Fitting to \(T_0\) and \(\tau_{eff}\)

Seems like the paramters \(\beta_{\mathrm{He}}\), \(\beta_{\mathrm{H}}\), and \(\Delta z_{\mathrm{He}}\) are constrained to a reasonable degree but there is no constrain for \(\Delta z_{\mathrm{H}}\).

Below is the interpolated evolution of \(\tau_{eff}\) for some values of \(\Delta z_{\mathrm{H}}\), it seems like there is something wrong for the \(\Delta z_{\mathrm{H}} = 0.15\) trajectories.

Below are the UVB rates for the simulates values of \(\Delta z_{\mathrm{H}}\) and all the other parameters constant, apparently nothing wrong here.