The contribution of faint Lyman-$\alpha$ emitters to extended Lyman-$\alpha$ halos constrained by MUSE clustering measurements

Abstract

Detections of extended Ly$\alpha$ halos (LAHs) around Ly$\alpha$ emitters (LAEs) have lately been reported on a regular basis, but their origin is still under investigation. Simulation studies predict that the outer regions of the extended LAHs contain a major contribution from the Ly$\alpha$ emission of faint, individually undetected LAEs. To address this matter from an observational angle, we use halo occupation distribution (HOD) modeling to reproduce the clustering of a spectroscopic sample of 1265 LAEs at $3<z<5$ from the MUSE-Wide survey. We integrate the Ly$\alpha$ luminosity function (LF) to estimate the background surface brightness due to discrete faint LAEs. We then extend the HOD statistics inwards towards small separations and compute the factor by which the measured Ly$\alpha$ surface brightness (SB) is enhanced by undetected close physical neighbors. We consider various clustering scenarios for the undetected sources and compare the corresponding radial profiles. The resulting inferred Ly$\alpha$ SB of faint LAEs ranges between $(0.4-2)\times10^{20}\;\rm{erg}\;\rm{s}^{-1}~\rm{cm}^{-2}~\rm{arcsec}^{-2}$, with a very slow radial decline outwards. Our results suggest that the outer regions of observed LAHs ($R\gtrsim50$~pkpc) could indeed contain a strong component from external (but physically associated) LAEs, possibly even be dominated by them. Only for a relatively shallow faint-end slope of the Ly$\alpha$ LF would this contribution from clustered LAEs become unimportant. We also confirm that the observed emission from the inner regions ($R\le20-30$~pkpc) is too bright to be significantly affected by clustering. We compare our findings with predicted profiles from simulations and find good overall agreement. We outline possible future measurements to further constrain the impact of discrete undetected LAEs on observed extended LAHs.