Phase-Space Spectral Line De-confusion in Intensity Mapping

Line intensity mapping (LIM) is a promising tool to eciently probe the three-dimensional large-scale structure by mapping the aggregate emission of a spectral line from all sources that trace thematter density eld. Spectral lines from dierent redshifts can fall in the same observed frequencyand be confused, however, which is a major challenge in LIM. In this work, we develop a line de-confusion technique in map space capable of reconstructing the three-dimensional spatial distributionof line-emitting sources. If multiple spectral lines of a source population are observable in multiplefrequencies, using the sparse approximation our technique iteratively extracts sources along a givenline-of-sight by tting the LIM data to a set of spectral templates. We demonstrate that the techniquesuccessfully extracts sources with emission lines present at a few sigma above the noise level, takinginto account uncertainties in the source modeling and presence of continuum foreground contaminationand noise uctuations. As an example, we consider a TIME/CONCERTO-like survey targeting [C II]at the Epoch of Reionization, and reliably reconstruct the 3D spatial distribution of the CO interlopersand their luminosity functions at 0:5 . z . 1:5. We also demonstrate a successful de-confusion for theSPHEREx mission in the near-infrared wavelengths.We discuss a formalism in which the reconstructedmaps can be further cross-correlated with a (galaxy) tracer population to estimate the total interloperpower. This technique is a general framework to extract the phase-space distribution of low-redshiftinterlopers, without the need of external information, for any line de-confusion problem.