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Dejan Urošević Department of Astronomy, Faculty of Mathematics, University of Belgrade Supernova remnants: evolution, statistics, spectra Hydrodynamic Evolution of SNRs • First phase – free expansion phase (Ms < Me), till 3/4Ek → U (Ms 3Me), (for 1/2Ek → U, Ms Me). • Second phase – adiabatic phase (Ms >> Me ) till 1/2Ek → radiation • Third phase – isothermal phase – formation of thick shell • Forth phase – dissipation into ISM Radio Brightness Evolution in the Adiabatic Phase • synchrotron emissivity K H1+ -, where K from N(E)=KE1+2 and spectral index from S - • surface brightness = S/ =Vshell/D22, D is SNR diameter where • magnetic field H = f1(D) and K = f2(D); both functions are power low functions • surface brightness becomes: Dfk() DfH() Vshell/D2 • finally we obtain so-called - D relation: = AD-, where =-(fk() +fH()+1) and A=const. 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 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 • 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 • Duric & Seaquist (1986) - for H D-2, =0.5 D-3.5 (D>>1pc), D-5 (D<<1pc) - for =0.5 and 1.5 x 2 -(2.75 3.5) D (D>>1pc) • Berezhko & Volk (2004) D-4.25 (time-dependent nonlinear kinetic theory) STATISTICS OF SNRs 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 Empirical -D Relations (Related Problems) • Critical analyses: Green (1984, 1991, 2004) • Galactic sample - distances determination problem - Malmquist Bias - volume selection - other selection effects (sensitivity, resolution, confusion) effect • Extragalactic samples - sensitivity (surface brightness () limits) - resolution (angular-size () limits) - confusion Updated Empirical - D Relations • Galactic relation (Milky Way (MW) 36 SNRs) D-2.4 (Case & Bhattacharya 1998) • 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) - the only one valid empirical -D relation is constructed for M82 (21 SNRs): -3.4 D , the validity was checked by Monte Carlo simulations and by L-D (luminositydiameter) dependences (Urošević et al. 2005, Arbutina et al. 2004) - also, this relation is appropriate for determination of distances to SNRs (Arbutina et al. 2004) Synchrotron spectra Thermal Emission from SNRs • Thermal Bremsstrahlung N2 T-1/2, where N is particle concentration and T is temperature There are two rare types of SNRs with strong thermal emission (Urošević and Pannuti 2005) • 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 ~ 106 K 1GHz, therm. 1GHz, synch. • 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 ~ 104 K 1GHz, therm. (0.1 - 10) 1GHz, synch. HB3 Urošević et al. 2007 HB3 – observational data • • • S1GHz = 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) HB3 - density of environment We recall (cgs)= 7x10-38 N2 T-1/2 if we suppose 104 < T < 106 K ↓↓↓ 10 < ne < 35 cm-3 SUMMARY • Some updated results related to: - evolution - statistic - spectra of SNRs are given. THANK YOU VERY MUCH ON YOUR PATIENT!!!