Shock acceleration of cosmic rays Tony Bell Imperial

Shock acceleration of cosmic rays Tony Bell Imperial College, London

SNR suitable CR source below 1015 e. V Typical max. radius of rapidly expanding SNR ~ 1017 m Radio image of SN 1006 Reynolds, 1986 x-ray image of SN 1006 Long, 2003

Shock in magnetised plasma Downstream shocked plasma B 1 High velocity plasma Shock Upstream ISM B 2>B 1 Low velocity plasma

Cosmic ray wanders around shock -scattered by magnetic field B 1 B 2 CR track High velocity plasma Low velocity plasma Due to scattering, CR recrosses shock many times

Shock acceleration gives right spectrum Upstream ISM B 1 High velocity plasma Downstream shocked plasma B 2 Shock velocity: vs b = vs/c B 2>B 1 Low velocity plasma Simple diffusion theory: Prob of CR crossing shock times is Average fractional energy gained at each crossing is Differential spectrum is Allowing for propagation matches observed spectrum

Cosmic ray wanders around shock -scattered by magnetic field B 1 B 2 CR track High velocity plasma Low velocity plasma Due to scattering, CR recrosses shock many times

‘Bohm diffusion’ Mean free path lcr ~ rg (proportional to 1/B) DBohm= crg /3 rg Requires disordered magnetic field: d. B/B ~ 1

CR distribution near shock Exponential distn shock upstream downstream L= rg c /3 vshock Balance between advection and ‘Bohm’ diffusion (lcr = rg ) Want small rg (large B) for rapid acceleration to high energy

Scaleheight must be less than SNR radius R sho ck L=(c/3 vshock)lcr L Need L<R CR pre-cursor (c/3 vshock)lcr < R lcr=rg , (proportional to 1/B) Rvshock. B must exceed certain value

Condition on Bv. R (Hillas, 1984) Get original version

Cosmic Ray spectrum arriving at earth Mainly protons

Reducing the CR mean free path Magnetic field amplification

CR/Alfven wave interaction (conventional theory) CR B If CR gyration length matches Alfven wavelength • CR scattered strongly by waves • Waves excited by CR

Currents driving Alfven waves CR B dominates in conventional theory dominates when CR current is large

For SNR conditions, instability strongly driven Dispersion relation Re(w) Im(w) krg=1 k in units of rg-1 w in units of v. S 2/crg

Growth time of fastest growing mode Uncertain efficiency factor Acceleration favoured by high velocity and high density Look to very young SNR for high energy CR eg SN 1993 J in M 81 (Bartel et al, 2002) After 1 year: vs =1. 5 x 107 ms-1 ne~106 cm-3 After 9 years: vs =0. 9 x 107 ms-1 ne~104 cm-3 SNR expand rapidly for ~1000 yrs

Instability mechanism jcr jthermal = -jcr helical field line jthermal x B causes helix expand extends field lines increases B

MHD simulations show magnetic field amplification Development of previous modelling, Lucek & Bell (2000)

t=0

t=6. 4 t=9. 5 t=12. 4 t=16. 8

Evolution of magnetic field rms field grows 30 x max. field grows 100 x Magnetic field (log) time linear non-linear Saturation magnetic field proportional to r 1/2 vshock 3/2

For SNR conditions, instability strongly driven Dispersion relation Re(w) Im(w) krg=1 k in units of rg-1 w in units of v. S 2/crg

CR collimate into Filaments and Beams

Filamentation & self-focussing B proton beam j velocity vbeam

MHD response to beam – mean |B| along line of sight t=2 t=4 x z t=8 t=6 Current, j

Slices of B and r in z at t=2 Magnetic field B (0. 71, 1. 32) Density r (0. 76, 1. 17)

Slices of B and r in z at t=4 Magnetic field Density B (0. 40, 2. 61) r (0. 54, 1. 59)

Slices of B and r in z at t=6 Magnetic field B (0. 11, 8. 53) Density r (0. 03, 4. 13) Low density & low B in filament

Slices of B and r in z at t=8 Magnetic field B (0. , 8. 59) Density r (0. , 4. 51)

MHD response to beam – mean |B| along line of sight t=2 t=4 x z t=8 t=6 Current, j

Filamentation & self-focussing B E=0 proton beam j velocity vbeam E=-ux. B R E=0 Energy conservation Magnetic field growth (focus CR, evacuates plasma) Ideal for focussing CR into beam

Power carried by filament/beam Alfven current: Beam radius = Larmor radius Power in individual filament/beam W =1015 e. V =1021 e. V 1. 7 x 1028 W = 3 x 10 -12 Moc 2 yr-1 1. 7 x 1040 W = 3 Moc 2 yr-1

Some questions: future directions

A revised perspective? Acceleration requires large Bv. R size magnetic field velocity B increases with energy density rv 2 Puts emphasis on v and r For >1015 e. V, look at high density, high velocity objects: young SNR expanding into dense medium supernovae AGN Could jets be driven by high energy CR?

Limits on shock acceleration at high density p-p loss time: tpp ~ 3 x 10 -9 rgm/cc-1 sec p-p Loss length: lpp ~ 0. 8 rgm/cc-1 m (Aharonian, 2004) p-p loss limit Max CR energy: e ~ 25 rgm/cc-1 BMG (vshock/c)2 Ge. V Other (larger? ) losses Can CR escape dense plasma?

Shock acceleration a natural explanation for CR Recent theory: 1) removes doubts about acceleration to the knee 2) acceleration beyond knee a possibility 3) directs attention to young SNR 4) filament/beaming intriguing 5) application to accretion systems/compact objects Lucek & Bell, MNRAS 314, 65 (2000) Bell, MNRAS 353, 550 (2004) Bell, MNRAS in press (2005)

Cassiopeia A (Chandra)

Instability mechanism jcr jthermal = -jcr helical field line jthermal x B causes helix expand extends field lines increases B