Constraining neutrino mass with tomographic weak lensing peak counts

Massive cosmic neutrinos change the structure formation history by suppressing perturbations on small scales. Weak lensing data from galaxy surveys probe the structure evolution and thereby can be used to constrain the total mass of the three active neutrinos. However, much of the information is at small scales where the dynamics are nonlinear. Traditional approaches with second-order statistics thus fail to fully extract the information in the lensing field. In this paper, we study constraints on the neutrino mass sum using lensing peak counts, a statistic which captures non-Gaussian information beyond the second order. We use the ray-traced weak lensing mocks from the Cosmological Massive Neutrino Simulations (MassiveNuS) and apply Large Synoptic Survey Telescope-like noise. We discuss the effects of redshift tomography, the multipole cutoff ${\ell }_{\max }$ for the power spectrum, the smoothing scale for the peak counts, and constraints from peaks of different heights. We find that combining peak counts with the traditional lensing power spectrum can improve the constraint on the neutrino mass sum, ${\mathrm{\Omega }}_m$, and $A_s$ by 39%, 32%, and 60%, respectively, over that from the power spectrum alone. We note that observational systematics such as baryonic effects, intrinsic alignments, and photometric redshift errors are not studied in this work, but will be an important next step.

Figure 1

The models (black) used in the MassiveNuS simulations, projected onto 2D planes. The fiducial model $\sum m_{\nu }=0.1\mathrm{eV}$, ${\mathrm{\Omega }}_m=0.3$, $A_s=2.1\times {10}^{-9}$ is highlighted in red.

Figure 2

The fractional interpolation error from the Gaussian process (GP) for peak counts (top panel, black line) and power spectrum (bottom panel, black line). We test the robustness of the interpolation by comparing the true statistic at the fiducial model with that obtained from our GP interpolator (built with the other 100 models). We also show the expected variance of a LSST-like survey (purple line).

Figure 3

Noiseless (left panel) and noisy (right panel) covariance matrices, normalized by the diagonal terms, for the power spectrum (bins 1–120) and peak counts (bins 121–326). We assume LSST noise (Sec. 3). Five source redshifts ($z_s=0.5$, 1, 1.5, 2, 2.5) are shown as the five miniblocks within each statistic.

Figure 4

Left panel: The impact of changes in the cosmological parameters on the noiseless lensing power spectrum at $z=1$, shown as fractional changes from the fiducial model (solid black, $\sum m_{\nu }=0.1\mathrm{eV}$, ${\mathrm{\Omega }}_m=0.3$, $A_s=2.1\times {10}^{-9}$). We generate the other three curves from our Gaussian process interpolator, while keeping the other two parameters fixed. By decreasing $A_s$ or ${\mathrm{\Omega }}_m$, and increasing $\sum m_{\nu }$, we decrease the overall lensing power spectrum, with very subtle changes in the shape of the curve, which explains the degeneracy among these parameters. Right panel: Same as left panel but for the peak counts. Similarly, the three parameters show degenerate behavior. However, a close examination of the bottom panel shows different crossing at $N=N_{\text{fid}}$ for the three parameters, hinting at the potential to break the degeneracy. Also shown in the top left is the amplitude of white noise for $n_{\text{gal}}=40\mathrm{per}{\mathrm{arcmin}}^2$.

Figure 5

The 95% confidence contours from the lensing power spectrum (left panel) and peak counts (right panel) assuming a single source plane at $z=1$ (black lines, “$1z$”) and source planes across five redshifts $z=\{0.5,1,1.52,2.5\}$ (orange lines, “$5z$”), with the total galaxy density held fixed. The fiducial values are shown in gray.

Figure 6

A comparison of cosmological parameter constraints from the lensing power spectrum for different maximum multipoles used in the analysis. The contours represent 95% confidence contours, taking information from multipoles ranging from $300<\ell <{\ell }_{\max }$, with ${\ell }_{\max }=2000$ (black), ${\ell }_{\max }=5000$ (orange), and ${\ell }_{\max }=8000$ (blue). The fiducial values are shown in gray.

Figure 7

Comparison of the power spectrum 95% confidence contours from our simulations (orange) to that from a simple Fisher forecast using Halofit (black).

Figure 8

A comparison of 95% confidence contours from lensing peak counts assuming different smoothing scales at 1 arcmin (orange), 2 arcmin (black), and 5 arcmin (blue). The fiducial values are shown in gray.

Figure 9

We split the peaks into three groups based on their height, separated by $\mathrm{S}/N=1$ and $\mathrm{S}/N=3$, as labeled “low,” “med,” and “high” peaks. We show the single redshift, noiseless peak count spectrum configuration “1z” with 2 arcmin smoothing scale for illustration.

Figure 10

The 95% confidence contours for the low (orange), med (blue), and high (black) peak height bins, as described in Fig. 9. The fiducial values are shown in gray.

Figure 11

The 95% confidence contours from the lensing power spectrum (“PS,” ${\ell }_{\max }=5000$), peak counts (2 arcmin smoothing), and the two combined. We use five tomographic redshift bins. The full covariance is assumed. The fiducial values are shown in gray.

Figure 12

The 95% confidence contours combined with the Planck prior (orange), the weak lensing power spectrum with five source planes (blue), and lensing peak counts with five source planes (black). The fiducial values are shown in gray.

Figure 13

Marginalized constraints on each parameter for forecasts made in this paper, showing the 2.5 and 97.5 percentiles for ${\mathrm{\Omega }}_m$ and $A_s$, as well as the 95% upper bound on $\sum m_{\nu }$. The values are listed in Table 1.