1 / 22

Mario A. Riquelme, Anatoly Spitkovsky Department of Astrophysical Sciences, Princeton University

Generation of magnetic field upstream of shocks: the cosmic ray current-driven (CRCD) instability. Mario A. Riquelme, Anatoly Spitkovsky Department of Astrophysical Sciences, Princeton University. Motivation. Observation of X-ray synchrotron emission from rims in SNRs suggest that:

ama
Download Presentation

Mario A. Riquelme, Anatoly Spitkovsky Department of Astrophysical Sciences, Princeton University

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Generation of magnetic field upstream of shocks: the cosmic ray current-driven (CRCD) instability Mario A. Riquelme, Anatoly Spitkovsky Department of Astrophysical Sciences, Princeton University

  2. Motivation • Observation of X-ray synchrotron emission from rims in SNRs suggest that: -Electrons are accelerated to ultrarelativistic energies in these environments. -Magnetic field can be a factor of ~100 bigger than the typical ISM field in the downstream medium. • Such amplification would ease the acceleration of galactic CRs in SNRs until the “knee” (~3x1015 eV).

  3. Possible mechanisms • Idea: field is amplified by the CRs themselves. • Resonant instability: amplification of Alfven waves due to their resonant interaction with CRs ( RL,CR ~ l ). • In 2004 A. Bell predicted that plasma waves can be amplified non-resonantly (RL,CR >> l)due to the presence ofthe cosmic ray current (JCR) . • This cosmic ray current-driven (CRCD) instability would have a growth rate much faster than the resonant instability.

  4. The CRCD instability Right handed, circularly polarized when B0 || Jcr z Je x Btr Dv B0 Jcr y Je x

  5. In this study... • We combine an analytical, kinetic model of the CRCD waves valid in the non-linear regime, with particle-in-cell (PIC) simulations. • We study the non-linear properties of the instability, mainly focused on its possible saturation mechanisms and its applications to the case of SNRs’ shocks.

  6. The CRCD waves properties • One-dimensional + constant CR current • We calulate analytically a non-linear, kinetic dispersion relation and obtain that the waves will grow exponentially with: • lmax = cB0 /Jcr and gmax= 2p Va,0 / lmaxuntilVa ~ Vd,cr. Our model allows for evolution of the phase velocity of the wave, Vf. Vf  Va2/Vd,cr This would explain the saturation at Va ~ Vd,cr, since at that point the plasma moves at a velocity of about Vd,crso, from the point of view of the plasma, the CR current has stopped. • Our model also predicts a transverse velocity of the plasma Vtr f Va,0, where f=Btr/B0 (important when multidimensional effects are considered). (confirmed by one-dimensional PIC simulations)

  7. Multidimensional effects Va,0/Vd,,cr = 1/100 ncr/ni = 0.04 mi/me= 10 Vd,cr = c z Jcr Je • The possible initial filamentation: (Vd,cr/ Va,0)(ncr / ni) = 4 B0 y x (See Niemiec et al. 2008)

  8. Multidimensional effects Va,0/Vd,,cr = 1/100 ncr/ni = 0.004 mi/me= 10 Vd,cr = c z Jcr Je • The possible initial filamentation: (Vd,cr/Va,0)(ncr / ni) = 0.4 B0 y x Requirement (Vd,cr/Va,0 )(ncr / ni)<< 1

  9. The 3D structure of the instability

  10. The 3D structure of the instability

  11. The 3D structure of the instability y (CR current still constant) electrons x CRs z Bo Va,0/Vd,,cr = 1/40 ncr/ni = 0.0125 mi/me= 10 Vd,cr = c Remember: Vtr ~ f Va,0, where f=Btr/B0 Growth rate, g, decreases but Va ~Vd,cr at saturation. Dominant wavelength, ld , grows. Plasma accelerates.

  12. The 3D structure of the instability y x CRs (CR current still constant) electrons Bo z Va,0/Vd,,cr = 1/40 ncr/ni = 0.0125 mi/me= 10 Vd,cr = c Remember: Vtr ~ f Va,0, where f=Btr/B0 Growth rate, g, decreases but Va ~Vd,cr at saturation. Dominant wavelength, ld , grows. Plasma accelerates.

  13. Migration to longer wavelengths Since Vturb~ Vtr~ f Va,0, then for a wavelength l • Time scale of suppression ~ l/fVa,0. • Time scale of growth ~ g-1(l) (from the dispersion relation). g-1(ld) ≈ b ld/fVa,0=> b  2 ldlmax((f/3)2 + 1)/2 (solid) where f = Btr/B0 This migration is faster than suggested by previous MHD studies (Bell 2004). Va,0/Vd,cr = 1/40, Vd,cr=c (dash-dotted) Va,0/Vd,cr = 1/20, Vd,cr=c/2 (dashed) Va,0/Vd,cr = 1/10, Vd,cr=c (dotted)

  14. The back-reaction on the CRs Vcr (semi-isotropic velocity distribution, => Vd,cr =c/2) x Red and green lines represent Btr2for one-dimensional runs with CR’s Lorentz factors, G, of 20 and 40. Here Va,0/Vd,cr=1/40 Orange lines show a three-dimensional simulation with G=30 (solid is Bx2 and dotted is Btr2). Here Va,0/Vd,cr=1/20. In all three simulations saturation occurs when RL,cr≈ld. Thus, in general, the CRCD instability will saturate either when Va ~ Vd,cr or when RL,cr ~ ld, whichever happens first. Also, many CRs are scattered back in the –x direction => efficient scattering mechanism

  15. Application An estimate for the magnetic amplification in SNRs (only considering the most energetic CRs that escape from the remnant): f((f/3)2+1) = 130 (Vsh/104km/sec)3(10km/sec/Va,0)2(hesc/0.05), where hesc = FE,cr/(nimiVsh3 /2). This would imply a typical amplification factor due only to the most energetic “escaping” particles of f ≈ 10.

  16. Conclusions • Using PIC simulations, we confirm the existence of the CRCD instability predicted by Bell (2004). • One-dimensional geometry + constant CR: CRCD waves grow exponentially until Va ~ Vd,cr (intrinsicsaturation is due to plasma moving at the drift velocity of CRs) • Including multidimensional effects we see the formation of significant turbulence in the plasma when the instability becomes non-linear (Btr ~ B0).

  17. Conclusions • Turbulence makes the instability evolve rapidly into longer wavelengths (ld ≈ lmax((f/3)2 + 1)/2), where f = Btr/B0. • Turbulence also reduces the growth rate of the field, but intrinsic saturation still happens due to plasma acceleration at Va ~Vd,cr. • However, the back-reaction on the CRs can stop the CR current and cause saturation whenRL,cr ≈ ld. • The magnetic amplification in SNRs (only considering the most energetic, or “escaping” CRs) could reach a factor of ~10.

  18. Conclusions • Open questions: -Does the CR current really exist? i..e. are CR only positively charged particles? (injection problem). -What happens in the region close to the shock? Can we expect further magnetic amplification due to the diffusing CRs current? -Why in almost all the cases (except SN1006) the amplification seems to happen symmetrically all around the remnant?

  19. Motivation Example: Cassiopeia A (Cas A) Red: infrared (Spitzer). Yellow: optical (Hubble). Blue and green: X-ray (Chandra).

  20. The CRCD waves properties • One-dimensional + constant CR current B0 Jcr Je

  21. The CRCD waves properties • Numerical confirmation (one-dimensional simulations): Va,0 /c = 1/10 • Our model also predicts a transverse velocity of the plasma Vtr ~ f Va,0, where f=Btr/B0 (important for turbulence generation). Solid-yellow: Vd,cr =1c Solid-green: Vd,cr =0.9c Solid-red: Vd,cr =0.8c Dotted-yellow: Vd,cr =0.6c Dotted-green: Vd,cr =0.4c Dotted-red: Vd,cr =0.2c

More Related