AstrOmatic software » Stuff

Refs:
http://adsabs.harvard.edu/abs/1995ApJ...441...18M
http://adsabs.harvard.edu/abs/1996MNRAS.283.1388M
http://adsabs.harvard.edu/abs/2005A&A...435..471I
http://heasarc.gsfc.nasa.gov/xanadu/xspec/models/zigm.html

We use the average model from Madau 1995 and Madau et al. 1996 for both Lyman absorbants:

(...) For $\lambda_{\beta}(1+z_{\rm em}) < \lambda_{\rm obs} < \lambda_{\alpha} (1+z_{\rm em})$, where $\lambda_{\alpha}=1216\,\mathring{A}$ and $\lambda_{\beta}=1026\,\mathring{A}$, a galaxy's continuum intensity is attenuated by the combined blanketing effect of many Ly$\alpha$ forest absorption lines, with effective opacity
$$ \tau_{\rm eff}=0.0036\left({\lambda_{\rm obs}\over \lambda_{\alpha}}\right) ^{3.46},$$
(Press, Rybicki, & Schneider 1993). Hence, line blanketing from Ly$\alpha$ alone will produce $\ge1\,$mag of attenuation in the continuum spectrum shortward of $6000\,\mathring{A}$ of a galaxy at $z_{\rm em}\ge 4$.

When $\lambda_{\rm obs}\le\lambda_{\beta}(1+z_{\rm em})$, a significant contribution to the blanketing opacity comes from the higher order lines of the Lyman series. A standard curve of growth analysis has been applied to numerically compute the attenuation expected from line blanketing of Ly$\beta$, $\gamma$, $\delta$ plus 13 higher order members. In the wavelength range $\lambda_{i+1}(1+z_{\rm em})<\lambda_{\rm obs}<\lambda_i(1+z_{\rm em})$, the total optical depth can be written as the sum of the contributions from the $j\rightarrow 1$ transitions,
$$ \tau_{\rm eff}=\sum_{j=2,i} A_j({\lambda_{\rm obs}\over \lambda_j})^{3.46}, $$
where $A_j=(1.7\times 10^{-3}, 1.2\times 10^{-3},9.3\times 10^{-4})$, and $\lambda_j=(1026, 973, 950\,\mathring{A})$ for Ly$\beta$, $\gamma$, and $\delta$, respectively. It is worth noting that heavy element absorbers make a negligible contribution to the blanketing optical depth at high redshifts, as this is dominated by those lines which lie at the transition between the linear and the flat part of the curve of growth, i.e., with $N_{\rm HI} \approx 10^{13.6}\,{\rm cm}^{-2}$ in the case of Ly$\alpha$.
Continuum absorption by HI affects photons observed at $\lambda_{\rm obs}<\lambda_L(1+z_{\rm em})$, where $\lambda_L=912\,\mathring{A}$ is the Lyman limit. An approximate (within 5%) integration of equation yields for the effective photoelectric optical depth along the line of sight:
$$\tau_{eff}=0.25x_c^3 (x_{em}^{0.46}-x_c^{0.46})+9.4x_c^{1.5} (x_{em}^{0.18}-x_c^{0.18})-0.7x_c^3(x_c^{-1.32}-x_{em}^{-1.32})-0.023 (x_{em}^{1.68}-x_c^{1.68})$$
(...)

and for metal lines (although Madau 1995 claims that their effect is negligible for $2.5\ge z\ge4.5$:

$$ \tau_{\rm eff}=0.0017\left({\lambda_{\rm obs}\over \lambda_{\alpha}}\right) ^{1.68}$$

The complete list of $\lambda_j$ and $A_j$ is taken from the xspec IGM attenuation module by Martin Still and Frank Marshall:

We obtain the following transmission curves for sources at $z=1,2,3,4,5,6$, plotted over MEGACAM 's global filter responses:

New "stuff":http://astromatic.net/software/stuff 1.26.0 with IGM extinction option (turned on by default) installed on the morpho cluster.