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Cosmic Ray Transport in the Galaxy Vladimir Ptuskin IZMIRAN, Russia

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Ncr ~ 10-10 cm-3- total number density

wcr ~ 1.5 eV/cm3- energy density

Emax ~ 3x1020 eV - max. observed energy

δcr ~ 10-3 at 1012 - 1014 eV - anisotropy

rg ~ 1E/(Z×3×1015 eV) pc - Larmor radius

ulsar

E-2.7

cosmic ray density

Ncr

T

source spectrum

E-(2.0 … 2.4)

Qcr

escape time

E-(0.3 … 0.6)

two power laws: source spectrum + propagation

secondary species:Qcr,2 = nvσ21N1

d, 3He, Li, Be, B … p, e+

escape length:X = ρvT

~ 10 g/cm2at 1 GeV/nucleon

basic empirical diffusion model

Ginzburg & Ptuskin 1976, Berezinskii et al. 1990, Strong & Moskalenko 1998 (GALPROPcode)

surface gas density 2.4 mg/cm2

cosmic-ray halo

Sun

escape length:

SNR

2H

galactic disk

r =20 kpc

- plain diffusion

break of D at 5 GV

- diffusion + reacceleration

Va = 30 km/s

some explanations of peak in sec./prim. ratio:

Xe

v

- convective transport
- Jones 1979

problem:

too broad

sec/prim peak

R-0.6

wind or

turbulent

diffusion

resonant

diffusion

E

- distributed reacceleration
- Simon et al. 1986; Seo & Ptuskin 1994
- Dpp~ p2Va2/D, D ~ vR1/3
- - Kolmogorov spectrum of turbulence

Icr

ΔE

problem:

low flux of

secondary

antiprotons

weak

reacceleration

strong

reaccele-

ration

E

- wave damping on cosmic rays

nonlinear

cascade

W(k)

problem:

cascade

availability

VSP, Moskalenko et al. 2004

damping

W(k) ~ k-3/2

D ~ vR1/2

Iroshnikov - Kraichnan cascade

D0 ~ vR1/2

k

1/1020cm

1/1012cm

radioactive secondaries

10Be (2.3 Myr) 26Al (1.3 Myr) 36Cl (0.43 Myr)

54Mn (0.9 Myr) 14C (0.0082 Myr)

decay time at rest

d

gas density

primaries

D = (2 – 5)×1028 cm2/s

at 0.5 GeV/n

H ~ 4 kpc, Tesc ~ 70 Myr

Ptuskin & Soutoul 1998

flat component of secondary nuclei produced by strong SNR shocks Wandel et al. 1987, Berezhko et al. 2003

production by primaries inside SNRs

reacceleration in ISM by strong shocks

grammage gained in SNR

volume filling

factor of SNRs

grammage gained

in interstellar gas

Berezhko et al. 2003

RUNJOB 2003

preliminary

plain diff.

reacceleration

nism = 0.003…1 cm-3

Bohm diffusion

TSNR = 105 yr

standard

plain diff.

reacceleration

“microscopic” theory of cosmic-ray diffusion

resonant interaction

rg~ 1 / k

p

Larmor

radius

resonant

wave number

parallel diffusion

Jokipii 1966

anomalous

perpendicular

diffusion

Jokipii & Parker 1970

Chuvilgin & Ptuskin 1993

Giacolone & Jokipii 1999

Casse et al 2001

Hall diffusion

< B > + δB

1017 eV

109 eV

Armstrong et al 1995

W(k) ~k-5/3… k-3/2

hot topic: anisotropic Alfvenic turbulence

Shebalin et al. 1983, Higdon 1984, Bieber et al. 1994, Montgomery

& Matthaeus 1995, Goldrreich & Shridhar 1995, Lazarian et al. 2003

Kolmogorov

Kraichnan

galactic wind driven by cosmic rays

Ipavich 1975, Breitschwerdt et al. 1991, 1993

cosmic ray streaming instability with nonlinear saturation

CR emissivity of Galactic disk per unit area

Zirakashvili et al. 1996, 2002 Ptuskin et al. 1997

uinf = 500km/s

Rsh = 300 kpc

stable secondaries:

radioactive secondaries:

effective halo

size H(p/Z)

empirical spectrum of galactic cosmic ray sources: problem for theory of diffusive shock acceleration

high energy asymptotic

R-2.15

low energies, R < 30 GV

plane

diffusion

D ~ βR0.54

R-2.35Davis et al. 2000

R-2.50Moskalenko et al. 2004

Q

concave spectrum

E

diffusion with

reacceleration

D ~ βR0.3

R-2.40(1+(2/RGV)2)-1/2Jones et al. 2001

Q

flattened at low energy

E

spectrum of very high energy electronsShen 1970, Cowsik & Lee 1979, Nishimura et al. 1979, 1997, Dorman et al. 1985,Aharonian et al. 1995, Kobayashi et al. 2004

plain diffusion

Vela

S147

Cygnus

SN185

HB21

G65.3

Monogem

G347.3

reacceleration

Golden et al. 1984

Tang et al. 1984

Barwick et al.1998

Kobayashi et al. 1999

Boezio et al. 2000

Tori et al. 2001

Vela

tloss = 2.3×105yr(ETeV)-1

Cygnus

Emax = 100 TeV

Monogem

G65.3

HB21

TeV

data:

Candia et al 2003

Galactic

disk

<B>

Hall diffusion in average Galactic magnetic field

Ptuskin et al.1993

Kalmykov & Pavlov 1999

Candia et al. 2003

ultra-high energies

J·E3

TUNKA collaboration 2005

extragalactic

p

Fe

p

two components:

Galactic (heavy) +

extragalactic (protons ?)

Bird et al. 1993

E, eV

limit for acceleration

In Galactic sources

knee

1015

1017

1019

J·E3

Fe

pure Galactic origin:

Pochepkin et al. 1998

p

problems with acceleration

and anisotropy

switch to free exit

from the Galaxy

knee

E, eV

1015

1017

1019

kyr

trajectory calculations

Zirakashvily et al. 1998

simple magnetic field structure:

average

field

random

field

B0 = 1 μG, a = 1.5 kpc, r1 = 0.5 kpc

Br/B0 = 3, L = 100 pc, R = 20 kpc

p

p

galactic?

galactic

trajectory

claculations

diffusion approximation

(protons)

knee

2nd knee

dispersion of SNs?

reacceleration?

early transition to extragalactic CRs?

Nagano & Watson 2000

Conclusion

Diffusion model provides reasonably good description of cosmic ray propagation in the Galaxy even under simplified assumptions on cosmic ray transport coefficients and geometry of propagation region.

The choice between plain diffusion model and the model with reacceleration is difficult to make:

Plain diffusion model predicts too large anisotropy at E > 100 TeV.Diffusion model with reacceleration is bearably compatible with data on cosmic ray anisotropy.

Source spectrum in the plain diffusion model is close to prediction of diffusive shock acceleration theory. Source spectrum in the model with reacceleration is considerably steeper.

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