Dejan Uro š evi ć Department of Astronomy, Faculty of Mathematics, University of Belgrade
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Dejan Urošević
Department of Astronomy, Faculty of Mathematics,
University of Belgrade
Supernova remnants: evolution, statistics, spectra
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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
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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
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• 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.
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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
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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
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• 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
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• 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)
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STATISTICS OF SNRs
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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
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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)
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• Extragalactic samples
- sensitivity (surface brightness () limits)
- resolution (angular-size () limits)
- confusion
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Updated Empirical - D Relations
• Galactic relation
(Milky Way (MW) 36 SNRs)
D-2.4 (Case & Bhattacharya 1998)
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• 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)
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- 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)
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Synchrotron spectra
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Thermal Emission from SNRs
• Thermal Bremsstrahlung
N2 T-1/2,
where N is particle concentration and T is temperature
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There are two rare types of SNRs with strong thermal emission
(Urošević and Pannuti 2005)
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• 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.
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• 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.
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HB3 Urošević et al. 2007
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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)
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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
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SUMMARY
• Some updated results related to:
- evolution
- statistic
- spectra
of SNRs are given.
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THANK YOU VERY MUCH
ON YOUR PATIENT!!!