Cosmic Ray Acceleration Beyond the Knee up to the Ankle in the

Galactic Wind Halo

V.N. Zirakashvili1,2

1Institute for Terrestrial Magnetism, Ionosphere and Radiowave Propagation, Russian Academy of Sciences, 142190 Troitsk, Moscow Region, Russia2Max-Planck-Institut für Kernphysik, Postfach 103980, 69029 Heidelberg, Germany• Enhanced Star/CR formation in spiral arms and

recurrent wind compressions

•Production of CR Population beyond the “knee”

• Shock formation in wind halo

• Reacceleration of disk CRs at large distance from Galaxy

• Role of termination shock

• CR sources in Galactic disk short-lived / small-scale pmax pknee

• Energy spectrum steepens beyond knee

Continuity problem for spectrum

Problems:

Proposed Solution:

• Reacceleration in extended Galactic Wind beyond knee

•Spiral Arms generate Galactic Wind Interaction Regions Shocks

Large spatial and temporal Scales

Spectral Continuity possible

Shocks in the Galactic Wind Flow:•Termination Shock

CR spectrum

Astrophysical reasons of the “knee”:

CR sources versus CR propagation

“knee” in CR spectrum at 1016 eV

Kulikov & Khristiansen 1958

Drift of CR particles in

inhomogeneous galactic

magnetic field

Ginzburg, Syrovatsky 1963

Drift velocity VdE, CR diffusion coefficient DEm, m=0.20.7 in thestandard diffusion modelDrift motion is negligible at small energies, but becomes essential at larger energies and can explain the “knee”

Ptuskin et al 1993, Kalmykov & Pavlov, 1999Power-low CR source spectrum up to 1017 eV was assumed

Change in energy dependence of diffusion can produce the same effect

CR sources: Diffusive Shock Acceleration

Krymsky 1977; Axford, Leer, & Scadron 1977; Bell 1978

Very attractive feature: power-low spectrum of particles accelerated, =(+2)/(-1), where is the shock compression ratio, for strong shocks =4 and =2Maximum energy for SN:

D0.1ushRsh, in the Bohm limit D=DB=crg/3 and for interstellar magnetic field

1

shsh14max skm3000pc3μG10

eV10uRB

ZE

Magnetic field amplification by CR streaming instability (Bell & Lucek 2001) Emax=Z•1017

eVHowever, rather steep spectrum beyond the knee =4.5, Ptuskin & Zirakashvili 2005 A&A 429, 755

One can conclude that

1. It seems that Supernovae are the best candidate for CR acceleration.

2. However, at present we can expect that SN effectively produce CR particles up to the “knee” region. For larger energies acceleration is ineffective.

3. In this case some mechanism is needed for producing CRs beyond the knee.

We suggest reacceleration by shocks in the Galactic Wind flow.

Mean Galactic Wind Flow

Cosmic rays are produced in the Galactic disk.

CR gas mag 1 eV cm-3

Gas is confined by gravity,

CRs are not

CR scale height is larger then the scale height of thermal gas

Galactic Wind flow driven by CR pressure gradient

• Rda(1 TeV) ≃ 15 kpc• Knee particles

diffusive

•Rda(1 PeV) ≃ 150 kpc

• Strong Termination shock: energy independent CR escape

Ipavich, 1975Breitschwerdt, McKenzie, & Völk, 1991Zirakashvili, Breitschwerdt, Ptuskin, & Völk, 1996

Kinetic energy power inthe Galactic wind

Distance to the Termination Shock, u2 PIG, PIG –is the intergalactic pressure

2/112/1

IG

3152/1

141 u

skm500

P

cmerg10

serg10 kpc180

sR

322 ur

Magnetic field in the Wind is almost azimuthal at large distances, is the galactic colatitude, is the angular velocity of Galactic rotaion

)/(sin)(2 ruRBB gg Maximum energy of accelerated (or confined) particles in the Bohm limit: DBuRs, DB=crg/3-Bohm diffusion coefficient

2

11616

max kpc15G2s105

)(sineV106

gg RB

ZE

Cosmic Ray Acceleration on the Termination Shock

was introduced by Jokipii and Morfill in 1987PROBLEMS

1. The condition of efficient acceleration on the Termination Shock D<<uRs coinsides with condition of strong CR modulation in the Galactic Wind flow. Soit is difficult to observe particles accelerated near the Terminaination Shock in the Galaxy.

2. If the Termination Shock reaccelerates galactic CRs, their number density near the shock is smaller in comparison with the density in the Galaxy. Thus it is difficult to obtain continiuty of the CR spectrum.

Cosmic ray propagation in the galactic wind flow

CR scattering and diffusion is determined by the spectrum of Alfven waves

Self-consistent CR diffusion coefficient Ptuskin, Völk, Zirakashvili, & Breitschwerdt 1997

Cosmic ray streaming instability of Alfven waves is balanced by nonlinear damping

Exact value depends on CR galactic sources power and nonlinear Alfven wave damping

D‖1027 p/(Zmpc) cm2 s-1

Cosmic Ray Propagation in the Galactic Wind Flow

NLp

NpNND

t

Nr

uu3

Equation for CR momentum distribution N. It isnormalized as nCR=4p2dpN

diffusion

Adiabatic energy gain or losses

advection

Reacceleration by spiral shocks

CR Reacceleration on the Galactic Wind Termination Shock

Numeric results

u=500 km s-1

=4

Q(p)p-4exp(-p2/p2max)

Pmax=3•106 Zmpc

Wind velocity

Termination shock compression ratio

galactic CR source spectrum

1) Spherical termination shock,

Rs=300 kpc, D‖=2.5•1025 p/(Zmpc)

2) Nonspherical termination shock (possible since CR sources are concentrated near galactic center)

Rs=150(1+3cos2)1/2 kpc, D‖=1026

p/(Zmpc(1+3cos2)) cm2s-1

Zirakashvili, & Völk 2004

CR proton spectrum at the spherical termination shock

CR proton spectrum in the Galaxy

modulation

Not very good but the simplest model

Rs=300 kpc, D‖=2.5•1025 p/(Zmpc)(a factor 40 smaller in order to get effective acceleration)

CR proton spectrum in the Galaxy

CR proton spectra at different colatitudes of nonspherical termination shock

=0

=/4

=/2

CR spectrum in the Galaxy is continuous because maximum energy depends on colatitude

Galaxy fast rotator, no backward shocks . Spiral pattern = Wave, rotates with angular velocity that differs from Galactic one. Spiral shocks are slipping across B-field. Wind CR-dominated: no injection (only reacceleration).

Fast wind from the active region on the Sun surface overtakes slow wind. Compression region and forward and backward shocks are formed at large distances. Spiral arms play the role of active regions in the Galaxy, since massive young stars and correspondent SN explosions are concentrated there. Difference:

Spiral shocks: Solar Wind-Galactic Wind analogy

Corotating Interaction Region

HST

M51

Spiral

Arms

Reacceleration by spiral shocks in the galactic wind flow

Particles with energies smaller then Z•1017eV are locked inside the Termination Shock and reaccelerated by almost perpen-dicular spiral shocks.

Relatively fast CR diffusion inside the termination shock. Strong turbulence and slow CR diffusion beyond the Termination Shock.

Völk, & Zirakashvili 2004

A&A 417, 807

velocity

Gas pressure

Results of numeric 2D MHD calculations of Slipping Interaction Region (SIR) shocks

Spiral modulation of CR sources in the Galactic disk results in modulation of G.Wind velocity

Nonlinear steepening produces shocks

CR pressure

velocity

Gas pressure

----

velocity

CR pressure

Gas pressure

Bt2/4

forward shocks (Sawtooth) =Slipping Interaction Regions (SIRs)

velocity

Reacceleration in

p

s

rpp

pNpN

p

p

p

dp

p

Np

L

uNL

s

0 )/'ln(ln

)()'('

'

'

3

Reacceleration by saw-tooth shock system

Adiabatic losses between shocks

Reacceleration on the shock fronts

u – velocity jump on the shock front,

s – shock compression ratio,

L – distance between neighboring shocks

• Disk-CR sources with Q(p) p-4 exp(-p/pmax)

• Reacceleration by about factor 30 in rigidity

From pmax = 3 x Z x 106 mpc, up to ∼ Z x 1017 Volt.

All-particle spectrum

Chemical composition fixed at energy 9 x 1014 eV

(Kampert et al. 2001)

p

He

Fe

C

Summary1. Supersonic Galactic Wind flow is bounded

by a so-called Termination Shock that can accelerate or confine CR particles up to energies Z•1017 eV.

2. Spiral structure of our Galaxy results in spiral shocks formation at large distances.

3. Shocks in the Galactic Wind flow can provide CR reacceleration beyond the “knee”.

4. Acceleration at the Termination Shock can be effective if CR diffusion coefficient is small enough.

5. It is easy to obtain the spectral continuity in the spiral shock reacceleration model (Völk, & Zirakashvili 2004).