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, where

D is SNR diameter

• 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= 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

D-(2.75 3.5) (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 effect - other selection effects (sensitivity,

resolution, confusion)

• 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):

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)

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!!!