Turbulence and Magnetic Field Amplification in the Supernova Remnants Tsuyoshi Inoue (NAOJ) Ryo Yamazaki (Hiroshima Univ.) Shu-ichiro Inutsuka (Kyoto Univ.) TI, Yamasaki & Inutsuka (2009) in preparation

Introduction Supernova remunants (SNRs): The site of CR acceleration SNRs emit radiations with various wavelengths (radio to TeV  ) Uchiyama+07, Uchiyama & Aharonian 08 discovered that There are bright X-ray hot spots in SNR RXJ1713 and CasA. The hot spots decrease its luminosity with the timescale of a few years. Synchrotron cooling time ： t synch years --> B ~ 1 mG (~ 200 × B ISM ) is necessary! --> Physical conditions of SNRs are very important to understand them.

Motivation of This Work A possible mechanism of B amplification in SNRs ( Balsara+01, Giacalone & Jokipii 07 ) Density fluctuations of preshock medium cause magnetic field amplification in the post shock medium (SNR). However, the realistic strength of turbulence cannot amplify B to the order of 1mG (Balsara+01). They assumed the caused by turbulence of ISM. Large amplitude  fluctuations are ubiquitously exist in ISM: Small-scale HI clouds generated by thermal instability HI clouds have density n ~ cm -3 >> diffuse medium n ~ 1 cm -3 --> Stronger amplification than the case of turbulent medium can be expected, if we consider complex (and realistic) ISM! --> In order to make hot spot (1mG level of B ), larger  fluctuations are needed.

Interstellar Medium ISM is an open system in which radiative cooling/heating are effective （ Field+ 69, Wofire+95, 03 ） Heating source : photoelectric heating by dust grains (PAHs) Cooling sources : line emissions (T>10 3 K: Ly-a, T<10 3 K: CII/OI fine structure) --> Diffuse warm gas and HI clouds can coexist under pressure equilibrium. Thermal equilibrium curve Diffuse gas HI cloud Diffuse warm gas HI clouds T ~ 8000 K, n ~ cm -3 T ~ 100 K, n ~ cm -3 Thermal instability: the equilibrium that connects warm/cold phase is unstable. unstable --> Unstable gas evolves into diffuse gas and HI clouds (Field 65, Balbus 95). Heating region Cooling region Number density Pressure

Evolution of Thermally Bistable ISM ISM is affected by (late-stage) supernova shock waves once/several Myr. 1. Shock compression 2. Cooling 3. Development of thermal instability Cooling region Heating region Timescale of this evolution is a few Myr （ timesacle of cooling/heating ）. Recent high-resolution MHD simulations have shown that ISM evolves as follows: T.I. & Inutsuka 08, Hennebelle & Audit 07 --> In general, ISM is two-phase medium composed of warm gas and HI clouds. (McKee & Ostriker 77) Number density Pressure

Generation of Two-phase Medium To generate two-phase medium as a consequence of thermal instability, we performed MHD simulation. basic equations: Result (density structure) Initial condition: thermally unstable equilibrium + B filed ( Bx=6  G, By=0 ) Results: Red region: diffuse warm gas ( n~1 cm -3, T ~ 5000 K ) Blue region: HI clouds ( n~30 cm -3, T ~ 100 K ) *Scale of HI clouds are determined by scale of thermal instability ( ~ 0.1 pc) *Small scale HI clouds are ubiquitously observed in ISM (Heiles & Troland 2003) Thermal conduction Heating/cooling fuction

Early-stage Supernova Shock wave Set the hot plasma (n=0.1 cm -3 ) at one of the boundary. ModelP hot /k B position to set hot plasma （ shock type ） Shock speed 13.0 X 10 8 K cm -3 y=0 (perpendicular shock)1300 km/s 23.0 X 10 8 K cm -3 x=0 (parallel shock)1300 km/s To investigate SNR formed by piling up the two-phase medium, we induced shock wave at a boundary of computational domain. Basic equations: ideal MHD equations. *Strength of induced shock wave corresponds to early-stage supernova shock of the age ~ 1,000 years.

Result of Model 1 Model 1: Perpendicular shock, v shock ~ 1300 km/s ） B field is strongly amplified to the level of 1 mG in some region! Number Density Magnetic Field Strength T.I. et al 09 in preparation

Result of Model 2 Model 1: Parallel shock, v shock ~ 1300 km/s ） B field is strongly amplified to the level of 1 mG in some regions! Number Density Magnetic Field Strength T.I. et al 09 in preparation

Evolutions of Maximum B and  Maximum magnetic field strength saturate at B ~ 1 mG. |B| max plasma  at B is max  B [  G] Maximum magnetic field strength is determined by the condition  = p thermal /p mag ~ 1. Model 1 (perp. shock) Model 2 (para. shock) Model 1 (perp. shock) Model 2 (para. shock)

Mechanism of B amplification Amplification mechanism of B By using the eq. of continuity and induction eq., we can obtain: --> B is amplified if velocity filed has shear along B filed line. Strong velocity shear is generated when HI clouds are swept by the shock. T.I. et al 09 in preparation v B Shock Perp. shock case (model 1) v B Shock Para. shock case (model 2) v shock in HI cloud << v shock in warm gas --> post shock gas flows to round HI cloud --> velocity shear is induced most strongly at transition layer between HI cloud and surrounding diffuse gas (scale of the transition layer l ~ ~ 0.05 pc T.I.+06)

Comparison with Observation X-ray image of SNR(RXJ1713) by Uchiyama+07 Scale of hot spots ~ 0.05 pc 10 arcsec = pc Hot spots seem to be located far behind the shock front

Comparison with Observation Scale of the regions where magnetic field is amplified to 1 mG agrees well with the scale of the X-ray hot spots. Result of our Simulation 0.05 pc Regions with high B are located far behind the shock as the X-ray hot spots. --> Regions with high B can make X-ray hot spots, if electrons are accelerated around there by secondary shock.

Summary Shocked shell generated by piling up two-phase medium is turbulent. In general, ISM has large amplitude fluctuations due to thermal instability, which generates small scale HI clouds ( l~0.1 pc ). Velocity shear along B line amplifies B at transition layer between HI cloud and diffuse warm gas. In the case V shock ~ 1000 km/s, B strength grows to the order of 1 mG （  ~ 1 ）. Scale of the regions where B is on the oreder of 1 mG is 0.05 pc, which agrees well with the scale of X-ray hot spots. The scale 0.05 pc is determined by the scale of transition layer between HI cloud and surrounding diffuse gas at which velocity shear is most strongly induced.