def sis_sigma_v2theta_E(self, v_sigma):
        """
        converts the velocity dispersion into an Einstein radius for a SIS profile
        :param v_sigma: velocity dispersion (km/s)
        :return: theta_E (arcsec)
        """
        theta_E = 4 * np.pi * (v_sigma * 1000./const.c)**2 * self.D_ds / self.D_s / const.arcsec
        return theta_E