1. 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

2. 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.

3. 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 ~ 10-100 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.

4. 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 ~ 0.1-1 cm -3 T ~ 100 K, n ~ 10-100 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

5. 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

6. 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

7. 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.

8. 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

9. 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

10. 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)

11. 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)

12. Comparison with Observation X-ray image of SNR(RXJ1713) by Uchiyama+07 Scale of hot spots ~ 0.05 pc 10 arcsec = 0.048 pc Hot spots seem to be located far behind the shock front

13. 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.

14. 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.