Cluster Cosmology Constraints from the 2500 deg$^2$ SPT-SZ Survey: Inclusion of Weak Gravitational Lensing Data from Magellan and the Hubble Space Telescope (1812.01679v2)

Abstract: We derive cosmological constraints using a galaxy cluster sample selected from the 2500~deg$^2$ SPT-SZ survey. The sample spans the redshift range $0.25< z<1.75$ and contains 343 clusters with SZ detection significance $\xi>5$. The sample is supplemented with optical weak gravitational lensing measurements of 32 clusters with $0.29<z<1.13$ (from Magellan and HST) and X-ray measurements of 89 clusters with $0.25<z<1.75$ (from Chandra). We rely on minimal modeling assumptions: i) weak lensing provides an accurate means of measuring halo masses, ii) the mean SZ and X-ray observables are related to the true halo mass through power-law relations in mass and dimensionless Hubble parameter $E(z)$ with a-priori unknown parameters, iii) there is (correlated, lognormal) intrinsic scatter and measurement noise relating these observables to their mean relations. We simultaneously fit for these astrophysical modeling parameters and for cosmology. Assuming a flat $\nu\Lambda$CDM model, in which the sum of neutrino masses is a free parameter, we measure $\Omega_\mathrm{m}=0.276\pm0.047$, $\sigma_8=0.781\pm0.037$, and $\sigma_8(\Omega_\mathrm{m}/0.3)^{0.2}=0.766\pm0.025$. The redshift evolution of the X-ray $Y_\mathrm{X}$-mass and $M_\mathrm{gas}$-mass relations are both consistent with self-similar evolution to within $1\sigma$. The mass-slope of the $Y_\mathrm{X}$-mass relation shows a $2.3\sigma$ deviation from self-similarity. Similarly, the mass-slope of the $M_\mathrm{gas}$-mass relation is steeper than self-similarity at the $2.5\sigma$ level. In a $\nu w$CDM cosmology, we measure the dark energy equation of state parameter $w=-1.55\pm0.41$ from the cluster data. We perform a measurement of the growth of structure since redshift $z\sim1.7$ and find no evidence for tension with the prediction from General Relativity. We provide updated redshift and mass estimates for the SPT sample. (abridged)

• The paper derives new cosmological constraints on parameters like Ωₘ, σ₈, and w using SPT-SZ clusters and direct weak-lensing mass calibration.
• The study identifies significant deviations in scaling relations, particularly in the X-ray Yₓ–mass and M_gas–mass slopes, compared to self-similar expectations.
• The integration of diverse datasets, including Magellan and Hubble weak-lensing observations, sets a robust framework for enhancing future cosmological surveys and neutrino mass assessments.

Cluster Cosmology Constraints from the SPT-SZ Survey with Weak-Lensing Mass Calibration

The paper by Bocquet et al. addresses the derivation of cosmological constraints from a galaxy cluster sample selected through the South Pole Telescope (SPT) SZ survey, supplemented with weak gravitational lensing data from Magellan and the Hubble Space Telescope. The paper involves a comprehensive investigation into the constraints that can be placed on cosmological parameters using cluster observations, leveraging minimal modeling assumptions to minimize potential biases.

Summary of Findings

1. Cosmological Parameters:
   • The analysis primarily focuses on the cosmological parameters $\Omega_\mathrm{m}$, $\sigma_8$, and $w$, assuming both a $\nu\Lambda$CDM and a $\nu w$CDM cosmology.
   • For a flat $\nu\Lambda$CDM model with a free parameter for the sum of neutrino masses, constraints are: $\Omega_\mathrm{m} = 0.276 \pm 0.047$, $\sigma_8 = 0.781 \pm 0.037$, with a specific combination $$\sigma_8 (\Omega_\mathrm{m}/0.3)^{0.2} = 0.766 \pm 0.025$$.
   • The findings include no significant tension with General Relativity predictions for the growth of cosmic structure from $z \sim 1.7$.
2. Weak-Lensing Mass Calibration:
   • This research represents the first analysis of the SPT cluster sample incorporating direct weak-lensing mass calibration, indicating significant advancements from previous analyses that did not have this refinement.
   • The paper also highlights the potential for utilizing the Dark Energy Survey's comprehensive weak-lensing data set in future analyses.
3. Scaling Relations and Cluster Properties:
   • The analysis finds the redshift evolution of the X-ray $Y_\mathrm{X}$--mass relation to be consistent with self-similar evolution to within $1\sigma$. However, the mass-slope of the $Y_\mathrm{X}$--mass relation exhibits a $2.3\sigma$ deviance from self-similarity.
   • Similarly, there's a $2.5\sigma$ divergence in the $M_\mathrm{gas}$--mass relation's mass-slope from self-similarity.
4. Dark Energy Equation of State:
   • Under the $\nu w$CDM cosmology, the dark energy equation of state parameter $w$ is constrained to $w = -1.55 \pm 0.41$. The cluster data suggest a slight deviation from the cosmological constant hypothesis ($w = -1$).
5. Neutrino Mass:
   • The paper presents the measurement results of the sum of neutrino masses, finding a moderate detection with constraints that align with other combined probe results when considering CMB measurements.

Implications and Future Directions

The integration of weak-lensing data with the SPT-SZ cluster sample sets a precedent for more precise cosmological measurements using galaxy clusters, highlighting the instrumental role of diverse astronomical datasets in improving mass calibrations. The demonstrated nuances in scaling relations and the constrained parameters provide a reliable framework for upcoming cosmological surveys.

Future advancements will be inclined towards enhancing weak-lensing mass calibration across a wider redshift range, potentially refining the observed discrepancies in scaling relations. The continually increasing sample size from SZ and weak-lensing surveys is poised to improve constraints on cosmological parameters, neutrino mass, and growth of cosmic structure, offering deeper insights into dark energy dynamics and the fundamental nature of the universe.

This paper not only strengthens our understanding of cosmological observations derived from clusters but also extends the methodological landscape for employing weak gravitational lensing as a robust calibration tool in cosmology. This work lays the groundwork for further integration with ongoing large-scale surveys, which will likely reveal further intricacies regarding the universe's structure and fundamental forces.