SNRTrueloveMcKee

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

Bases: 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 \(t_{ST} \approx 0.52 t_{ch}\).

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:

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

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:

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

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.

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:

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

Parameters:

tQuantity

Time after birth of the SNR.