In addition to the photons from the UVB, accounted for in Haardt Madau (2001) (HM01), ionizing photons ($\rm h\nu \ge 1\, Ryd$) emitted by nearby young stars, in particular these belonging to the halo in consideration, can contribute substantially to the total Ly emission of star-forming galaxies. The strength of this contribution depends strongly on the interstellar dust and gas geometry and kinematics (Kunth etal. 2003; Verhamme etal. 2012), as those determine how many Ly photons escape from the star-forming regions. In a first, conservative approximation, we assume that all the ionizing photons from stars are absorbed by dust or photoionizing neutral gas in the ISM. Since the dust attenuation is poorly constrained at low redshift, we will consider a simplistic model for the emitted Ly$\rm \alpha$ photons. We start with the prescription from Furlanetto etal. (2005) to estimate the intrinsic Ly luminosity from ionizing photons in the absence of dust: $L\rm ^{stars}_{Ly\alpha } \ [erg\, s^{-1}] = 10^{42}\ SFR\ [M_{\odot }\ yr^{-1}]$. We compute the SFR of each halo from the mass of young stars, using the continuous star formation approximation (Kennicutt 1998):

(1)
$$\begin{eqnarray*}
\rm SFR [M_{\odot }\, yr^{-1}] = \frac{\mathit{ M}_{stars \lt 10^8\ yr}\ [M_{\odot }]}{10^8\ [yr]}.
\end{eqnarray*}
$$
Using COS data of low-redshift ($z \sim 0.03$) star-forming galaxies, Wofford, Leitherer Salzer (2013) measured a Ly escape fraction ranging from 1percent to $\rm 10{{\ \rm per\ cent}}$. They estimate that this fraction is sensitive to the presence of dust and to the Hi column density, the Ly photons escaping more easily from holes of low Hi and dust column densities, resulting in a large scatter. Winds can also have a strong effect and can help Ly photons to escape (Dijkstra Jeeson-Daniel 2013) but we do not consider winds in our model. As we do not have any model for either the dust or radiative transfer, we will stay conservative in our assumptions. Hayes etal. (2011) find Ly escape fractions between $\rm 0.1{{\ \rm per\ cent}}$ and $\rm 1{{\ \rm per\ cent}}$ for low-z galaxies. Therefore, we will consider two extreme cases for the Ly luminosity from the stellar contribution at low redshift: one with a Ly escape fraction of $\rm 1{{\ \rm per\ cent}}$, and another with a Ly escape fraction of $\rm 0.1{{\ \rm per\ cent}}$. At higher redshift (z  1), we adopt a Ly escape fraction of $\rm 10{{\ \rm per\ cent}}$ that is within the prediction of Hayes etal. (2011). We are aware that different works predict very different escape fractions for Ly (e.g. Wofford etal. 2013; Naidu etal. 2017, but we choose to follow the trend observed in Hayes etal. (2011). Predicting the spatial and spectral profiles of such emission would require the full calculation from radiative transfer techniques (Verhamme etal. 2006, 2012; Rosdahl etal. 2013; Lake etal. 2015), which is beyond the scope of this work. However, as our goal is to study the detectability of such emission with upcoming instruments, we chose to make the simple assumption that all the Ly photons only go through one absorption/re-emission process before leaving the cloud. Also, we assume that all of the Ly photons are emitted from the centre of the galaxy. We then weigh the profile proportionally to the total hydrogen density of the gas cell and by its inverse squared distance to the centre. This gives us, for each cell j the luminosity $L_{j}^{\star }$:

(2)
$$\begin{eqnarray*}
L_{j}^{\star }\rm [erg\, s^{-1}] = \mathit{ f}_{esc} (Ly\alpha) \frac{\frac{\mathit{ n}_{\mathit{ j},H}}{\mathit{ R}_\mathit{ j}^2}}{\int _{\mathit{ R}_{vir}} \frac{\mathit{ n}_H}{\mathit{ R}^2}} 10^{42} SFR_\mathit{ j}\, [M_{\odot }\, yr^{-1}] .
\end{eqnarray*}
$$
Citation: Kennicutt 1998
Citation function: Uses; Uses