# SNRTrueloveMcKee#

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

SNR model according to Truelove & McKee (1999).

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. Outer shell radius at age t. radius_inner(t[, fraction]) Inner radius at age t of the SNR shell. Reverse shock radius at age t.

Attributes Documentation

sedov_taylor_begin#

Characteristic time scale when the Sedov-Taylor phase starts.

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

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:

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

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:

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

Parameters
tQuantity

Time after birth of the SNR

energy_minQuantity

Lower energy limit for the luminosity

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:

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

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

Inner radius at age t of the SNR shell.

Parameters
tQuantity

Time after birth of the SNR

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:

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

Time after birth of the SNR