Tijana Prodanović, University of Novi Sad · Tijana Prodanović, University of Novi Sad Brian D. Fields, University of Illinois at Urbana Champaign. Tijana Prodanović. Fundamental

Tijana ProdanoviTijana Prodanovićć, University of Novi Sad, University of Novi SadBrian D. Fields, University of Illinois at Urbana Champaign

Tijana Prodanović

Fundamental Interactions, Serbia -

2007

September 28th, 2007

Tijana

Prodanović


2007

High-energy charged particlesAccelerated in astrophysical shocksDiffusive shock accelerationAny shock source is a candidate! (Blandford & Eichler 1987)

SitesSupernova remnants

Structure formation shocks

VLA image of Tycho

SNR Reynolds & Chevalier

Tijana Prodanović


2007


6Li only made by cosmic rays viafusion and spallation6Li very fragile – all other processes (stars) destroy Li more than they produce itPerfect cosmic ray probe!Standard assumption: measured 66LiLiSolarSolar made by Galactic made by Galactic CRsCRsLow-metallicity galactic halo stars stars (old age; older = lower metals) : 6Li plateau (Asplund et al. 2006) → indicates new lithium-6 source!?

Tijana Prodanović


2007


Li6→+αα LiCNO, 6→+αp

METALLICITY

Li A

BU

ND

AN

CE

6Li plateauUnexpected!New 6Li source?

Asplund et al. (2006)

Normalized to Sun

6Li only made by cosmic rays viaStandard assumption: 6LiSolar made by Galactic CRsBut new observations indicate a 6LiSolar plateauNeed new source?But Li observations are very difficult...maybe some observational effect

Is Is 66Li really in trouble?Li really in trouble?

Make an independent testMake an independent test


2007

September 28th, 2007Tijana Prodanović

Li6→+αα

Tijana Prodanović


2007


Hadronic cosmic-ray interactions make both

Lithium - 6 Pionic Gamma RaysLiCNO, 6→+αp ππγγπ →→+ 0pp

Any cosmic-ray source produces both gamma-rays and lithiumConnected essentially with ratio of reaction rates (Fields and Prodanović 2005)

Li abundance: local CR fluence (time integrated flux)Diffuse extragalactic : CR fluence across Universe

Use gamma rays to learn about Li!πγ

Fundamental Interactions, Serbia –

2007


αα

γ

αα

π

σ

σγ

crism yy ,,

1Li

∝

Pionic gamma-ray fraction Normalized to the Milky Way (blue)~30% of the total EGRB (normal gal.)

6Li production channels includedfusionspallation2-step reactions, eg.

Account for astrationsome gas was processed in stars – some Li was destroyedestimate astration from Deuterium: ~ 25% of gas was processed

Li6→+ααLiCNO, 6→+αp


2007


LiHBHO 611 →+→+

Prodanović

& Fields (2006)

Only ~ 50% of solar 6Li can be explained by GCRs without overproducing gamma-raysNeed newnew important 66Li sourceLi source

Recent observations in halo stars: 6Li plateau? But at 10% level of solar (Asplund et al. 2006)

Astrophysics to the rescue!Milky Way GCR flux higher than the cosmic mean? Implications for star-formation rateLow-energy CR component? Energetics and LiBeBratio constraints

Physics to the rescue!New, yet unknown production channel? Decaying dark matter? New physics?

Tijana Prodanović


2007


Tijana Prodanović


2007


It remains to be seen…

Use Li-gamma connection to check if things add upNumerically

GCR spectrumSolve propagation equation for Leaky Box model

Gamma-ray spectrumNumerically calculate from Dermer (1986) model

Tijana Prodanovic

Fundamental Interactions in Serbia


Pfrommer & Enßlin (2003) fit

Numerical: Dermer (1986) model

Below 3 GeV: isobar model

Above 12 GeV: scaling model based on accelerator data for

cross-sectionsLinearly connected

( ) ( )[ ] δαδπ

δπγ

/00 /2/2~)(

−−+ mEmEEF


September 28th, 2007Tijana Prodanovic

02/3 πppppp →Δ→

0πpppp →

Tijana Prodanovic



),(),(),(),(),(),( ,,Li txntxtxYytxntxtxq bcrp

ismcrgas

cr rrrrrr μσσ αααααααα Φ=Φ=

),()',()',(

'),( ,0

LiLi txFYytxqtxn

dttxY pism

cr

t

b

rrr

rαααα σ== ∫

)',()',('),(0

txtxdttxF crp

t

prrr

Φ= ∫ μ

),(),(),(),(, tsntststsq comp

comH

rrrrΦ= γπγ σμ

∫∫=

≡

)(

)()(

2 0

εεφ

εσεεφσ

σςξσππαγ

p

p

d

d

)(4

)'('4

)( 0,

0, tFY

cntqdtctI p

ismH

bt

comγγπγ σ

ππ== ∫

)',()',()',(')(0 0,

tsn

tsntsdttF p

t

b

comb

pr

rr

Φ= ∫ μ

),()(

4),(

)(

,,Li

, 0

txFtF

yycn

txY

tI

p

pi

ismcr

b

i

rrαα

γ

αα

πγ

σσ

π=

∫

∫ ∫

∫

∞Λ

−

∞−

∫=

Λ−=

≡

∫∫=

Λ===

+−=

=

=−+=

ε

εδερδ

ε

ε

τε

τε

ε

ε

εε

εεε

εφ

δερδ

ετερ

εεφ

ρττφ

φτδε

δφφ

τδεδ

δδ

'

'

00

")(1

")(

"

'

)'(')(

1)(

)(1

)'('

1

0)(

ism

esciesci

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iii

i

ism

esci

ism

ii

bd

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i

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ii

iesci

i

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esc

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i

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bd

vb

w

eQbvde

qqvQv

Qbv

b

vn

nnbQ

tn

⎩⎨⎧

<ℜ>ℜℜ

=Λ

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛=

=

GV4, 10.8GV4,)/4(g/cm8.10

2ln4

)(

6.02

2

222

2

42e

ββ

γπεεε

ρ

cv

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vmmAzZ

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ddR

dtvd

e

e

ism



)2(2,2/)('

2/)(,2/),1(

)]}'1('),'1(';[)''2(

)]}'1('),'1(';[)''2{(2

1),;(

])[()(

tantan)(

),;()()(),(

),()(

),(

),()(4)(

)(2)(

222

22***

1

1

1220

01

01

)(

)4/(22

0

min

2

pppp

pccc

p

pppr

p

ms

mmpr

p

pp

p

TT

ppppH

m

mTmsmmmmm

smmsms

H

Hm

mTTf

mmmB

mmmmmsTw

mTTfmBdmTwdT

TTdN

dTTTdN

TdT

TTd

dTTTd

TdTnEF

mE

EFdEF

p

p

p

+=−+=

−+==±=

+−+

+−=

Γ+−Γ

=

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

Γ

−+−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

Γ

−−=

⋅⋅=

=

=

−=

ΔΔ

ΔΔΔΔ±

Δ

−Δ

−Δ

−Δ

−Δ

−−Δ

−Δ

+Δ

+Δ

+Δ

+Δ

−+Δ

+ΔΔ

−ΔΔΔ

Δ−Δ−

Δ

−

+ΔΔ

∞

∞

+

∫

∫

∫

πππ

π

πππππππ

ππππππππ

π

π

ππ

π

π

ππ

π

π

π

πππ

εε ππ

πππγγ

γ

γγββγγγ

ββγγββγγγγβγβ

ββγγββγγγγβγβ

π

π

ςσσ

σφπ

ε

π

π

γπγ

Tijana Prodanovic



f –

normalized energy spectrum+ forward moving isobar- backward moving isobarΓ

–

resonance width=0.115/2 GeVB –

Breit-Wigner

distributionγπ’

–

Lorentz

factor in rest frame of isobarγc

–

LF in center of momentum sys.γΔ* -

LF in lab sys

)/(cossintan

)cos(

2/)4()(

/)]([cos

cos)(

2),(

*

*

22*max

*maxmax

*3

*3*

1

cos

22

max

ππ

ππ

π

ππ

π

ππ

π

π

βγ

βγ

γβγ

σςσ

π

pE

pEE

smmssE

psEE

dpdEd

TmE

dTTTdN

cc

cc

p

ccc

p

p

−ΘΘ

=Θ

Θ−=

+−=

−=Θ

⎟⎟⎠

⎞⎜⎜⎝

⎛Θ

−= ∫

Θ

π

π

σ

2max

2max

*max

**||

*||

2*22*||

2

*23

*21

26.2

2**3

*3*

,/

/)(4~

/41

)/41)(231()(

)]/41/(exp[)~1()(

mEpppx

smpxx

sm

pcpccq

smEEf

smBpxEfAdpdE

p

rppp

pq

p

−==

++=

+

+−=

−+=

+−⋅−⋅⋅=

⊥

⊥⊥

−

⊥

Tijana Prodanovic



Θ

–

angle of emission

Lorentz

invariant x-section

* is in center of massp –

pion

momentum

Tijana

Prodanović


2007

High-energy charged particlesAccelerated in astrophysical shocksSpectrum:

Strong shocks (diffusive shock acceleraton): Flux~E-2

Measured at Earth (JACEE 1998) : Flux~E-2.75

Tijana

Prodanović


2007

Diffusive shock accelerationAny shock source is a candidate! (Blandford & Eichler 1987)

SitesSupernova remnants

Structure formation shocks

VLA image of Tycho

SNR Reynolds & Chevalier

7Li made significantly in the Big Bang Nucleosynthesis (Cyburt, Fields, Schramm) but also in CR interactionsLow-metallicity galactic halo stars (old age; older = lower metals): 7Li plateau (Spite & Spite 1982) →indicates primordial lithium

Tijana Prodanović


2007


7Li plateau Expected but below theoretical predictions

METALLICITY

Li A

BU

ND

AN

CE

Asplund et al. (2006)

Normalized to Sun

TIME

2−∝ pφ


2007


75.2)( −+∝ Empφ


2007

June, 13th

2007Tijana Prodanović

“Pionic” gamma-rays

Distinctive spectrum – pion “bump”; peaks at mπ/2 (Stecker 1971; Dermer 1986)

But no strong evidence for pion “bump” either in the EGRB or in the MW diffuse gamma-ray spectrumUse the shapeshape of the spectrum (Pfrommer & Enßlin 2003) to find max max ““pionicpionic”” fraction fraction (Prodanović & Fields 2004)

0π+→+ pppp ismcr

γγ


2007

June, 13th

2007Tijana Prodanović

Documents

Tijana Prodanović, University of Novi Sad · Tijana Prodanović, University of Novi Sad Brian D. Fields, University of Illinois at Urbana Champaign. Tijana Prodanović. Fundamental