darkhistory.electrons.ics.ics_spectrum.rel_spec

darkhistory.electrons.ics.ics_spectrum.rel_spec(eleceng, photeng, T, inf_upp_bound=False, as_pairs=False)

Relativistic ICS spectrum of secondary photons.

Parameters:

elecengndarray

Incoming electron energy.

photengndarray

Outgoing photon energy.

Tfloat

CMB temperature.

inf_upp_boundbool

If True, calculates the approximate spectrum that is used for fast interpolation over different values of T. See Notes for more details. Default is False.

as_pairsbool

If true, treats eleceng and photeng as a paired list: produces eleceng.size == photeng.size values. Otherwise, gets the spectrum at each photeng for each eleceng, returning an array of length eleceng.size*photeng.size.

Returns:

TransFuncAtRedshift or ndarray

dN/(dt dE) of the outgoing photons (dt = 1 s). If as_pairs == False, returns a TransFuncAtRedshift, with abscissa given by (eleceng, photeng). Otherwise, returns an ndarray, with abscissa given by each pair of (eleceng, photeng).

See also

:function:`.rel_spec_Jones_corr`

Notes

This function accepts the energy of the electron as one of the arguments and not the kinetic energy, unlike the other related ICS functions.

The flag inf_upp_bound determines whether an approximation is taken that only gets the shape of the spectrum correct for \(E_{\gamma,\text{final}} \gtrsim T_\text{CMB}\). This is sufficient from an energy conservation perspective, and is used for building a table that can be interpolated over different values of T quickly.

If inf_upp_bound == False, the spectrum up to \(\mathcal{O}(1/\gamma^2)\) corrections is given. This is a combination of the spectrum derived in Eq. (2.48) of Ref. [1]_ and Eq. (9) of Ref. [2]_, which assumes that electrons only lose energy, and Eq. (8) of Ref. [2]_, which contains the spectrum of photons produced electrons getting upscattered.