HeII Optical Depth

HeII Optical Depth Data

HeII Effective Optical Depth from P19

HeII Effective Optical Depth from P19 Modified

HeII Effective Optical depth along a skewer

Optical Depth:

\[\tau_{u_0}=\frac{\pi e^{2} \lambda_0}{m_{e} c H} f \int \frac{n_{\mathrm{HeII}}}{\sqrt{\pi} b} \exp \left[-\left(\frac{u-u_0}{b}\right)^{2}\right] d u.\]

Thermal Velocities:

\[b=\sqrt{ \frac {2 k_{\mathrm{B}} T }{ 4*m_{\mathrm{H}}} }\]

Cross Section:

\[\sigma = \frac {\pi e^2}{ m_e c^2 } \lambda_0 f\] \[\sigma_{\mathrm{HeII}} = \frac{ \sigma_{\mathrm{HI}} }{ 4}\]

source here.