Compute the average surface brightness [mag arcsec^-2] within the half-light radius

    abs_mag = absolute magnitude [mag]
    r_physical = half-light radius [kpc] 
    distance = [kpc]

    The factor 2 in the c_v equation below account for half the luminosity 
    within the half-light radius. The 3600.**2 is conversion from deg^2 to arcsec^2

    c_v = 2.5 * np.log10(2.) + 2.5 * np.log10(np.pi * 3600.**2) = 19.78

def surfaceBrightness(abs_mag, r_physical, distance):
    """
    Compute the average surface brightness [mag arcsec^-2] within the half-light radius

    abs_mag = absolute magnitude [mag]
    r_physical = half-light radius [kpc] 
    distance = [kpc]

    The factor 2 in the c_v equation below account for half the luminosity 
    within the half-light radius. The 3600.**2 is conversion from deg^2 to arcsec^2

    c_v = 2.5 * np.log10(2.) + 2.5 * np.log10(np.pi * 3600.**2) = 19.78
    """
    r_angle = np.degrees(np.arctan(r_physical / distance))
    c_v = 19.78 # mag/arcsec^2
    return abs_mag + dist2mod(distance) + c_v + 2.5 * np.log10(r_angle**2)