Abstract
We develop a comprehensive theoretical model for Lyman-alpha (Ly$\alpha$) emission, from the scale of individual Ly$\alpha$ emitters (LAEs) to Ly$\alpha$ halos (LAHs), Ly$\alpha$ blobs (LABs), and Ly$\alpha$ filaments (LAFs) of the diffuse cosmic web itself. To do so, we post-process the high-resolution TNG50 cosmological magnetohydrodynamical simulation with a Monte Carlo radiative transfer method to capture the resonant scattering process of Ly$\alpha$ photons. We build an emission model incorporating recombinations and collisions in diffuse gas, including radiative effects from nearby AGN, as well as emission sourced by stellar populations. Our treatment includes a physically motivated dust model, which we empirically calibrate to the observed LAE luminosity function. We then focus on the observability, and physical origin, of the Ly$\alpha$ cosmic web at $z=2$, studying the dominant emission mechanisms and spatial origins. We find that diffuse Ly$\alpha$ filaments are, in fact, illuminated by photons which originate, not from the intergalactic medium itself, but from within galaxies and their gaseous halos. In our model, this emission is primarily sourced by intermediate mass halos ($10^{10} - 10^{11}$ M$_\odot$), principally due to collisional excitations in their circumgalactic media as well as central, young stellar populations. Observationally, we make predictions for the abundance, area, linear size, and embedded halo/emitter populations within filaments. Adopting an isophotal surface brightness threshold of $10^{-20}$erg s$^{-1}$ cm$^{-2}$ arcsec$^{-2}$, we predict a volume abundance of Ly$\alpha$ filaments of ${\sim}10^{-3}$ cMpc$^{-3}$ for lengths above $400$ pkpc. Given sufficiently large survey footprints, detection of the Ly$\alpha$ cosmic web is within reach of modern integral field spectrographs, including MUSE, VIRUS, and KCWI.