[PPT] - Cosmic antimatter from dark matter annihilation: effects of PowerPoint Presentation

SLIDE 1

Cosmic antimatter from dark matter annihilation: effects of cosmological subhalos and uncertainties

Julien Lavalle (Dept of Theoretical Physics, University of Turin)

Refs (arXiv) : 0603796, 0712.0468, 0709.3634, 0704.2543, 0808.0332, 0809.5268, 0902.3665 Collab: Delahaye, Salati, Taillet (LAPTH) – Maurin (LPNHE) – Nezri (LAM) Ling (Brussels) – Donato, Fornengo, Lineros (Turin) – Bi, Yuan (Beijing) – Bringmann (Stockholm)

1st Tango in Paris — IAP Tuesday, May 5th 2009

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 1

SLIDE 2

Requirements from PAMELA

e+ background (Delahaye et al, arXiv:0809.5268)

E [GeV]

1

10 1 10

2

10

]

1

.GeV

1

.s

1

.sr

2

/dE [cm φ d

+

e 3.5

∈

6

10

5

10

4

10

3

10

2

10

Propagation MIN MED MAX Full allowed

flux

+

Secondary e = 600 MV) φ TOA ( IS MS98 (IS)

CAPRICE 94 HEAT 94-95 AMS 01

E [GeV]

1 10

2

10

)

+e

+

/(e

+

positron fraction e

2

10

1

10

Propagation MIN MED MAX MS98

spectrum)

fraction (med e

+

e

= 600 MV φ HEAT 94-95 HEAT 00 AMS1 07 PAMELA 08

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 2

SLIDE 3

Requirements from PAMELA

e+ background (Delahaye et al, arXiv:0809.5268)

E [GeV]

1

10 1 10

2

10

]

1

.GeV

1

.s

1

.sr

2

/dE [cm φ d

+

e 3.5

∈

6

10

5

10

4

10

3

10

2

10

Propagation MIN MED MAX Full allowed

flux

+

Secondary e = 600 MV) φ TOA ( IS MS98 (IS)

CAPRICE 94 HEAT 94-95 AMS 01

E [GeV]

1 10

2

10

)

+e

+

/(e

+

positron fraction e

2

10

1

10

Propagation MIN MED MAX MS98

spectrum)

fraction (med e

+

e

= 600 MV φ HEAT 94-95 HEAT 00 AMS1 07 PAMELA 08

Orders of magnitude for χχ → e+e− (for E → mχ = 100 GeV). From PAMELA, the excess is 5 × φbg(100 GeV) ∼ 1.5 · 10−9cm−2.s−1.GeV−1.sr−1. φbg(100 GeV) ≃ 3 · 10−10 „ E 100 GeV «−3.5 cm−2.s−1.GeV−1.sr−1 φχχ(E → mχ) ≃ δβc 4π τE0 E2 σv 2 „ ρ⊙ mχ «2 ≃ 3 · 10−10 “ τ 1016s ” „ ρ⊙ 0.3 GeV/cm3 « „ 100 GeV mχ «4 „ σv 3 · 10−26cm3/s « For mχ ≃ 100 GeV, need for an amplification of: B ≃ 5.

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 2

SLIDE 4

Smooth NFW halo and generic predictions

E [GeV]

1

10 1 10

2

10

3

10

]

1

.sr

1

.s

1

.GeV

2

/dE [cm φ d

3.5

E

10

10

9

10

8

10

7

10

6

10

5

10

4

10

3

10

2

10

from WIMPs

+

e line

+

e

W

+

W b b Bg Del08 CAPRICE 94 HEAT 94-95 AMS 01 100 GeV 500 GeV 1000 GeV

Boost to get ∼ 5 × φbg at ∼100 GeV: WIMP mass 100 GeV 500 GeV 1 TeV final state e+e− 5 100 350 W +W − 80 500 1000 b¯ b 250 500 1000

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 3

SLIDE 5

Smooth NFW halo and generic predictions

E [GeV]

1

10 1 10

2

10

3

10

]

1

.sr

1

.s

1

.GeV

2

/dE [cm φ d

3.5

E

10

10

9

10

8

10

7

10

6

10

5

10

4

10

3

10

2

10

from WIMPs

+

e line

+

e

W

+

W b b Bg Del08 CAPRICE 94 HEAT 94-95 AMS 01 100 GeV 500 GeV 1000 GeV

Boost to get ∼ 5 × φbg at ∼100 GeV: WIMP mass 100 GeV 500 GeV 1 TeV final state e+e− 5 100 350 W +W − 80 500 1000 b¯ b 250 500 1000

10

2

10

1

1 10 10

2

10

3

Bkg. Signal Signal + bkg.

Bkg. only fit

HEAT 94+95

Positron energy (GeV) Positron fraction, e+ / (e+ + e-)

E.A. Baltz and J. Edsjö, 1998

mχ = 130.3 GeV ks = 54.6 χ2/7 = 1.35 (d) Example 4

Baltz & Edsjö, 98 Boost factor of 55

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 3

SLIDE 6

Inhomogeneous halo and boosted annihilation rate

Though the topic is still controversial, clumps are predicted by theory and simulations of hierarchical formation of structures (in the frame of ΛCDM) Annihilation rate is increased in a characteristic volume, because < n2

dm >≥< ndm >2

(Silk & Stebbins ApJ’93) The boost factor to the annihilation rate is related to the statistical variance via Bann ∼

<n2

dm>

<ndm>2

There is some scatter in N-body experiments: how to translate theoretical uncertainties to flux uncertainties ? what and where are the less ambiguous sig- natures, if so ? (Fig. from Diemand et al, MNRAS’04)

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 4

SLIDE 7

Inhomogeneous halo and boosted annihilation rate

Though the topic is still controversial, clumps are predicted by theory and simulations of hierarchical formation of structures (in the frame of ΛCDM) Annihilation rate is increased in a characteristic volume, because < n2

dm >≥< ndm >2

(Silk & Stebbins ApJ’93) The boost factor to the annihilation rate is related to the statistical variance via Bann ∼

<n2

dm>

<ndm>2

There is some scatter in N-body experiments: how to translate theoretical uncertainties to flux uncertainties ? what and where are the less ambiguous sig- natures, if so ? (Fig. from Diemand et al, MNRAS’04) Minimal mass from free streaming ∼ 10−6M⊙ (e.g. Bringmann arXiv:0903.0189). . Nbody resolution: ∼ 105M⊙ — ∼ 105 subhalos in the MW (e.g. Diemand et al 08, Springel et al 08). .. Mass distribution ∼ M−1.9, various concentration models. ⇒∼ 1015 Earth-mass objects in the MW! .. Antibiased spatial distribution. (What for small

bjects ?)

.. Limits: spatial and mass resolutions (numerical) + NO BARYONS (physical)!

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 4

SLIDE 8

Gamma-rays versus antimatter cosmic rays

The annihilation signal is integrated:

ver a small solid angle around the line
f sight for γ−rays and neutrinos
ver a rather small volume around the

Earth for antimatter CRs, due to diffusion processes = ⇒ Boost factors are not the same ! Courtesy P . Salati

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 5

SLIDE 9

Boost from few objects

Few massive subhalos are expected in the MW: ∼ 100 × “

M 108M⊙

”−1 By chance, one or few could wander close to the Earth ... Predictions: move a single (or few) object(s) around Very small probability: fine tuned models !!! (∼ O(103−4)objects/MW volume) Multimessenger analysis: check radio, γ-ray and antiproton constraints Not a clean prediction of clumpiness ⇒ What about global effects?.

E (GeV)

1 10

2

10

)

+e

+

/(e

+

positron fraction e

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Primary contribution Background from MS98 Total HEAT data Closest clump at ~0.5 kpc = 50 GeV

LZP

m = 6 TeV)

KK

(m E [GeV]

1

10 1 10

2

10

]

1

.sr

1

.s

1

.GeV

2

/dE [cm φ d

3.5

E

10

10

9

10

8

10

7

10

6

10

5

10

4

10

3

10

2

10

1

10 1

from WIMPs

+

e smooth Clump at 2 kpc

Lavalle, Pochon, Salati & Taillet astro-ph/0603796

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 6

SLIDE 10

Boost from few objects

Few massive subhalos are expected in the MW: ∼ 100 × “

M 108M⊙

”−1 By chance, one or few could wander close to the Earth ... Predictions: move a single (or few) object(s) around Very small probability: fine tuned models !!! (∼ O(103−4)objects/MW volume) Multimessenger analysis: check radio, γ-ray and antiproton constraints Not a clean prediction of clumpiness ⇒ What about global effects?.

E (GeV)

1 10

2

10

)

+e

+

/(e

+

positron fraction e

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Primary contribution Background from MS98 Total HEAT data Closest clump at ~0.25 kpc = 50 GeV

LZP

m = 6 TeV)

KK

(m E [GeV]

1

10 1 10

2

10

]

1

.sr

1

.s

1

.GeV

2

/dE [cm φ d

3.5

E

10

10

9

10

8

10

7

10

6

10

5

10

4

10

3

10

2

10

1

10 1

from WIMPs

+

e smooth Clump at 1 kpc

Lavalle, Pochon, Salati & Taillet astro-ph/0603796

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 6

SLIDE 11

Boost from few objects

Few massive subhalos are expected in the MW: ∼ 100 × “

M 108M⊙

”−1 By chance, one or few could wander close to the Earth ... Predictions: move a single (or few) object(s) around Very small probability: fine tuned models !!! (∼ O(103−4)objects/MW volume) Multimessenger analysis: check radio, γ-ray and antiproton constraints Not a clean prediction of clumpiness ⇒ What about global effects?.

E (GeV)

1 10

2

10

)

+e

+

/(e

+

positron fraction e

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Primary contribution Background from MS98 Total HEAT data Closest clump at ~0.12 kpc = 50 GeV

LZP

m = 6 TeV)

KK

(m E [GeV]

1

10 1 10

2

10

]

1

.sr

1

.s

1

.GeV

2

/dE [cm φ d

3.5

E

10

10

9

10

8

10

7

10

6

10

5

10

4

10

3

10

2

10

1

10 1

from WIMPs

+

e smooth Clump at 0.5 kpc

Lavalle, Pochon, Salati & Taillet astro-ph/0603796

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 6

SLIDE 12

Boost from few objects

Few massive subhalos are expected in the MW: ∼ 100 × “

M 108M⊙

”−1 By chance, one or few could wander close to the Earth ... Predictions: move a single (or few) object(s) around Very small probability: fine tuned models !!! (∼ O(103−4)objects/MW volume) Multimessenger analysis: check radio, γ-ray and antiproton constraints Not a clean prediction of clumpiness ⇒ What about global effects?.

E [GeV]

1 10

2

10

3

10

)

+e

+

/(e

+

positron fraction e

2

10

1

10

HEAT 94-95 HEAT 00 AMS1 07 PAMELA 08

min med max 1.00 0.50 5.00 0.10 0.05 1033 1034 1035 1036 1037 1038

Bringmann, Lavalle & Salati (2009)

d [kpc] Γ [s−1]

0.1 × ΓMilky Way PAMELA (fit) EGRET (constraint)

mχ = 1 TeV (UED)

.

Bringmann, Lavalle & Salati arXiv:0902.3665

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 6

SLIDE 13

Boost from few objects

Few massive subhalos are expected in the MW: ∼ 100 × “

M 108M⊙

”−1 By chance, one or few could wander close to the Earth ... Predictions: move a single (or few) object(s) around Very small probability: fine tuned models !!! (∼ O(103−4)objects/MW volume) Multimessenger analysis: check radio, γ-ray and antiproton constraints Not a clean prediction of clumpiness ⇒ What about global effects?.

min med max 1.00 0.50 5.00 0.10 0.05 1034 1035 1036 1037 1038 1039 1040

Bringmann, Lavalle & Salati (2009)

d [kpc] Γ [s−1]

0.1 × ΓMilky Way PAMELA (fit) EGRET (constraint)

mχ = 1 TeV (100% to e+e−)

.

min med max 1.00 0.50 5.00 0.10 0.05 1033 1034 1035 1036 1037 1038

Bringmann, Lavalle & Salati (2009)

d [kpc] Γ [s−1]

0.1 × ΓMilky Way PAMELA (fit) EGRET (constraint)

mχ = 1 TeV (UED)

.

Bringmann, Lavalle & Salati arXiv:0902.3665

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 6

SLIDE 14

Energy-dependent diffusion scales for e+ and p

] p for

max

] or [ E / E

+

for e

S

/ E

D

[ E

4

10

3

10

2

10

1

10

/ L

D

λ

1

10 1 10

Characteristic diffusion length (for L = 4 kpc) = 1 TeV]

max

anti-proton [E = 1 TeV]

S

positron [E = 0.5 TeV]

S

positron [E = 0.25 TeV]

S

positron [E

Lavalle, Nezri, Ling et al – PRD 78 (2008)

e+’s lose energy: survey larger and larger volumes when detected at lower and lower energies → importance of energy loss parameters: magnetic field, interstellar radiation field. p’s do not lose energy, but convective wind and spallation processes very efficient at low energy: survey larger volume at high energies

.

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 7

SLIDE 15

Energy-dependent diffusion scales for e+ and p

] p for

max

] or [ E / E

+

for e

S

/ E

D

[ E

4

10

3

10

2

10

1

10

/ L

D

λ

1

10 1 10

Characteristic diffusion length (for L = 4 kpc) = 1 TeV]

max

anti-proton [E = 1 TeV]

S

positron [E = 0.5 TeV]

S

positron [E = 0.25 TeV]

S

positron [E

Lavalle, Nezri, Ling et al – PRD 78 (2008)

e+’s lose energy: survey larger and larger volumes when detected at lower and lower energies → importance of energy loss parameters: magnetic field, interstellar radiation field. p’s do not lose energy, but convective wind and spallation processes very efficient at low energy: survey larger volume at high energies

.

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 7

SLIDE 16

Effective volume picture for the smooth contribution Inject a 200 GeV e+ with Q(r) = ρ2(r) ∝ r−2 ...

GC Earth Simplest view of propagation G ∝ exp „ − |

xS− x⊙|2 λ2

D

« with λD = p 4K0∆˜ t = f(ES, ED) → Detection volume scaling a sphere of radius λD Figures: galactic plane at z=0 kpc x and y from -20 to 20 kpc Earth located at (x = 8, y = 0) kpc 2D plots of G( x, 200GeV → ˜ x⊙, E) × ρ2

← − 2 × R = 40 kpc − → @190 GeV @150 GeV @100 GeV @10 GeV

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 8

SLIDE 17

Primary fluxes for a 200 GeV e+ line / antiprotons

T [GeV]

1 10

2

10

]

1

.GeV

1

.sr

1

.s

2

/dT [cm φ d

12

10

11

10

10

10

9

10

8

10

7

10

6

10

Contributions smooth halo only ) σ 5 ± sub-halos (

sun

M

6

+ 10 = 200 GeV

χ

Fiducial WIMPs with m (from b) p (line)

+

e = 200 GeV

χ

Fiducial WIMPs with m (from b) p (line)

+

e

T [GeV]

1 10

2

10

]

1

.GeV

1

.sr

1

.s

2

/dT [cm φ d

12

10

11

10

10

10

9

10

8

10

7

10

6

10

Contributions smooth halo only ) σ 5 ± sub-halos (

sun

M

6

+ 10 = 200 GeV

χ

Fiducial WIMPs with m (from b) p (line)

+

e = 200 GeV

χ

Fiducial WIMPs with m (from b) p (line)

+

e

Configurations: Mmin = 10−6|106M⊙, αm = 2.0, inner-NFW, B01, smooth-like space distribution (smooth = NFW) Lavalle, Maurin et al – A&A 429, 427 (2008) Lavalle, Nezri, Ling et al – PRD 78 (2008)

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 9

SLIDE 18

Boost factors for a 200 GeV e+ line / antiprotons

E [GeV]

1 10

2

10

+

for e

eff

B

1 10

Max, Inter and Min boost configurations = 1.8 α ,

6

= 10

min

Min: cored, inner NFW, M = 1.9 α ,

6

= 10

min

Inter: NFW, inner NFW, M = 2 α ,

6

= 10

min

Max: NFW, inner Moore, M

T [GeV]

1

10 1 10

2

10

p for

eff

B

1 10

Max, Inter and Min boost configurations = 1.8 α ,

6

= 10

min

Min: cored, inner NFW, M = 1.9 α ,

6

= 10

min

Inter: NFW, inner NFW, M = 2 α ,

6

= 10

min

Max: NFW, inner Moore, M

Lavalle, Yuan, Maurin & Bi — A&A 429, 427 (2008)

e+ ¯ p

Extreme configurations Mmin = 10−6|106M⊙, αm = 1.8|2.0, inner-NFW/Moore, B01/ENS01, cored/smooth-like space distribution (smooth = NFW)

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 10

SLIDE 19

Boost factors for a 200 GeV e+ line / antiprotons

E [GeV]

1 10

2

10

+

for e

eff

B

1 10

Varying sub-halo spatial distribution cored + inner NFW smooth NFW + inner NFW smooth NFW + inner Moore

T [GeV]

1

10 1 10

2

10

p for

eff

B

1 10

Varying sub-halo spatial distribution cored + inner NFW smooth NFW + inner NFW smooth NFW + inner Moore

Mmin = 10−6M⊙, αm = 1.9, inner-NFW vs Moore, B01, cored vs smooth-like space distribution (smooth = NFW) Lavalle, Yuan, Maurin & Bi — A&A 429, 427 (2008)

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 11

SLIDE 20

Summary

Clumps are predicted and observed in pure DM Nbody simulations: what will happen with baryons? (more efficient tidal disruption expected, but small scales should survive) Invoking a nearby clump = playing the Galactic Lottery Global clumpiness effects cannot amplify the signal, BOOST 20 for usual WIMP models (VLII analysis — Bertone et al, in progress) Complementarity with other messengers (multiwavelength photons and ¯ p) is very important Clumpiness can boost the Sommerfeld boost (Lattanzi & Silk, 2008 — Lattanzi, Lavalle, Salati & Silk, in progress) If DM is made of WIMPs, clumps should be there ... seen or unseen ... Uncomfortable to look for exotic explanations when standard astrophysics (e.g. pulsars) pro- vides significant contributions: local e+s at the GeV scale may not be interesting anymore to look for DM

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 12

SLIDE 21

Backup

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 13

SLIDE 22

Prediction of the secondary e+ flux and uncertanties

The Alpine connection e+ background (Annecy & Torino) Delahaye et al, arXiv:0809.5268

E [GeV]

1

10 1 10

2

10

]

1

.GeV

1

.s

1

.sr

2

/dE [cm φ d

+

e 3.5

∈

6

10

5

10

4

10

3

10

2

10

Propagation MIN MED MAX Full allowed

flux

+

Secondary e = 600 MV) φ TOA ( IS MS98 (IS)

CAPRICE 94 HEAT 94-95 AMS 01

R [kpc]

1

10 1 10

Signal fraction f

2

10

1

10 1

Signal fraction E = 0.1 GeV E = 1 GeV E = 10 GeV E = 100 GeV E = 500 GeV

Secondary positron flux Spatial origin vs energy

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 14

SLIDE 23

PAMELA: to predict the e+ fraction, we need e−s!

The Alpine connection e+ background (Annecy & Torino) Delahaye et al, arXiv:0809.5268

E [GeV]

1

10 1 10

2

10

]

1

.GeV

1

.s

1

.sr

2

/dE [cm φ d

+

e 3.5

∈

6

10

5

10

4

10

3

10

2

10

Propagation MIN MED MAX Full allowed

flux

+

Secondary e = 600 MV) φ TOA ( IS MS98 (IS)

CAPRICE 94 HEAT 94-95 AMS 01

E [GeV]

1

10 1 10

]

1

.GeV

1

.s

1

.sr

2

/dE [cm φ d

e

3.45

∈

6

10

5

10

4

10

3

10

2

10

1

10 1

0.1 ± = 3.44 γ index hard index fit med index fit soft index fit MS98 (IS) Electron CR data CAPRICE 94 HEAT 94-95 AMS01 98

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 15

SLIDE 24

PAMELA: to predict the e+ fraction, we need e−s!

The Alpine connection e+ background (Annecy & Torino) Delahaye et al, arXiv:0809.5268

E [GeV]

1

10 1 10

2

10

]

1

.GeV

1

.s

1

.sr

2

/dE [cm φ d

+

e 3.5

∈

6

10

5

10

4

10

3

10

2

10

Propagation MIN MED MAX Full allowed

flux

+

Secondary e = 600 MV) φ TOA ( IS MS98 (IS)

CAPRICE 94 HEAT 94-95 AMS 01

E [GeV]

1

10 1 10

]

1

.GeV

1

.s

1

.sr

2

/dE [cm φ d

e

3.45

∈

6

10

5

10

4

10

3

10

2

10

1

10 1

0.1 ± = 3.44 γ index hard index fit med index fit soft index fit MS98 (IS) Electron CR data CAPRICE 94 HEAT 94-95 AMS01 98

E [GeV]

1 10

2

10

)

+e

+

/(e

+

positron fraction e

2

10

1

10

Propagation MIN MED MAX MS98

spectrum)

fraction (hard e

+

e

= 600 MV φ HEAT 94-95 HEAT 00 AMS1 07 PAMELA 08

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 15

SLIDE 25

PAMELA: to predict the e+ fraction, we need e−s!

The Alpine connection e+ background (Annecy & Torino) Delahaye et al, arXiv:0809.5268

E [GeV]

1

10 1 10

2

10

]

1

.GeV

1

.s

1

.sr

2

/dE [cm φ d

+

e 3.5

∈

6

10

5

10

4

10

3

10

2

10

Propagation MIN MED MAX Full allowed

flux

+

Secondary e = 600 MV) φ TOA ( IS MS98 (IS)

CAPRICE 94 HEAT 94-95 AMS 01

E [GeV]

1

10 1 10

]

1

.GeV

1

.s

1

.sr

2

/dE [cm φ d

e

3.45

∈

6

10

5

10

4

10

3

10

2

10

1

10 1

0.1 ± = 3.44 γ index hard index fit med index fit soft index fit MS98 (IS) Electron CR data CAPRICE 94 HEAT 94-95 AMS01 98

E [GeV]

1 10

2

10

)

+e

+

/(e

+

positron fraction e

2

10

1

10

Propagation MIN MED MAX MS98

spectrum)

fraction (hard e

+

e

= 600 MV φ HEAT 94-95 HEAT 00 AMS1 07 PAMELA 08

E [GeV]

1 10

2

10

)

+e

+

/(e

+

positron fraction e

2

10

1

10

Propagation MIN MED MAX MS98

spectrum)

fraction (soft e

+

e

= 600 MV φ HEAT 94-95 HEAT 00 AMS1 07 PAMELA 08

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 15

SLIDE 26

Sub-TeV Cosmic ray propagation in the Galaxy

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 16

SLIDE 27

Sub-TeV Cosmic ray propagation in the Galaxy

cf. e.g. Berezinsky (1990)

Cylindrical diffusive halo : R ∼ 20kpc, L ∼ 3kpc diffusion off magnetic inhomogeneities, reacceleration. Gaseous disc (h ∼ 0.1kpc) : spallation + convection upside down. free parameters: K(E), L, R, VC, VA ....... (Figure by D. Maurin)

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 16

SLIDE 28

Sub-TeV Cosmic ray propagation in the Galaxy

cf. e.g. Berezinsky (1990)

Cylindrical diffusive halo : R ∼ 20kpc, L ∼ 3kpc diffusion off magnetic inhomogeneities, reacceleration. Gaseous disc (h ∼ 0.1kpc) : spallation + convection upside down. free parameters: K(E), L, R, VC, VA ....... (Figure by D. Maurin)

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 16

SLIDE 29

Diffusion equation for e+/− or p¯ p

e+/−, cf. Bulanov & Dogel 73, Baltz & Edsjö 98, Lavalle et al 07, Delahaye et al 08 Nuclei, cf. Strong et al (98-08), Maurin et al (01-08) ∂t dn dE = Q(E, x, t) +

∇(K(E,

x) ∇ − Vc) dn dE −

∂E(dE

dt − ∂EE2Kpp∂pE−2) dn dE −

Γspal

dn dE

source: injected spectrum spatial current: diffusion and convection K(E) = K0 “

E E0

”α

Vc(z) = sign(z) × Vc

Energy losses and reacceleration spallation (nuclei) Uncertainties and degeneracies in parameters (Maurin et al 01) (Complementary & full numerical: Galprop, Strong et al)

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 17

SLIDE 30

Many-object method: Define the phase space of substructures

The phase space distribution depends on two main quantities: the spatial distribution of objects the luminosity function of objects

dncl dL (L,

x) =

dNcl dV dL(L,

x) = N0 × dP

dV (

x) × dP

dL(L,

x)

PDFs allow to compute mean values and associated statistical variances for some physical quantities

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 18

SLIDE 31

Computing the odds of the Galactic Lottery: Identical clumps tracking the smooth halo

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 19

SLIDE 32

Computing the odds of the Galactic Lottery: Identical clumps tracking the smooth halo

Boost for antimatter CRs: Long believed to be simple rescaling of fluxes ... This picture is wrong. Due to propagation effects, boost is a non-trivial function of energy (J.L, Pochon, Salati & Taillet, 2006). Variance depends on the number of clumps within the volume bounded by diffusion length λD: increases when the population when λD decreases (∼ 1/√Neff). The recipe applies to any kind of sources Predictions for N-body-like models ??? Lavalle et al, A&A 462 (2007)

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 20

SLIDE 33

Cosmological sub-halos: Results of the state-of-the-art N-body experiments

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 21

SLIDE 34

Cosmological sub-halos: Results of the state-of-the-art N-body experiments

N-body results as input ingredients, and allowed [ranges]: Mass distribution: minimal clump mass Mmin [106 − 10−6M⊙], logarithmic slope αm [1.8-2.0] Spatial distribution: . [cored isothermal – smooth-like] Spherical inner profile(s) for clumps ∝ r−γ, with γ ∈[NFW-Moore]=[1,1.5] and concentration [Eke et al 01 – Bullock et al 01]

radius [kpc]

1

10 1 10

2

10

]

3

(r) [kpc dV dP

10

10

9

10

8

10

7

10

6

10

5

10

4

10

3

10 Space distribution of clumps NFW Cored isoth

NFW vs cored isothermal

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 22

SLIDE 35

Luminosity profiles: effects of αm

sol

r / R

1 2 3 4 5 6

sol

L / L

4

10

3

10

2

10

1

10 1 10

2

10

3

10 Luminosity profiles (f=0.13) smooth (NFW) )

2

cored r ∝ subhalos ( total Range mass contribution = 1.9

m

α

sol

M

3
10
6

10

sol

1 M
3

10

sol

M

3

1-10

sol

M

6

10

3

10

sol

M

9

10

6

10

Luminosity profiles for different mass ranges Li = N0 × dPV (r) dV Z

∆i=3

d log(m) dPm d log(m)ξ(m) luminosity ∝ local number of annihilations N(> Mref) ∝ M1−αm: if ξ ∝ Mβ and each decade of mass contributes the same to the annihilation rate when αm − β = 1 (for B01, β ∼ 0.9 )

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 23

SLIDE 36

Luminosity profiles: effects of αm

sol

r / R

1 2 3 4 5 6

sol

L / L

4

10

3

10

2

10

1

10 1 10

2

10

3

10 Luminosity profiles (f=0.09) smooth (NFW) )

2

cored r ∝ subhalos ( total Range mass contribution = 1.8

m

α

sol

M

3
10
6

10

sol

1 M
3

10

sol

M

3

1-10

sol

M

6

10

3

10

sol

M

9

10

6

10

Luminosity profiles for different mass ranges Li = N0 × dPV (r) dV Z

∆i=3

d log(m) dPm d log(m)ξ(m) luminosity ∝ local number of annihilations N(> Mref) ∝ M1−αm: if ξ ∝ Mβ and each decade of mass contributes the same to the annihilation rate when αm − β = 1 (for B01, β ∼ 0.9 )

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 23

SLIDE 37

Luminosity profiles: effects of αm

sol

r / R

1 2 3 4 5 6

sol

L / L

4

10

3

10

2

10

1

10 1 10

2

10

3

10 Luminosity profiles (f=0.34) smooth (NFW) )

2

cored r ∝ subhalos ( total Range mass contribution = 2.0

m

α

sol

M

3
10
6

10

sol

1 M
3

10

sol

M

3

1-10

sol

M

6

10

3

10

sol

M

9

10

6

10

Luminosity profiles for different mass ranges Li = N0 × dPV (r) dV Z

∆i=3

d log(m) dPm d log(m)ξ(m) luminosity ∝ local number of annihilations N(> Mref) ∝ M1−αm: if ξ ∝ Mβ and each decade of mass contributes the same to the annihilation rate when αm − β = 1 (for B01, β ∼ 0.9 )

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 23

SLIDE 38

Luminosity profiles: effects of dP/dV

sol

r / R

1 2 3 4 5 6

sol

L / L

4

10

3

10

2

10

1

10 1 10

2

10

3

10 Luminosity profiles (f=0.13) smooth (NFW) (r))

sm

ρ ∝ subhalos ( total Range mass contribution = 1.9

m

α

sol

M

3
10
6

10

sol

1 M
3

10

sol

M

3

1-10

sol

M

6

10

3

10

sol

M

9

10

6

10

sol

r / R

1 2 3 4 5 6

sol

L / L

4

10

3

10

2

10

1

10 1 10

2

10

3

10 Luminosity profiles (f=0.13) smooth (NFW) )

2

cored r ∝ subhalos ( total Range mass contribution = 1.9

m

α

sol

M

3
10
6

10

sol

1 M
3

10

sol

M

3

1-10

sol

M

6

10

3

10

sol

M

9

10

6

10

Julien Lavalle, TANGO in Paris — IAP , 4-7/V/2009 – p. 24