Constraints on massive neutrinos from the pairwise kinematic Sunyaev-Zel’dovich effect

We present the mean pairwise momentum of clusters, as observed through the kinematic Sunyaev-Zel’dovich (kSZ) effect, as a novel probe of massive neutrinos. We find that kSZ measurements with current and upcoming surveys will provide complementary constraints on the sum of neutrino masses from large scale structure and will improve on Planck satellite measurements of the primordial cosmic microwave background (CMB) and CMB lensing. Central to the constraints is a distinctive scale dependency of the kSZ neutrino signature on the mean pairwise momentum of clusters that we do not expect to be mirrored in systematic effects that change the overall amplitude of the signal, like the cluster optical depth. Assuming a minimal $\mathrm{\Lambda }\mathrm{CDM}$ cosmology including massive neutrinos with Planck primordial CMB priors combined with conservative kSZ specifications, we forecast 68% upper limits on the neutrino mass sum of 310, 240, and 110 meV for “Stage II” ($\mathrm{ACTPol}+\mathrm{BOSS}$), “Stage III” (Advanced $\mathrm{ACTPol}+\mathrm{BOSS}$), and “Stage IV” ($\mathrm{CMB}\text{−}\mathrm{S}4+\mathrm{DESI}$) surveys respectively, compared to the Planck alone forecast of 540 meV. These forecasts include the ability to simultaneously constrain the neutrino mass sum and the mass-averaged optical depth of the cluster sample in each redshift bin. If the averaged optical depth of clusters can be measured with few percent accuracy and a lower limiting mass is assumed, the projected kSZ constraints improve further to 100, 85 and 33 meV (Stage II, III and IV). These forecasts represent a conservative estimate of neutrino constraints using cross-correlations of arcminute-resolution CMB measurements and spectroscopic galaxy surveys. More information relevant for neutrino constraints is available from these surveys, such as galaxy clustering, weak lensing, and CMB temperature and polarization.

Figure 1

Upper panel: The mean pairwise cluster velocity, $V(r)$, for different neutrino mass sums, $\sum m_{\nu }$. $V(r)$ is calculated at $z=0.15$ and assuming a minimum cluster mass of $M_{\min }=1\times {10}^{14}{M}_{\odot }$ with other cosmological parameters, including ${\mathrm{\Omega }}_m{h}^2$ and $A_s$, fixed to fiducial values. Here we assume a normal neutrino hierarchy ($m_1\approx m_2\approx 0,m_3\ne 0$). Lower panel: Ratio of the mean pairwise velocity, $V(r)$, for the different scenarios to the fiducial model with $\sum m_{\nu }=0$ (black line in upper panel). Massive neutrinos clearly leave a scale-dependent imprint on $V(r)$, which is highlighted by the different slopes of the lower curves.

Figure 2

Ratio of the mean pairwise velocity, $V(r)$, for the different neutrino models to the normal hierarchy ($m_1<m_2\ll m_3$), $V(r{)}^{\text{norm}}$. The inverted hierarchy ($m_3\ll m_1\simeq m_2$) deviates more strongly from the normal hierarchy assuming a total mass of $\sum m_{\nu }=110\mathrm{meV}$ (blue, dashed-dotted line) than for $\sum m_{\nu }=150\mathrm{meV}$ (red, dashed line). A degenerate model ($m_1\approx m_2\approx m_3$, black, solid line) with $\sum m_{\nu }=150\mathrm{meV}$ exhibits a slightly different behavior from the normal and inverted hierarchies. This shows that there is a mild sensitivity to the different masses of the individual neutrinos even when $\sum m_{\nu }$ is constant.

Figure 3

Constraints on the neutrino mass sum, $\sum m_{\nu }$, versus the matter density, ${\mathrm{\Omega }}_m{h}^2$ (left); the dark energy equation of state, $w_0$ (middle); and its evolution, $w_a$ (right). Contours show 2D 68% confidence levels for the following data sets: Planck (black), Planck and kSZ Stage IV (blue), Planck including CMB lensing (green), and Planck including CMB lensing plus kSZ Stage IV(red). Solid lines assume no prior on the average cluster optical depth evolution, $b_{\tau }(z)$, while dashed lines assume a 1% prior on $b_{\tau }(z)$.

Figure 4

The impact of imposing a prior on a potential systematic offset in the mass-averaged optical depth, parametrized by a multiplicative bias in each redshift bin, $b_{\tau }(\mathrm{z})$, for Stage II (blue), Stage III (green) and Stage IV (red) surveys, on the $1\text{−}\sigma$ constraints on $\sum m_{\nu }$. This assumes a mass cutoff of $M_{\min }=4\times {10}^{13}{M}_{\odot }$ for Stage II and III and $M_{\min }=1\times {10}^{13}{M}_{\odot }$ for Stage IV as well as including CMB temperature and polarization priors. This shows that $\sum m_{\nu }$ constraints are more weakly dependent on $\tau$ than the dark energy and gravity parameters studied in [17].