The Escape Fraction

The LyC escape fraction, \(f_{\rm esc}\), is one of the main quantities we need to calculate for the simulated galaxies (see this post).This quantity is the fraction of photons that escape galaxies to ionize intergalactic hydrogen, and is therefore a dimensionless number between 0 and 1.

Current constraints

\(f_{\rm esc}\) is the least constrained out of the three parameters needed to calculate \(\dot{n_{\rm ion}}\). It is especially difficult to measure at the epoch of reionization, since neutral hydrogen absorbs LyC photons; in reality, it can’t be measured directly except at low redshifts

Here is some information pulled from a couple papers:

• Negligible \(f_{\rm esc}\) measured in deep stacks at z~0–1 (e.g., Siana et al. 2010; Rutkowski et al. 2016)
• Less than 5 per cent in the local Universe (Grimes et al. 2009; Vanzella et al. 2010; Leitherer et al. 2016; Naidu et al. 2018)
• \(f_{\rm esc}\)~10% at z~2.5–4 (Marchi et al. 2017; Steidel et al. 2018; Fletcher et al. 2019; P. A. Oesch et al. 2020).
• During EoR \(f_{\rm esc}\) must be >15–20 per cent for star-forming galaxies to reionize the universe (Ouchi et al. 2009b; Robertson et al. 2013, 2015; Finkelstein et al. 2019; Naidu et al. 2020).

Models

Constant escape fraction

It is common to assume the \(f_{\rm esc}\) is a constant number in reionization studies (e.g., Robertson2015, Ishigaki2018). This can be interperated as an average escape fraction.

fesc depends on SFR surface density

I will largely follow Naidu et. al 2020. They assume escape fraction solely depends on the SFR surface density:

\[f_{\rm esc} = a \times \left( \dfrac{ \Sigma_{\rm SFR} } {1000 M_\odot {\rm yr}^{-1} {\rm kpc}^{-2} } \right)^b\]

with \(a=1.6 \pm 0.3\) and \(b=0.4 \pm 0.1\)

Calculation

\[\Sigma_{\rm SFR} = \dfrac{SFR}{2 \pi R_{\rm gal}^2}\]

where \(R_{\rm gal}\) is the effective radii of the galaxy (e.g. Shibuya2019). I calculate this from the galaxy catalog as \(R_{\rm gal} = \sqrt{q} R_{\rm eff}\)

Then I use the best fit parameters from Naidu2020 (\(a=1.6\) and \(b=0.4\)), and constrain the values so that they fall between 0 and 1.

Results

Here is what I get (using the test catalog, that only contains more massive galaxies)

This roughly agrees with the values above. I need to check what range of galaxy masses/luminosities they used in their measurements to make a fair comparison. For now, this seems pretty good though!

Questions/Thoughts/Next steps

1. This obviously depends a lot on the galaxy effective sizes. There was some concern that my catalog has a (small number) of galaxies that have unrealistically small sizes for their brightness. This is something I want to look into a bit more, by plotting the SFR surface density. I might also do some comparisons to Shibuya et al. 2019.

2. Now I have all the ingredients to calculate the ionization contribution of the galaxies (modulo some debugging on the \(xi_{\rm ion}\) values). I will go ahead soon and get the calculation for \(\dot{n_{\rm ion}}\).

3. My end goal is to compare different galaxy surveys abilities to constrain reionization. I need to think about if I want to alter these models. I could use e.g. different models for the escape fraction, alter the spectral modelling, change the luminosity functions, change the IGM absorption model in the spectra. An easier approach would be to alter the values by e..g 10 percent and seeing how it affects things.

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