Calculate the relativistic synchrotron emission coefficient η_ν.

    This is Dulk (1985) equation 40, which is an approximation assuming a
    power-law electron population. Arguments are:

    b
      Magnetic field strength in Gauss
    ne
      The density of electrons per cubic centimeter with energies greater than E0.
    delta
      The power-law index defining the energy distribution of the electron population,
      with ``n(E) ~ E^(-delta)``. The equation is valid for ``2 <~ delta <~ 5``.
    sinth
      The sine of the angle between the line of sight and the magnetic field direction.
      It's not specified for what range of values the expressions work well.
    nu
      The frequency at which to calculate η, in Hz. The equation is valid for
      It's not specified for what range of values the expressions work well.
    E0
      The minimum energy of electrons to consider, in MeV. Defaults to 1 so that
      these functions can be called identically to the gyrosynchrotron functions.

    The return value is the emission coefficient (AKA "emissivity"), in units
    of ``erg s^-1 Hz^-1 cm^-3 sr^-1``.

    No complaints are raised if you attempt to use the equation outside of its
    range of validity.

def calc_synch_eta(b, ne, delta, sinth, nu, E0=1.):
    """Calculate the relativistic synchrotron emission coefficient η_ν.

    This is Dulk (1985) equation 40, which is an approximation assuming a
    power-law electron population. Arguments are:

    b
      Magnetic field strength in Gauss
    ne
      The density of electrons per cubic centimeter with energies greater than E0.
    delta
      The power-law index defining the energy distribution of the electron population,
      with ``n(E) ~ E^(-delta)``. The equation is valid for ``2 <~ delta <~ 5``.
    sinth
      The sine of the angle between the line of sight and the magnetic field direction.
      It's not specified for what range of values the expressions work well.
    nu
      The frequency at which to calculate η, in Hz. The equation is valid for
      It's not specified for what range of values the expressions work well.
    E0
      The minimum energy of electrons to consider, in MeV. Defaults to 1 so that
      these functions can be called identically to the gyrosynchrotron functions.

    The return value is the emission coefficient (AKA "emissivity"), in units
    of ``erg s^-1 Hz^-1 cm^-3 sr^-1``.

    No complaints are raised if you attempt to use the equation outside of its
    range of validity.

    """
    s = nu / calc_nu_b(b)
    return (b * ne *
            8.6e-24 * (delta - 1) * sinth *
            (0.175 * s / (E0**2 * sinth))**(0.5 * (1 - delta)))