Planck 2013 results. XVIII. Gravitational lensing-infrared background correlation

TL;DR

Planck 2013 results XVIII reports the first detection of a cross-correlation between the cosmic infrared background (CIB) and the CMB lensing potential, exploiting Planck's multi-frequency data to probe the connection between dark and luminous matter at $1 \lesssim z \lesssim 3$. A three-point statistic linked to the CIB and the reconstructed lensing field yields cross-spectra across $100$–$857$ GHz that align with a simple halo-based model, with a peak correlation of up to about $80\%$ and a detection significance reaching $42\sigma$ at $545$ GHz. By leveraging the frequency dependence, the authors isolate the high-redshift CIB contribution and directly constrain the star-formation-rate density for redshifts $z>1$, achieving approximately $2\sigma$ significance across three redshift bins between $z=1$ and $z=7$. The results illuminate the relationship between dark and luminous matter in the early universe and demonstrate Planck's capability to extract high-fidelity non-Gaussian cross-correlations despite foregrounds, with implications for halo occupation and the history of star formation.

Abstract

The multi-frequency capability of the Planck satellite provides information both on the integrated history of star formation (via the cosmic infrared background, or CIB) and on the distribution of dark matter (via the lensing effect on the cosmic microwave background, or CMB). The conjunction of these two unique probes allows us to measure directly the connection between dark and luminous matter in the high redshift (1 < z <3) Universe. We use a three-point statistic optimized to detect the correlation between these two tracers. Following a thorough discussion of possible contaminants and a suite of consistency tests, using lens reconstructions at 100, 143 and 217 GHz and CIB measurements at 100-857 GHz, we report the first detection of the correlation between the CIB and CMB lensing. The well matched redshift distribution of these two signals leads to a detection significance with a peak value of 42 σat 545 GHz and a correlation as high as 80% across these two tracers. Our full set of multi-frequency measurements (both CIB auto- and CIB-lensing cross-spectra) are consistent with a simple halo-based model, with a characteristic mass scale for the halos hosting CIB sources of log_{10}(M/M_sun) = 10.5 \pm 0.6. Leveraging the frequency dependence of our signal, we isolate the high redshift contribution to the CIB, and constrain the star formation rate (SFR) density at z>1. We measure directly the SFR density with around 2 sigma significance for three redshift bins between z=1 and 7, thus opening a new window into the study of the formation of stars at early times.

Figures (8)

• Figure 2: Combined Galactic, point-source and Hi mask with sky fractions 16, 30 and 43%.
• Figure 3: Angular cross-spectra between the reconstructed lensing map and the temperature map at the six HFI frequencies. The error bars correspond to the scatter within each band. The solid line is the expected result based on the PER model and is not a fit to these data (see Fig. \ref{['fig:autos_fit']} for an adjusted model), although it is already a satisfying model. In each panel we also show the correlation between the lens reconstruction at 143GHz and the 143GHz temperature map in grey. This is a simple illustration of the frequency scaling of our measured signal and also the strength of our signal as compared to possible intra-frequency systematic errors.
• Figure 4: Temperature maps of size $1{\rm deg}^2$ at 545 and 857GHz stacked on the 20,000 brightest peaks (left column), troughs (centre column) and random map locations (right column). The stacked (averaged) temperature maps is in K. The arrows indicate the lensing deflection angle deduced from the gradient of the band-pass filtered lensing potential map stacked on the same peaks. The longest arrow corresponds to a deflection of 6.3 $^{\prime\prime}$, which is only a fraction of the total deflection angle because of our filtering. This stacking allows us to visualize in real space the lensing of the CMB by the galaxies that generate the CIB. A small and expected offset ($\simeq$1) was corrected by hand when displaying the deflection field.
• Figure 5: Naive analytical estimates of the contribution to the $C_\ell^{\mathrm{T}\phi}$ variance as a function of multipole and frequency as given in Eq. \ref{['eqn:error_breakdown']}. We assume the same bin sizes as in Fig. \ref{['fig:nominal_results']}. The different lines are the contribution to the analytical error from the signal only: $C_\ell^{\phi\phi} C_\ell^{\rm CIB} + \left(C_\ell^{{\rm CIB} \phi}\right)^2$ (green), noise only: $\hat{C}_\ell^{\phi\phi,{\rm N}}\hat{C}_\ell^{{\rm CIB,N}}$ (blue), and the mixed signal and noise terms: $C_\ell^{\phi\phi}\hat{C}_\ell^{\rm CIB, N}$ (yellow) and $\hat{C}_\ell^{\phi\phi,{\rm N}} C_\ell^{\rm CIB}$ (orange). The total contribution is the solid black line, and the theory spectrum, $\left(C_\ell^{CIB \phi}\right)^2$, is the dashed line.
• Figure 6: Null tests at 545GHz. Left: difference spectra obtained by nulling the signal in the HR temperature map before correlating it with our nominal $\phi$ reconstruction. Middle: temperature signal nulled using different detectors at 545GHz. Right: temperature signal nulled using the first and second survey maps. The black error bars correspond to the scatter measured within an $\ell$-bin, while the coloured bands correspond to the analytical estimate. Except for the survey null test (see text for details), these tests are passed satisfactorily except, as illustrated by the quoted $\chi^2$ and $N_{\rm dof}$, thus strengthening confidence in our signal.