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Cosmological Constraints from Sunyaev-Zel'dovich-Selected Clusters with X-ray Observations in the First 178 Square Degrees of the South Pole Telescope Survey

B. A. Benson, T. de Haan, J. P. Dudley, C. L. Reichardt, K. A. Aird, K. Andersson, R. Armstrong, M. Bautz, M. Bayliss, G. Bazin, L. E. Bleem, M. Brodwin, J. E. Carlstrom, C. L. Chang, H. M. Cho, A. Clocchiatti, T. M. Crawford, A. T. Crites, S. Desai, M. A. Dobbs, R. J. Foley, W. R. Forman, E. M. George, M. D. Gladders, N. W. Halverson, F. W. High, G. P. Holder, W. L. Holzapfel, S. Hoover, J. D. Hrubes, C. Jones, M. Joy, R. Keisler, L. Knox, A. T. Lee, E. M. Leitch, J. Liu, M. Lueker, D. Luong-Van, A. Mantz, D. P. Marrone, M. McDonald, J. J. McMahon, J. Mehl, S. S. Meyer, L. Mocanu, J. J. Mohr, T. E. Montroy, S. S. Murray, T. Natoli, S. Padin, T. Plagge, C. Pryke, A. Rest, J. Ruel, J. E. Ruhl, B. R. Saliwanchik, A. Saro, K. K. Schaffer, L. Shaw, E. Shirokoff, J. Song, H. G. Spieler, B. Stalder, Z. Staniszewski, A. A. Stark, K. Story, C. W. Stubbs, R. Suhada, A. van Engelen, K. Vanderlinde, J. D. Vieira, A. Vikhlinin, R. Williamson, O. Zahn, A. Zenteno

TL;DR

This paper presents a self-consistent framework to constrain cosmology by jointly modeling SZ and X-ray cluster observables and their mass scaling relations, while explicitly accounting for the SZ selection function. Applying the method to 18 SZ-selected clusters with X-ray follow-up in the first 178 deg$^2$ of the SPT-SZ survey, it achieves a ΛCDM constraint of $\sigma_8(\Omega_m/0.25)^{0.30}=0.785\pm0.037$ and, when combined with CMB data, $\sigma_8=0.795\pm0.016$ and $\Omega_m=0.255\pm0.016$, representing a ~1.5x improvement over CMB alone. The analysis also explores extensions to ΛCDM, finding tightened constraints on the dark energy equation of state $w$, the sum of neutrino masses $\Sigma m_\nu$, and the effective number of relativistic species $N_{\mathrm{eff}}$, with $w=-0.973\pm0.063$ and $\Sigma m_\nu<0.28$ eV (95% CL) when including external data. The work demonstrates that incorporating X-ray mass calibration with SZ data significantly reduces mass calibration systematics and will enable even stronger cosmological tests with the full SPT-SZ survey, especially when complemented by weak-lensing and dynamical mass measurements. The methodology provides a generalizable path to combine multiple cluster observables for robust cosmology and scaling-relations constraints.

Abstract

We use measurements from the South Pole Telescope (SPT) Sunyaev Zel'dovich (SZ) cluster survey in combination with X-ray measurements to constrain cosmological parameters. We present a statistical method that fits for the scaling relations of the SZ and X-ray cluster observables with mass while jointly fitting for cosmology. The method is generalizable to multiple cluster observables, and self-consistently accounts for the effects of the cluster selection and uncertainties in cluster mass calibration on the derived cosmological constraints. We apply this method to a data set consisting of an SZ-selected catalog of 18 galaxy clusters at z > 0.3 from the first 178 deg2 of the 2500 deg2 SPT-SZ survey, with 14 clusters having X-ray observations from either Chandra or XMM. Assuming a spatially flat LCDM cosmological model, we find the SPT cluster sample constrain sigma_8 (Omega_m/0.25)^0.30 = 0.785 +- 0.037. In combination with measurements of the CMB power spectrum from the SPT and the seven-year WMAP data, the SPT cluster sample constrain sigma_8 = 0.795 +- 0.016 and Omega_m = 0.255 +- 0.016, a factor of 1.5 improvement on each parameter over the CMB data alone. We consider several extensions beyond the LCDM model by including the following as free parameters: the dark energy equation of state (w), the sum of the neutrino masses (sum mnu), the effective number of relativistic species (Neff), and a primordial non-Gaussianity (fNL). We find that adding the SPT cluster data significantly improves the constraints on w and sum mnu beyond those found when using measurements of the CMB, supernovae, baryon acoustic oscillations, and the Hubble constant. Considering each extension independently, we best constrain w=-0.973 +- 0.063 and the sum of neutrino masses sum mnu < 0.28 eV at 95% confidence, a factor of 1.25 and 1.4 improvement, respectively, over the constraints without clusters. [abbrev.]

Cosmological Constraints from Sunyaev-Zel'dovich-Selected Clusters with X-ray Observations in the First 178 Square Degrees of the South Pole Telescope Survey

TL;DR

This paper presents a self-consistent framework to constrain cosmology by jointly modeling SZ and X-ray cluster observables and their mass scaling relations, while explicitly accounting for the SZ selection function. Applying the method to 18 SZ-selected clusters with X-ray follow-up in the first 178 deg of the SPT-SZ survey, it achieves a ΛCDM constraint of and, when combined with CMB data, and , representing a ~1.5x improvement over CMB alone. The analysis also explores extensions to ΛCDM, finding tightened constraints on the dark energy equation of state , the sum of neutrino masses , and the effective number of relativistic species , with and eV (95% CL) when including external data. The work demonstrates that incorporating X-ray mass calibration with SZ data significantly reduces mass calibration systematics and will enable even stronger cosmological tests with the full SPT-SZ survey, especially when complemented by weak-lensing and dynamical mass measurements. The methodology provides a generalizable path to combine multiple cluster observables for robust cosmology and scaling-relations constraints.

Abstract

We use measurements from the South Pole Telescope (SPT) Sunyaev Zel'dovich (SZ) cluster survey in combination with X-ray measurements to constrain cosmological parameters. We present a statistical method that fits for the scaling relations of the SZ and X-ray cluster observables with mass while jointly fitting for cosmology. The method is generalizable to multiple cluster observables, and self-consistently accounts for the effects of the cluster selection and uncertainties in cluster mass calibration on the derived cosmological constraints. We apply this method to a data set consisting of an SZ-selected catalog of 18 galaxy clusters at z > 0.3 from the first 178 deg2 of the 2500 deg2 SPT-SZ survey, with 14 clusters having X-ray observations from either Chandra or XMM. Assuming a spatially flat LCDM cosmological model, we find the SPT cluster sample constrain sigma_8 (Omega_m/0.25)^0.30 = 0.785 +- 0.037. In combination with measurements of the CMB power spectrum from the SPT and the seven-year WMAP data, the SPT cluster sample constrain sigma_8 = 0.795 +- 0.016 and Omega_m = 0.255 +- 0.016, a factor of 1.5 improvement on each parameter over the CMB data alone. We consider several extensions beyond the LCDM model by including the following as free parameters: the dark energy equation of state (w), the sum of the neutrino masses (sum mnu), the effective number of relativistic species (Neff), and a primordial non-Gaussianity (fNL). We find that adding the SPT cluster data significantly improves the constraints on w and sum mnu beyond those found when using measurements of the CMB, supernovae, baryon acoustic oscillations, and the Hubble constant. Considering each extension independently, we best constrain w=-0.973 +- 0.063 and the sum of neutrino masses sum mnu < 0.28 eV at 95% confidence, a factor of 1.25 and 1.4 improvement, respectively, over the constraints without clusters. [abbrev.]

Paper Structure

This paper contains 33 sections, 7 equations, 8 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Data and Observations
  3. Cluster Data and Observations
  4. SZ Observations and the Cluster Sample
  5. Optical Redshifts
  6. X-ray Observations
  7. External Cosmological Data Sets
  8. Cosmological Analysis
  9. Scaling Relation Parameterization
  10. X-ray: $Y_{X}-M_{500}$
  11. SZ: $\zeta-M_{500}$
  12. Likelihood Model
  13. $\Lambda$CDM Results
  14. Cosmological Constraints
  15. Scaling Relation Constraints
  16. ...and 18 more sections

Figures (8)

  • Figure 1: Assuming a $\Lambda$CDM cosmology, the two-dimensional marginalized constraints on $\sigma_8$ and $\Omega_{m}$. Contours show the 68% and 95% confidence regions for the SPT$_{\hbox{\scriptsize CL}}$+$H_0$+BBN (red), CMB (gray), and CMB+SPT$_{\hbox{\scriptsize CL}}$ (blue) data sets. The black lines are the best-fit constraint (solid) and 68% confidence region (dashed) for the combination of parameters that the SPT$_{\hbox{\scriptsize CL}}$+$H_0$+BBN data set best constrains: $\sigma_8 (\Omega_m/0.25)^{0.30} = 0.785 \pm 0.037$.
  • Figure 2: A plot of the SZ-significance, $\xi$, versus the X-ray observable $Y_{X}$ for the 14 SPT clusters with X-ray measurements. From the CMB+SPT$_{\hbox{\scriptsize CL}}$ data set fit to a $\Lambda$CDM cosmology, we use the best-fit $\zeta-M_{500}$ and $Y_{X}-M_{500}$ scaling relations to calculate the expected form and redshift evolution of the $\xi$-$Y_{X}$ relation (solid-line), where $E_{\rm piv} \equiv E(z=0.6)$. With the best-fit cosmology parameters, we also predict the effective 68 and 95% confidence intervals for the expected distribution of clusters in the $\xi$-$Y_{X}$ plane (red contours). The measured and predicted cluster distribution show qualitatively good agreement.
  • Figure 3: Assuming a $w$CDM cosmology, the two-dimensional marginalized constraints on $w$ and $\sigma_8$. Contours show the 68% and 95% confidence regions for the SPT$_{\hbox{\scriptsize CL}}$+$H_0$+BBN (red) and CMB (gray) data sets.
  • Figure 4: Assuming a $w$CDM cosmology, the constraints on $\Omega_{m}$, $\sigma_8$, and $w$. The plots along the diagonal are the one-dimensional marginalized likelihood. The off-diagonal plots are the two-dimensional marginalized constraints showing the 68% and 95% confidence regions. We show the constraints for the CMB+BAO+SNe (gray, dashed), and CMB+BAO+SNe+SPT$_{\hbox{\scriptsize CL}}$ (green, solid) data sets. The SPT$_{\hbox{\scriptsize CL}}$ data improves the constraints on $\sigma_8$ and $w$, by factors of 1.4 and 1.25, respectively.
  • Figure 5: Assuming a $w$CDM cosmology, the two-dimensional marginalized constraints on $A_{SZ}$ and $\sigma_8$. Contours show the 68% and 95% confidence regions for the SPT$_{\hbox{\scriptsize CL}}$+$H_0$+BBN (red) and CMB+BAO+SNe+SPT$_{\hbox{\scriptsize CL}}$ (green) data sets. The horizontal black dashed line is the center of the theory prior on $A_{SZ}$.
  • ...and 3 more figures