Toward accurate modeling of line-intensity mapping one-point statistics: Including extended profiles

Line-intensity mapping (LIM) is quickly attracting attention as an alternative technique to probe large-scale structure and galaxy formation and evolution at high redshift. LIM one-point statistics are motivated because they provide access to the highly non-Gaussian information present in line-intensity maps and contribute to break degeneracies between cosmology and astrophysics. Now that promising surveys are underway, an accurate model for the LIM probability distribution function (PDF) is necessary to employ one-point statistics. We consider the impact of extended emission and limited experimental resolution in the LIM PDF for the first time. We find that these effects result in a lower and broader peak at low intensities and a lower tail towards high intensities. Focusing on the distribution of intensities in the observed map, we perform the first model validation of LIM one-point statistics with simulations and find good qualitative agreement. We also discuss the impact on the covariance, and demonstrate that if not accounted for, large biases in the astrophysical parameters can be expected in parameter inference. These effects are also relevant for any summary statistic estimated from the LIM PDF, and must be implemented to avoid biased results. The comparison with simulations shows, however, that there are still deviations, mostly related with the modeling of the clustering of emitters, which encourage further development of the modeling of LIM one-point statistics.

Figure 1

Top panel: extended profiles in the direction along the line of sight for our example under different assumptions: we show a point source in light green, the effects of the limited resolution in purple, and adding line broadening with and without random inclination (dotted and dashed lines, respectively) with different colors for different halo masses. The grid in the horizontal axis corresponds to the voxel division. Bottom panel: luminosity-weighted distribution (top) and cumulative distribution (bottom) of the line broadening with and without random inclinations (blue and red, respectively). We also show the line broadening ${\sigma }_v$ for edge-on emitters for the same masses considered in the top panel, the standard deviation ${\sigma }_{\parallel }$ of the line-spread function and the voxel size ${\sigma }_{\parallel }^{\mathrm{FWHM}}$.

Figure 2

VID of the signal (top) and including the contribution from the instrumental noise (bottom) for our example. We show the VID for point sources in red, including the effects from limited resolution in blue, adding line broadening for edge-on galaxies in magenta and marginalizing also over their inclination in orange. The inset enlarges the deviation over the noise-alone VID (black dotted).

Figure 3

VID including the contribution from the instrumental noise for our example and accounting for experimental resolution and the line broadening for randomly oriented galaxies. We show the prediction for several values of ${\sigma }_{\mathrm{vox}}^2$ with different colors, as indicated in the legend, and the noise-only VID with a black-dotted line. The inset in the bottom panel enlarges the deviation over the noise-alone VID.

Figure 4

Mean measured VID from 1008 independent log-normal realizations including instrumental noise (solid step lines) and the prediction using the formalism described in this work (dotted lines). Shaded regions correspond to the square root of the diagonal of the covariance. We show results for point sources in red, including the effects from resolution in blue, adding line broadening in purple and marginalizing over inclinations in orange.

Figure 5

Relative deviation between the theoretical prediction and the mean from Poisson realizations and log-normal simulations, considering point sources and extended profiles as indicated by the titles of the panels. For the cases with clustering (log-normal), we vary ${\sigma }_{\mathrm{vox}}^2$, highlighting the fiducial value used throughout the rest of the study in magenta. Shaded gray areas show the relative uncertainties related with the diagonal of the covariance matrix. Note the change of scale in the $y$ axis between the two top and the two bottom panels.

Figure 6

Correlation matrices computed numerically from 1008 log-normal realizations. We consider four cases as indicated by the titles at the top of each panel.

Figure 7

68% and 95% confidence level forecasted marginalized constraints on the parameters controlling the $L(M)$ relation for the experimental set up described in Secs. 3b and 4. We compare the results for point sources (red) and modeling the limited resolution of the experiment and line broadening marginalizing over the emitter inclination (orange), assuming that the latter is the correct description of the data. True parameter values are marked by a star, while the best fit assuming point sources is marked by a black dot.