Probing the Warm Dark Matter mass with [C II] intensity mapping

TL;DR

This work investigates the potential of [CII] line-intensity mapping to constrain warm dark matter using a halo-model description of the [CII] power spectrum. By introducing two LF parameterisations (optimistic and pessimistic) and performing Bayesian inference on mock data for the Deep Spectroscopic Survey at $z\approx3.6$, the authors quantify how survey design and the faint-end slope of the [CII] LF affect constraints on $m_\mathrm{WDM}$ and its FDM counterpart. They find that, under a CDM background, the reference DSS yields 95% CL lower limits of $m_\mathrm{WDM}=1.10$ keV (optimistic LF) and $0.58$ keV (pessimistic LF), with more ambitious surveys pushing to several keV; a steeper faint-end slope can further tighten bounds. However, for realistic small-halo contributions, the [CII] PS provides limited leverage on WDM unless survey capabilities are greatly expanded and multiple redshifts/lines are combined, highlighting the value of multi-tracer LIM campaigns for competitive DM constraints.

Abstract

The nature of dark matter (DM) is still debated. While cold DM (CDM) is the standard paradigm, warm DM (WDM) may ease some small-scale tensions in the $Λ$CDM framework. Line-intensity mapping (LIM) offers a novel probe of DM properties. To explore the potential of LIM surveys in constraining the WDM particle mass ($m_\mathrm{WDM}$) by means of the [C II] power spectrum (PS), we provide forecasts for the Deep Spectroscopic Survey (DSS) at $z\simeq3.6$ and extend the analysis to larger sky coverage, higher sensitivity, and/or increased spectral resolution. We develop a formulation for the [C II] PS based on the halo-model approach, incorporating the uncertainty in the luminosity function (LF) through two alternative parameterisations. We perform a Bayesian analysis on mock data to derive constraints on $m_\mathrm{WDM}$. In a CDM universe, the DSS yields lower limits on $m_\mathrm{WDM}$ at $95\%$ credibility level (CL) of $1.10$ keV and $0.58$ keV when considering the optimistic and pessimistic LF ($α= -1.1$), respectively. Ambitious surveys can improve these figures to $5.82$ keV and $1.90$ keV, and assuming a steeper faint-end slope ($α= -1.9$) further boosts these limits. A fivefold increase in spectral resolution enhances sensitivity to the damping scale associated to redshift-space distortions, tightening the constraints on $m_\mathrm{WDM}$ by a factor of up to $\sim1.8$. Finally, Bayesian inference on mock data with $m_\mathrm{WDM}=3$ keV results in a well-constrained and unbiased posterior only in futuristic survey setups. Upcoming LIM surveys can provide meaningful limits on $m_\mathrm{WDM}$, although the negligible contribution from small haloes reduces the constraining power of the [C II] PS. Future progress will benefit from combining multiple redshifts and emission lines, opening the way to competitive constraints on the nature of DM.

Figures (11)

• Figure 1: [CII] luminosity--halo mass relation inferred from abundance matching. In both panels, the solid lines correspond to the $L(M)$ relations derived from our Schechter fits to the ALPINE data with fixed values for $\alpha$. The dashed red line is based on the fit by yan_20. The left and right panels assume a CDM and a $0.5\ \mathrm{keV}$ HMF, respectively (see Appendix \ref{['app:HMF_bias']} for a direct comparison between the two scenarios). In the left panel, for comparison, the dot-dashed black line indicates the $L(M)$ relation obtained by Silva+15, while the dotted gold and dark gold lines show results from the Marigold simulations Khatri+24_marigold at $z=5$ and $z=4$, respectively.
• Figure 2: Reconstructed [CII] LFs obtained by combining the abundance-matched $L(M)$ relations with the HMFs of the CDM and WDM cosmologies. The figure uses the LF of our optimistic case and adopts a WDM particle mass of $0.5\ \mathrm{keV}$. While the CDM model reproduces the input LF across all luminosities, the WDM case shows a sharp downturn at the faint end, reflecting the dearth of low-mass haloes and the corresponding minimum luminosity imposed by the abundance-matching procedure.
• Figure 3: Left: $\Delta^2(k,z\simeq 3.6)$ computed in the CDM scenario for our optimistic (solid red line) and pessimistic (solid blue line) cases for $\alpha=-1.1$. The shaded areas represent the associated statistical uncertainty as for our survey reference setup. The dotted line is a graphical representation of the white-noise level, $P_\mathrm{WN}$, while the dashed and dot-dashed lines refer to the clustering and shot-noise components, respectively. Right: Ratio between the WDM and CDM power spectra. The dashed and dotted black lines correspond to WDM models with $m_\mathrm{WDM} = 10$ keV and $0.5$ keV, respectively. The shaded regions reflect the CDM uncertainties from the left panel. In both panels, the markers illustrate the adopted binning scheme.
• Figure 4: Left: The likelihood ratio $\ell$ computed for the optimistic case in our reference setup. Centre: Same as left panel but with $R=500$. Right: Graphical explanation of the banana-shaped $\ell$ shown in the left panel. Each pair of values $(w,\sigma)$ in the legend indicates the inverse particle mass in keV$^{-1}$ and the RSD displacement parameter in units of $h^{-1} \ \mathrm{Mpc}$, respectively. The stars of corresponding colours in the left panel serve as identifiers for each combination in the parameter space, while the red circle denotes the true values used to generate the data.
• Figure 5: The marginalised posterior (over $\sigma$) computed for the whole set of sky areas in the optimistic scenario, with $R=100$ and $P_\mathrm{WN} \simeq 2.4\times 10^{10} \,h^{-3}\,\mathrm{Mpc}^3 \,\mathrm{Jy}^2 \,\mathrm{sr}^{-2}$. The left panel shows the posterior for a fixed $\beta=0$ (uniform prior in $w$), while the right panel shows the result marginalised over $\beta$. The dashed lines of corresponding colours indicate the $m_\mathrm{WDM}$ threshold up to which CDM and WDM can be distinguished (95% CL). The dotted lines show the assumed prior distribution for $w$.