

90
180
90
45

45 90

300
200
100

100 200 300

300
200
100

100 200 300 10-20erg/Hz/s/cm2/sr

Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

SLIDE 11

Intro Model Method Spectra

Method

1. Separate Q(E,

x0) 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, xi = Q(Ei, x0)

4. Matrix A maps x to predicted signals,

Aij is the contribution to data point i for energy bin j

5. Fit to data minus background, b
6. Minimize

χ2 = (A · x − b)TC−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

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Intro Model Method Spectra

Summary of fit

Linear fit parameters:

◮ Q(E,

x0) of new source in 17 log-spaced bins from 5-5000 GeV

◮ NICS: normalization of background IC ◮ Ns, Np, ∆Iwmap

Nonlinear fit parameters:

◮ rB = 4.5, 6.5, and 8.5kpc ◮ γe, ΦAMS, 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

SLIDE 13

Intro Model Method Spectra

Source Modification Best Fit Spectrum

1 10 100 1000 Ee [GeV] 0.001 0.010 0.100 E3 dN/dE [GeV2/cm2/s/sr] e+ +e- flux ΦAMS = 0.52 Np = 1.0, Ns = 1.8 1 10 100 Ee [GeV] 0.0001 0.0010 0.0100 E3 dN/dE [GeV2/cm2/s/sr] e+ flux ΦPAM

+ = 0.08, Ns = 1.8

0.1 1.0 10.0 100.0 1000.0 Ee [GeV] 0.01 0.10 φe+/(φe++φe-) e+ fraction ΦPAM

+ = 0.08, ΦPAM

= -0.01
40
30
20
10

b (degrees) 5 10 15 Intensity [10-20erg/Hz/s/cm2/sr] WMAP synch 23 GHz ∆ S = 0.0

40
30
20
10

b (degrees) 5 10 15 Intensity [10-20erg/Hz/s/cm2/sr] WMAP synch 33 GHz ∆ S = 0.0

40
30
20
10

b (degrees) 5 10 15 Intensity [10-20erg/Hz/s/cm2/sr] WMAP synch 23 GHz, high l ∆ S = 0.0

40
30
20
10

b (degrees) 500 1000 1500 2000 Intensity [10-20erg/Hz/s/cm2/sr] Haslam 408 MHz Nh = 1.0 0.1 1.0 10.0 100.0 1000.0 Eγ [GeV] 10-5 10-4 10-3 10-2 E2 dN/dE [MeV/cm2/sr/s] Fermi IC + brem NIC = 1.8 10 100 1000 Injection energy [GeV]

50

50 100 150 200 250 Local injection [10-30GeV/cm3/s] Source injection χ2 =29.7

γe = 2.65 rB = 8.5kpc PAMELA data above 10 GeV and WMAP haze data NOT included in fit.

Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

SLIDE 14

Intro Model Method Spectra

Annihilation Best Fit Spectrum

1 10 100 1000 Ee [GeV] 0.001 0.010 0.100 E3 dN/dE [GeV2/cm2/s/sr] e+ +e- flux ΦAMS = 0.42 Np = 1.1, Ns = 0.9 1 10 100 Ee [GeV] 0.0001 0.0010 0.0100 E3 dN/dE [GeV2/cm2/s/sr] e+ flux ΦPAM

+ = 0.20, Ns = 0.9

0.1 1.0 10.0 100.0 1000.0 Ee [GeV] 0.01 0.10 φe+/(φe++φe-) e+ fraction ΦPAM

+ = 0.20, ΦPAM

= 0.29
40
30
20
10

b (degrees) 5 10 15 Intensity [10-20erg/Hz/s/cm2/sr] WMAP synch 23 GHz ∆ S = -0.7

40
30
20
10

b (degrees) 5 10 15 Intensity [10-20erg/Hz/s/cm2/sr] WMAP synch 33 GHz ∆ S = -0.5

40
30
20
10

b (degrees) 5 10 15 Intensity [10-20erg/Hz/s/cm2/sr] WMAP synch 23 GHz, high l ∆ S = -1.1

40
30
20
10

b (degrees) 500 1000 1500 2000 Intensity [10-20erg/Hz/s/cm2/sr] Haslam 408 MHz Nh = 1.3 0.1 1.0 10.0 100.0 1000.0 Eγ [GeV] 10-5 10-4 10-3 10-2 E2 dN/dE [MeV/cm2/sr/s] Fermi IC + brem NIC = 1.3 10 100 1000 Injection energy [GeV]

50

50 100 150 200 250 Local injection [10-30GeV/cm3/s] M = 1000GeV, BF*fE = 70 χ2 =138.5

Einasto α = 0.22 γe = 2.5 rB = 8.5kpc

mχ ≈ 1 TeV BF × fE(e+ + e−) ∼ 70 · Fit is equally good for

rB = 4.5, 6.5kpc

· Normalization factors

N ∼ 1

Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

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Intro Model Method Spectra

Decay Best Fit Spectrum

1 10 100 1000 Ee [GeV] 0.001 0.010 0.100 E3 dN/dE [GeV2/cm2/s/sr] e+ +e- flux ΦAMS = 0.46 Np = 1.0, Ns = 0.6 1 10 100 Ee [GeV] 0.0001 0.0010 0.0100 E3 dN/dE [GeV2/cm2/s/sr] e+ flux ΦPAM

+ = 0.04, Ns = 0.6

0.1 1.0 10.0 100.0 1000.0 Ee [GeV] 0.01 0.10 φe+/(φe++φe-) e+ fraction ΦPAM

+ = 0.04, ΦPAM

= 0.34
40
30
20
10

b (degrees) 5 10 15 Intensity [10-20erg/Hz/s/cm2/sr] WMAP synch 23 GHz ∆ S = -0.5

40
30
20
10

b (degrees) 5 10 15 Intensity [10-20erg/Hz/s/cm2/sr] WMAP synch 33 GHz ∆ S = -0.3

40
30
20
10

b (degrees) 5 10 15 Intensity [10-20erg/Hz/s/cm2/sr] WMAP synch 23 GHz, high l ∆ S = -0.9

40
30
20
10

b (degrees) 500 1000 1500 2000 Intensity [10-20erg/Hz/s/cm2/sr] Haslam 408 MHz Nh = 0.6 0.1 1.0 10.0 100.0 1000.0 Eγ [GeV] 10-5 10-4 10-3 10-2 E2 dN/dE [MeV/cm2/sr/s] Fermi IC + brem NIC = 2.5 10 100 1000 Injection energy [GeV]

50

50 100 150 200 250 Local injection [10-30GeV/cm3/s] M > 16TeV, τ/fE = 4× 1026 s χ2 =128.7

Einasto α = 0.12 γe = 2.6 rB = 4.5kpc

mχ 16 TeV τχ/fE(e+ +e−) ∼ 4×1026 s · rB = 4.5kpc needed to

produce WMAP haze

·Some normalization factors

N ∼ 2 − 3

· Many low energy e±

injected

Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

SLIDE 16

Intro Model Method Spectra

Pulsar Best Fit Spectrum

1 10 100 1000 Ee [GeV] 0.001 0.010 0.100 E3 dN/dE [GeV2/cm2/s/sr] e+ +e- flux ΦAMS = 0.42 Np = 1.0, Ns = 0.5 1 10 100 Ee [GeV] 0.0001 0.0010 0.0100 E3 dN/dE [GeV2/cm2/s/sr] e+ flux ΦPAM

+ = 0.02, Ns = 0.5

0.1 1.0 10.0 100.0 1000.0 Ee [GeV] 0.01 0.10 φe+/(φe++φe-) e+ fraction ΦPAM

+ = 0.02, ΦPAM

= 0.34
40
30
20
10

b (degrees) 5 10 15 Intensity [10-20erg/Hz/s/cm2/sr] WMAP synch 23 GHz ∆ S = -0.5

40
30
20
10

b (degrees) 5 10 15 Intensity [10-20erg/Hz/s/cm2/sr] WMAP synch 33 GHz ∆ S = -0.0

40
30
20
10

b (degrees) 5 10 15 Intensity [10-20erg/Hz/s/cm2/sr] WMAP synch 23 GHz, high l ∆ S = -0.8

40
30
20
10

b (degrees) 500 1000 1500 2000 Intensity [10-20erg/Hz/s/cm2/sr] Haslam 408 MHz Nh = 0.6 0.1 1.0 10.0 100.0 1000.0 Eγ [GeV] 10-5 10-4 10-3 10-2 E2 dN/dE [MeV/cm2/sr/s] Fermi IC + brem NIC = 2.6 10 100 1000 Injection energy [GeV]

50

50 100 150 200 250 Local injection [10-30GeV/cm3/s] Pulsar injection χ2 =148.2

γe = 2.6 rB = 4.5kpc

· rB = 4.5kpc needed to

produce WMAP haze

· Some normalization

factors N ∼ 2 − 3

· Many low energy e±

injected

Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

SLIDE 17

Intro Model Method Spectra

Comments

◮ Fit spectrum of e± for DM Annihilation, DM Decay, Pulsars, ...

to explain CR, gamma ray and microwave excesses all at once

◮ DM Annihilation

→ mχ ∼ 1TeV, BF × Br ∼ 80 → self-consistent model in GALPROP with rB = 8.5kpc

◮ DM Decay and Pulsars

→ high magnetic fields, radiation fields needed to fit haze

◮ Spectra qualitatively the same despite large range of background

model freedom

◮ Source + DM Annihilation and Pulsar + DM Annihilation do

well, but too much freedom

Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

SLIDE 18

Intro Model Method Spectra

Annihilation + Source Mod Best Fit Spectrum

1 10 100 1000 Ee [GeV] 0.001 0.010 0.100 E3 dN/dE [GeV2/cm2/s/sr] e+ +e- flux ΦAMS = 0.48 Np = 0.9, Ns = 1.6 1 10 100 Ee [GeV] 0.0001 0.0010 0.0100 E3 dN/dE [GeV2/cm2/s/sr] e+ flux ΦPAM

+ = 0.18, Ns = 1.6

0.1 1.0 10.0 100.0 1000.0 Ee [GeV] 0.01 0.10 φe+/(φe++φe-) e+ fraction ΦPAM

+ = 0.18, ΦPAM

= 0.07
40
30
20
10

b (degrees) 5 10 15 Intensity [10-20erg/Hz/s/cm2/sr] WMAP synch 23 GHz ∆ S = -0.8

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30
20
10

b (degrees) 5 10 15 Intensity [10-20erg/Hz/s/cm2/sr] WMAP synch 33 GHz ∆ S = -0.6

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30
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b (degrees) 5 10 15 Intensity [10-20erg/Hz/s/cm2/sr] WMAP synch 23 GHz, high l ∆ S = -1.3

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10

b (degrees) 500 1000 1500 2000 Intensity [10-20erg/Hz/s/cm2/sr] Haslam 408 MHz Nh = 1.2

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b (degrees) 500 1000 1500 2000 Intensity [10-20erg/Hz/s/cm2/sr] Haslam 408 MHz Nh = 1.2

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b (degrees) 500 1000 1500 2000 Intensity [10-20erg/Hz/s/cm2/sr] Haslam 408 MHz Nh = 1.2 0.1 1.0 10.0 100.0 1000.0 Eγ [GeV] 10-5 10-4 10-3 10-2 E2 dN/dE [MeV/cm2/sr/s] Fermi IC + brem NIC = 1.3 10 100 1000 Injection energy [GeV]

50

50 100 150 200 250 Local injection [10-30GeV/cm3/s] total ann source χ2 =109.6

Einasto α = 0.17, γe = 2.55 rB = 8.5kpc

· LARGE error bars,

not shown

· mχ ∼ 300GeV, BF × fE(e+ + e−) ∼ 10

Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

SLIDE 19

Intro Model Method Spectra

Annihilation + Pulsars Best Fit Spectrum

1 10 100 1000 Ee [GeV] 0.001 0.010 0.100 E3 dN/dE [GeV2/cm2/s/sr] e+ +e- flux ΦAMS = 0.48 Np = 1.0, Ns = 0.9 1 10 100 Ee [GeV] 0.0001 0.0010 0.0100 E3 dN/dE [GeV2/cm2/s/sr] e+ flux ΦPAM

+ = 0.12, Ns = 0.9

0.1 1.0 10.0 100.0 1000.0 Ee [GeV] 0.01 0.10 φe+/(φe++φe-) e+ fraction ΦPAM

+ = 0.12, ΦPAM

= 0.27
40
30
20
10

b (degrees) 5 10 15 Intensity [10-20erg/Hz/s/cm2/sr] WMAP synch 23 GHz ∆ S = -0.6

40
30
20
10

b (degrees) 5 10 15 Intensity [10-20erg/Hz/s/cm2/sr] WMAP synch 33 GHz ∆ S = -0.5

40
30
20
10

b (degrees) 5 10 15 Intensity [10-20erg/Hz/s/cm2/sr] WMAP synch 23 GHz, high l ∆ S = -0.8

40
30
20
10

b (degrees) 500 1000 1500 2000 Intensity [10-20erg/Hz/s/cm2/sr] Haslam 408 MHz Nh = 1.0

40
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10

b (degrees) 500 1000 1500 2000 Intensity [10-20erg/Hz/s/cm2/sr] Haslam 408 MHz Nh = 1.0

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10

b (degrees) 500 1000 1500 2000 Intensity [10-20erg/Hz/s/cm2/sr] Haslam 408 MHz Nh = 1.0 0.1 1.0 10.0 100.0 1000.0 Eγ [GeV] 10-5 10-4 10-3 10-2 E2 dN/dE [MeV/cm2/sr/s] Fermi IC + brem NIC = 1.4 10 100 1000 Injection energy [GeV]

50

50 100 150 200 250 Local injection [10-30GeV/cm3/s] total ann pulsar χ2 =108.8

Einasto α = 0.17, γe = 2.65 rB = 8.5kpc

· LARGE error bars,

not shown

· mχ ∼ 300GeV, BF × fE(e+ + e−) ∼ 10

Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

SLIDE 20

Intro Model Method Spectra

Propagation

10 100 1000 Injection energy [GeV]

50

50 100 150 200 250 Local injection [10-30GeV/cm3/s] default best fit smooth fit MED M1

Annihilating dark matter fits

10 100 1000 Injection energy [GeV]

50

50 100 150 200 250 Local injection [10-30GeV/cm3/s] default fit smooth fit MED M1

Decaying dark matter fits 10 100 1000 Injection energy [GeV]

50

50 100 150 200 250 Local injection [10-30GeV/cm3/s]

default fit smooth fit MED M1

Pulsar fits

K0 δ L Default 0.097 0.43 4 M1 0.0765 0.46 15 MED 0.0112 0.70 4

Table: K0 in kpc2/Myr, L in kpc.

Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

SLIDE 21

Intro Model Method Spectra

Injected primary electrons

dN dE ∝      (E/4GeV)1.6 E < 4GeV (E/4GeV)γe 4GeV < E < 2200GeV (E/2200GeV)3.3 E > 2200GeV (2) We use γe= 2.45, 2.50, 2.55, 2.60, 2.65, 2.70 Spatial distribution: ne( x) ∝ r r⊙ α exp

−β r

r⊙ − |z| .2kpc

Θ(rmax − r)

(3) where r is distance to the center of galaxy projected on the galactic

plane. The parameters are α = 2.35, β = 5.56283, and rmax = 15kpc .

Normalization fixed using Haslam 408 MHz signal.

Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

SLIDE 22

Intro Model Method Spectra

Spectrum for different rB, γe

10 100 1000 Injection energy [GeV] 50 100 150 200 250 300 Local injection [10-30GeV/cm3/s]

γe = 2.65 γe = 2.55 γe = 2.45 Annihilation Br=4.5 kpc

10 100 1000 Injection energy [GeV] 50 100 150 200 250 300 Local injection [10-30GeV/cm3/s]

γe = 2.65 γe = 2.55 γe = 2.45 Annihilation Br=6.5 kpc

10 100 1000 Injection energy [GeV] 50 100 150 200 250 300 Local injection [10-30GeV/cm3/s]

γe = 2.65 γe = 2.55 γe = 2.45 Annihilation Br=8.5 kpc

10 100 1000 Injection energy [GeV] 50 100 150 200 250 300 Local injection [10-30GeV/cm3/s]

γe = 2.65 γe = 2.55 γe = 2.45 Decay Br=4.5 kpc

10 100 1000 Injection energy [GeV] 50 100 150 200 250 300 Local injection [10-30GeV/cm3/s]

γe = 2.65 γe = 2.55 γe = 2.45 Decay Br=6.5 kpc

10 100 1000 Injection energy [GeV] 50 100 150 200 250 300 Local injection [10-30GeV/cm3/s]

γe = 2.65 γe = 2.55 γe = 2.45 Decay Br=8.5 kpc

10 100 1000 Injection energy [GeV] 50 100 150 200 250 300 Local injection [10-30GeV/cm3/s]

γe = 2.65 γe = 2.55 γe = 2.45 Pulsar Br=4.5 kpc

10 100 1000 Injection energy [GeV] 50 100 150 200 250 300 Local injection [10-30GeV/cm3/s]

γe = 2.65 γe = 2.55 γe = 2.45 Pulsar Br=6.5 kpc

10 100 1000 Injection energy [GeV] 50 100 150 200 250 300 Local injection [10-30GeV/cm3/s]

γe = 2.65 γe = 2.55 γe = 2.45 Pulsar Br=8.5 kpc

Figure:

All fit results for the three scenarios, over a 3 × 3 grid in background electron injection index (γe = 2.45, 2.55, 2.65) and scale for the magnetic field Br = 4.5, 6.5, and 8.5 kpc. These spectra were obtained from non-negative fits; the interpolated local injection density is plotted. Despite a wide range of assumptions about the background model, the results remain the same, qualitatively, for each scenario. Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

SLIDE 23

Intro Model Method Spectra

Spectrum for different α, γe

10 100 1000 Injection energy [GeV] 50 100 150 200 250 300 Local injection [10-30GeV/cm3/s]

γe = 2.65 γe = 2.55 γe = 2.45 Ann, α=.17 Br=4.5 kpc

10 100 1000 Injection energy [GeV] 50 100 150 200 250 300 Local injection [10-30GeV/cm3/s]

γe = 2.65 γe = 2.55 γe = 2.45 Ann, α=.17 Br=6.5 kpc

10 100 1000 Injection energy [GeV] 50 100 150 200 250 300 Local injection [10-30GeV/cm3/s]

γe = 2.65 γe = 2.55 γe = 2.45 Ann, α=.17 Br=8.5 kpc

10 100 1000 Injection energy [GeV] 50 100 150 200 250 300 Local injection [10-30GeV/cm3/s]

γe = 2.65 γe = 2.55 γe = 2.45 Ann, α=.22 Br=4.5 kpc

10 100 1000 Injection energy [GeV] 50 100 150 200 250 300 Local injection [10-30GeV/cm3/s]

γe = 2.65 γe = 2.55 γe = 2.45 Ann, α=.22 Br=6.5 kpc

10 100 1000 Injection energy [GeV] 50 100 150 200 250 300 Local injection [10-30GeV/cm3/s]

γe = 2.65 γe = 2.55 γe = 2.45 Ann, α=.22 Br=8.5 kpc

10 100 1000 Injection energy [GeV] 50 100 150 200 250 300 Local injection [10-30GeV/cm3/s]

γe = 2.65 γe = 2.55 γe = 2.45 Ann, α=.17, v~r.5 Br=4.5 kpc

10 100 1000 Injection energy [GeV] 50 100 150 200 250 300 Local injection [10-30GeV/cm3/s]

γe = 2.65 γe = 2.55 γe = 2.45 Ann, α=.17, v~r.5 Br=6.5 kpc

10 100 1000 Injection energy [GeV] 50 100 150 200 250 300 Local injection [10-30GeV/cm3/s]

γe = 2.65 γe = 2.55 γe = 2.45 Ann, α=.17, v~r.5 Br=8.5 kpc

Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

SLIDE 24

Intro Model Method Spectra

Results: DM Annihilation

◮ mχ ∼ 1TeV, BF ∗ Br ∼ 80 ◮ Einasto α = 0.22, γe = 2.5, Br = 8.5kpc

10 100 1000 Injection energy [GeV]

50

50 100 150 200 250 Local injection [10-30GeV/cm3/s] default best fit smooth fit MED M1

Annihilating dark matter fits

Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

SLIDE 25

Intro Model Method Spectra

Results: DM Decay

◮ mχ 3TeV, τ/Br ∼ 2 × 1026s ◮ Einasto α = 0.12, γe = 2.6, Br = 4.5kpc

10 100 1000 Injection energy [GeV]

50

50 100 150 200 250 Local injection [10-30GeV/cm3/s] default fit smooth fit MED M1

Decaying dark matter fits

Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

SLIDE 26

Intro Model Method Spectra

Results: Pulsar

◮ γe = 2.6, Br = 4.5kpc 10 100 1000 Injection energy [GeV]

50

50 100 150 200 250 Local injection [10-30GeV/cm3/s]

default fit smooth fit MED M1

Pulsar fits

Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

SLIDE 27

Intro Model Method Spectra

Haze morphology

WMAP haze

Fermi gamma ray haze

0.1

0.3 Temperature [mK]

23 GHz WMAP residual

40 20

20
40
20
10

10 20

0.64

1.60 [keV cm-2 s-1 sr-1]

5 < E < 10 GeV residual (1 < E < 2 GeV)

40 20

20
40
20
10

10 20

DM Ann 23 GHz, rB = 4.5kpc

Pulsar 23 GHz, rB = 4.5kpc

40
20

20 40

20
10

10 20

40
20

20 40

20
10

10 20

DM Ann 23 GHz, rB = 6.5kpc

Pulsar 23 GHz, rB = 6.5kpc

40
20

20 40

20
10

10 20

40
20

20 40

20
10

10 20

Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

SLIDE 28

Intro Model Method Spectra

Error Bars

10 100 1000 Injection energy [GeV]

50

50 100 150 200 250 Local injection [10-30GeV/cm3/s] best fit ± 1 sigma Annihilating dark matter fits 10 100 1000 Injection energy [GeV]

50

50 100 150 200 250 Local injection [10-30GeV/cm3/s] best fit ± 1 sigma Decaying dark matter fits 10 100 1000 Injection energy [GeV]

50

50 100 150 200 250 Local injection [10-30GeV/cm3/s] best fit ± 1 sigma Pulsar fits

Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

SLIDE 29

Intro Model Method Spectra

Gamma rays near Galaxy center

1 10 100 1000 Energy [GeV] 10-7 10-6 10-5 10-4 E2 dN/dE [GeV/cm2/sr/s] ann decay pulsar

Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

SLIDE 30

Intro Model Method Spectra

Solar Modulation

Low-energy (below ∼ 1 − 10GeV) CR data affected by solar physics. Solar modulation correction: J⊙(E) E2 − m2

e

= JLIS(E + Φ) (E + Φ)2 − m2

e

Conversion of PAMELA positron fraction to a positron flux JP AM(e+) =

φ(e+)

φ(e−) + φ(e+)

P AM

× ˆ SΦ−

P AM

ˆ

S−1

ΦAMS

JAMS(e+ + e−)
Parameters: ΦAMS, Φ−

P AM, Φ+ P AM - allow two different PAMELA

parameters to allow for charge sign dependence of modulation affects.

Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

SLIDE 31

Intro Model Method Spectra

Dark matter parameters

Annihilation:

E dN

dE dE = mχ (4) Therefore, integrating the local injection multiplied by energy gives

E Q(E,

x0)dE = σv0 × BF × (ρ0)2 mχ × Br(e+e−) 2 . (5) Decay:

E dN

dE = mχ (6) Again, we integrate the local injection multiplied by energy, giving

E Q(E,

x0)dE = τ −1

χ

× ρ0 × Br(e+e−) 2 . (7)

Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da

SLIDE 32

Intro Model Method Spectra

Some standard spectra

Electrons Gamma-rays

1 10 100 1000 E [GeV] 20 40 60 80 100 E^2 dN/dE b higgs lightquarks W Z tau XDMpions XDMtau 1 10 100 1000 E [GeV] 20 40 60 80 100 E^2 dN/dE b higgs lightquarks W Z tau XDMpions XDMtau

Tongyan Lin Harvard The Electron Injection Spectrum Determined By Anomalous Excesses in Cosmic Ray, Microwave, and Gamma Ray Da