# Power-Law Sources¶

PowerLawSourceModel assumes that the emission can be described by a pure power law:

$\varepsilon(E) = K\left(\frac{E}{E_0}\right)^{-\alpha}, E_{\rm min} \leq E \leq E_{\rm max}$

between the energies emin and emax, with a power-law spectral index alpha. The power law normalization $$K$$ is represented by an emission_field specified by the user, which must have units of counts/s/keV in the source rest frame. alpha may be a single floating-point number (implying the spectral index is the same everywhere), or a field specification corresponding to a spatially varying spectral index. A reference energy e0 (see above equation) must also be specified.

## Examples¶

An example where the spectral index is the same everywhere:

e0 = (1.0, "keV") # Reference energy
emin = (0.01, "keV") # Minimum energy
emax = (11.0, "keV") # Maximum energy
emission_field = "hard_emission" # The name of the field to use (normalization)
alpha = 1.0 # The spectral index

plaw_model = pyxsim.PowerLawSourceModel(e0, emin, emax, emission_field, alpha)


Another example where you have a spatially varying spectral index:

e0 = YTQuantity(2.0, "keV") # Reference energy
emin = YTQuantity(0.2, "keV") # Minimum energy
emax = YTQuantity(30.0, "keV") # Maximum energy
emission_field = "inverse_compton_emission" # The name of the field to use (normalization)
alpha = ("gas", "spectral_index") # The spectral index field

plaw_model = pyxsim.PowerLawSourceModel(e0, emin, emax, emission_field, alpha)