EFFECTS OF REACCELERATION AND SOURCE GRAMMAGE ON SECONDARY COSMIC - - PowerPoint PPT Presentation

EFFECTS OF REACCELERATION AND SOURCE GRAMMAGE ON SECONDARY COSMIC RAYS SPECTRA

28/11/19 - Virginia Bresci PHYSICS and ASTROPHYSICS of COSMIC RAYS OHP Saint Michel l'Observatoire, France

GALACTIC DISK hd ≪ H

,Li..

GALACTIC HALO nH ≪ nd

2

THE TRANSPORT EQUATION

− ∂ ∂z [Dα Iα ∂z ] + vA ∂Iα ∂z + 2hdndvασαIα δ(z)− − 2 3 vAAαp3∂Fα ∂p δ(z) + 2hdδ(z) ∂ ∂p [( dp dt )α,Ion. Iα] = = Aαp2Qα(p)δ(z)

3

2h

d

Galactic Halo

d

R

Disc

z-direction

Iα(z, Ek)dEk = vα(p)Fα(z, p)p2dp

…What experiments really measure:

THE TRANSPORT EQUATION

− 2 3 vAAαp3∂Fα ∂p δ(z) + 2hdδ(z) ∂ ∂p [( dp dt )α,Ion. Iα] = = Aαp2Qα(p)δ(z)

4

2h

d

Galactic Halo

d

R

Disc

z-direction

Iα(z, Ek)dEk = vα(p)Fα(z, p)p2dp

…What experiments really measure:

− ∂ ∂z [Dα Iα ∂z ]

+vA ∂Iα ∂z + 2hdndvασαIα δ(z)−

Spatial Diffusion

THE TRANSPORT EQUATION

− 2 3 vAAαp3∂Fα ∂p δ(z) + 2hdδ(z) ∂ ∂p [( dp dt )α,Ion. Iα] = = Aαp2Qα(p)δ(z)

5

2h

d

Galactic Halo

d

R

Disc

z-direction

Iα(z, Ek)dEk = vα(p)Fα(z, p)p2dp

…What experiments really measure:

Advection

− ∂ ∂z [Dα Iα ∂z ] +vA

∂Iα ∂z

+2hdndvασαIα δ(z)−

THE TRANSPORT EQUATION

= Aαp2Qα(p)δ(z)

6

2h

d

Galactic Halo

d

R

Disc

z-direction

Iα(z, Ek)dEk = vα(p)Fα(z, p)p2dp

…What experiments really measure:

Spallation reactions

− ∂ ∂z [Dα Iα ∂z ] +vA ∂Iα ∂z

+2hdndvασαIα δ(z)− − 2 3 vAAαp3 ∂Fα ∂p δ(z) + 2hdδ(z) ∂ ∂p [( dp dt )α,Ion. Iα] =

Adiabatic expansion Ionization of the medium

THE TRANSPORT EQUATION

− 2 3 vAAαp3 ∂Fα ∂p δ(z) + 2hdδ(z) ∂ ∂p [( dp dt )α,Ion. Iα] =

= Aαp2Qα(p)δ(z)

7

2h

d

Galactic Halo

d

R

Disc

z-direction

Iα(z, Ek)dEk = vα(p)Fα(z, p)p2dp

…What experiments really measure:

− ∂ ∂z [Dα Iα ∂z]+vA ∂Iα ∂z + 2hdndvασαIα δ(z)−

Source term

SOURCE TERM

Primary nuclei Secondary CRs

∂ ∂z [D(p) ∂f(z, p) ∂z ] − u ∂f(z, p) ∂z + + 1 3 ( du dz ) p ∂f(z, p) ∂p + η n1u1 4πp2

inj

δ(p − pinj) δ(z) = 0

Diffusion Advection Compression Injection at the shock surface Power law in momentum, slope s=3r/ (r-1) depends ONLY on the compression ratio r=u1/u2 -> 4 No dependence upon diffusion

Created in interactions between primaries - ISM:

Aαp2Qα(p) = ∑

α′>α

2hdndvα′(Ek)σα′αIα′,0(Ek)

Nuclei

p2Q¯

p = 2hdv¯ pnd,j∫ +∞ Eth

dEk,α′Iα′,0(Ek,α′) dσα′,j dEk,¯

p

Antiparticles

f0(p) = s ηn1 4πp3

inj (

p pinj)

−s

8

TRANSPORT EQUATION: THE HIGH ENERGY LIMIT

− ∂ ∂z [Dα Iα ∂z] + vA ∂Iα ∂z + 2hdndvασαIα δ(z)− 2 3 vAAαp3∂Fα ∂p δ(z) + 2hdδ(z) ∂ ∂p [( dp dt )α,Ion. Iα] = = Aαp2Qα(p)δ(z)

Primary CRs Secondary CRs

Dα ∝ Eδ

k

p2Qα ∝ E−s′

k

Dα ∝ Eδ

k

p2Qα′ ∝ Iα(Ek) ∝ E−s′−δ

k

Iα′(Ek) Iα (Ek) ∝ Xα(Ek) ∝ E−δ

k

Secondary to Primary (nuclei) Ratios: 9

“GRAMMAGE”

RECENT AMS-02 OBSERVATIONS

( R = A Z E2

k + 2mpc2Ek )

Helium Boron Boron over Carbon

10

NON-LINEAR EFFECTS

• Super-Alfvenic streaming of cosmic rays instability growth of

Alfvén waves

• Transition from this regime to Galactic turbulence generates a break in

the diffusion coefficient just around 200 GV :

(e.g. Blasi+ 2012 PRL 109,061101)

PURPLE VS CYAN LINE:

δ1 ≠ δ2 δ1 = δ2

ENOUGH NOT ENOUGH

(Blasi 2017)

A. REACCELERATION EFFECT:

The same shock waves at supernovae explosions that accelerate primary CRs in the first place are expected to pick up and re-energize any other charged particle in the upstream above the threshold of injection

f(−∞, p) = g(p)

SOURCE TERM NOW ?

f0(p) = s ηn1 4πp3

inj (

p pinj )

−s

+ s∫

p p0

dp′ p′ ( p′ p )

s

g(p′)

AS BEFORE.. (NOT FOR SECONDARIES) ..RE-ACCELERATION TERM (EVERYONE)

Aαp2Qα(p) = Aαp2 f0(p)VSNℛSN πR2

d

DIFFERENT BOUNDARY CONDITION:

12

A. REACCELERATION EFFECT:

The same shock waves at supernovae explosions that accelerate primary CRs in the first place are expected to pick up and re-energize any other charged particle in the upstream above the threshold of injection

f(−∞, p) = g(p)

SOURCE TERM NOW ?

f0(p) = s ηn1 4πp3

inj (

p pinj )

−s

+ s∫

p p0

dp′ p′ ( p′ p )

s

g(p′)

AS BEFORE.. (NOT FOR SECONDARIES) ..RE-ACCELERATION TERM (EVERYONE)

Aαp2Qα(p) = Aαp2 f0(p)VSNℛSN πR2

d

DIFFERENT BOUNDARY CONDITION:

13

• Distribution of SNRs that CRs found in the Galactic disk as a function of

their radius in the S-T phase

• Maximum energy cut-off

EMax(t) ≈ 100 ( t tST )

− 4

5

TeV = 100 ( rSN rST )

−2

TeV

A. REACCELERATION EFFECT:

14

P (rSN) drSN = KP dt(rSN) TMax ; TMax ≈ 3 × 104 yr

• Distribution of SNRs that CRs found in the Galactic disk as a function of

their radius in the S-T phase

• Maximum energy cut-off

EMax(t) ≈ 100 ( t tST )

− 4

5

TeV = 100 ( rSN rST )

−2

TeV

A. REACCELERATION EFFECT:

15

f0(p) = s ηn1 4πp3

inj(

p pinj)

−s

+ s∫

p p0

dp′ p′ ( p′ p )

s

I(i−1)(p′)

e−p/pMax(rSN) P (rSN) drSN = KP dt(rSN) TMax ; TMax ≈ 3 × 104 yr

• Distribution of SNRs that CRs found in the Galactic disk as a function of

their radius in the S-T phase

• Maximum energy cut-off

EMax(t) ≈ 100 ( t tST )

− 4

5

TeV = 100 ( rSN rST )

−2

TeV

A. REACCELERATION EFFECT:

16

f0(p) = s ηn1 4πp3

inj(

p pinj)

−s

+ s∫

p p0

dp′ p′ ( p′ p )

s

I(i−1)(p′)

¯ VSN = ∫

rMax rST

P(rSN)4 3 πr3

SNdrSN = 20

33 π r11/2

Max − r11/2 ST

r5/2

Max − r5/2 ST

AVERAGE VOLUME

P (rSN) drSN = KP dt(rSN) TMax ; TMax ≈ 3 × 104 yr e−p/pMax(rSN)

• Distribution of SNRs that CRs found in the Galactic disk as a function of

their radius in the S-T phase

• Maximum energy cut-off

P (rSN) drSN = KP dt(rSN) TMax ; TMax ≈ 3 × 104 yr EMax(t) ≈ 100 ( t tST )

− 4

5

TeV = 100 ( rSN rST )

−2

TeV

A. REACCELERATION EFFECT:

17

f0(p) = s ηn1 4πp3

inj(

p pinj)

−s

+ s∫

p p0

dp′ p′ ( p′ p )

s

I(i−1)(p′)

¯ VSN = ∫

rMax rST

P(rSN)4 3 πr3

SNdrSN = 20

33 π r11/2

Max − r11/2 ST

r5/2

Max − r5/2 ST

AVERAGE VOLUME

e−p/pMax(rSN)

B. SOURCE GRAMMAGE

18

Particles up to TeV/n are typically confined for a time yr inside the sources A non-negligible production of secondaries might come from interactions

• ccurring inside the SNR BEFORE the escape of primaries:

Ek ∼ TSN ≈ 3 × 104

CONTRIBUTION FROM PRIMARY PARTICLES THAT ARE STILL LOCATED INSIDE THE SOURCES

Qsrc,α = vα r(s) nsrc,j sVSNTSNℛ πR2

d

× × Aα′Kα′∫

+∞ Eth

dE′

k,α′

dσα′,j dEk,α ( p′(E′

k,α′)

pinj,α′ )

2−s

NB: for spallation processes

dσα′,j dEk,α ≡ σα,α′ δ(E′

k,α′ − Ek,α)

RESULTS

RESULTS

Model without Reacceleration Model with Reacceleration before solar modulation is included Model with Reacceleration Model without Reacceleration Model with Reacceleration before solar modulation is included Model with Reacceleration Model without Reacceleration Model with Reacceleration before solar modulation is included Model with Reacceleration

VB, E. Amato, P. Blasi, G. Morlino, MNRAS 488, 2068–2078 (2019)

RESULTS

21

Models without Reacceleration Models with Reacceleration Models without Reacceleration & source grammage Models with Reacceleration & source grammage Models with Reacceleration before solar modulation is included

RESULTS

22

Models without Reacceleration Models with Reacceleration Models without Reacceleration & source grammage Models with Reacceleration & source grammage Models with Reacceleration before solar modulation is included

RESULTS

23

Models without Reacceleration Models with Reacceleration Models without Reacceleration & source grammage Models with Reacceleration & source grammage Models with Reacceleration before solar modulation is included

RESULTS

24

Models without Reacceleration Models with Reacceleration Models without Reacceleration & source grammage Models with Reacceleration & source grammage Models without Reacceleration Models with Reacceleration Models without Reacceleration & source grammage Models with Reacceleration & source grammage Models with Reacceleration before solar modulation is included

… REACCELERATION & GRAMMAGE INSIDE SOURCES allow us to well-reproduce the spectra

• f CNO, p, He and B/C, B, Li, pbar without

requiring alternative descriptions of CRs transport