SNRTrueloveMcKee

class gammapy.astro.source.SNRTrueloveMcKee(*args, **kwargs)

Bases: gammapy.astro.source.snr.SNR

SNR model according to Truelove & McKee (1999).

Reference: https://ui.adsabs.harvard.edu/abs/1999ApJS..120..299T

Attributes Summary

sedov_taylor_begin	Characteristic time scale when the Sedov-Taylor phase starts.
sedov_taylor_end	Characteristic time scale when the Sedov-Taylor phase of the SNR's evolution ends.

Methods Summary

luminosity_tev(t[, energy_min])	Gamma-ray luminosity above energy_min at age t.
radius(t)	Outer shell radius at age t.
radius_inner(t[, fraction])	Inner radius at age t of the SNR shell.
radius_reverse_shock(t)	Reverse shock radius at age t.

Attributes Documentation

sedov_taylor_begin

Characteristic time scale when the Sedov-Taylor phase starts.

Given by $t_{ST}\approx 0.52t_{ch}$.

sedov_taylor_end

Characteristic time scale when the Sedov-Taylor phase of the SNR’s evolution ends.

The end of the Sedov-Taylor phase of the SNR is defined by the condition, that the temperature at the shock drops below T = 10^6 K.

The time scale is given by:

$$t_{end}\approx 43000{\left(\frac{m}{1.66\cdot {10}^{-24}g}\right)}^{5/6}{\left(\frac{E_{SN}}{{10}^{51}erg}\right)}^{1/3}{\left(\frac{{\rho }_{ISM}}{1.66\cdot {10}^{-24}g/c{m}^3}\right)}^{-1/3}\text{yr}$$

Methods Documentation

luminosity_tev(t, energy_min='1 TeV')

Gamma-ray luminosity above energy_min at age t.

The luminosity is assumed constant in a given age interval and zero before and after. The assumed spectral index is 2.1.

The gamma-ray luminosity above 1 TeV is given by:

$$L_{\gamma }(\ge 1TeV)\approx {10}^{34}\theta \left(\frac{E_{SN}}{{10}^{51}erg}\right)\left(\frac{{\rho }_{ISM}}{1.66\cdot {10}^{-24}g/c{m}^3}\right){\text{ s}}^{-1}$$

Reference: https://ui.adsabs.harvard.edu/abs/1994A%26A…287..959D (Formula (7)).

Parameters

tQuantity

Time after birth of the SNR

energy_minQuantity

Lower energy limit for the luminosity

radius(t)

Outer shell radius at age t.

The radius during the free expansion phase is given by:

$$R_{SNR}(t)=1.12R_{ch}{\left(\frac{t}{t_{ch}}\right)}^{2/3}$$

The radius during the Sedov-Taylor phase evolves like:

$$R_{SNR}(t)={[R_{SNR,ST}^{5/2}+{\left(2.026\frac{E_{SN}}{{\rho }_{ISM}}\right)}^{1/2}(t-t_{ST})]}^{2/5}$$

Using the characteristic dimensions:

$$R_{ch}=M_{ej}^{1/3}{\rho }_{ISM}^{-1/3}\text{and}{t}_{ch}=E_{SN}^{-1/2}{M}_{ej}^{5/6}{\rho }_{ISM}^{-1/3}$$

Parameters

tQuantity

Time after birth of the SNR

radius_inner(t, fraction=0.0914)

Inner radius at age t of the SNR shell.

Parameters

tQuantity

Time after birth of the SNR

radius_reverse_shock(t)

Reverse shock radius at age t.

Initially the reverse shock co-evolves with the radius of the SNR:

$$R_{RS}(t)=\frac{1}{1.19}{r}_{SNR}(t)$$

After a time $t_{core}\simeq 0.25t_{ch}$ the reverse shock reaches the core and then propagates as:

$$R_{RS}(t)=[1.49-0.16\frac{t-t_{core}}{t_{ch}}-0.46\ln \left(\frac{t}{t_{core}}\right)]\frac{R_{ch}}{t_{ch}}t$$

Parameters

tQuantity

Time after birth of the SNR