barak.absorb.tau_LL¶

barak.absorb.tau_LL(logN, wa, wstart=912)[source]¶

Find the optical depth at the neutral hydrogen Lyman limit.

Parameters :	logN : float log10 of neutral hydrogen column density in cm^-2. wa : array_like Wavelength in Angstroms. wstart : float (912.) Tau values at wavelengths above this are set to zero.
Returns :	tau : ndarray or float if wa is scalar The optical depth at each wavelength.

Notes

At the Lyman limit, the optical depth tau is given by:

tau = N(HI) * sigma_0

where sigma_0 = 6.304 e-18 cm^2 and N(HI) is the HI column density in cm^-2. The energy dependence of the cross section is:

sigma_nu ~ sigma_0 * (h*nu / I_H)^-3 = sigma_0 * (lam / 912)^3

where I_H is the energy needed to ionise hydrogen (1 Rydberg, 13.6 eV), nu is frequency and lam is the wavelength in Angstroms. This expression is valid for I_H < I < 100* I_H.

So the normalised continuum bluewards of the Lyman limit is:

F/F_cont = exp(-tau) = exp(-N(HI) * sigma_lam)
         = exp(-N(HI) * sigma_0 * (lam/912)^3)

Where F is the absorbed flux and F_cont is the unabsorbed continuum.

References

Draine, 2011, “Physics of the Interstellar Medium”. ISBN 978-0-691-12214-4: p84, and p128 for the photoionization cross section.

Examples

>>> wa = np.linspace(100, 912, 100)
>>> z = 2.24
>>> for logN in np.arange(17, 21., 0.5):
...    fl = exp(-tau_LL(logN, wa))
...    plt.plot(wa*(1+z), fl, lw=2, label='%.2f' % logN)
>>> plt.legend()