# ReHILAE: Is Re-ionisation of Hydrogen due to Lyman-alpha emitters (LAEs)?

### Week 4 Research Update:

Our first task this week was to investigate why our $L_{Ly\alpha}$ graph had such small values. This was due to a simple logic error in the code, we had hardcoded the data from D. Sobral, S. Santos and J. Matthee (Table 6 p.17) and did not account for the fact that every data point was divided by $10^{40}$. After we had fixed this, we replotted the $L_{Ly\alpha}$, $\dot{n}_{ion}$ and $\dot{Q}_{ion, Ly\alpha}$ plots:

These plots are much better than the previous week’s plots and it can be seen that the $Ly\alpha$ luminosity density was causing the error in the top two plots. The plots are still not ideal however, here, we are still capping the luminosity to zero when it is negative. What we implemented towards the end of today’s session was logging the data and then SciPy to fit a curve to this data.

After we produced these plots we realised we had accidentally missed out one re-ionisation process. There are three models which we should have reproduced before moving onto implementing the $Ly\alpha$ methodology, they are listed below. All three models use the following use the following equation to calculate the availability of LyC photons.

$\dot{n}_{ion} = f_{esc}\xi_{ion}\rho_{UV}$

• Robertson et al. This model uses the following assumptions: $log\xi_{ion}=25.2, \ f_{esc}=20\%$
• Lyman Break Galaxies (LBGs) uses the following assumptions: $log\xi_{ion}=25.3, \ f_{esc}\approx 3 \%$
• LAEs. This model makes the following assumptions: $f(z)\rho_{UV}; \ log\xi_{ion}=25.6, \ f_{esc}\approx 13 \%$

For the first two models we assume that sources ionising the universe account for 100% of $\rho_{UV}$ whereas with LAEs, we assume a redshift dependent $\rho_{UV}$ coefficient. We have plotted these three models below (the time dependent redshift coefficient has not yet been implemented).

We would expect the re-ionisation models to behave like this from looking at the ionisation efficiency and escape fractions. Once the redshift dependent coefficient is implemented, the LAE re-ionisation model will slow, but we still expect it to be the quickest.

Earlier we discussed using SciPy to fit a curve to our data. Not only is it a better fit than the one generated by pylab’s polyfit function, it also gives the errors for the parameters of the curve. To visualise this, we have plotted the $Ly\alpha$ luminosity density against redshift using SciPy’s average optimised data, its maximum, its minimum and finally the polyfit:

SciPy returns the error on the fits parameters, we can choose a random fit that lies between the error bound fits and run our simulation multiple times, for multiple different fits. This is what will be working on during our next lab session. For now, we have ran our re-ionisation model with the UV framework using the SciPy average optimised data rather than the polyfit data.