The dynamical effects of self generated magnetic fields in cosmic ray modified shocks
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The dynamical effects of self-generated magnetic fields in cosmic-ray-modified shocks. Damiano Caprioli Scuola Normale Superiore – Pisa, Italy. Tycho. Tycho. Warren et al. 2005. SN 1006. X-ray observations of young SNRs. Bright narrow rims at the blast wave Non-thermal spectra

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The dynamical effects of self generated magnetic fields in cosmic ray modified shocks

The dynamical effects of self-generated magnetic fields in cosmic-ray-modified shocks

Damiano Caprioli

Scuola Normale Superiore – Pisa, Italy

Krakow 2008


X ray observations of young snrs

Tycho

Tycho

Warren et al. 2005

SN 1006

X-ray observations of young SNRs

  • Bright narrow rims at the blast wave

  • Non-thermal spectra

  • Synchrotron radiationby electrons up to 10-100 TeV

Krakow 2008


Magnetic field amplification mfa

240¹G

240¹G

360¹G

360¹G

240¹G

240¹G

360¹G

360¹G

VBK 2005

VBK 2005

Magnetic field amplification (MFA)

  • The width of the rims requires

    Bds» 90-500¹G À B0

    • Völk, Berezhko & Ksenofontov 2005

    • Parizot et al. 2006

  • Lower Bds if the thickness of the rims were due to magnetic field damping

    • Pohl et al. 2005

Krakow 2008


Mfa models
MFA models

  • Cosmic ray induced Streaming Instability (SI)

    • Resonant(standard) Skilling 1975, Bell 1978

    • Non-resonantBell 2004, Amato & Blasi 2008

  • Phenomenological models: isotropization of magnetic irregularities with opposite helicities

    • Bell & Lucek 2001; Vladimirov, Ellison & Bykov 2007

  • Amplification of the magnetic field downstream due to upstream clumpiness and shock corrugation

    • Giacalone & Jokipii 2007

Krakow 2008


The snr paradigm for galactic cr

Velocity Profile

Subshock Precursor

Blasi, Amato & DC 2007

Self-generatedD(x,p)

Bohm diffusion in B0

Amato & Blasi 2006

The SNR paradigm for galactic CR

  • 10-20% of SN kinetic energy converted in CR

    • The upstream fluid is slowed down: CRmodified shock

  • Power law spectra

    • In modified shocks becomes rather concave

  • Energies up to the knee

    Eknee»3£106 GeV

    achievable only with MFA

    • Blasi, Amato, CD 2007

Krakow 2008


Snr hydrodynamics
SNR Hydrodynamics

  • Relative positions of forward shock

    and contact discontinuity

    • Tycho, Warren et al. 2005;

    • SN 1006, Cassam-Chenaï et al. 2007.

  • Multiwavelength analysis

    • Berezhko & Voelk 2004 and following;

  • Barely consistent with predictions of

    Rtot / M03/4¼ 10-100

    • Berezhko & Ellison 1999; Amato & Blasi 2006

  • Non-adiabatic heating in the precursor?

    • Alfvén heating: McKenzie & Völk 1982

    • Acoustic instability: Wagner et al. 2007

Ellison et al. 2007

Ellison et al. 2007

Rtot» 6-10

Krakow 2008


The dynamical feedback of mfa
The dynamical feedback of MFA

  • Three-fluid model (plasma-cosmic rays-magnetic field)

    • Resonant Alfvén waves excited by standard SI

    • At the subshock:

      • Wave reflection and trasmission; Scholer-Belcher 1971

      • Magnetized jump conditions;Vainio-Schlickeiser 1999

  • Conservation of mass, momentum and energy lead to

    which is the standard one a part from the factor ¤B

Ratio between magnetic and plasma pressure upstream

CD et al. 2008, ApJL

Krakow 2008


Magnetization of snrs

Normalized magnetic pressure downstream

Pw,ds» 2 - 4%

imply at leastW ¸ 0.3

TypicallyW»1-100

The magnetic field can not be neglected!

Relevant reduction of Rtot

The effect is driven by:

Unmagnetized case

Magnetization of SNRs

DC et al. 2008, ApJL

Krakow 2008


The kinetic calculation
The kinetic calculation

Fluid velocity

CR Spectrum

CR pressure

Spectral slope

B0=10¹G; Age of SNR=1000yr

DC et al., sbt. to MNRAS

Bohm diffusion in the self-generated magentic field

Krakow 2008


Turbulent alfv n heating
Turbulent (Alfvén) Heating

  • Often invoked in order to smooth the precursor, BUT it:

    • Is relevant only if Vsh¿ 4000 T51/2 km/s; Völk & McKenzie 1981; Ptuskin & Zirakasvhili 2005

    • Cannot be too efficient, otherwise no MFA

    • Has no severe effects on the precursor; DC et al. 2008;Vladimirov, Bykov & Ellison 2008

³< 1

DC et al. 2008,sbt. to MNRAS

B0=10¹G; Age=1000yr; T0=105 K

Krakow 2008


Conclusions
Conclusions

  • The magnetic feedback is always relevant for young SNRs

  • The inclusion of the amplified magnetic field provides

    • A smoothening of the precursor (Rtot» 6-10)

    • Mildly-concave spectra (/p-3.5 at highest momenta)

    • Higher pmax

    • No dependence on M0

    • Higher temperature and pressure downstream

    • No need for turbulent heating

  • The details can be analytically worked out only for resonant SI

    • Need for a theory of non-resonant turbulence

    • CR transport equation / pressure and energy densities

Krakow 2008


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