SHOCK ACCELERATION SHOCK ACCELERATION IN PARTIALLY IONIZED PLASMAS IN PARTIALLY IONIZED PLASMAS Giovanni Morlino Giovanni Morlino INAF/Osservatorio Astrofisico di Arcetri In collaboration with: Elena Amato, Pasquale Blasi, Damiano Caprioli, Rino Bandiera TeV Particle Astrophysics Paris, July 19 th - 23 th , 2010 G. Morlino, Paris - 22 July 2010
OUTLINE Acceleration at collisionless shocks propagating in partially neutral plasmas Why it is relevant: the environment of SNRs Balmer shocks Observational evidences of CRs influence onto Balmer shocks Theoretical model Conclusions G. Morlino, Paris - 22 July 2010
Why Shocks in Partially Neutral Plasmas are Important? Theory of shock acceleration is usually developed in totally ionized plasma - Good approximation for Type II SNR which expand in the pre-stellar wind ( T~ 10 5 -10 7 K ) → hydrogen is totally ionized - Bad approximation for Type I/a SNR which expand in the ISM ( T~ 10 4 K ) → hydrogen is partially ionized → even if T < 10 4 K → minimum degree of ionization for young SNR is ~20% due to the ionizing radiation coming from the remnant itself G. Morlino, Paris - 22 July 2010
Why Shocks in Partially Neutral Plasmas are Important? 1) Does the shock structure change when expanding in partially neutral plasma? 2) Can neutral particle affect the CR production efficiency? At zeroth order the neutral component does not feel the electromagnetic shock discontinuity downsteam upstream Velocity of neutral component U i0 U i2 Velocity of ionized L prec BUT... component Collisionless subshock G. Morlino, Paris - 22 July 2010
Balmer-Dominated Shocks … neutral particles do produce radiation associated with shock transition Balmer-dominated shocks are associated with faint optical filaments observed around young SNRs 1) Shock speed ~ 200 - 9000 km/s 2) Typical ISM density ~ 0.1 - 1 cm -3 3) Presence of strong hydrogen lines with narrow (10 km/s) and broad (1000 km/s) components 4) General lack of non-thermal X-ray emission SN 1006 – H α emission G. Morlino, Paris - 22 July 2010
Balmer-Dominated Shocks Optical Balmer shocks Optical bow shocks associated with SNRs associated with PWNe SN 1006 RCW 86 Kepler Tycho G. Morlino, Paris - 22 July 2010
Balmer-dominated Shocks: Basic Principles VELOCITY PROFILE L CE upstream L ion downstream Downstream of the shock cold hydrogen DENSITY PROFILE atoms can charge exchange with hot shocked shock upstream downstream protons, giving rise to a population of hot hydrogen atoms Interaction Rate = n p v rel CE v rel CE ion G. Morlino, Paris - 22 July 2010
Balmer-dominated Shocks: Basic Principles VELOCITY PROFILE L CE upstream L ion downstream DENSITY PROFILE shock upstream downstream FWHM of narrow line W n = = 21 km / s 4 K 1 / 2 k T 0 T 0 8ln2 m H 10 W b = FWHM of broad line k T 2 4 v sh 1 ln2 − 1 = 1.02 v sh = 8ln2 m H G. Morlino, Paris - 22 July 2010
Balmer-dominated Shocks: Basic Principles There are evidences that Balmer shock physics is not so simple... Let analyse three different observational evidences of shock modification G. Morlino, Paris - 22 July 2010
1) Balmer-Dominated Shocks associated with X-ray Emission From Helder et al., 2009 Dowstream temperature from broad H α line W broad = 1100 ± 63 km / s T 2 = 2.3 ± 0.3 keV Shock speed from proper motion v shock = 6000 ± 2800 km / s 2.5 ± .5 kpc − 1 T 2 = 20 − 150 keV noequilibration ˙ obs d 12 − 90 keV equilibration 0.5 ± .2 ' ' yr Helder et al. infer that > 50% of the post shock pressure is due to CRs. G. Morlino, Paris - 22 July 2010
2) Narrow H α Lines with Unusual Broad Width From Sollerman at al., 2003 The H α FWHM of narrow lines measured from Balmer Shocks gives an estimate of upstream temperature W n = = 21 km / s 4 K 1 / 2 k T 0 T 0 8ln2 m H 10 4 K W n ~ 30 − 50 km / s T ~ 2 − 610 But for temperature above 10 4 K hydrogen is expected to be completely ionized → We need a mechanism able to heat the neutral ISM component in a time less than the ionization time G. Morlino, Paris - 22 July 2010
3) Precursor in Balmer-Dominated Shocks: the Case of Tycho Lee et al., 2010 (Observation with the Hubble Space Telescope) KPNO Lee et al. 2007 Chandra 1) Evidence of H α emission from the precursor which contribute up to 30-40% of the total narrow H α emission: → different temperature and/or different bulk speed between ions and neutrals in the precursor region 2) The knot g in Tycho remnant is associated with non-thermal Warren et al. 2005 X-ray emission → the shock may accelerate particles efficiently Knot g G. Morlino, Paris - 22 July 2010
3) Precursor in Balmer-Dominated Shocks: the Case of Tycho Can we explain all these features with the presence of accelerated CRs? 1) Shock speed inferred from Broad lines < measured speed → a fraction of kinetic energy is converted into nonthermal particles 2) Broad narrow component imply upstream T 0 > 10 4 K → neutral hydrogen has to be heated ahead of the shock in a time < collisional time Need the presence of a 3) Evidence of H α (narrow line) emission ahead of the shock: precursor → protons and neutral hydrogen have different temperatures and/or different bulk velocities in the precursor G. Morlino, Paris - 22 July 2010
Balmer-Dominated Shocks with CRs Acceleration Sub-shock thickness 3000 km / s velocity profile u(x) in the shock frame 10 cm G − 1 u 0 B L s ~ r L p th ≃ 10 U n2 =U n0 U n0 =U i0 L CE Unmodified Ionization and charge-exchange length shock U i2 L ion 16 cm − 3 − 1 u 2 n p L ion ~ u 0 ion = ≃ 10 n p ion v rel downstream upstream 1 cm 15 cm − 3 − 1 u 2 n p L CE ~ u 0 CE = ≃ 10 n p CE v rel 1 cm U i0 v rel ≠ 0 Shock Precursor length TeV 3000 km / s modified 17 cm G − 1 − 1 D p max u 0 B E L prec ~ ≃ 10 by CRs U i2 u 0 L prec Ionization and charge exchange length in the L CE U n2 upstream U 0 Shock with L prec / L ion 0.1 CRs and U i1 U i2 neutrals L prec / L CE ~ 10 − 100 G. Morlino, Paris - 22 July 2010
Modified Shocks in Plasma with Neutral Component: Fluid Equations Time-independent Boltzmann equation ∂ f v ⋅∇ f = f x , v R x , v ∂ t Ionized component (interacting with CRs) Neutral component ∂ ∂ ∂ x [ n u n ] = − q M ∂ x [ i u i ] = q M MASS FLUX ∂ ∂ ∂ x [ n u n 2 P n ] = − q m ∂ x [ i u i 2 P i P CR ] = q m MOMENTUM FLUX ∂ x [ − 1 u n P n ] = − q e ∂ x [ − 1 u i P i ] = − u i ∂ P CR 3 ∂ ∂ 1 1 2 n u n 2 i u i 3 ∂ x q e ENERGY FLUX q M x = ∫ dv n dv i ion ∣ v rel ∣ f n x ,v n f i x ,v i MASS TRANSFER We assume both the distribution functions to be maxwellian q m x = ∫ dv n dv i v n − v i ion CE ∣ v rel ∣ f n x ,v n f i x ,v i MOMENTUM TRANSFER q e x = ∫ dv n dv i 1 2 ion CE ∣ v rel ∣ f n x ,v n f i x ,v i 2 v n 2 − v i ENRGY TRANSFER G. Morlino, Paris - 22 July 2010
Effect of Charge-Exchange in the Upstream Acceleration Upstream Velocity profile Upstream Temperature profile efficiency T i x U i x T n x inj = 4.0 ; U n x P CR / i ,0 u 0 2 = 0.06 P CR x Initial conditions T 0 = 10 4 K ; B 0 = 10 G inj = 3.9 ; − 3 ; n 0 = 1 cm P CR / i ,0 u 0 2 = 0.15 f N = 0.5 ; u 0 = 3000 km / s; p max = 10 4 m p c inj = 3.7 ; P CR / i ,0 u 0 2 = 0.8 G. Morlino, Paris - 22 July 2010
Temperature of Neutral Hydrogen CR pressure and upstream Mach Upstream Temperature as function number as function of injection of injection efficiency efficiency T i ,1 M i ,1 T n ,1 P CR / i ,0 u 0 2 Region of observed temperature Region of inferred CR efficiency Even a modest acceleration efficiency (around few %) is able to heat the neutral plasma To explain the observed temperature of neutral hydrogen (T < 10 5 ) we need a CR efficiency < 10% G. Morlino, Paris - 22 July 2010
Which are the (indirect) effects of Neutral Hydrogen on CRs Spectrum? Initial conditions: − 3 ; f N = 0.5 ; u 0 = 3000 km / s; p max = 10 T 0 = 10 4 K ; B 0 = 10 G; n 0 = 1 cm 4 m p c ; inj = 3.7 ; Upstream Velocity profile − q p f p ∝ p Spectrum slope and CRs pressure P CR x U i x U i x P CR : 0.98 0.81 ; f N = 0 ; R t : 81 7.8 ; f N = 0.5 ; R s : 2.25 3.56 ; 5 K 6 K ; T 1 : 1.910 5.510 G. Morlino, Paris - 22 July 2010
CONCLUSIONS CRs acceleration at shocks is strongly affected by the presence of a non negligible fraction of neutral hydrogen because the charge exchange process 1) The neutral hydrogen can be efficiently heated in the precursor even in the case of inefficient shock acceleration ( є CR ~few%) → this can explain the broad narrow lines → predicts the presence of narrow lines ahead of the shock 2) Also the ionized component is heated in the precursor and as a consequence → the shock modification and the CR spectrum concavity are reduced (the same effect is produced by turbulent heating and magnetic field amplification ) We are currently applying the theory to single SNR → detailed results will be available soon G. Morlino, Paris - 22 July 2010
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