1. Dejan Urošević Department of Astronomy, Faculty of Mathematics, University of Belgrade Supernova remnants: evolution, statistics, spectra

2. Hydrodynamic Evolution of SNRs First phase – free expansion phase (M s < M e ), till 3/4E k → U (M s  3M e ), (for 1/2E k → U, M s  M e ). Second phase – adiabatic phase (M s >> M e ) till 1/2E k → radiation Third phase – isothermal phase – formation of thick shell Forth phase – dissipation into ISM

5. Radio Brightness Evolution in the Adiabatic Phase synchrotron emissivity   K H 1+  - , where K from N(E)=KE 1+2  and spectral index  from S  -  surface brightness  = S /  =  V shell / D 2  2, where D is SNR diameter

6. magnetic field H = f 1 (D) and K = f 2 (D); both functions are power low functions surface brightness becomes:   D fk(  ) D fH(  ) V shell / D 2  = AD - finally we obtain so-called  - D relation:  = AD - , where  =-(fk(  ) +fH(  )+1) and A=const.

7. Trivial Theoretical  - D Relation if the luminosity is constant (or independent on D) during SNR expansion we have:   D -2 this is trivial form of the theoretical  - D relation

8. Short History of the Theoretical  - D relation Shklovsky (1960) - spherical model with: H  D -2  =0.5    D -6 Lequeux (1962) - shell model with: H  D -2  =0.5    D -5.8

9. Poveda & Woltjer (1968) - using van der Laan (1962) model with: H = const.,  =0.5    D -3 Kesteven (1968) - shell of constant thickness: H  D -1,  =0.5    D -4.5

10. Duric & Seaquist (1986) - for H  D -2  =0.5    D -3.5 (D>>1pc),   D -5 (D >1pc) Berezhko & Volk (2004)   D -4.25 (time-dependent nonlinear kinetic theory)

11. STATISTICS OF SNRs

12. Empirical  -D Relation Necessary for determination of distances to Galactic SNRs identified only in radio continuum Necessary for confirmation of the theory in order to define valid evolutionary tracks

13. Empirical  -D Relations (Related Problems) Critical analyses: Green (1984, 1991, 2004) Galactic sample - distances determination problem - Malmquist Bias - volume selection effect - other selection effects (sensitivity, resolution, confusion)

14. Extragalactic samples - sensitivity (surface brightness (  ) limits) - resolution (angular-size (  ) limits) - confusion

15. Updated Empirical  - D Relations Galactic relation (Milky Way (MW) 36 SNRs)   D -2.4 (Case & Bhattacharya 1998)

17. Extragalactic sample (11 galaxies) LMC, SMC, M31, M33, IC1613, NGC300, NGC6946, NGC7793, M82, NGC1569, NGC2146 (148 SNRs) - Monte Carlo simulations suggest that the effect of survey sensitivity tending to flatten the slopes toward the trivial relation (opposite to effect of Malmquist bias) (Urošević et al. 2005)

19. -the only one valid empirical  -D relation is constructed for M82 (21 SNRs):   D -3.4, the validity was checked by Monte Carlo simulations and by L-D (luminosity- diameter) dependences (Urošević et al. 2005, Arbutina et al. 2004) - also, this relation is appropriate for determination of distances to SNRs (Arbutina et al. 2004)

21. Synchrotron spectra

22. Thermal Emission from SNRs Thermal Bremsstrahlung   N 2 T -1/2, where N is particle concentration and T is temperature

23.  There are two rare types of SNRs with strong thermal emission (Urošević and Pannuti 2005)

24. the first type – the relatively young SNRs in the adiabatic phase of evolution that evolve in the dense molecular cloud (MC) – D  20 pc,  1GHz ~ 10 -20 (SI) – for N  300 cm -3 and T ~ 10 6 K   1GHz, therm.   1GHz, synch.

25. the second type – the extremely evolved SNRs in the late adiabatic phase expanded in denser warm medium – D  200 pc,  1GHz ~ 10 -22 (SI) – for N  1 - 10 cm -3 and T ~ 10 4 K   1GHz, therm.  (0.1 - 10)  1GHz, synch.

28. HB3 Urošević et al. 2007

30. HB3 – observational data S 1GHz = 50 Jy D= 70 pc (for distance of 2 kpc) Shell thickness = 0.05 D ↓ ↓ ↓ Emissivity  1GHz =1.67 x 10 -37 (ergs sec -1 cm -3 Hz -1 )

32. HB3 - density of environment We recall  (cgs)= 7x10 -38 N 2 T -1/2 if we suppose 10 4 < T < 10 6 K ↓ ↓ ↓ 10 < n e < 35 cm -3

33. SUMMARY Some updated results related to: - evolution - statistic - spectra of SNRs are given.

34. THANK YOU VERY MUCH ON YOUR PATIENT!!!