| We recover the intrinsic distribution of observed Lyman-alpha (Lya) halo properties at z~4, correcting for selection biases and the effects of flux-limited samples. Relating extended gas halos (CGM) to their host galaxies is a critical issue in galaxy evolution, but diffuse CGM gas is difficult to detect at high redshifts, and we rely on observational tracers such as the Lya emission line. Scattered Lya emission produces broad, complicated spatial and spectral profiles that trace the extended CGM, but variations in these halo properties also affect line detectability. We develop a generalized selection function for model Lya halos set in deep VLT/MUSE observations, enabling completeness correction as a function of flux and specific halo properties: spectral line width, halo scale length, and halo flux fraction. With our selection function, we uncover the intrinsic distributions of these properties for z~4 halos, and show that extended halos are more common than observed distributions indicate. We compare our results with mock spectra of a simulated Lya galaxy to make further inferences on detection biases and link halo properties to host galaxy recent star formation. Finally, we explore available data from JWST to relate host galaxy stellar population characteristics to the observed halo distributions. |
