def rho_MC(delta, rhoeq=4.39e-38):
    """
   returns the characteristic density of an 
   axion minicluster in [solar masses/km^3]
   forming from an overdensity with 
   overdensity parameter delta.
   rhoeq is the matter density at matter 
   radiation equality in [solar masses/km^3]
   """
    return 140 * (1 + delta) * delta**3 * rhoeq