PowerLaw2

class gammapy.spectrum.models.PowerLaw2(amplitude, index, emin, emax)

Bases: gammapy.spectrum.models.SpectralModel

Spectral power-law model with integral as norm parameter

See http://fermi.gsfc.nasa.gov/ssc/data/analysis/scitools/source_models.html for further details.

\[\phi(E) = F_0 \cdot \frac{\Gamma + 1}{E_{0, max}^{\Gamma + 1} - E_{0, min}^{\Gamma + 1}} \cdot E^{-\Gamma}\]

Parameters:

index : Quantity

Spectral index \(\Gamma\)

amplitude : Quantity

Integral flux \(F_0\).

emin : Quantity

Lower energy limit \(E_{0, min}\).

emax : Quantity

Upper energy limit \(E_{0, max}\).

Methods Summary

evaluate(energy, amplitude, index, emin, emax)
integral(emin, emax)	Integrate power law analytically.
integral_error(emin, emax, **kwargs)	Integrate power law analytically with error propagation.
inverse(value)	Return energy for a given function value of the spectral model.

Methods Documentation

static evaluate(energy, amplitude, index, emin, emax)

integral(emin, emax)

Integrate power law analytically.

\[F(E_{min}, E_{max}) = F_0 \cdot \frac{E_{max}^{\Gamma + 1} \ - E_{min}^{\Gamma + 1}}{E_{0, max}^{\Gamma + 1} \ - E_{0, min}^{\Gamma + 1}}\]

Parameters:

emin, emax : Quantity

Lower and upper bound of integration range.

integral_error(emin, emax, **kwargs)

Integrate power law analytically with error propagation.

Parameters:

emin, emax : Quantity

Lower and upper bound of integration range.

Returns:

integral, integral_error : tuple of Quantity

Tuple of integral flux and integral flux error.

inverse(value)

Return energy for a given function value of the spectral model.

Parameters:

value : Quantity

Function value of the spectral model.