Detecting Features in the Detecting Features in the Cosmic Ray Positron Cosmic Ray Positron

Spectrum with PAMELA Spectrum with PAMELA and AMS-02 and AMS-02

D.T. CumberbatchD.T. Cumberbatch

Oxford UniversityOxford University

Motivation for Dark Motivation for Dark MatterMatter

Rotation Curves of spiral galaxies:• M/L ratio

Abell 1689, HST

Galaxy clusters:•Proper motion

• X-ray emissions from hot gas•Gravitational lensing

Large-scale structure

2dFGRS

WMAP

Anisotropies in the CMB

Dark Matter CandidatesDark Matter Candidates

… … AND MANY MORE!!! AND MANY MORE!!! (e.g. Light DM, Kaluza-Klein bosons, …)(e.g. Light DM, Kaluza-Klein bosons, …)

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˜ χ 10 = N11

˜ B 0 + N12˜ W 3 + N13

˜ H 10 + N14

˜ H 20

Weakly Interacting Massive Particles (WIMPS)Weakly Interacting Massive Particles (WIMPS) (Lightest) Neutralino, stable in R-Parity conserving SUSY models(Lightest) Neutralino, stable in R-Parity conserving SUSY models Superposition of Higgsinos, Winos and Binos:Superposition of Higgsinos, Winos and Binos:

Sterile NeutrinosSterile Neutrinos Predominantly generated through (non) resonant oscillations e.g. Dodelson-Widrow (DW) mechanism, during QCD epoch.Predominantly generated through (non) resonant oscillations e.g. Dodelson-Widrow (DW) mechanism, during QCD epoch. Parameter space still available for subdominant DW Sterile Neutrino Dark Matter (Palazzo, Cumberbatch, Slosar & Silk arXiv:0707.1495). Parameter space still available for subdominant DW Sterile Neutrino Dark Matter (Palazzo, Cumberbatch, Slosar & Silk arXiv:0707.1495).

Primordial Long-lived Decaying ParticlesPrimordial Long-lived Decaying Particles Generated in early Universe with lifetimes >1sec (e.g. Gravitinos).Generated in early Universe with lifetimes >1sec (e.g. Gravitinos). Hadronic decay products can solve Li abundance problems (Cumberbatch et al. arXiv:0708.0095).Hadronic decay products can solve Li abundance problems (Cumberbatch et al. arXiv:0708.0095).

DM Detection MethodsDM Detection MethodsTwo Complementary Methods: Two Complementary Methods:

Direct DetectionDirect Detection Measure phonon, charge or light signals produced from elastic scattering Measure phonon, charge or light signals produced from elastic scattering

of WIMPS with a nuclear targetof WIMPS with a nuclear target DAMA, CDMS, EDELWEISS, ZEPLIN, CRESSTDAMA, CDMS, EDELWEISS, ZEPLIN, CRESST

ã

dd,

pp,

e,e

v,v ii

−+ Indirect DetectionIndirect Detection Measure excess in antiparticle flux from DM annihilationsMeasure excess in antiparticle flux from DM annihilations PAMELA, AMS-01/02, HEAT, BESS (antiprotons, positrons, antideuterons)PAMELA, AMS-01/02, HEAT, BESS (antiprotons, positrons, antideuterons) GLAST, HESS, EGRET (photons)GLAST, HESS, EGRET (photons)

Astrophysical Sources?Astrophysical Sources?

Supernovae and Wolf-Supernovae and Wolf-Rayet starsRayet stars

(Ramaty et al.)(Ramaty et al.) Neutron stars, Pulsars & Neutron stars, Pulsars &

BH’sBH’s

(Milne et al., Sturrock)(Milne et al., Sturrock) Solar Modulation effects Solar Modulation effects

(M&S)(M&S) Cosmic Ray interactions Cosmic Ray interactions

with ISMwith ISM

(Kozlovsky et al.)(Kozlovsky et al.)

Astrophysical sources are Astrophysical sources are insufficient!!!insufficient!!!

Positron ExcessPositron Excess

EXCESS!

Background (Moskalenko & Strong)

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(GeV)

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94/95HEAT

Positron Fraction=Positron Fraction= Total Positron FluxTotal Positron FluxTotal Positron Flux + Total Electron FluxTotal Positron Flux + Total Electron Flux

Positrons from decays involving Positrons from decays involving HHii00, W, W, Z, Z00 and and ff

Positron Production from Positron Production from 1100

annihilationannihilation via Gauge Bosons (favoured by Higgsinos and Winos) via Gauge Bosons (favoured by Higgsinos and Winos)

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˜ χ 10 ˜ χ 1

0 →W +W − + ... → e+v + ...

˜ χ 10 ˜ χ 1

0 → Z 0Z 0 + ... → e+e− + ...

⎫ ⎬ ⎭E

e + ≈ mW ,Z /2

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˜ χ 10 ˜ χ 1

0 → W +W − + ... → μ +v + ...→ e+vv v + ...

˜ χ 10 ˜ χ 1

0 → Z 0Z 0 + ...→ e+e− or μ +μ− + ...→ e+vv e− + ...

→ τ + + ... → e+ + hadrons

→ π + +... → μ +v + ... → e+vv v + ...

⎫

⎬

⎪ ⎪

⎭

⎪ ⎪

⇒ Continuum

via heavy quarks (favoured by Binos)via heavy quarks (favoured by Binos)

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˜ χ 10 ˜ χ 1

0 → tt + ... →( ) b b + ... → hadrons + l± → e+ + ...} ⇒ Continuum

Characteristic “cliff ” Characteristic “cliff ”

via leptons (producing a much harder spectrum)via leptons (producing a much harder spectrum)

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˜ χ 10 ˜ χ 1

0 → τ +τ − or μ +μ− + ... → e+ + ...} ⇒ Continuum

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˜ χ 10 ˜ χ 1

0 → e+e− + ...} ⇒ Ee + = mχ “ “saw-tooth”-shaped flux saw-tooth”-shaped flux

b b favoured because of tan favoured because of tan(()) suppression factorsuppression factor

Cosmic Ray PropagationCosmic Ray Propagation Injection spectrum modified by particle diffusion through ISMInjection spectrum modified by particle diffusion through ISM Scattering off galactic B-field, CMB radiation and starlight result in energy lossesScattering off galactic B-field, CMB radiation and starlight result in energy losses Diffusion can be well-approximated to a random walkDiffusion can be well-approximated to a random walk

Diffusion ConstantDiffusion Constant

Energy loss rateEnergy loss rateAssuming a constant B-field:Assuming a constant B-field:

Source TermSource TermProportional to haloProportional to halo

annihilation rate per unit vol.annihilation rate per unit vol.

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∂∂t

∂n

∂ε

⎛

⎝ ⎜

⎞

⎠ ⎟= ∇ K(ε,

r r )∇

∂n

∂ε

⎛

⎝ ⎜

⎞

⎠ ⎟

⎛

⎝ ⎜

⎞

⎠ ⎟+

∂

∂εb(ε,

r r )

∂n

∂Ee +

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟+ Q(ε,

r r )

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K ≈ K0 Cα + εα( )

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α ≈O(0.1), K0 ≈ O 1023( ) m2 s-1(Webber et al.)(Webber et al.)€

b ≈ b(ε) = τ E−1ε 2

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τE ≈1016 s(Maurin et al.)(Maurin et al.)

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ksρ2(

r r ) σv

dφ

dε

Cosmic Ray PropagationCosmic Ray Propagation Solve for the Solve for the locallocal differential positron flux (z=0, r=8.5 kpc) differential positron flux (z=0, r=8.5 kpc)

Diffusion zone half-thickness, L~4 kpc (Webber et Diffusion zone half-thickness, L~4 kpc (Webber et al.)al.) Investigate sensitivity of this flux to diffusion Investigate sensitivity of this flux to diffusion parameters parameters αα, L, K, b, , L, K, b,

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∂Φ∂ε z= 0

r= rsol.

= ks

c

2πβ (ε)τ Eε−2 σv

mχ2

δ fac. dε 'ε '=ε

mχ∫ D−2(ε,ε')dφ

dε 'H(L,D(ε,ε'))

× dr'r'ρ 2(r')exp −(r

sol.

2 + r'2 )

D2(ε,ε')

⎛

⎝ ⎜

⎞

⎠ ⎟

r= 0

∞

∫ I2rsol.r'

D2(ε,ε')

⎛

⎝ ⎜

⎞

⎠ ⎟,

D(ε,ε ') = 4K0τ E (v(ε) −ν (ε '))[ ]1/ 2

, v(ε) = ε (α −1) /(1−α ),

H(L,D) = erfL

D

⎛

⎝ ⎜

⎞

⎠ ⎟+ −2erf

(4m -1)L

D

⎛

⎝ ⎜

⎞

⎠ ⎟+ erf

(4m +1)L

D

⎛

⎝ ⎜

⎞

⎠ ⎟+ erf

(4m - 3)L

D

⎛

⎝ ⎜

⎞

⎠ ⎟

⎧ ⎨ ⎩

⎫ ⎬ ⎭m∈Z

m>0

∞

∑

L L = 2, 4, 10 kpc= 2, 4, 10 kpc KK0 0 = (0.25, 1, 4) x 3x10= (0.25, 1, 4) x 3x102323 m m2 2 ss-1-1

ττE E = (0.25, 1, 4) x 10= (0.25, 1, 4) x 101616 s s αα = 0.2, 0.6, 0.9= 0.2, 0.6, 0.9

Cosmic Ray PropagationCosmic Ray PropagationVariation with density profileVariation with density profile

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NFW =ρ s

r /rs( ) 1+ r /rs( )2 , rs = 25 kpc

ρ ISO =ρ s

rs

2 + r2( )

, rs = 5 kpc

ρ MOORE =ρ s

r /rs( )1.5

1+ r /rs( )1.5

( ), rs = 28 kpc

Positron FractionPositron Fraction NFW profile used, NFW profile used, rrss=25 kpc, =25 kpc, 00==0.3 GeV cm0.3 GeV cm--

33

Calculate PF using injection spectra calculated by DarkSUSY (Edsjo et al.)Calculate PF using injection spectra calculated by DarkSUSY (Edsjo et al.)

Normalisation of positron components left as a free parameters, nNormalisation of positron components left as a free parameters, nss and k and kss

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mχ = 988.4 GeV

Ωh2 = 0.162

Zg = 0.020

ks = 969

ns = 0.70

χ 2 /(12 − 2) = 0.33

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mχ = 335.7 GeV

Ωh2 = 0.029

Zg = 0.9951

ks = 35.8

ns = 0.6

χ 2 /(12 − 2) = 0.4830

Gaugino-dominatedGaugino-dominated Higgsino-dominatedHiggsino-dominated

Positron FractionPositron Fraction

To discern which models are relevant we need better instrumentation…To discern which models are relevant we need better instrumentation…

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mχ =101.6 GeV

Ωh2 = 0.042

Zg = 0.99927

ks = 45.50

ns = 0.26

χ 2 /(12 − 2) = 0.40

Γ( ˜ χ 10 ˜ χ 1

0 → 2e+e−) = 0.05

Gaugino-dominatedGaugino-dominated

++

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Γ( ˜ χ 10 ˜ χ 1

0 → 2e+e−)finitefinite

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mχ =130.3 GeV

Ωh2 = 0.058

Zg = 0.660

ks = 77.3

ns = 0.40

χ 2 /(12 − 2) = 0.38

Mixed Gaugino/HiggsinoMixed Gaugino/Higgsino

PAMELA & AMS-02PAMELA & AMS-02PAMELAPAMELA

AMS-02AMS-02

Primary objectives include measurement Primary objectives include measurement

Designed to study (anti)matter asymmetryDesigned to study (anti)matter asymmetry

of cosmic positron spectrum up to 270 GeVof cosmic positron spectrum up to 270 GeV Large acceptance of 20.5 cmLarge acceptance of 20.5 cm2 2 s s

Extensive exposure time of 3-years Extensive exposure time of 3-years

Balloon-based experiment (like HEAT) Balloon-based experiment (like HEAT)

To be deployed on ISS for 3-yr missionTo be deployed on ISS for 3-yr mission

Large acceptance of 20.5 cmLarge acceptance of 20.5 cm2 2 s (!)s (!)

Superior energy resolution and bkg rejectionSuperior energy resolution and bkg rejection

Sensitivity of PAMELA & AMS-02Sensitivity of PAMELA & AMS-02We attempt to identify at what annihilation rate the unique We attempt to identify at what annihilation rate the unique

features of our cosmic ray spectra are statistically significant features of our cosmic ray spectra are statistically significant by evaluating the following parameterby evaluating the following parameter

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Θ2 =f

e + ,obs.− f

e + ,bkg.( )2

Δ fe + ,bkg.( )

2∑

Where the sum is over each data point, Where the sum is over each data point, taken to have taken to have

the estimated sensitivity for each the estimated sensitivity for each instrumentinstrument

Sensitivity of PAMELA & AMS-02Sensitivity of PAMELA & AMS-02 Mixed Gaugino/Higgsino Neutralino annihilationsMixed Gaugino/Higgsino Neutralino annihilations

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mχ =130.3 GeV

Ωh2 = 0.058

Zg = 0.660

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ks = [8, 80], ns =1, Θ2 =[0.89, 81.14] (PAMELA)

[1.21, 109.25] (AMS - 02)

⎧ ⎨ ⎩

Sensitivity of PAMELA & AMS-02Sensitivity of PAMELA & AMS-02 Gaugino-dominated Neutralinos, with Gaugino-dominated Neutralinos, with

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Γ( ˜ χ 10 ˜ χ 1

0 → 2e+e−) = 0.05

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mχ =101.6 GeV

Ωh2 = 0.042

Zg = 0.99927

Γ( ˜ χ 10 ˜ χ 1

0 → 2e+e−) = 0.05

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ks = [5, 50], ns =1, Θ2 =[1.46, 127.75] (PAMELA)

[3.22, 266.48] (AMS - 02)

⎧ ⎨ ⎩

Potential of PAMELA & AMS-02Potential of PAMELA & AMS-02 Annihilation rates needed to be distinguished from the bkg at 95% C.L. ( Hooper & Silk , 2004 ) Annihilation rates needed to be distinguished from the bkg at 95% C.L. ( Hooper & Silk , 2004 )

AMS-02, BF=1AMS-02, BF=1

Pure HiggsinosPure Higgsinos

Pure WinosPure Winos

BinosBinos<<vv>>[10>>[10-26-26,10,10-27-27]] cmcm33ss-1 -1 (PAMELA, (PAMELA, AMS-02)AMS-02) Prospects improve for large tan(Prospects improve for large tan( )) NB: <NB: <vv>>can.can.~3x10~3x10-26-26cmcm33ss-1-1

WinosWinos AMSB for AMSB for m>m>[0.55,1] TeV (PAMELA, AMS-02)[0.55,1] TeV (PAMELA, AMS-02)

HiggsinosHiggsinos m>m>[230,400] GeV (PAMELA, AMS-02)[230,400] GeV (PAMELA, AMS-02)

WE NEED A BETTER UNDERSTANDING OF DM SUBSTRUCTURE IN MW!!!WE NEED A BETTER UNDERSTANDING OF DM SUBSTRUCTURE IN MW!!!