magnificationcurve.py 文件源码

def _B_1_function(self, z, B_0=None):
        """
        calculate B_1(z) function defined in:

        Gould A. 1994 ApJ 421L, 71 "Proper motions of MACHOs
        http://adsabs.harvard.edu/abs/1994ApJ...421L..71G

        Yoo J. et al. 2004 ApJ 603, 139 "OGLE-2003-BLG-262: Finite-Source
        Effects from a Point-Mass Lens"
        http://adsabs.harvard.edu/abs/2004ApJ...603..139Y

        """
        if B_0 is None:
            B_0 = self._B_0_function(z)

        function = (lambda r, theta: r * np.sqrt(1.-r**2) /
            self.parameters.rho / np.sqrt(r**2+zz**2-2.*r*zz*np.cos(theta)))
        lim_0 = lambda x: 0
        lim_1 = lambda x: 1
        W_1 = 0. * z
        for (i, zz) in enumerate(z):
            W_1[i] = integrate.dblquad(function, 0., 2.*np.pi, lim_0, lim_1)[0]

        W_1 /= np.pi
        return B_0 - 1.5 * z * self.parameters.rho * W_1