Cluster Gas Mass Research Articles

Non-parametric reconstruction of the fine structure constant with galaxy clusters

Testing possible variations in fundamental constants of nature is a crucial endeavor in observational cosmology. This paper investigates potential cosmological variations in the fine structure constant (α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}) through a non-parametric approach, using galaxy cluster observations as the primary cosmological probe. We employ two methodologies based on galaxy cluster gas mass fraction measurements derived from X-ray and Sunyaev–Zeldovich observations, along with luminosity distances from type Ia supernovae. We also explore how different values of the Hubble constant (H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document}) impact the variation of α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} across cosmic history. When using the Planck satellite’s H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document} observations, a constant α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} is ruled out at approximately the 3σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document} confidence level for z≲0.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z \\lesssim 0.5$$\\end{document}. Conversely, employing local estimates of H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document} restores agreement with a constant α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}.

Unveiling the Hubble constant through galaxy cluster gas mass fractions

In this work, we obtain Hubble constant (H0) estimates by using two galaxy cluster gas mass fraction measurement samples, Type Ia supernovae luminosity distances, and the validity of the cosmic distance duality relation. Notably, the angular diameter distance (ADD) to each galaxy cluster in the samples is determined by combining its gas mass fraction measurement with galaxy clustering observations, more precisely, the Ωb/Ωm ratio. Such a combination results in a H0 estimate that is independent of a specific cosmological framework. In one of the samples, the gas fraction measurements were calculated in spherical shells at radii near r2500 (44 data points), while in the other (103 data points) the measurements were calculated within r500. We find H0=72.7−5.6+6.3 km/s/Mpc at 68% CL for the joint analysis of these data sets. We also investigate the impact on the H0 determination by exploring the precision and number of gas mass fraction data by performing a data Monte Carlo simulation. Our simulations show that future measurements could achieve a precision of up to 5% for H0.

Painting baryons on to N-body simulations of galaxy clusters with image-to-image deep learning

ABSTRACT Galaxy cluster mass functions are a function of cosmology, but mass is not a direct observable, and systematic errors abound in all its observable proxies. Mass-free inference can bypass this challenge, but it requires large suites of simulations spanning a range of cosmologies and models for directly observable quantities. In this work, we devise a U-net – an image-to-image machine learning algorithm – to ‘paint’ the illustristng model of baryons on to dark matter-only (DMO) simulations of galaxy clusters. Using 761 galaxy clusters with M200c ≳ 1014 M⊙ from the TNG300 simulation at z < 1, we train the algorithm to read in maps of projected dark matter mass and output maps of projected gas density, temperature, and X-ray flux. Despite being trained on individual images, the model reproduces the true scaling relation and scatter for the MDM–LX, as well as the distribution functions of the cluster X-ray luminosity and gas mass. For just one decade in cluster mass, the model reproduces three orders of magnitude in LX. The model is biased slightly high when using dark matter maps from the DMO simulation. The model performs well on inputs from TNG300-2, whose mass resolution is eight times coarser; further degrading the resolution biases the predicted luminosity function high. We conclude that U-net-based baryon painting is a promising technique to build large simulated cluster catalogues, which can be used to improve cluster cosmology by combining existing full-physics and large N-body simulations.

Observational constraints on varying fundamental constants in a minimal CPC model

ABSTRACT A minimal model based on the Co-varying Physical Couplings (CPC) framework for gravity is proposed. The CPC framework is based on the assumptions of a metric-compatible four-dimensional Riemannian manifold, where a covariantly conserved stress-energy tensor acts as source of the field equations, which are formally the same as Einstein field equations, but where the couplings {G, c, Λ} are allowed to vary simultaneously. The minimal CPC model takes Λ as a genuine constant while c and G vary in an entangled way that is consistent with Bianchi identity and the aforementioned assumptions. The model is constrained using the most recent galaxy cluster gas mass fraction observational data. Our result indicates that the functions c(z) and G (z) = G0 (c/c0)4 are compatible with constant couplings for the two different parametrizations of c = c(z) adopted here.

A test of the standard dark matter density evolution law using galaxy clusters and cosmic chronometers

In this paper, we implement a test of the standard law for the dark matter density evolution as a function of redshift. For this purpose, only a flat universe and the validity of the FRW metric are assumed. A deformed dark matter density evolution law is considered, given by rho _c(z) propto (1+z)^{3+epsilon }, and constraints on epsilon are obtained by combining the galaxy cluster gas mass fractions with cosmic chronometers measurements. We find that epsilon =0 within 2sigma c.l., in full agreement with other recent analyses.

A search for the variation of speed of light using galaxy cluster gas mass fraction measurements

In this paper, we implement a new method to test the invariance of the speed of light (c) as a function of redshift, by combining the measurements of galaxy cluster gas mass fraction, H(z) from cosmic chronometers, and Type-Ia supernovae (SNe Ia). In our analyses, we consider both a constant depletion factor (which corresponds to the ratio by which the cluster gas mass fraction is depleted with respect to the universal baryonic mean) and one varying with redshift. We also consider the influence of different H 0 estimates on our results. We look for a variation of c, given by c(z) = c 0(1+c 1 z). We find a degeneracy between our final results on c variation and the assumptions on the gas mass fraction depletion factor. Most of our analyses indicate negligible variation ofthe speed of light.

Galaxy clusters, cosmic chronometers and the Einstein equivalence principle

The Einstein equivalence principle in the electromagnetic sector can be violated in modifications of gravity theory generated by a multiplicative coupling of a scalar field to the electromagnetic Lagrangian. In such theories, deviations of the standard result for the cosmic distance duality relation, and a variation of the fine structure constant are expected and are unequivocally intertwined. In this paper, we search for these possible cosmological signatures by using galaxy cluster gas mass fraction measurements and cosmic chronometers. No significant departure from general relativity is found regardless of our assumptions about cosmic curvature or a possible depletion factor evolution in cluster measurements.

Outflows from Super Star Clusters in the Central Starburst of NGC 253

Abstract Young massive clusters play an important role in the evolution of their host galaxies, and feedback from the high-mass stars in these clusters can have profound effects on the surrounding interstellar medium. The nuclear starburst in the nearby galaxy NGC 253 at a distance of 3.5 Mpc is a key laboratory in which to study star formation in an extreme environment. Previous high-resolution (1.9 pc) dust continuum observations from the Atacama Large Millimeter/submillimeter Array (ALMA) discovered 14 compact, massive super star clusters (SSCs) still in formation. We present here ALMA data at 350 GHz with 28 mas (0.5 pc) resolution. We detect blueshifted absorption and redshifted emission (P-Cygni profiles) toward three of these SSCs in multiple lines, including CS 7−6 and H13CN 4−3, which represent direct evidence for previously unobserved outflows. The mass contained in these outflows is a significant fraction of the cluster gas masses, which suggests we are witnessing a short but important phase. Further evidence of this is the finding of a molecular shell around the only SSC visible at near-IR wavelengths. We model the P-Cygni line profiles to constrain the outflow geometry, finding that the outflows must be nearly spherical. Through a comparison of the outflow properties with predictions from simulations, we find that none of the available mechanisms completely explains the observations, although dust-reprocessed radiation pressure and O star stellar winds are the most likely candidates. The observed outflows will have a very substantial effect on the clusters’ evolution and star formation efficiency.

Cosmological Constraints from Galaxy Cluster Sparsity, Cluster Gas Mass Fraction, and Baryon Acoustic Oscillation Data

Abstract In recent years, the availability of large, complete cluster samples has enabled numerous cosmological parameter inference analyses using cluster number counts. These have provided constraints on the cosmic matter density Ω m and the amplitude of matter density fluctuations σ 8 alternative to that obtained from other standard probes. However, systematics uncertainties, such as the mass calibration bias and selection effects, may still significantly affect these data analyses. Hence, it is timely to explore other proxies of galaxy cluster cosmology that can provide cosmological constraints complementary to those obtained from cluster number counts. Here we use measurements of the cluster sparsity from weak-lensing mass estimates of the LC2-single and HSC-XXL cluster catalogs to infer constraints on a flat ΛCDM model. The cluster sparsity has the advantage of being insensitive to selection and mass calibration bias. On the other hand, it primarily constrains a degenerate combination of Ω m and σ 8 (along approximately constant curves of and, to a lesser extent, the reduced Hubble parameter h. Hence, in order to break the internal parameter degeneracies, we perform a combined likelihood analysis of the cluster sparsity estimates with cluster gas mass fraction measurements and BAO data. We find marginal constraints that are competitive with those from other standard cosmic probes: Ω m = 0.316 ± 0.013, σ 8 = 0.757 ± 0.067 (corresponding to S 8 = 0.776 ± 0.064), and h = 0.696 ± 0.017 at 1σ. Moreover, assuming a conservative Gaussian prior on the mass bias of gas mass fraction data, we find a lower limit on the gas depletion factor Y b,500c ≳ 0.89.

A model-independent test of the evolution of gas depletion factor for SPT-SZ and Planck ESZ clusters

The gas mass fraction in galaxy clusters has been widely used to determine cosmological parameters. This method assumes that the ratio of the cluster gas mass fraction to the cosmic baryon fraction (gamma (z)) is constant as a function of redshift. In this work, we look for a time evolution of gamma (z) at R_{500} by using both the SPT-SZ and Planck Early SZ (ESZ) cluster data, in a model-independent fashion without any explicit dependence on the underlying cosmology. For this calculation, we use a non-parametric functional form for the Hubble parameter obtained from Gaussian Process regression using cosmic chronometers. We parameterize gamma (z) as: gamma (z)= gamma _0(1+gamma _1 z) to constrain the redshift evolution. We find contradictory results between both the samples. For SPT-SZ, gamma (z) decreases as a function of redshift (at more than 5sigma ), whereas a positive trend with redshift is found for Planck ESZ data (at more than 4sigma ). We however find that the gamma _1 values for a subset of SPT-SZ and Planck ESZ clusters between the same redshift interval agree to within 1sigma . When we allow for a dependence on the halo mass in the evolution of the gas depletion factor, the 4-5sigma discrepancy reduces to 2sigma .

A low Hubble constant from galaxy distribution observations

An accurate determination of the Hubble constant remains a puzzle in observational cosmology. The possibility of a new physics has emerged with a significant tension between the current expansion rate of our Universe measured from the cosmic microwave background by the Planck satellite and from local methods. In this paper, new tight estimates on this parameter are obtained by considering two data sets from galaxy distribution observations: galaxy cluster gas mass fractions and baryon acoustic oscillation measurements. Priors from the Big Bang nucleosynthesis (BBN) were also considered. By considering the flat ΛCDM and XCDM models, and the non-flat ΛCDM model, our main results are: H0=65.9+1.5−1.5 km s−1 Mpc−1, H0=65.9+4.4−4.0 km s−1 Mpc−1 and H0=64.3+ 4.5− 4.4 km s−1 Mpc−1 in 2σ c.l., respectively. These estimates are in full agreement with the Planck satellite results. Our analyses in these cosmological scenarios also support a negative value for the deceleration parameter at least in 3σ c.l. .

Sunyaev–Zel’dovich effect and X-ray scaling relations from weak lensing mass calibration of 32 South Pole Telescope selected galaxy clusters

Uncertainty in the mass-observable scaling relations is currently the limiting factor for galaxy cluster based cosmology. Weak gravitational lensing can provide a direct mass calibration and reduce the mass uncertainty. We present new ground-based weak lensing observations of 19 South Pole Telescope (SPT) selected clusters at redshifts $0.29 \leq z \leq 0.61$ and combine them with previously reported space-based observations of 13 galaxy clusters at redshifts $0.576 \leq z \leq 1.132$ to constrain the cluster mass scaling relations with the Sunyaev-Zel'dovich effect (SZE), the cluster gas mass \mgas, and \yx, the product of \mgas\ and X-ray temperature. We extend a previously used framework for the analysis of scaling relations and cosmological constraints obtained from SPT-selected clusters to make use of weak lensing information. We introduce a new approach to estimate the effective average redshift distribution of background galaxies and quantify a number of systematic errors affecting the weak lensing modelling. These errors include a calibration of the bias incurred by fitting a Navarro-Frenk-White profile to the reduced shear using $N$-body simulations. We blind the analysis to avoid confirmation bias. We are able to limit the systematic uncertainties to 5.6% in cluster mass (68% confidence). Our constraints on the mass--X-ray observable scaling relations parameters are consistent with those obtained by earlier studies, and our constraints for the mass--SZE scaling relation are consistent with the simulation-based prior used in the most recent SPT-SZ cosmology analysis. We can now replace the external mass calibration priors used in previous SPT-SZ cosmology studies with a direct, internal calibration obtained on the same clusters.

A Model for Protostellar Cluster Luminosities and the Impact on the CO–H2 Conversion Factor

Abstract We construct a semianalytic model to study the effect of far-ultraviolet (FUV) radiation on gas chemistry from embedded protostars. We use the protostellar luminosity function (PLF) formalism of Offner & McKee to calculate the total, FUV, and ionizing cluster luminosity for various protostellar accretion histories and cluster sizes. We2 compare the model predictions with surveys of Gould Belt star-forming regions and find that the tapered turbulent core model matches best the mean luminosities and the spread in the data. We combine the cluster model with the photodissociation region astrochemistry code, 3d-pdr, to compute the impact of the FUV luminosity from embedded protostars on the CO-to-H2 conversion factor, X CO, as a function of cluster size, gas mass, and star formation efficiency. We find that X CO has a weak dependence on the FUV radiation from embedded sources for large clusters owing to high cloud optical depths. In smaller and more efficient clusters the embedded FUV increases X CO to levels consistent with the average Milky Way values. The internal physical and chemical structures of the cloud are significantly altered, and X CO depends strongly on the protostellar cluster mass for small efficient clouds.

Is the non-isothermal double β-model incompatible with no time evolution of galaxy cluster gas mass fraction?

In this paper, we propose a new method to obtain the depletion factor γ(z), the ratio by which the measured baryon fraction in galaxy clusters is depleted with respect to the universal mean. We use exclusively galaxy cluster data, namely, X-ray gas mass fraction (fgas) and angular diameter distance measurements from Sunyaev–Zel’dovich effect plus X-ray observations. The galaxy clusters are the same in both data set and the non-isothermal spherical double β-model was used to describe their electron density and temperature profiles. In order to compare our results with those from recent cosmological hydrodynamical simulations, we suppose a possible time evolution for γ(z), such as, γ(z)=γ0(1+γ1z). As main conclusions we found that: the γ0 value is in full agreement with the simulations. On the other hand, although the γ1 value found in our analysis is compatible with γ1=0 within 2σ c.l., our results show a non-negligible time evolution for the depletion factor, unlike the results of the simulations. However, we also put constraints on γ(z) by using the fgas measurements and angular diameter distances obtained from the flat ΛCDM model (Planck results) and from a sample of galaxy clusters described by an elliptical profile. For these cases no significant time evolution for γ(z) was found. Then, if a constant depletion factor is an inherent characteristic of these structures, our results show that the spherical double β-model used to describe the galaxy clusters considered does not affect the quality of their fgas measurements.

Weighing the giants– V. Galaxy cluster scaling relations

We present constraints on the scaling relations of galaxy cluster X-ray luminosity, temperature and gas mass (and derived quantities) with mass and redshift, employing masses from robust weak gravitational lensing measurements. These are the first such results obtained from an analysis that simultaneously accounts for selection effects and the underlying mass function, and directly incorporates lensing data to constrain total masses. Our constraints on the scaling relations and their intrinsic scatters are in good agreement with previous studies, and reinforce a picture in which departures from self-similar scaling laws are primarily limited to cluster cores. However, the data are beginning to reveal new features that have implications for cluster astrophysics and provide new tests for hydrodynamical simulations. We find a positive correlation in the intrinsic scatters of luminosity and temperature at fixed mass, which is related to the dynamical state of the clusters. While the evolution of the nominal scaling relations over the redshift range $0.0<z<0.5$ is consistent with self similarity, we find tentative evidence that the luminosity and temperature scatters respectively decrease and increase with redshift. Physically, this likely related to the development of cool cores and the rate of major mergers. We also examine the scaling relations of redMaPPer richness and Compton $Y$ from Planck. While the richness--mass relation is in excellent agreement with recent work, the measured $Y$--mass relation departs strongly from that assumed in the Planck cluster cosmology analysis. The latter result is consistent with earlier comparisons of lensing and Planck scaling-relation-derived masses.

Galaxy cluster scaling relations measured with APEX-SZ

We present thermal Sunyaev-Zel'dovich effect (SZE) measurements for 42 galaxy clusters observed at 150 GHz with the APEX-SZ experiment. For each cluster, we model the pressure profile and calculate the integrated Comptonization $Y$ to estimate the total thermal energy of the intracluster medium (ICM). We compare the measured $Y$ values to X-ray observables of the ICM from the literature (cluster gas mass $M_{\rm{gas}}$, temperature $T_X$, and $Y_X =M_{\rm{gas}}T_X$) that relate to total cluster mass. We measure power law scaling relations, including an intrinsic scatter, between the SZE and X-ray observables for three subsamples within the set of 42 clusters that have uniform X-ray analysis in the literature. We observe that differences between these X-ray analyses introduce significant variability into the measured scaling relations, particularly affecting the normalization. For all three subsamples, we find results consistent with a self-similar model of cluster evolution dominated by gravitational effects. Comparing to predictions from numerical simulations, these scaling relations prefer models that include cooling and feedback in the ICM. Lastly, we measure an intrinsic scatter of $\sim28$ per cent in the $Y-Y_X\,$ scaling relation for all three subsamples.

Cosmology and astrophysics from relaxed galaxy clusters – IV. Robustly calibrating hydrostatic masses with weak lensing

This is the fourth in a series of papers studying the astrophysics and cosmology of massive, dynamically relaxed galaxy clusters. Here, we use measurements of weak gravitational lensing from the Weighing the Giants project to calibrate Chandra X-ray measurements of total mass that rely on the assumption of hydrostatic equilibrium. This comparison of X-ray and lensing masses provides a measurement of the combined bias of X-ray hydrostatic masses due to both astrophysical and instrumental sources. Assuming a fixed cosmology, and within a characteristic radius (r_2500) determined from the X-ray data, we measure a lensing to X-ray mass ratio of 0.96 +/- 9% (stat) +/- 9% (sys). We find no significant trends of this ratio with mass, redshift or the morphological indicators used to select the sample. In accordance with predictions from hydro simulations for the most massive, relaxed clusters, our results disfavor strong, tens-of-percent departures from hydrostatic equilibrium at these radii. In addition, we find a mean concentration of the sample measured from lensing data of c_200 = $3.0_{-1.8}^{+4.4}$. Anticipated short-term improvements in lensing systematics, and a modest expansion of the relaxed lensing sample, can easily increase the measurement precision by 30--50%, leading to similar improvements in cosmological constraints that employ X-ray hydrostatic mass estimates, such as on Omega_m from the cluster gas mass fraction.

Testing the gas mass density profile of galaxy clusters with distance duality relation

In this paper, assuming the validity of distance duality relation, $\eta=D_L(z)(1+z)^{-2}/D_A(z)=1$, where $D_A(z)$ and $D_L(z)$ are the angular and the luminosity distance respectively, we explore two kinds of gas mass density profiles of clusters: the isothermal $\beta$ model and the non-isothermal double-$\beta$ model. In our analysis, performed on 38 massive galaxy clusters observed by \textit{Chandra} (within the redshift range of $0.14<z<0.89$), we use two types of cluster gas mass fraction data corresponding to different mass density profiles fitted to the X-ray data. Using two general parameterizations of $\eta(z)$ (phenomenologically allowing for distance duality violation), we find that the non-isothermal double-$\beta$ model agrees better with the distance duality relation, while the isothermal $\beta$ model tends to be marginally incompatible with the Etherington theorem at 68.3% CL. However, current accuracy of the data does not allow to distinguish between the two models for the gas-density distribution at a significant level.

Testing X-ray measurements of galaxy cluster gas mass fraction using the cosmic distance-duality relation

We propose a consistency test for some recent X-ray gas mass fraction (fgas) measurements in galaxy clusters, using the cosmic distance-duality relation, ηtheory = DL(1 + z)−2/DA, with luminosity distance (DL) data from the Union2 compilation of type Ia supernovae. We set ηtheory ≡ 1, instead of assigning any redshift parameterizations to it, and constrain the cosmological information preferred by fgas data along with supernova observations. We adopt a new binning method in the reduction of the Union2 data, in order to minimize the statistical errors. Four data sets of X-ray gas mass fraction, which are reported by Allen et al. (two samples), LaRoque et al. and Ettori et al., are analyzed in detail in the context of two theoretical models of fgas. The results from the analysis of Allen et al.'s samples demonstrate the feasibility of our method. It is found that the preferred cosmology by LaRoque et al.'s sample is consistent with its reference cosmology within the 1σ confidence level. However, for Ettori et al.'s fgas sample, the inconsistency can reach more than a 3σ confidence level and this dataset shows special preference to an ΩΛ = 0 cosmology.

Optimizing observational strategy for futurefgasconstraints

The Planck cluster catalog is expected to contain of order one thousand galaxy clusters, both newly discovered and previously known, detected through the Sunyaev-Zeldovich effect over the redshift range $0\ensuremath{\lesssim}z\ensuremath{\lesssim}1$. Follow-up x-ray observations of a dynamically relaxed subsample of newly discovered Planck clusters will improve constraints on the dark energy equation of state found through measurement of the cluster gas mass fraction (${f}_{\mathrm{gas}}$). In view of follow-up campaigns with XMM-Newton and Chandra satellites, we determine the optimal redshift distribution of a cluster sample to most tightly constrain the dark energy equation of state. The distribution is nontrivial even for the standard ${w}_{0}\mathrm{\text{\ensuremath{-}}}{w}_{\mathrm{a}}$ parametrization. We then determine how much the combination of expected data from the Planck satellite and ${f}_{\mathrm{gas}}$ data will be able to constrain the dark energy equation of state. Our analysis employs a Markov Chain Monte Carlo method as well as a Fisher Matrix analysis. With a suitably large program of observational time to observe only hot relaxed clusters, we find that these upcoming data would be able to improve the figure of merit by at least a factor two.