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The emission and escape of Lyman-alpha photons from star-forming galaxies is determined through complex interactions between the emitted photons and a galaxy's interstellar and circumgalactic gas. \ This causes Lyman-alpha emitters (LAEs) to commonly appear not as point sources but in spatially extended halos with complex spectral profiles. We developed a 3D spatial-spectral model of Lyman-alpha halos (LAHs) to replicate LAH observations in integral field spectroscopic studies, such as those made with VLT/MUSE. The profile of this model is a function of six key halo properties: the halo- and compact-source exponential scale lengths sH and r_ sC), the halo flux fraction (fH), the compact component ellipticity (q), the spectral line width (sigma), and the spectral line skewness parameter (gamma). Placing a series of model LAHs into datacubes that reflect observing conditions in the MUSE UDF-Mosaic survey, we tested their detection recoverability and determine that sigma, r_ sH, and fH are expected to have the most significant effect on the detectability of the overall LAH at a given central wavelength and intrinsic line luminosity. We developed a general selection function model that spans a grid of these halo parameters. Using it with a sample of 145 LAHs with measured halo properties observed in the UDF-Mosaic survey, we derived completeness-corrected, intrinsic distributions of the values of sigma, r_ sH, and fH for 3<z<5 LAHs. We present the best-fit functional forms of the distributions as well as a sigma distribution corrected for instrumental line-spread function broadening, and thereby show the physical line-spread distribution of the intrinsic population. Finally, we discuss possible implications for these distributions for the nature of Lyalpha emission through the circumgalactic medium, finding that observations may undercount LAHs with extended halo scale lengths compared to the intrinsic population.
Pharo et al. (Sat,) studied this question.