text:
\section{\label{sec:level1}First-level heading}

\section{Introduction}

Galaxy clusters are the most massive virialized objects in the universe and provide wonderful laboratories for studying a wide range of topics from galaxy evolution to cosmology~\cite{Vikhlininrev,allen11} to fundamental Physics~\cite{Desai}.  They  are also key in pinning down the dark energy equation of state, as they probe both the geometry of the Universe and the growth of structure~\cite{Huterer,Weinberg}. Galaxy clusters are   therefore, one of the flagship probes for Stage IV dark energy experiments~\cite{Albrecht}. In the past two decades, a large number of galaxy clusters have been discovered upto very high redshifts, thanks to myriad multi-wavelength surveys, which have greatly facilitated these  science goals.

Since galaxy clusters are the largest gravitationally bound objects, their matter content present in the intracluster medium has provided a powerful probe to constrain the cosmological parameters. The X-ray emitting gas in the intra-cluster medium  dominates the baryon budget in clusters. The idea of using the gas mass fraction as a cosmological tool was first introduced by White et al~\cite{white93}.  The gas mass fraction, which is defined as $f_{gas} \equiv M_{gas} / M_{tot}$ is expected to  match closely  the cosmic baryon fraction, viz. $\Omega_b / \Omega_m$, where $\Omega_b$ and  $\Omega_m$ are the cosmic baryon density and total matter density respectively, in units of critical density ($\rho_c$).
There have been a large number of studies, constraining the matter density ($\Omega_m$), dark energy equation of state parameter ($\omega$), and the curvature density ($\Omega_k$)  using the $f_{gas}$ measurements~\cite{Sasaki96,Pen,lima03,allen02,allen04,allen08,ettori03,ettori09,mantz14}. The $f_{gas}$ test has also been used to test alternatives to $\Lambda$CDM such as $R_h=ct$ universe~\cite{Melia16}. The main assumption in these studies is that  the gas fraction doesn't evolve with redshift for hot, massive and relatively relaxed clusters.
However, the  evolution  of $f_{gas}$  as a function of redshift needs to be determined in a model-independent method, in order to probe the robustness of these results.
This evolution is usually parametrized  using the   gas depletion factor $\gamma$, which is the ratio by which the baryonic gas fraction in galaxy cluster gets depleted by the cosmic mean baryon fraction, and is given by: $\gamma  =  f_{gas} (\Omega_b / \Omega_m)^{-1}$~\cite{allen08}. So the study of gas depletion factor and it's evolution with redshift  play a pivotal  role in the  robustness of  the $f_{gas}$ test. As argued in ~\cite{holanda1706}, the results for  the gas depletion factor obtained using only  the data could  then be used as a prior for any cosmology studies with $f_{gas}$.

Therefore, a large number of studies have been undertaken using both simulations and data to test the variation  of the gas depletion factor $\gamma(z)$ as a function of redshift. This evolution  is usually  modeled using the following function.
\begin{equation}
    \gamma(z)= \gamma_0(1+\gamma_1 z)
    \label{eq:gammavariation}
\end{equation}
 where $\gamma_0$ is the normalization factor and $\gamma_1$ represents the evolution of gas depletion factor with redshift.

Battaglia et al~\cite{battaglia13} studied the measurement biases of $f_{gas}$ using   hydrodynamical simulations including different kinds of processes like star formation, AGN feedback and radiative physics. They found a constant gas mass fraction at $R_{500}.$\footnote{$R_{500}$ is the radius at which the mass density is 500 times the critical density for Einstein-DeSitter universe~\cite{White01}.}
Thereafter, Planelles et al~\cite{planelles13} studied the baryon fraction within $R_{2500}$, $R_{500}$, and $R_{200}$ by using three different suites of  simulations of  galaxy clusters in the redshift range $0 \leqslant z \leqslant 1$ for different physical processes in clusters. The first set of simulations (NR) involved non-radiative  hydrodynamical simulations. The second suite (CSF)  studied  the effects of cooling,  supernovae feedback, and star formation. Finally the third set of simulations (AGN) included the same physics as CSF, along with   AGN feedback. Furthermore, they discussed the baryon  and gas depletion factor and its dependence on the  cluster radius, redshift and baryonic physics. They concluded that the evolution of the depletion factor is negligible with redshift (for $z < 1$) regardless of the cluster radius and baryonic physics. This aforementioned work obtained: $\gamma_0 = 0.79\pm0.07$ and $\gamma_1 = 0.07\pm0.12$ at $R_{2500}$, $\gamma_0 = 0.85\pm0.03$ and $\gamma_1 = 0.02\pm0.05$ at $R_{500}$, $\gamma_0 = 0.86\pm0.02$ and $\gamma_1 = 0.00\pm0.04$ at $R_{200}$~\cite{planelles13}. We note that all these aforementioned simulations assumed $\Lambda$CDM as the base cosmological model.

Holanda et al.~\cite{holanda1706} made the first attempt to study the gas depletion factor using only  observations. They carried out an analysis using 40 $f_{gas}$ measurements~\cite{mantz14} observed by the Chandra X-ray telescope spanning the redshift range $0.078 \leqslant z \leqslant 1.063$ characterized as massive, morphologically relaxed systems and with $kT \geqslant 5$~keV. In their work, $f_{gas}$ measurements were obtained from inside a shell with radii between (0.8 - 1.2) $R_{2500}$. Their analysis assumed the validity of cosmic distance duality relation (CDDR)~\cite{ellis07}, and  the use of different distance indicators, e.g. Type Ia SNe (from Union 2.1 and JLA compilation) and $\Lambda$CDM model.  They  obtained  $\gamma_0 = 0.86\pm0.04$ and  $\gamma_1 = -0.04\pm0.12$~\cite{holanda1706}.  Therefore, their analysis showed no evolution of  the gas depletion factor with redshift.

Then, in a followup work, ~\citet{holanda1711} used 38 Chandra X-ray  $f_{gas}$ measurements  from~\cite{laRoque06} in the redshift range $0.14 \leqslant z \leqslant 0.89$, along with angular diameter distances from X-ray/SZ measurements. Unlike ~\cite{holanda1706}, they did not use CDDR to derive the angular diameter distance. They reported $\gamma_0$ =  $0.76\pm0.14$ and $\gamma_1$ = $-0.42_{-0.40}^{+0.42}$ at $R_{2500}$, which also indicates no time evolution for the  gas depletion factor.

Most recently, ~\citet{zheng19} (Z19, hereafter) did a similar study using data for 182 clusters with  the SZ~\cite{SZ,birki,carl} selected sample from the  Atacama Cosmology Telescope Polarization experiment (ACTPol) spanning the redshift range $0.1 \leqslant z \leqslant 1.4$~\cite{actpol}.  The main difference between Z19 and the previous works~\cite{holanda1706,holanda1711} is that Z19 considered the data at $R_{500}$, whereas the latter considered $R_{2500}$.
However,  Z19
did not use direct $f_{gas}$ measurements, but instead
resorted to  a  semi-empirical relation between  the gas mass fraction   and the total cluster mass~\cite{vikhlinin09}. To estimate the angular diameter distance (needed for the estimation of the  gas depletion factor), a model-independent approach using Gaussian Processes regression was used. They reported that the  gas depletion factor decreases as a function of redshift.
Similar to Z19, we study  the evolution of  the gas depletion factor for two different SZ selected cluster samples. The first set comprises  a sample 94 South Pole Telescope (SPT) selected clusters in the redshift range $0.278 \leqslant z \leqslant 1.32$, and the second set uses 120 Planck Early SZ (ESZ) data covering the redshift range $0.059 \leqslant z \leqslant 0.546$.

This paper is structured as follows. In section~\ref{sec:sample}, we briefly describe both our cluster samples, and their $f_{gas}$ measurements. In section~\ref{sec:method}, we describe the procedure used to determine the evolution of  gas mass fraction. Our analysis along with results are discussed in section~\ref{sec:analysis}. A discussion of our results can be found in section~\ref{sec:dicussions}. Finally, we conclude in section~\ref{sec:conclusion}.

\section{Galaxy Cluster Sample and their \boldmath$f_{gas}$ measurements}
\label{sec:sample}

\subsection{For SPT-SZ Sample}
The SPT-SZ cluster sample used for this analysis, consists of  91 SPT clusters from~\cite{chiu18} (C18, hereafter) and three additional SPT-SZ clusters: namely SPT-CLJ 0205-5829, SPT-CLJ 0615-5746 and SPT-CLJ2040-5726 from~\cite{chiu16}, giving a total of 94 clusters, with a mass threshold of   $M_{500} \geqslant 2.5 \times 10^{14}$ $M_\odot$, and  in the redshift range of $0.278 \leqslant z \leqslant 1.32$. These clusters  were detected in the  2,500 deg$^2$ South Pole Telescope (SPT) SZ survey~\cite{carlstrom11}. In this work, we used redshifts for each of these clusters from ~\citet{bocquet19}.  The SPT is a 10~m telescope at the South Pole, that  has imaged the sky at three different frequencies, viz. 95 GHz, 150 GHz, and 220 GHz~\cite{carlstrom11}. The SPT collaboration  carried out a 2500 square degree survey between 2007 and 2011 to detect galaxy clusters using the SZ effect.
This SPT-SZ survey detected 516 galaxy clusters with a mass threshold of $3 \times 10^{14} M_{\odot}$ upto redshift of  1.8~\cite{bleem15,bocquet19}. Detailed properties of the SPT  clusters  are discussed in~\cite{bleem15}. Their redshifts  have been obtained using survey data as well as   pointed spectroscopic and photometric observations~\cite{song12,ruel14,bayliss17,desai12,saro15}.
The first step in estimating the gas mass fraction consists of  determining  the total mass of the cluster at $R_{500}$, known as  $M_{500}$. This was estimated from the SZ
detection significance or signal to noise ratio, using SZ observable to mass scaling relations discussed  in ~\cite{bocquet15,dehaan16}. These scaling relations have  been self-consistently calibrated  using
a combination of X-ray, weak lensing, and number count distributions~\cite{chiu18}.
Here, we briefly describe the procedure used to derive the $f_{gas}$ measurements below. More details can be found in the aforementioned works.

 C18 estimated the total mass (denoted by $M_{500}$) and gas mass (which they refer to as intra-cluster medium mass, denoted by $M_{ICM}$) from the analysis of Chandra X-ray observations. All the 91 clusters have been imaged with Chandra, either through the Chandra X-ray Visionary Project led by the SPT collaboration as well as  other proposals led by non-SPT members.

To estimate $M_{ICM}$, a modified-$\beta$~\cite{vikhlinin06} model is used  to fit the gas density, which was estimated from the observed surface brightness  profile in the energy range 0.7-2.0 keV out to 1.5 $R_{500}$. This surface profile was then fit to the  modified $\beta$-model~\cite{vikhlinin06}. More details of this analysis can be found in ~\cite{mcdonald13}.
We then calculate the gas mass fraction $f_{gas}$, as the ratio of $M_{ICM}$ to $M_{500}$. This estimated gas mass fraction as a function of redshift is shown in Fig.~\ref{fig:f1}. We note that C18  also investigated the trends of gas mass  fraction as a function of redshift. However the parametric form which they have considered (Eq. 6 in C18) is different than that considered in this work (cf. Eq.~\ref{eq:gamma_obs}), and their analysis also includes a dependence  on $M_{500}$. A comparison between our results will be discussed in Sec.~\ref{sec:dicussions}.

Another thing to point out is that for calculating this gas mass fraction, $M_{500}$ was estimated using the observable SZ to mass scaling relation derived in a previous SPT work~\cite{dehaan16}. However, this scaling relation can change when using the cosmology priors from the Planck CMB anisotropy observations~\cite{bocquet15}. If this cosmology is adopted, $M_{500}$ would be larger by about 22\%, which in turn would also effect the baryon fraction numbers computed in C18.  However, the Planck Cosmology prior is disfavored, since the weak lensing and dynamical masses are in agreement with the standard SPT cluster analysis~\cite{chiu18}. In this work, we therefore do not consider the impact from the Planck cosmology prior.

\subsection{For Planck ESZ Sample}
In this work, we use the gas mass fraction measurements of  120 Planck Early SZ (ESZ) clusters~\cite{Planck11}  spanning the redshift range $0.059 \leqslant z \leqslant 0.546$~\cite{lovisari20}. All these clusters were also  imaged  with XMM-Newton up to $R_{500}$~\cite{lovisari17}. The only difference compared to this dataset  is that we used updated redshifts from Planck SZ2 catalog~\cite{PlanckSZ2}, instead of the ESZ redshifts used in ~\cite{lovisari17}.  These redshifts have also been obtained  using pointed optical follow-ups with various telescopes (eg.~\cite{Liu15})
and are still been continuously refined (eg.~\cite{Klein,Zaznobin}). Therefore, the redshifts of some of these clusters have further been updated after the publication of the Planck SZ2 catalog. The redshifts used for this analysis can be found in Table~\ref{tab:updated z}.

Lovisari et al.~\cite{lovisari20}  derived the total mass of the cluster at $R_{500}$ from the equation of hydrostatic equilibrium  and assuming spherical symmetry:
\begin{equation}
	\label{eq:hydrostatic}
    M(r<r_{500}) = -\frac{kT_{gas}}{G\mu m_p{}{}} {\left[\frac{d\log\rho_{gas}}{d\log r}  + \frac{d\log T_{gas}}{d\log r}\right]}
\end{equation}
where $T_{gas}(r)$ and $\rho_{gas}(r)$ denote the temperature and density profiles (see~\cite{lovisari20,lovisari17}), $k$ is the Boltzmann's constant and $\mu m_p$ represents the mean molecular weight of the intra-cluster gas.

\begin{longtable}[t]{|l|c|c|}
\caption{ Redshifts of Planck-ESZ clusters used for this analysis.} \label{tab:updated z} \\
	\hline
	 \textbf{Cluster} & \textbf{Redshift} & \textbf{Reference} \\
	\hline
PSZ2 G000.40-41.86 & 0.1651 & ~\cite{PlanckSZ2}\\
PSZ2 G002.77-56.16 & 0.1411 & ~\cite{PlanckSZ2}\\
PSZ2 G003.93-59.41 & 0.151 & ~\cite{PlanckSZ2}\\
PSZ2 G006.68-35.55 & 0.0894 & ~\cite{PlanckSZ2}\\
PSZ2 G006.76+30.45 & 0.203 & ~\cite{PlanckSZ2}\\
PSZ2 G008.47-56.34 & 0.1486 & ~\cite{PlanckSZ2}\\
PSZ2 G008.94-81.22 & 0.3066 & ~\cite{PlanckSZ2}\\
PSZ2 G021.10+33.24 & 0.1514 & ~\cite{PlanckSZ2}\\
PSZ2 G036.73+14.93 & 0.1525 & ~\cite{PlanckSZ2}\\
PSZ2 G039.85-39.96 & 0.176 & ~\cite{PlanckSZ2}\\
PSZ2 G042.81+56.61 & 0.0731 & ~\cite{rines16}\\
PSZ2 G046.10+27.18 & 0.389 & ~\cite{PlanckSZ2}\\
PSZ2 G046.47-49.44 & 0.0846 & ~\cite{PlanckSZ2}\\
PSZ2 G049.22+30.87 & 0.1604 & ~\cite{rines16}\\
PSZ2 G049.32+44.37 & 0.096 & ~\cite{rines16}\\
PSZ2 G049.69-49.46 & 0.098 & ~\cite{PlanckSZ2}\\
PSZ2 G053.53+59.52 & 0.1132 & ~\cite{rines16}\\
PSZ2 G055.59+31.85 & 0.2242 & ~\cite{rines16}\\
PSZ2 G055.95-34.89 & 0.2306 & ~\cite{rykoff16}\\
PSZ2 G056.77+36.32 & 0.0997 & ~\cite{rines16}\\
PSZ2 G056.93-55.08 & 0.4393 & ~\cite{rykoff16}\\
PSZ2 G057.25-45.34 & 0.4265 & ~\cite{rykoff16}\\
PSZ2 G058.29+18.55 & 0.065 & ~\cite{PlanckSZ2}\\
PSZ2 G062.44-46.43 & 0.0909 & ~\cite{rines16}\\
PSZ2 G067.17+67.46 & 0.166 & ~\cite{rines16}\\
PSZ2 G071.63+29.78 & 0.1579 & ~\cite{rines16}\\
PSZ2 G072.62+41.46 & 0.2257 & ~\cite{rines16}\\
PSZ2 G072.79-18.73 & 0.143 & ~\cite{PlanckSZ2}\\
PSZ2 G073.97-27.82 & 0.2302 & ~\cite{rykoff16}\\
PSZ2 G080.41-33.24 & 0.1102 & ~\cite{rines16}\\
PSZ2 G081.00-50.93 & 0.2998 & ~\cite{PlanckSZ2}\\
PSZ2 G083.29-31.03 & 0.412 & ~\cite{PlanckSZ2}\\
PSZ2 G085.98+26.69 & 0.179 & ~\cite{PlanckSZ2}\\
PSZ2 G086.47+15.31 & 0.26 & ~\cite{PlanckSZ2}\\
PSZ2 G092.71+73.46 & 0.2312 & ~\cite{rines16}\\
PSZ2 G093.92+34.92 & 0.0801 & ~\cite{rines16}\\
PSZ2 G096.88+24.18 & 0.37 & ~\cite{planck_canary16}\\
PSZ2 G097.72+38.12 & 0.1709 & ~\cite{PlanckSZ2}\\
PSZ2 G098.97+24.86 & 0.0928 & ~\cite{PlanckSZ2}\\
PSZ2 G106.87-83.23 & 0.2924 & ~\cite{PlanckSZ2}\\
PSZ2 G107.10+65.32 & 0.2799 & ~\cite{PlanckSZ2}\\
PSZ2 G113.81+44.35 & 0.225 & ~\cite{PlanckSZ2}\\
PSZ2 G124.20-36.48 & 0.1971 & ~\cite{PlanckSZ2}\\
PSZ2 G125.71+53.86 & 0.3019 & ~\cite{PlanckSZ2}\\
PSZ2 G139.18+56.37 & 0.322 & ~\cite{PlanckSZ2}\\
PSZ2 G149.75+34.68 & 0.1818 & ~\cite{PlanckSZ2}\\
PSZ2 G157.43+30.34 & 0.407 & ~\cite{barrena18}\\
PSZ2 G159.91-73.50 & 0.206 & ~\cite{PlanckSZ2}\\
PSZ2 G164.18-38.88 & 0.0739 & ~\cite{PlanckSZ2}\\
PSZ2 G166.09+43.38 & 0.2173 & ~\cite{rines16}\\
PSZ2 G167.67+17.63 & 0.174 & ~\cite{PlanckSZ2}\\
PSZ2 G171.98-40.66 & 0.272 & ~\cite{planck_canary16}\\
PSZ2 G180.25+21.03 & 0.546 & ~\cite{PlanckSZ2}\\
PSZ2 G182.42-28.28 & 0.0882 & ~\cite{PlanckSZ2}\\
PSZ2 G182.59+55.83 & 0.2041 & ~\cite{rines16}\\
PSZ2 G186.37+37.26 & 0.2812 & ~\cite{rines16}\\
PSZ2 G195.60+44.06 & 0.293 & ~\cite{mehrtens16}\\
PSZ2 G195.75-24.32 & 0.203 & ~\cite{PlanckSZ2}\\
PSZ2 G218.81+35.51 & 0.1751 & ~\cite{PlanckSZ2}\\
PSZ2 G225.93-19.99 & 0.46 & ~\cite{PlanckSZ2}\\
PSZ2 G226.16-21.95 & 0.0989 & ~\cite{PlanckSZ2}\\
PSZ2 G226.18+76.79 & 0.1412 & ~\cite{rines16}\\
PSZ2 G228.16+75.20 & 0.545 & ~\cite{PlanckSZ2}\\
PSZ2 G227.61+54.87 & 0.3188 & ~\cite{PlanckSZ2}\\
PSZ2 G229.23-17.23 & 0.171 & ~\cite{PlanckSZ2}\\
PSZ2 G229.93+15.30 & 0.0704 & ~\cite{PlanckSZ2}\\
PSZ2 G236.92-26.65 & 0.1483 & ~\cite{PlanckSZ2}\\
PSZ2 G241.76-30.88 & 0.2708 & ~\cite{PlanckSZ2}\\
PSZ2 G241.79-24.01 & 0.1392 & ~\cite{PlanckSZ2}\\
PSZ2 G241.98+14.87 & 0.1687 & ~\cite{PlanckSZ2}\\
PSZ2 G244.37-32.15 & 0.2839 & ~\cite{PlanckSZ2}\\
PSZ2 G244.71+32.50 & 0.1535 & ~\cite{PlanckSZ2}\\
PSZ2 G247.19-23.31 & 0.152 & ~\cite{PlanckSZ2}\\
PSZ2 G249.91-39.86 & 0.1501 & ~\cite{PlanckSZ2}\\
PSZ2 G250.89-36.24 & 0.2 & ~\cite{PlanckSZ2}\\
PSZ2 G252.99-56.09 & 0.0752 & ~\cite{PlanckSZ2}\\
PSZ2 G253.48-33.72 & 0.191 & ~\cite{PlanckSZ2}\\
PSZ2 G256.53-65.70 & 0.2195 & ~\cite{PlanckSZ2}\\
PSZ2 G257.32-22.19 & 0.203 & ~\cite{PlanckSZ2}\\
PSZ2 G259.98-63.43 & 0.2836 & ~\cite{PlanckSZ2}\\
PSZ2 G262.27-35.38 & 0.2952 & ~\cite{PlanckSZ2}\\
PSZ2 G262.73-40.92 & 0.4224 & ~\cite{bayliss16}\\
PSZ2 G263.14-23.41 & 0.226 & ~\cite{bleem15}\\
PSZ2 G263.68-22.55 & 0.1644 & ~\cite{PlanckSZ2}\\
PSZ2 G266.04-21.25 & 0.2965 & ~\cite{PlanckSZ2}\\
PSZ2 G269.31-49.87 & 0.0853 & ~\cite{PlanckSZ2}\\
PSZ2 G271.18-30.95 & 0.376 & ~\cite{bleem15}\\
PSZ2 G271.53-56.57 & 0.3 & ~\cite{PlanckSZ2}\\
PSZ2 G272.08-40.16 & 0.0589 & ~\cite{PlanckSZ2}\\
PSZ2 G277.76-51.74 & 0.438 & ~\cite{PlanckSZ2}\\
PSZ2 G278.58+39.16 & 0.3075 & ~\cite{PlanckSZ2}\\
PSZ2 G280.17+47.83 & 0.1557 & ~\cite{PlanckSZ2}\\
PSZ2 G286.39+64.06 & 0.2287 & ~\cite{rykoff16}\\
PSZ2 G283.16-22.91 & 0.45 & ~\cite{PlanckSZ2}\\
PSZ2 G284.41+52.45 & 0.4414 & ~\cite{PlanckSZ2}\\
PSZ2 G284.97-23.69 & 0.39 & ~\cite{PlanckSZ2}\\
PSZ2 G285.63-17.23 & 0.35 & ~\cite{PlanckSZ2}\\
PSZ2 G286.62-31.24 & 0.21 & ~\cite{PlanckSZ2}\\
PSZ2 G286.98+32.90 & 0.39 & ~\cite{PlanckSZ2}\\
PSZ2 G288.63-37.66 & 0.127 & ~\cite{PlanckSZ2}\\
PSZ2 G292.56+21.97 & 0.3 & ~\cite{PlanckSZ2}\\
PSZ2 G294.68-37.01 & 0.2742 & ~\cite{PlanckSZ2}\\
PSZ2 G304.65-31.66 & 0.1934 & ~\cite{PlanckSZ2}\\
PSZ2 G304.84-41.40 & 0.41 & ~\cite{PlanckSZ2}\\
PSZ2 G306.66+61.06 & 0.0843 & ~\cite{rines16}\\
PSZ2 G306.77+58.61 & 0.0845 & ~\cite{PlanckSZ2}\\
PSZ2 G308.33-20.21 & 0.48 & ~\cite{PlanckSZ2}\\
PSZ2 G313.33+61.13 & 0.1842 & ~\cite{rines16}\\
PSZ2 G313.88-17.11 & 0.153 & ~\cite{PlanckSZ2}\\
PSZ2 G318.14-29.57 & 0.217 & ~\cite{PlanckSZ2}\\
PSZ2 G321.98-47.96 & 0.094 & ~\cite{PlanckSZ2}\\
PSZ2 G324.54-44.97 & 0.0951 & ~\cite{PlanckSZ2}\\
PSZ2 G332.23-46.37 & 0.098 & ~\cite{PlanckSZ2}\\
PSZ2 G332.87-19.26 & 0.147 & ~\cite{PlanckSZ2}\\
PSZ2 G335.58-46.44 & 0.076 & ~\cite{PlanckSZ2}\\
PSZ2 G336.60-55.43 & 0.0965 & ~\cite{PlanckSZ2}\\
PSZ2 G337.14-25.98 & 0.26 & ~\cite{PlanckSZ2}\\
PSZ2 G342.33-34.93 & 0.232 & ~\cite{PlanckSZ2}\\
PSZ2 G347.17-27.36 & 0.2371 & ~\cite{PlanckSZ2}\\
PSZ2 G349.46-59.95 & 0.351 & ~\cite{bleem15}\\
\hline
\end{longtable}

\newpage

The gas density was obtained from the X-ray surface brightness profile in the 0.3-2 keV energy band after fitting a double-$\beta$ model~\cite{lovisari17}. The temperatures were obtained by fitting the X-ray spectra to a thermal plasma emission model~\cite{lovisari17}. The gas mass $M_{gas}$ was then  estimated by integrating the density profile upto  $R_{500}$ after assuming spherical symmetry.
Both $M_{gas}$ and $M_{500}$, along with their errors are tabulated in  ~\citet{lovisari20}.
Thereafter, their ratio $M_{gas}/M_{500}$ gives the desired gas mass fraction $f_{gas}$ values for each cluster. Fig.~\ref{fig:f1} shows the derived $f_{gas}$ values for Planck ESZ clusters as a function of redshift.

\begin{figure*}

   \includegraphics[width=17cm, height=10cm]{combined1_2.pdf}
    \caption{$f_{gas}$ data of 94 SPT-SZ clusters sample taken from~\cite{chiu18,chiu16} and 120 Planck ESZ galaxy clusters sample taken from~\cite{lovisari20}  as a function of $z$.}
    \label{fig:f1}
\end{figure*}

\section{Method}
\label{sec:method}
The gas mass fraction in galaxy clusters has been used as a cosmological probe. The expression for  $f_{gas}$ with respect  to a reference cosmological model is given by~\cite{allen08}:

\begin{equation}
    f_{gas}^{ref}= K(z)A(z)\gamma(z)\left(\frac{\Omega_b}{\Omega_m}\right) {\left[\frac{D_A^{ref}(z)}{D_A(z)}\right]}^{3/2}
	\label{eq:fgas}
\end{equation}
where $\Omega_b$ and $\Omega_m$ denote the cosmic baryon and matter fraction density (obtained from Planck 18 Cosmological analysis~\cite{planck18}) scaled by the critical density $\rho_c$; $K(z)$ = $1.0\pm0.1$~\cite{allen08} is the instrument calibration constant, which also accounts for any bias in mass due to non-thermal pressure and bulk motions in baryonic gas; $A(z)$ represents the angular correction factor which is almost in all cases, close to unity, and hence can be neglected.  The terms in the square parenthesis denote the variation in $f_{gas}$ value as the underlying cosmology is changed. $D_{A}$ is the angular diameter distance and $ref$ indicates the fiducial cosmology. For our  reference cosmology, we have used a  flat $\Lambda$CDM cosmology ($\Omega_m$ = 0.3 and $H_0$ = 70 km/sec/Mpc~\cite{lovisari20}).

Assuming flat $\Lambda$CDM cosmology, the angular diameter distance for a reference cosmology can be calculated as follows~\cite{Hogg}:
\begin{equation}
    D_{A}^{ref} = \frac{c}{H_0} \left(\frac{1}{1+z}\right) \int_{0}^{z}\frac{dz^{'}}{\sqrt{\Omega_m{(1+z^{'})^3}+(1 - \Omega_m)}}
   \label{eq:ADD}
\end{equation}
From Eq.~\ref{eq:fgas}, we can write the gas depletion factor, $\gamma(z)$ as follows:
\begin{equation}
\label{eq:gamma_obs}
    \gamma(z)= \frac{f_{gas}^{ref}}{ A(z) K(z)} \left(\frac{\Omega_m}{\Omega_b}\right) {\left[\frac{D_A(z)}{D_A^{ref}(z)}\right]}^{3/2}
\end{equation}
This equation shows that $\gamma(z)$ is sensitive to  measurements of angular diameter distance.
In this work, similar to Z19 we have used Gaussian Process Regression to derive the angular diameter distances  by using $H(z)$ data from cosmic chronometers, which are agnostic to the underlying cosmology. $D_A(z)$ is given by
\begin{equation}
D_{A} (z) =  \left(\frac{c}{1+z}\right)\int_{0}^{z}\frac{dz^{'}}{H(z')}
\label{eq:daz}
\end{equation}
where $H(z')$ is the non-parametric  estimate of the Hubble parameter, whose determination will be described in the next section.

\begin{figure*}[t]

    \includegraphics[width=17cm, height=10cm]{Figure_3.pdf}
    \caption{Reconstruction of $H(z)$ using Gaussian Processes Regression. The data points represent the 31 $H(z)$ cosmic chronometer measurements taken from ~\citet{li19}. The blue line indicates the best GP fit to data along with $1\sigma$ and $2\sigma$ error bands shown by two different shades of green bands.}
    \label{fig:f3}
\end{figure*}

\section{Analysis and results}
\label{sec:analysis}
Cosmic chronometers provide a model-independent
measurement of $H(z)$, based on the age difference between two passively evolving galaxies~\cite{Jimenez}. Therefore, they have been widely used for a variety of tests of the  standard cosmological model, as well as a whole suite of  cosmological measurements~\cite{Seikel,Meliachrono,ChenRatra,Amendola,Yang19,Haridasu2,Jesus,Rana,Ratra13,Moresco_2016,HS}. For this work, we used cosmic chronometer data to provide a non-parametric estimate of the expansion history, needed to evaluate Eq.~\ref{eq:daz}.

Gaussian Processes (GPs) extend the idea of Gaussian distribution, and are characterized by the mean function and the covariance (kernel) function. They offer a non-parametric way to model a function~\cite{Seikel}. In this work, we choose a squared exponential (RBF) kernel function which is defined as,
\begin{equation}
 \label{eq:kernal}
  K(x,\Tilde{x}) = \sigma_f^2 exp  {\left[\frac{-(x-\Tilde{x})^2}{2l^2}\right]},
\end{equation}
where $\sigma_f^2$ and $l$ are the hyperparameters of the kernel function. The length parameter $l$ controls the smoothness of the function. To implement the GPs, we used the GaPP (Gaussian Process in Python) code~\cite{GaPP}.

Following Z19, we used the 31 $H(z)$ cosmic chronometer measurements from~\citet{li19} (same  as that  used in ~\cite{HS}) in the redshift range $0.07 \leqslant z \leqslant 1.965$
to obtain non-parametric estimates of $H(z)$ at any redshift.
Fig.~\ref{fig:f3} shows the GP reconstructed $H(z)$ from cosmic chronometers along with  $1\sigma$ and $2\sigma$ uncertainties.
We then reconstruct the GP reconstructed $H(z)$ values for SPT-SZ and  Planck ESZ  redshifts in order to obtain the angular diameter distances. Thereafter, these $H(z)$ values were used to derive the angular diameter distances $D_A$ using
Eq.~\ref{eq:daz}. $D_A^{ref}$ is calculated from Eq.~\ref{eq:ADD} by assuming  the cosmological parameters outlined in Sect.~\ref{sec:method}.

Finally, we reconstructed the gas depletion factor $\gamma (z)$  using Gaussian Process, after incorporating all  the other factors presented in  Eq.~\ref{eq:gamma_obs}. We also propagated the errors in $\Omega_b$, $\Omega_M$, $K$, angular diameter distance,  and redshifts, if they were provided.
Figs.~\ref{fig:f4} and ~\ref{fig:f5} display our reconstructed $\gamma(z)$ as a function of $z$ for both SPT-SZ and Planck ESZ data, respectively. Both these data  show opposite  trends for the  gas depletion factor with redshift. We find a decreasing  $\gamma$ for  SPT-SZ data, whereas for Planck ESZ data, a slightly increasing trend is observed. For comparison,~\citet{planelles13} reported a negligible evolution of gas depletion factor by using Eq.~\ref{eq:gammavariation} for their NR simulations. They obtained $\gamma_0 = 0.85\pm0.03$ and  $\gamma_1 = 0.02\pm 0.05$ at $R_{500}$. The simulation results can be found in the red shaded region in  Figs.~\ref{fig:f4} and  ~\ref{fig:f5}. \rthis{Therefore, at face value, our results do not agree with these hydrodynamical simulations based on $\Lambda$CDM.}

\begin{figure}[t]
    \centering
    \includegraphics[width=10cm,height=8cm]{Figure_4.pdf}
    \caption{Reconstructed $\gamma(z)$ as a function of $z$. The blue line represents the best GP reconstructed fit for the SPT-SZ data along with the $1\sigma$ error band (shown by blue shaded region). The red band shows the NR simulation results at $R_{500}$ from~\cite{planelles13} by assuming the Eq.~\ref{eq:gammavariation}. }
    \label{fig:f4}
\end{figure}

\begin{figure}[t]
    \centering
    \includegraphics[width=10cm, height=8cm]{Figure_5.pdf}
    \caption{Reconstructed $\gamma(z)$ as a function of $z$. The green line represents the best GP reconstructed fit for the Planck ESZ data along with the $1\sigma$ error band(shown by green shaded region). The red region shows the NR simulation results at $R_{500}$ from~\cite{planelles13} by assuming the Eq.~\ref{eq:gammavariation}.}
    \label{fig:f5}
\end{figure}

To confirm and quantify the significance of the trends seen in  $\gamma(z)$, we also did a  parametric  fit of our estimated depletion factor measurements  to Eq.~\ref{eq:gammavariation}.
We maximize the following likelihood function $\mathcal{L}$ in our analysis, where
\begin{equation}
    \label{eq:logL}
   -2\ln\mathcal{L} = \sum_{obs} \ln 2\pi{\sigma_{obs}^2}+ \sum_{i=1}^{n}\frac{(\gamma_{model}(z_i)-\gamma_{obs}(z_i))^2}{\sigma_{i,obs}^2} ,
\end{equation}
where $\gamma_{model}$ is defined in Eq.~\ref{eq:gammavariation}, $\gamma_{obs}$ is obtained from Eq.~\ref{eq:gamma_obs}, and  $\sigma_{i,obs}^2$ represents the error  in $\gamma_{obs}$.  $\sigma_{i,obs}$ is calculated by propagating the errors in $f_{gas}^{ref}$, $K$, $\Omega_m$,  cluster $z$, $\Omega_b$, $D_A(z)$, and $D_A^{ref}$. In addition to these observational errors, $\sigma_{obs}$ also includes an unknown  intrinsic scatter ($\sigma_{int}$) added in quadrature, similar to our recent works on galaxy cluster scaling relations~\cite{Gopika,Bora,Pradyumna}.

To estimate the model parameters($\gamma_0$ and $\gamma_1$), we maximize the likelihood using the {\tt emcee} MCMC sampler~\cite{emcee}.
For both the datasets, we adopt uniform priors on $\gamma_0$  and $\gamma_1$: $-1.5 \leqslant \gamma_0 \leqslant 1.5$ and $-2.0 \leqslant \gamma_1 \leqslant 3.0$. For the intrinsic scatter, similar to ~\cite{Tian}, we assume log-uniform priors between $10^{-5}$ and 0.1. \rthis{The log-uniform prior ensures that the intrinsic scatter is greater than zero.}
The 68\%, 95\%, and 99\% 2-D marginalized credible intervals, along with the marginalized one-dimensional likelihoods for each parameters  are displayed in Fig.~\ref{fig:f6} and Fig.~\ref{fig:f7} respectively.

From this analysis, we get $\gamma_0 = 0.915\pm0.050$ and $\gamma_1 = -0.305_{-0.058}^{+0.064}$ for SPT-SZ data, and  $\gamma_0 = 0.741\pm0.029$ and $\gamma_1 = 0.834_{-0.199}^{+0.214}$ for Planck ESZ data. The SPT-SZ data results indicate a decreasing  trend of $\gamma$(z) with redshift at about 5$\sigma$ significance. On the other hand, the Planck ESZ results show an increasing $\gamma$ as a function of redshift at about $4\sigma$. Both the results contradict those  from hydrodynamical simulations ~\cite{planelles13}. Table~\ref{tab:summary_table} summarizes the constraints on parameters $\gamma_0$ and $\gamma_1$,  which we have obtained from the datasets, along with a summary of previous compilations in literature using both data and simulations. We note that among the  previous observational results, only Z19 had found $\gamma(z)$ decreasing with redshift at about $1.6\sigma$.

\begin{table*}
	\caption{Constraints on parameters $\gamma_0$ and $\gamma_1$ (cf. Eq.~\ref{eq:gammavariation}) from different estimates in literature (including this work). The last two rows show the gas depletion factors for a subset of SPT-SZ  and Planck ESZ clusters within the same redshift range. }
	\label{tab:summary_table}
	\begin{tabular}{|l|c|c|c|c|r|}
		\hline
		\boldmath{$f_{gas}$} & \textbf{Redshift range} & \textbf{Cluster Radius} &  \boldmath$\gamma_0$ & \boldmath$\gamma_1$ & \textbf{Reference}\\
		\hline

	    NR Simulation & $0.0  \leqslant z  \leqslant 1.0$ & $R_{200}$ & $0.86\pm0.02$ & $0.00\pm0.04$ & ~\cite{planelles13}  \\
	    NR Simulation & $0.0  \leqslant z  \leqslant 1.0$ & $R_{500}$ & $0.85\pm0.03$ & $0.02\pm0.05$ &  ~\cite{planelles13} \\
	    NR Simulation & $0.0  \leqslant z  \leqslant 1.0$ & $R_{2500}$ & $0.79\pm0.07$ & $0.07\pm0.12$ & ~\cite{planelles13} \\
	    CSF Simulation & $0.0  \leqslant z  \leqslant 1.0$ & $R_{200}$ & $0.68\pm0.03$ & $0.00\pm0.06$ & ~\cite{planelles13}  \\
	    CSF Simulation & $0.0  \leqslant z  \leqslant 1.0$ & $R_{500}$ & $0.63\pm0.03$ & $0.01\pm0.08$ &  ~\cite{planelles13} \\
	    CSF Simulation & $0.0  \leqslant z  \leqslant 1.0$ & $R_{2500}$ & $0.49\pm0.06$ & $-0.04\pm0.18$ & ~\cite{planelles13} \\
	    AGN Simulation & $0.0  \leqslant z  \leqslant 1.0$ & $R_{200}$ & $0.75\pm0.03$ & $-0.03\pm0.05$ & ~\cite{planelles13}  \\
	    AGN Simulation & $0.0  \leqslant z  \leqslant 1.0$ & $R_{500}$ & $0.71\pm0.03$ & $-0.03\pm0.06$ &  ~\cite{planelles13} \\
	    AGN Simulation & $0.0  \leqslant z  \leqslant 1.0$ & $R_{2500}$ & $0.55\pm0.07$ & $-0.04\pm0.18$ & ~\cite{planelles13} \\
	    \hline
	    $f_{gas}$/SNIa & $ 0.078  \leqslant z  \leqslant 1.063$ & $R_{2500}$ & $0.86\pm0.04$ & $-0.04\pm0.12$ & ~\cite{holanda1706} \\
	    \hline
	    $f_{gas}$/Cluster I & $0.14  \leqslant z  \leqslant 0.89$ & $R_{2500}$ & $0.76\pm0.14$ & $-0.42_{-0.40}^{+0.42}$ & ~\cite{holanda1711} \\
	     $f_{gas}$/Cluster II & $0.14  \leqslant z  \leqslant 0.89$ & $R_{2500}$ & $0.72\pm0.01$ & $0.16\pm0.36$ &  ~\cite{holanda1711} \\
	     $f_{gas}$/$\Lambda$CDM & $0.12  \leqslant z  \leqslant 0.78$ & $R_{2500}$ & $0.84\pm0.07$ & $-0.02\pm0.14$ & ~\cite{holanda1711} \\
	     \hline
		ACTPol & $0.1  \leqslant z  \leqslant 1.4$ & $R_{500}$ & $0.840\pm0.025$ & $-0.072_{-0.049}^{+0.044}$ & ~\cite{zheng19} \\
	    ACTPol-re & $0.1  \leqslant z  \leqslant 1.0$  & $R_{500}$ &  $0.835\pm0.028$ & $-0.060_{-0.063}^{+0.056}$ & ~\cite{zheng19} \\
	    \hline
		\textbf{SPT-SZ} & $0.278  \leqslant z  \leqslant 1.32$  & $R_{500}$ & $\mathbf{0.911\pm0.05} $ & $\mathbf{-0.288_{-0.06}^{+0.07}} $ & \textbf{This work} \\
		\textbf{Planck ESZ} & $0.059  \leqslant z  \leqslant 0.546$  & $R_{500}$ &  $\mathbf{0.753\pm0.03}$ & $\mathbf{0.823^{+0.24}_{-0.22}} $ & \textbf{This work} \\
		\hline
		\textbf{SPT-SZ (subset)} & $0.278  \leqslant z  \leqslant 0.546$  & $R_{500}$ & $\mathbf{0.537\pm0.16} $ & $\mathbf{1.02_{-0.79}^{+1.44}} $ & \textbf{This work} \\
		\textbf{Planck-ESZ (subset)} & $0.278  \leqslant z  \leqslant 0.546$  & $R_{500}$ & $\mathbf{ 0.884\pm0.17 } $ & $\mathbf{0.24_{-0.47}^{+0.7}} $ & \textbf{This work}
		\\ \hline
	\end{tabular}
\end{table*}

\begin{figure*}[h]

 \includegraphics[width=10cm, height=10cm]{Figure_6.pdf}    \caption{\textbf{For SPT-SZ dataset:} Constraints on the parameters $\gamma_0$ and $\gamma_1$ along with $\ln(\sigma_{int})$, defined in Eq.~\ref{eq:logL}. The plots along the diagonal are the one-dimensional marginalized likelihood distributions. The contour plots represents the two-dimensional marginalized constraints showing the 68\%, 95\%, and 99\% credible regions. These contours have been obtained using the {\tt Corner} python module~\cite{corner}. }
 \label{fig:f6}
\end{figure*}

\begin{figure*}[h]

 \includegraphics[width=10cm, height=10cm]{Figure_7.pdf}    \caption{\textbf{For Planck ESZ dataset:} Constraints on the parameters $\gamma_0$ and $\gamma_1$ along with $\ln(\sigma_{int})$. The plots along the diagonal are the one-dimensional marginalized likelihood distributions. The contour plot represents the two-dimensional marginalized constraints showing the 68\%, 95\%, and 99\% credible regions. These contours have been obtained using the {\tt Corner} python module~\cite{corner}. }
    \label{fig:f7}
\end{figure*}

\section{Discussions}
\label{sec:dicussions}
Given the contradictory results for $\gamma(z)$ between the SPT-SZ and Planck-ESZ datasets as well as with previous results in literature, we carry out various sanity checks of our results along with  extensions of tests carried  out earlier, to verify the robustness of our conclusions, and to see if there is one deciding parameter, which governs the difference between the results.

\subsection{Comparison with C18}
A test of the variation of the gas mass fraction with redshift  (using different parametric forms) for the SPT-SZ sample was also carried out in C18, and no evidence for a variation of the depletion factor for redshift was found (cf. Table 6 in C18.) At prima facie, it may seem that our results contradict those in C18. However, $\gamma(z)$ defined in this work (cf. Eq.~\ref{eq:gammavariation}) is a function of $\Omega_b$, $\Omega_M$, and $D_A(z)$, besides the gas mass fraction. On the other hand, C18 carried out a joint  test for the variation of gas mass fraction with redshift and $M_{500}$.
 The functional forms used in C18 to test for  redshift trends are $\propto (1+z)^{\alpha}$ and $(E(z))^{\gamma}$, where $E(z)$ is the cosmic expansion factor in $\Lambda$CDM~\cite{Ratra13}. Here, $\gamma(z)$ estimated in this work is proportional to $\left[D_A(z)\right]^{3/2}$ (cf. Eq.~\ref{eq:gamma_obs}), which is the integral of the reciprocal of $E(z)$.  $\gamma(z)$ studies in this work also does not have an explicit dependence on the mass. We have also reconstructed $D_A(z)$ in a non-parameteric way using cosmic chronometers.

However, in order to test the consistency of our results with C18 (for SPT-SZ), we  now check  for a  variation of only the raw $f_{gas}$ data  to a few different parametric functions (including those used in C18).
The full list of functions used to test variations of gas mass fraction are indicated below:
\begin{eqnarray}
f_{gas} &=& f_0(1 + f_1 z)  \label{eq:9}\\
f_{gas} &=& \left(\frac{1+z}{1+z_{pivot}}\right)^{\alpha} \label{eq:10} \\
f_{gas} &=& \left(\frac{E(z)}{E(z_{pivot})}\right)^{\beta} \label{eq:11}
\end{eqnarray}
where $z_{pivot}$ is the pivot value of the redshift, equal to 0.6 for SPT and 0.2 for Planck.  With these functional forms, we remove any explicit dependence on the angular diameter distance ratio.
The best-fit values of the free parameters in the above equations for both the datasets were found by constructing a likelihood similar to Eq.~\ref{eq:logL}. These best-fit parameters can be found in Table~\ref{tab:extendedanalysis} for both SPT-SZ and Planck-ESZ. We find that for the SPT-SZ sample, the parameters $f_1$, $\alpha$, and $\beta$, which encode the dependence on redshift are consistent with no variation (within 1$\sigma$). Therefore, this agrees with the results in C18, which found no redshift dependence.

However, for the Planck sample $f_1$ in Eq.~\ref{eq:9} is equal to $0.85 \pm 0.17$, indicating a positive slope which is 5$\sigma$ discrepant from zero (which corresponds to no redshift evolution). This is one of the main determining factors for the positive $\gamma_1$ for Planck-ESZ. The deviations for $\alpha$ and $\beta$ from  a zero value are within $1-2\sigma$.

\subsection{$\gamma(z)$ within the overlapping redshift range}
The SPT sample extends upto very high redshift ($z=1.32$) compared to Planck, whose most distant cluster is located at $z=0.546$. Similarly, the Planck sample contains about 84 low redshift clusters with $z<0.278$, which is the lowest redshift for the SPT sample. We now check if the gas depletion factor for both the samples within the overlapping redshift range ($0.278\leqslant z \leqslant  0.546$)  display the same trend. We get a total of 34 SPT and 36 Planck clusters with these redshift cuts. We applied the same procedure as in Sect.~\ref{sec:analysis} to determine $\gamma_0$ and $\gamma_1$ for these sub-samples. These values can be found in the last two rows of Table~\ref{tab:summary_table}. The best-fit value of $\gamma_1$ for SPT-SZ and Planck-SZ is equal to $1.02_{-0.79}^{+1.44}$ and $0.24_{-0.47}^{+0.7}$, respectively. Therefore, we see that although there is a mild deviation of $\gamma_1$ from a zero value for SPT-SZ, their values are consistent between the two datasets within $1\sigma$.

\subsection{Dependence on $M_{500}$}
\rthis{The fits to $f_{gas}$  done in C18 also had an explicit dependence on $M_{500}$ given by $f_{gas} \propto M_{500}^{\zeta}$.}
C18 then found $\zeta =0.33 \pm 0.07$ with a $4.5\sigma$ deviation from self-similarity (\rthis{where, self-similarity  corresponds to $\zeta=0$}) in agreement with previous works~\cite{Mohr99,Neumann01,vikhlinin06,vikhlinin09}. So far, we have not accounted for any dependence on the halo mass, while estimating the gas depletion factor as a function of redshift.

In order to check the possible dependence on the mass of the cluster,  and evaluate its impact on  the gas depletion factor, we augment Eq.~\ref{eq:gammavariation} with an additional dependence on $M_{500}$ as follows:
\begin{equation}
 \gamma(z)= \gamma_0(1+\gamma_1 z)\left(\frac{M_{500}}{M_{pivot}}\right)^{\zeta}
\label{eq:gammavariationwithmass}
\end{equation}
 where $M_{pivot}$ corresponds \rthis{to the median mass for the SPT and Planck samples.} These are equal to
$ 4.8 \times 10^{14}M_{\odot}$  and $6.0 \times 10^{14}M_{\odot}$ for  SPT-SZ and Planck ESZ, respectively. To determine these parameters,  we use an extension of the same procedure as in Sect.~\ref{sec:analysis}, by including an additional dependence on $M_{500}$.
While constructing  the likelihood, the errors in $M_{500}$ were also included.
The marginalized posterior intervals for the gas depletion parameters along with $\zeta$, which encodes the variation with $M_{500}$, can be found in Fig.~\ref{fig:f14} and Fig.~\ref{fig:f15} for SPT-SZ and Planck-ESZ, respectively. The best-fit values for these parameters can be found in Table~\ref{tab:extendedanalysis}. For SPT-SZ, we  find that
$\zeta= 0.257 \pm 0.09$, indicating  a 2.9$\sigma$ deviation from self-similarity. For Planck-ESZ, we have  $\zeta=0.083 \pm 0.06$, with only a 1.4$\sigma$, deviation from self-similarity.
After allowing for this dependence on
$M_{500}$, we find that $\gamma_1=-0.23 \pm 0.08$ and $0.57 \pm 0.26$ for SPT-SZ and Planck-ESZ respectively. This shows that the discrepancy with respect to a constant depletion factor as a function of redshift decreases to $2.9\sigma$ and $2.2\sigma$ for SPT-SZ and Planck-ESZ, respectively, as  compared to the $4-5\sigma$ significance, which we had obtained earlier without including an explicit dependence on the halo mass.
Therefore, we conclude that although the statistical significance of the rising/falling slope  as a function of redshift decreases, it does not completely go away, when we include a dependence on the total mass. Only its significance reduces to between $2-3\sigma$. \rthis{However, given that the inclusion of halo mass in our fit reduces the discrepancy with respect to no evolution of $\gamma_1$, one cannot decouple the two factors while testing for a redshift of the gas depletion factor.}

\subsection{Other possible sources of systematics}
Here, we list other possible sources of errors, which could affect our estimates of $\gamma(z)$. A detailed study of the impact of  each of these effects is beyond the scope of this work. The most crucial ingredient is the determination of cluster masses, which are obtained from the observable to halo mass scaling relations and is limited by the systematic uncertainties. The gas mass can be sensitive to the assumed temperature profile ~\cite{ettori09}. Errors due to hydrostatic equilibrium assumption could be upto 15-20\%~\cite{biffi}. Other possible sources of systematic errors in the gas mass fraction determination such as magnetic field, thermal evaporation, and non-linear translation of analysis variables are discussed in ~\cite{Loeb,Linder,Jain}. Finally, we point out that the list of SPT-SZ and Planck-SZ analyzed in this work is not the full sample. The PSZ2 catalog contains 1653  cluster candidates (with 1,203 confirmed clusters) with signal to noise ratio above 4.5~\cite{PlanckSZ2}. This work has analyzed only about 10\% of the full sample, which was followed up in X-rays at the time of Planck ESZ release. Optical and X-ray studies  of Planck SZ clusters is still in progress~\cite{Melin19,Zaznobin}. Similarly, the SPT-SZ dataset  analyzed in this work is only a quarter of the full 2500 sq. degree survey sample used for the cosmological analysis in ~\cite{bocquet19}. However, the SPT clusters are also been imaged in X-rays through dedicated Chandra~\cite{mcdonald13} and XMM~\cite{Bulbul} based follow-ups. Since our currently analyzed  subset may not be representative of the full SPT and Planck SZ sample, it would be interesting to carryout a followup analysis, once  the follow-up data for the full sample is available.

\begin{table*}[]
\caption{\label{tab:extendedanalysis}. Constraints on the  parameters  of various extended tests of  the gas depletion factors as discussed in Sect.~\ref{sec:dicussions} for  both  SPT and Planck clusters.}
    \centering
    \begin{tabular}{|l|c|c|r|} \hline
    \textbf{Parameter} & \textbf{Equation} & \textbf{SPT-SZ} &   \textbf{Planck-ESZ}\\ \hline
      $f_0$ & Eq.~\ref{eq:9} & $0.12\pm0.006$  &  $0.11 \pm 0.004$ \\
      $f_1$ & Eq.~\ref{eq:9}     & $-0.06^{+0.084}_{-0.075}$ & $0.85^{+0.18}_{-0.17}$ \\
      $\alpha$ &  Eq.~\ref{eq:10}  & $-0.26^{+0.43}_{-0.39}$ & $-0.7^{+0.62}_{-0.61}$\\
      $\beta$ &  Eq.~\ref{eq:11}  & $-0.55^{+0.46}_{-0.48}$ & $-1.64^{+0.98}_{-1.0}$\\
      $\gamma_0$ &  Eq.~\ref{eq:gammavariationwithmass}  &  $0.86\pm 0.05$ & $0.79\pm0.04$ \\
      $\gamma_1$ &  Eq.~\ref{eq:gammavariationwithmass}  & $-0.23_{-0.07}^{+0.08}$  & $0.57_{-0.25}^{+0.27}$\\
      $\zeta$ &  Eq.~\ref{eq:gammavariationwithmass}  & $0.257\pm0.09$ & $0.083\pm0.06$ \\ \hline
    \end{tabular}
\end{table*}
\section{Conclusions}
\label{sec:conclusion}

The gas mass fraction ($f_{gas}$)  in galaxy clusters has been used as a cosmological probe in a number of works. A key assumption in these analyses is that the gas mass fraction  (at the particular radius used for cosmological measurements)  does not vary with redshift. This has also been confirmed with  hydrodynamical simulations  of galaxy clusters which use $\Lambda$CDM as the base model,  which show no evolution of the gas depletion factor with redshift ($z< 1$)~\cite{planelles13}.

To verify this {\it ansatz} with real data in a model-independent method without any dependence on the underlying cosmology,  Z19 carried out a model-independent test  for the variation of gas depletion factor using 182 clusters  from ACTPol. Using the parameterization in Eq.~\ref{eq:gammavariation}, they found that  $\gamma_0 = 0.840\pm0.025$ and $\gamma_1 = -0.072_{-0.049}^{+0.044}$, which indicates a decreasing trend at about $1.4\sigma$. In this work, we  apply the same procedure as Z19 using the data sets from SPT-SZ and Planck ESZ in the redshift range $0.278 \leqslant z \leqslant 1.32$ and $0.059 \leqslant z \leqslant 0.546$, respectively. One difference with respect to Z19, however is that we used direct gas mass fraction measurements
from SPT and Planck, instead of the empirical relation between halo and gas mass used in Z19.
These measurements  were obtained using a combination of SZ data along with follow-up X-ray observations from Chandra and XMM, for SPT and Planck, respectively.

Our  $f_{gas}$ measurements as a function of redshift can be found  in Fig.~\ref{fig:f1} for SPT-SZ and Planck ESZ clusters. We derived the angular diameter distance for both the datasets using GP fitting from $H(z)$ data reconstructed using cosmic chronometers. The reconstructed  gas depletion factor can be found in  Fig.~\ref{fig:f4} and Fig.~\ref{fig:f5} for SPT-SZ and Planck ESZ data respectively. To quantify the significance  of  our results obtained from GP reconstruction, we also did a maximum likelihood fit using Eq.~\ref{eq:gammavariation}. We find that $\gamma_0 = 0.915\pm0.05$ and $\gamma_1 = -0.305_{-0.058}^{+0.064}$ for SPT-SZ data; whereas  $\gamma_0 = 0.741\pm0.029$ and $\gamma_1 = 0.834 \pm 0.2$ for Planck ESZ data.
 The credible intervals  for  $\gamma_0$ as well as $\gamma_1$ along with marginalized 1-D distributions are shown in  Fig.~\ref{fig:f6} and Fig.~\ref{fig:f7} for SPT-SZ and Planck ESZ data respectively.   We find  $\gamma$ decreases with redshift (at about 5$\sigma$) for SPT-SZ clusters,  whereas it increases with  redshift for Planck ESZ clusters (at about 4$\sigma$). Both these findings  also contradict  hydrodynamical simulations which show a constant gas depletion factor. Previously, only Z19 had found a slightly decreasing trend  with redshift for $\gamma(z)$ using ACT-Pol data.

 Given the contradictory results between the two datasets, we carried out a series of cross-checks on our results using various extended tests, as outlined in Sect.~\ref{sec:dicussions}. We used simple parametric forms to model only the gas mass fraction, without any explicit dependence on the angular diameter distance (cf. Eqs.~\ref{eq:9},~\ref{eq:10},~\ref{eq:11}.)
 We then evaluated the gas depletion factor for both the datasets within the overlapping redshift range. Finally, we also added an explicit dependence on $M_{500}$ in the parameterization used for the gas depletion factor (cf. Eq.~\ref{eq:gammavariationwithmass}). The results of these extended tests are tabulated in Table~\ref{tab:extendedanalysis} and in Fig.~\ref{fig:f14} (SPT-SZ) and Fig.~\ref{fig:f15} (Planck ESZ). We find that the coefficients for the redshift dependent terms in Eqs.~\ref{eq:9},~\ref{eq:10},~\ref{eq:11} are consistent with no variation within 1$\sigma$. For Planck-ESZ, $f_1$ in Eq.~\ref{eq:9} is 5$\sigma$ deviant with respect to zero, which is one of the main underlying causes for a positive value for $\gamma_1$. If we analyze the evolution of the gas depletion factor for a subset of SPT-SZ and Planck ESZ clusters within the same redshift range, we find that $\gamma_1$ is consistent for both the datasets within $1\sigma$ (cf. last two rows in  Table~\ref{tab:summary_table}). Finally, when we allow for  a variation of the gas depletion factor with halo mass, we find that the decreasing/increasing trends with redshift for SPT-SZ (Planck ESZ) still persist, albeit with reduced significance of about $2-3\sigma$.

 \rthis{Therefore, our investigations on a model-independent test of the evolution of $f_{gas}$ reveal that the redshift evolution of the gas depletion factor depends on the redshift range,  and also changes depending on whether one includes/excludes a dependence on the halo mass. One possible reason for these changes is that the sample analyzed here is not the full SPT-SZ or  the Planck SZ sample as the optical/X-ray followups  is still ongoing.  Another possibility is that  the error in  $f_{gas}$ also depends on additional systematics such as observable to halo mass relation (which in turn is somewhat cosmology dependent), gas temperature and density profiles, hydrostatic equilibrium assumption, magnetic fields, thermal evaporation, which have not been completely accounted for, and could be redshift dependent.
 Nevertheless, given the observed  deviation from self-similarity found for both the cluster samples (and in C18)  and the significant change in the redshift dependence of $f_{gas}$ without reference to any underlying cosmology, one must include the dependence in halo mass for modelling  any evolution of $f_{gas}$ with redshift.}

 We note that, our results do not affect any cosmological parameter estimations with $f_{gas}$,  since most of those results were obtained with $f_{gas}$  estimated at $R_{2500}$~\cite{allen02,allen04,allen08,allen11}, whereas we used $f_{gas}$ measurements  at $R_{500}$.  Only a handful of works have used gas fraction measurements at $R_{500}$ for cosmology studies~\cite{Pen,ettori09}.
 However, if  the conflicting results for the two SZ datasets at $R_{500}$ \rthis{persist when extended to the full SZ dataset from both the telescopes, then it implies that  one cannot use  $f_{gas}$ values  at $R_{500}$ as a stand-alone probe  for any cosmological tests.}

\begin{figure*}[h]

 \includegraphics[width=12cm, height=10cm]{Figure_14.pdf}    \caption{Marginalized credible intervals (68\%, 95\%, 99\%) for $\gamma_0$, $\gamma_1$, $\zeta$, and $\ln (\sigma_{int})$ for the SPT-SZ dataset. The parameter $\zeta$ encodes the variation of the gas depletion factor as a function of $M_{500}$ (cf. Eq.~\ref{eq:gammavariationwithmass}).  }
 \label{fig:f14}
\end{figure*}

\begin{figure*}[h]

 \includegraphics[width=12cm, height=10cm]{Figure_15.pdf}    \caption{ Same as Fig.~\ref{fig:f14} for the Planck ESZ dataset. }
 \label{fig:f15}
\end{figure*}

\section*{ACKNOWLEDGEMENT}
We are grateful to Xiaogang Zheng for useful correspondence about Z19 and to the anonymous referee for many constructive suggestions on the manuscript, which helped us improve the draft.
KB would like to acknowledge the Department of Science and Technology, Government of India for providing the financial support under DST-INSPIRE Fellowship program.

redpajama_set_name: RedPajamaArXiv


It is the "original" St. Stanislaus Church in Modesto. The new, & much larger one, was built in 2008, right next to St. Stanislaus School. And while 18 million dollars was spent on the new church, it seems that the old church has been strikingly neglected.
McGurgan said the large number of preaching commitments in the Church — daily Mass, multiple Sunday Masses, weddings, and funerals — means Catholic homilists have to hone their craft constantly, so they welcome help.
First responders from across Stanislaus County gathered at St. Joseph's Catholic Church in Modesto on Saturday for the annual Blue Mass, a chance to thank the emergency personnel and offer prayers as they go back out to serve in the new year.
Catholic Dads » …..But Mass Is So Boring!
The Orthodox Christian Faith proclaims the Gospel of Jesus Christ, the teachings of the Apostles, and the tradition and life of the living Church worldwide through worship, communion, witness, and service.
by Carol Glatz, Catholic News Service Jul 21, 2018 Vatican City: According to tradition, the Holy Stairs are the ones Jesus climbed when Pontius Pilate brought him before the crowd and handed him over to be crucified. It's said that Constantine's mother, St. Helen, brought the stairs to Rome from Jerusalem in 326 A.D.
She was a line worker for Husman Hatchery. She was a parishioner of St. Joseph's Catholic Church in Modesto, former parishioner of St. Joachim's Catholic Church in Newman and a member of the Catholic Daughters of Newman.
Services Offered by Precision Line Boring & Welding. Line Boring services Houston, a wide range of services, Mobile Welding, Fabrication, Mobile Machining.
Find 23 listings related to Holy Trinity in Modesto on . See reviews, photos, directions, phone numbers and more for Holy Trinity locations in Modesto, CA.
The background of the Chaldean Catholic Church is the Church of Assyria and Mosul, formed out of the Church of the East in 1552 by Patriarch Shimun VIII Yohannan Sulaqa, recognised as "of the Chaldeans" by the Holy See.
Join us for Weekly Line Dancing in Our Lady of Fatima Shrine Church Hall Every Friday evening (except first Friday) from 6:00 – 7:30 pm Beginner or Pro come out and shake a leg, have fun and meet new friends.


The autum in Høvringen has a charm of it's own. Mother nature has already begun to prepare for a long winter, and can show off a sparkling explosion of colour without comparison. By then, you'll have more of Rondane all to yourself, giving you the space and time to peacefully and quietly enjoy the mountain landscape at it's best. Late summer and autumn is also the time to collect berries and fungi. Blueberries and mountain cranberries cover the forest floor of the valley sides, and on the mountains you can hunt for hidden gold- cloudberries.
Høvringen Fjellstue is one of the oldest mountain Lodges in Rondane which has been in the same Family for more than 120 years. Our guestbooks date back to 1903, but we have been welcoming guests since the 1890's.
Today the Lodge is run by mother and son - the 3rd and 4th generation.


Oiselle staffer Shanna, a mother runner expecting her second child, reviewed running strollers for Running Times.
Check out the April 2013 issue of Running Times to read Shanna's review and see her stylin' Oiselle threads.
The rainy season isn't over yet! Women's Running featured Oiselle's Clearly Jacket for rainy runs and the Stride Short for indoor workouts in their April 2013 issue.
Find the April 2013 issue of Women's Running on your newsstand this month.
Women's Running quoted Oiselle bird Shanna Burnette in a feature on mother runners.
Sally was recently featured in SGB Weekly, the digital magazine of the sporting goods industry.
Read Sally's insight into the women's running apparel industry on page 26 here.


It seems the numeric designation for Burnout 5 was just a place-holder for the real name: Burnout Paradise. While we've had a few bits and pieces of news and glimpses of screens screens about the game before, it's all official now, with a release slated for this winter. The press release accompanying the (rather blurry) screens states that the game is currently under development for both the Xbox 360 and the PS3, making earlier statements about the game hitting Sony's console first look a little unlikely. While a simultaneous release wasn't confirmed, given the way things are selling right now, that may wind up being the case. We will of course let you know more when we hear it.
GameSpot has had the opportunity to spend a little time with upcoming Xbox 360 smash-up racer FlatOut: Ultimate Carnage, due in the US and Europe later this summer. Without a doubt, they like what they see.
The main body of content in FlatOut: Ultimate Carnage is basically the same as in FlatOut 2, although it looks a little different. You jump in one of more than 40 different cars, and then try and win races, not just by being the fastest on the track, but by smashing up the opposition as well. You're also rewarded for driving on the edge and receive a boost bonus for power slides and other risky manoeuvres. However, anybody who played the old game will still find plenty that's new this time around, with some fantastic visuals, a couple of new vehicles, and a raft of new gameplay modes included.
There are now 12 cars in every race, each containing around 25,000 polygons, along with 40 distinct deformable panels, which deteriorate throughout each race as you collide with objects or other cars. The effects feel more dynamic than in the previous game, and while you can fail to finish a race if your car is completely destroyed, your ride will take quite a beating before that happens.
To read the rest and check out their 360-degree screenshot head on over to GameSpot.
It was just over a month ago that MotorStorm finally got an update to include a friend's list, along with a few other minor tweaks. There's another fix coming, version 1.2, that will make those friends lists even longer (maximum of 50 friends), will fix a few exploits some racers have been utilizing, and will also finally force races to start after a set time, hopefully helping to prevent having to wait forever for someone to ready up. You can read the full details at Pro-G.
Word comes from Pro-G that SBK 07 will be hitting the PS2 and PSP in Europe on May 18. This is a month's delay from the earlier plans for a release in April. No real updates on the Xbox 360 and PC versions, but those weren't due until October anyway.
It seems Voodoo Extreme have a copy of Forza Motorsport 2 to play with, and are showing off by posting up a lengthy video showing a Camaro SS vs. a Toyota MR-2 at the always exciting Suzuka circuit. Head on over to watch.
As at least one of you noticed, the site went a bit stagnant last week. Apologies but as of now this is largely a one-man-shop and, when that one man is unavailable, the shop gets a bit stale. But, we (I mean me) are back and will be trying to get caught up this am. Also, this is a lovely time to say we (I mean me) are always looking for those who can contribute to write up a news post or two in the morning. If you're interested post a comment and I'll get back to ya.
Alas, it seems last week's May 29 delay of Forza Motorsport 2 was only for the US. The game's release, which had been planned be release simultaneous in the US and abroad, has apparently been split and the game won't find it's way to the UK and elsewhere in Europe until June 8 according to Pro-G. Not terrible, especially considering the long delays many games see as they get localized from one continent to the other, but that'll still be a long week for European Xbox 360 owners.
It seems this morning's good news including the complete car list for Forza Motorsport 2 has unfortunately been tempered by some bad news: the game won't ship on May 15 as most recently planned. It's getting pushed back another two weeks to May 29. What impact this means for the demo, slated to ship by the end of April, remains to be seen.


The UEA is committed to helping educators be successful in their career. That includes "taking the lead" by providing resources to navigate evaluation requirements. Resources available for members include an evaluation toolkit, discussion guides for each of the Utah Effective Teaching Standards, tools for implementing student learning objectives (SLO), a five-module curriculum on assessment literacy, training on having a successful "critical conversation" and more. For more information about the resources available in your school district, contact your local UniServ office or log onto the UEA members-only website.
Significant changes to educator evaluations have been made over the past few years. Both Utah State Board of Education (USBE) rule and Utah State code have been modified to address educator evaluation with the goal of improving educator effectiveness and instructional quality.
The weight given to each of these components will be determined by each district.
According to state code, the evaluation system must categorize educators into one of four levels of performance. If an educator's evaluation identifies unsatisfactory performance, the district must "develop and implement a plan of assistance" to allow the educator "an opportunity to improve performance". An educator receiving the lowest rating ("not effective") on an evaluation may not advance on the salary schedule.
Educators will receive a performance rating based on data from multiple evaluation components. There is no requirement, either in state code or Board rule, that there be a certain number of educators rated in each category of performance ratings. In other words, there is no requirement for a "bell curve" distribution.
The UEA will continue to represent educators with the legislature, on USBE committees, and with the USBE. Count on local association leaders to also represent teachers at the district level.


Budweiser has made it a tradition to create emotional Super Bowl ads. But this year, the brand's "Lost Puppy" commercial is enough to make a grown man cry. And you thought you were a cat lover. Ha ha ha.
Sorry cats, but you can't win 'em all.
Check out this year's ad made even more incredible when set to Ginuwine's "Pony." (Everything's better when tied back to Channing Tatum, right?) You're welcome.


text:
Bob Stilger
May 15 ~ Bob Stilger's Notes from Japan #15: Reasons for Hope
My friend Val, from Elos Institute in Brazil wrote me recently:
I love your questions about what can be done right now, what are the possible solutions. Yesterday I attended a philosophy class and people's perspectives about the world were so dark and hopeless… I immediately remembered of you and other people giving a step towards what you believe can be done to make things better. I would like to hear what are the things that are being done now. I remember wrote about an afternoon with Bob in which people wrote down the questions they wanted you to answer: it was very clear for me how this kind of conversation can make space for healing and care in a community. People are looking for inspiration and hope that the world is worthy and so are the human beings.
Val asked that I write something for Elos's newsletter for Warriors Without Weapons along these themes and I realized if might be something good to write for others as well.
Imagine waking up one morning to your normal life and its routines. Imagine that by day's end, your normal life has vanished — toppled in an earthquake, washed away by a tsunami, hammered by invisible radiation. Or imagine that you're in a downtown office building in Tokyo, ten miles from your home. The building sways back and forth and things begin to pile on the floor. Eventually it quiets and you make your way downstairs to the street which is dark, filled with people and cars, and the trains are no longer moving. Imagine you are hundreds of miles away and you begin to see horrific images on television. Where does one find hope?
One man, an executive at a television station in Shikoku, told me that the afternoon of 3.11 he was shaken to his core and was convinced that Japan must surely die that day. He could not imagine how life could continue. And yet it did.
There's the story of my new colleague from Tohoku University in Sendai. I wrote about her earlier. In her third floor office when the earthquake hit, she and an assistant hid under a table as the building shook and all her books came flying off the wall. When she eventually made it back to her home, it was without power and everything was a mess. She ended up sleeping side-by-side with neighbors she did not know from her same apartment building. After two days, they returned to their building. One man, on the ground floor, said "I have a kerosene stove, bring all the food you have here and we can prepare together." And so they did, eating two hot meals a day together as they began to restore their apartments. And they began to make community.
I think of the sake shop owner whose building we cleaned out during a trip to Ishinomaki City near Sendai. I don't know if any of his family members were killed. Clearly his business was destroyed. While we rescued some inventory as we cleaned, I'm not sure that even the shell of the building can be used again. And business? Customers? Not for a long time. And when we finished cleaning up, he radiated gratitude. I am sure he goes through different cycles, but on that day he seemed so much more in touch with what he had than bitter about what he had lost.
And yet, of course, there are those who are in deep pain and grief. The fishermen who managed to stay safe at sea, only to and find their families missing and homes destroyed. Or the people who have become lost in despair and are taking their own lives, because they see no hope for the future. return
I don't know about hope and hopelessness. Mostly I am attracted to a Buddhist orientation in which we travel to a place beyond hope and despair where in some ways hope simply becomes irrelevant. The invitation in this space is to just live one's life, dealing with what is present, and not get caught up in endless cycles of hope and hopelessness. There's something important about doing the work in front of us because it is the right work to do and not worrying about whether it will ultimately make a difference or not. HOWEVER, most people don't see it that way. So what to do?
Many things are happening at once in Japan. Everyone is doing their best. Many people have different ideas about what is right. There's some time spent trying to find someone to blame. Lots of people are still in deep shock, ripped apart from their lives. People all over Japan and all over the world want to help. The people I spend my time with here believe we must support people in Tohoku in building their own communities again. We must help create conditions that support them in coming together to have conversations that matter — conversations which can host deep grief, deal with the practical matters of how to live daily lives now, and begin to envision and build a future. In some ways it is the same everywhere. We must turn to one another and become community again.
Going back to Val's question "is the world worthy and are human beings?" Heck, I don't know — but this is the life we have been blessed to live and we might as well give it a go. I can't see spending much time complaining!
Bob Stilger is the Founder and currently President of New Stories, a nonprofit that uses the power of story to help people regenerate community. After leading a local community development corporation in Spokane, Washington for 25 years, Bob's work has stretched to many parts of the world including Japan, Zimbabwe, South Africa, Brazil, Australia. Co-President of The Berkana Institute from 2005-2009, Bob has a PhD in Learning and Change in Human Systems from the California Institute of Integral Studies. Since 2010 he has done extensive work in Japan, introducing collaborative spaces called "Future Sessions" as well as many participatory leadership processes. Eiji Press of Tokyo published "AfterNow: When We Cannot See the Future, Where Do We Begin" in June, 2015. New Stories published the English Edition in 2017. The current focus of Bob's work is helping communities transform after disaster strikes.
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The mammoth İzmit Bay Bridge, a key part of the Gebze-Orhangazi-İzmir Highway Project which will shorten the travel time between Istanbul and the Aegean city of İzmir dramatically, has been named after Osman Gazi, the founder of the Ottoman Empire.
The last section of the bridge was mounted on April 21 in an official ceremony, attended by President Recep Tayyip Erdoğan and Prime Minister Ahmet Davutoğlu as well as several ministers.
Erdoğan announced the name of the bridge as the "Osman Gazi Bridge" during his speech.
The bridge is expected to be opened by the end of May and will shorten the time to travel to the other side of İzmit Bay drastically. As a part of the Istanbul-İzmir Highway Project, the İzmit Bay Bridge will be the fourth largest in the world by the length of its central span.


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text:
Home >> News
PM Skerrit among regional leaders and organizations to condemn attack on St. Vincent PM
Dominica News Online - Tuesday, August 10th, 2021 at 8:44 AM
Various Caribbean leaders and authoritative bodies have spoken out against the recent violent attack on Saint Vincent and the Grenadines Prime Minister Ralph Gonsalves, who was injured by a demonstrator during a protest in his country last week.
Prime Minister Roosevelt Skerrit, one of the latest leaders to denounce the attack, said in a live radio interview aired on DBS Radio and Kairi FM on Sunday August 8, 2021, that such behavior must be condemned from all sides.
Gonsalves was struck with an object in the head while making his way back to parliament in Kingstown on Thursday August 5, 2021. Bleeding profusely, he was rushed to the hospital and then flown to Barbados that same evening for a magnetic resonance imaging (MRI) or head scan.
Fifty-six-year-old female vendor Anna May Lewis was arrested and charged with wounding in connection with the incident. She has since been bailed in the sum of $3,000.
"Clearly the person who sent this projectile intended to harm the prime minister. Every right thinking citizen of this Caribbean and this world should condemn such violence on anybody, whether it is a prime minister or an ordinary citizen," Skerrit said.
He warned that while everyone has a right to protest, the law must be adhered to.
"Politicians must understand that debate can't be won by violence. Debates have to be won based on your argument, on your point [and] on your ability to research and to articulate your point in the parliament. That's what democracy is about. And politicians these days, when they believe they cannot win the battle [and] they cannot win by the polls, [or] they cannot win the debate in the parliament they want to resort to violence and every one of us must condemn this," he stated.
"We've always maintained that people have a right to protest but your right to protest should not be a justification for your action of disobeying the law and causing harm to an individual and everybody must condemn this action…" he also said.
Skerrit took the opportunity to lash back at politicians whom he said are "glorifying" the violent incident instead of taking a stance against it.
"I mean, are we that uncivilized? Are we that desperate to be in power… they believe that is by violence that they can get into government?" he asked.
According to Skerrit, doctors have indicated that had the projectile hit Gonsalves a bit lower on the head, he could have been dead.
Meanwhile, the Caribbean Community (CARICOM) has issued a statement further condemning the attack "in the strongest terms."
The organization said, "This reprehensible act is an affront to our democratic principles and practices. The conduct of peaceful protest is a fundamental civil and political right that represents a healthy element of our democracy. Its degeneration into violence and physical assault must be denounced unreservedly."
Calling for peace and calm, CARICOM wished Gonsalves a speedy recovery and said that it looks forward to the perpetrator of this "aggressive act" being brought to justice.
The Christian Council in St. Vincent also lent its voice saying it was concerned about the recent development.
It said that while democracy allows for the freedom of expression, this freedom brings with it personal and social responsibility.
The council said that such an incident indicates an intolerance of divergent views opinions and positions, and added that it abhors violence and urged those who choose to protest to do so peacefully and responsibly.
The Organization of Eastern Caribbean States (OECS) Chairman Dr. Keith Mitchel labelled the attack as heartbreaking and said it was not a true representation "of our true nature as Caribbean people, for this is not how we settle differences, political and otherwise."
"Within the OECS, we strongly uphold the tenets of democracy and the right of citizens to protest and to have their voices heard, but to do so peacefully and in accordance with the law. The OECS Authority unequivocally condemns the use of violence of any kind and any expressions of protest, such as the burning of police barriers in the street, as was witnessed in St. Vincent on Thursday," he said in a statement.
The OECS authority also called on the opposition forces to "unambiguously disassociate themselves from such anarchistic acts and to encourage supporters to keep their protest within the ambits of the law."
Similar sentiments have been echoed by various other country leaders including Anguilla and Montserrat.
"As Caribbean nations we are interrelated, interconnected and mutually vulnerable to what grows when the roots of violence are allowed to spread. We cannot afford for such to happen, if not for ourselves for the generations looking on," Anguilla's Prime Minister Ellis Webster said.
Montserrat's Premier and Minister of Foreign Affairs, Joseph E. Farrell said that violence and personal assaults have no place in Caribbean politics.
He maintains "that there can be no compromise on this front as such acts of violence are a threat to national security and do not in any way help our democracies."
Woman arrested in connection with assault of Ralph Gonsalves; two protesters also attacked
PM Skerrit to attend OECS Heads summit in Antigua
Congratulatory message to Prime Minister Ralph Gonsalves of St. Vincent and Grenadines on election victory and fifth term in office
PM Skerrit in St. Kitts for OECS Authority meeting
St Vincent PM urging citizens to think seriously about withdrawing funds from RBTT
I sincerely apologize to % & Ibo France. It was not intentional but, I should be more professional and intelligent in my approach.
@ Ibo France, I give up. Thanks for your advice. I wish % well in all his endeavours.
Francisco Etienne-Dods Telemaque
Citizens of the Caribbean, and the rest of the world should not condemned any actions, violent or otherwise taken against the corrupted politicians, across the Caribbean.
People do get tired; and when frustration sets in; they get angry, and snap!
The Gonzales' and Roosevelt's are shaking, urinating, and defecating in their shoe!
Because Gonzales recently won an election in St. Vincent does not mean he is loved by the entire population, the same thing applies to Dominica where elections are bought and paid for.
There is something some need to know; most of the time the abuse victims usually cleave to the abuser, that is what has happened in Dominica and St. Vincent, it is not love for the corrupted Roosevelt.
"President Thomas Jefferson on Politics and Government. Compiled and edited by Eyler Robert Coates:
Sr. "A Little Rebellion Now and Then is a Good Thing: A Letter from Thomas Jefferson to James Madison." Early America Review."
Gonzales getting his…
LifeandDeath
They fail to see the symbolism in the burst head and blood stained shirt. Although Ralph looks pensive (shocked, more likely) in that picture he, like many of the other Caribbean leaders including Skerrit are devoid of vision, consumed and deceived by their very own in vindictiveness and Glutton.
Their modus operandi is to continue to play with the emotions of the people while they enrich themselves. How many citizens have suffered much more from the arrogance and poor management style of these mis-leaders? Who are they fooling to come talk like they hold some high level of esteem and respect?
There is a lesson in the burst head and the blood stained shirt!!..#wakeup #takenote.
Jonathan Y St Jean
Is Skerritt implying that the woman who threw the projectile is a politician or that some politician directed her to throw it at Gonsalves? What a rediculous statement for him to want to rebuke opposition politicians for the misguided actions of one individual. Why hasn't he painted with such a broad brush regrading the behavior of the few misguided police who killed Slobbie. He knows it was not the entire body of the police force who are responsible for that atrocity, so why does he go there when one person acts crazy and hurts Gonsalves. He should exhort his Caribbean colleagues to act with wisdom and not provoke angry citizens by seeking to walk through a crowd protesting against a law which they find infringes upon their rights. This crop of leaders in the region are using the police to repress the rights of citizens who don't agree with them and this needs to stop. Nothing wrong with safely burning things to dramatize disagreement, it happens all over the world.
You can condemn as much as you want, its like the fox who condemns the hunter whose fowl he killed. All you guys will pay for all your dead…
Comrade Ralph, the man with the Hitler moustache and the Apex Dunce in Dominica have proven that:
*Politics and Honesty are eternal enemies
*Politics and Lies are identical twins
*Politics and Selfishness are bosom friends
*Politics and Empathy are fierce rivals
*Politics and Corruption are an inseparable couple
*Politics and Self-enrichment are bedfellows
Politics changes a man with honorable intentions to an egotistical, villainous, unloving infidel.
What level of leadership did Gonsalves display when he decided to get out of his vehicle and walk through a crowd protesting against his proposed legislation? It reveals a pig headedness and arrogance by a moronic leader. Ralph Gonsalves got what he deserved. Where were the voices of the other leaders and the regional bodies when Salisbury residents were tear gassed in their beds by OECS power hungry military wannabe types? This cult of like-minded thinking politicians and technocrats who they have put to staff these organizations to help them achieve their misguided missions of riding roughshod over a majority of their citizens, deserve nothing but scorn. None of them expressed an opinion on the issue of forcing people to take a vaccines which only have emergency use authorization and have not been fully approved yet. We will look back and realize that this period of our history is a troubling and backwards looking one for governance. Gonsalves bears blame too.
Talking in tongues
I too agree with PM Skerrit because in Dominica we must go all the way and make it to the finish line. Is only when we get to the finish line we are true winners
Mag way ca
Uncle take a lesson from that. People won't accept nonsense for much longer. Don't try to force people to take anything they don't want to . People will object and u won't like the outcome
Caricom has condemned the attack on Gonzales??? OMG!!!
What a disgraceful grouping Caricom is..This same grouping (Caricom) knew that Jovenel Moise was a dictator, plundering the wealth of Haiti, his police and special gangs were killing opposition supporters, kidnapping was going out of style. As a member of Caricom those atrocities were never condemned by Caricom. Caricom knew of the alleged kidnapping of Choksi, and the two countries, Dominica and Antigua allegedly invoved. Caricom knew there was no place for RSS in Dominica on the eve of the 2019 general elections. Caricom knows about the dictatotial tendencies of Skerrit, Gonzales,etc. Caricom knows that in both St Vincent and Dominica most of their important institutions of state are dysfunctional..
So CARICOM is a big farce. A boys club, serving themselves, not the people. SHAME ON CARICOM!!!
Do you know its Gaston that's the present chair of Caricom..OMG!!!
😄😄😄😄😄😄😄😄😄😄😄😄😄😄😄😄😄😄😄😄😄😄😄😄😄😄😄😄😄😄😄�
Did you apply to head one of the dysfunctional Institutions and you were rejected? I am not surprised. You probably would not know where to start.
Die Hard Dominique
Skeritt said that? WOW!!! What is worse Mr. "AM" I mean PM? A little burst head? (well deserved) or to tear gas men, women and children in the wee hours of the morning while they slept?? This guy Skeritt, is unbelievably evil and has no qualities of any kind of a leader. What a deplorable human "bean head." You have no shame, no dignity, no human decency, no morals, no qualifications for the post you cheat to keep, no remorse for the evils you continue to Demon – strate, no intellect for reasoning and understanding, no manners, no guilt for cheating the poor people and country….you will find no pardon down here, up there, or nowhere. You are a lost soul. My name is: Die hard Dominique, and I approve this message.
I don't condone the physical attack on Comrade Ralph. However, we should use discernment, at all times, especially in volatile situations.
I didn't read all of Skerrit's statement on this issue. I knew he would want his five (5) minutes of attention in the media. Can't take his smelly cow pie. These roguish occupants of the highest office of government ( Gaston, Roosevelt and Comrade Ralph) blame the Opposition in their countries for everything wrong., even for the bad weather.
In any incident, I don't focus on the main issue alone. I also look at the peripheral issues. Why would Comrade Raphie choose to walk through a sea of very livid protesters? No intelligent person would even attempt such. Many people conflate education with intelligence. They are not the same. That was not an intelligent thing to do.
You don't deliberately walk into trouble. The sensible thing to do is to avoid it. I hope Comrade Ralph has learnt a valuable lesson from this unfortunate incident.
RandyX
Skerrit, once you guys learn to behave in a way that is expected of leaders, then you might get some sympathy. You guys always forget that you got 'elected' to SERVE your country and not the other way round. By law you are required to account properly for state funds and state expenditures. How often have you been asked and reminded to do so? How often have you been asked to deliver fair and transparent elections? How often have you been asked to conduct yourself in a professional and law abiding manner in Parliament. How often have you been asked to refrain to use the police force in a manner that is at best questionable and at worst breaking the law? How often have you been asked not to interfere with court matters wether that be directly or indirectly? You see all these things I just mentioned should not have a place in Caribbean politics but unfortunately they do. With it comes violence eventually, when people feel they haven't got a voice anymore or a being taken for a ride. Stop!
Skerrit is by far the emptiest, duncest and most poorly lettered politician in the region. 99.999% of his speeches are confusing and directed to his base. He also butchers the english language. What the Vincentians are frustrated about is 20 years of Gonzales rule that have impoverished St Vincent, the missing hundreds of millions that they want, the lack of health care, the bribing at election times, etc,etc. In fact Gonzales is so wicked after 20years he still cannot trust healthcare in his own country. He is a corrupt politician like others in Antigua, Dominica, etc.
His idiocy almost caused his death. Among charged up demonstrators be has impoverished, he wanted to walk amongst them???
Political office must always be transient.. It's only dishonest leaders who cheat, lie and steal rule for more than at least 2 terms..
I am wondering whether you have a good command of the English language. I wonder what you mean by butchering the language? Did you take some remedial courses in English since you became an older person? Every Prime Minister today has impoverished their country. At least, that is the way % see it thru his lenses. They also cheat, lie, and steal – something % cannot do and will never do in the highest office of the land. Why? He simply does not possess what it takes to be a PM. All he gets is vicarious thrills out of watching and listening to Skerrit. He is a batiman.
Go read a book to enlighten yourself.
It's summer time!!!
I still read a lot of Mills & Boons and Barbara Cartland. Should I change my books. Which ones do you suggest? Help your brother. I guess what you cant do for self, you cant turn no one else.
Why don't you refrain from stalking %? Stalking is a crime. Your obsession with another man is unnatural. Go and stalk a member of the opposite sex. Stop harassing the man. He's not that inclined.
Only a dunce stalker (ds) would be fatally attracted to another person like you're to %. Every statement the man makes you feel compelled to criticize because you compulsively yearn for his attention. Leave the man alone.
Yes we too condemn violence on anyone whether its the PM or a garbage man. But one must ask the question, that is light of the death of the Haitian President what was Gonsalves doing walking into an angry protesting mob? That arrogance is jus too much knowing that people are hurting so much + Covid and more.
Lessons anyone?


We are here to provide quality childcare to all parents so that they can feel at ease and content that their little ones are properly cared for.
Children in Pre School who attend out of term time are automatically in the Holiday Club. We also welcome other children under eight who wish to use the Holiday Club.
Children will be able to use our computer area to play interactive games to help with their knowledge and understanding of ICT and further encouraged to play with our extensive range of resources and equipment both indoors and outdoors.
Your child will be encouraged to complete homework tasks related to specific areas. Your child will be encouraged to complete homework tasks such as reading, writing or mathematics. They will have help from a qualified member of staff to complete their work. This will provide you with the opportunity when arriving home to spend quality time and relaxation with your child.
Your child will have the opportunity to explore our outside play area experiencing resources and equipment suitable for their age and stage of development.
At Dickory Docks, we plan every child's day to make sure that it is fun and educational. All activities are carefully planned and are prepared appropriate to each age group.
Daily feedback is given to parents and guardians as well as parent's/curriculum evenings held twice a year. Parent/guardian's are encouraged to discuss their children's progress regularly with staff, and our nursery has an "Open Door" Policy, recognising the importance of parents having trust and confidence in our care of their children.
Our interactive website hosts a variety of educational games to support individual children's learning at home with the support of parents/guardians. Games are specifically chosen to meet the diverse backgrounds, culture, language and needs of all our children at Dickory Docks. We strongly encourage feedback on how the interactive games have supported your child. The information is used to form an assessment and next steps in your child's development target which are chosen and discussed in partnership with all parent/guardians.
Your child will be offered the opportunity to play games sometimes adult led that are developmentally correct for your child's age and stage of development. They are all designed to provide your child with your child's learning and a bit of fun thrown in!!!
Your child will have a selection of books to look at, read and learn from whilst they are at the club. They will all be developmentally suitable for your children.
Your child will be encouraged to take part in physical play such as skipping, dancing, football and running games. We will try to help keep your child as healthy as possible!!
Your child will also be encouraged to join in with our extra curriculum activities which include Drama and Dance through Expressive Arts and Design.
Dickory Docks has a strong commitment to children with Special Educational Needs and operates an inclusive environment for each child's needs. The Nursery has a designated Special Needs Coordinator who is fully qualified and vast experience of children with a number of health and educational needs. All children are encouraged to take part in Nursery activities.
The Nursery has achieved the Healthy Eating Award.
We have also been rated the highest grade 5H from Environmental Health.
Menus are displayed at various prominent places. We aim to provide well balanced and nutritional meals with an emphasis on healthy eating and healthy lifestyles. All meals are cooked in our own kitchen.
Staff should be informed if your child has any allergies or dietary requirements during the admission procedure.
We have our own cook on site who prepares food on site using fresh ingredients.
Breakfast commences at approximately 8 O'clock, we provide a range of cereals for your child to choose from.
Snack Commences at approximately 10 O'clock, we provide two different types of either fruit or vegetable.
Lunch commences at approximately 12 O'clock, the children will be given a hot meal, and a dessert.
Afternoon snack commences at approximately 2 O'clock.
Drinks Water and milk are available throughout the day.
Parents who wish to provide their own drinks for their child must only send in cartons or plastic bottles, for Health and Safety reasons. Under no circumstances are cans or glass bottles to be on the nursery premises. We promote drinking water and healthy drinks as necessary.
Designated members of staff hold a current Food and Hygiene certificate.
Children's religious and cultural needs are catered for upon request. Different foods and meals are incorporated into the weekly menus from around the world offering children new experiences and taste and also reflecting our setting's multi- cultural diversity.
Children have access to water throughout the day. Children are offered different fruits every day.
*Please note that if your child should be late coming into nursery please telephone before l0am so that a dinner can be reserved.
Children of working parents will be provided with a breakfast on arrival at nursery. All children receive a morning time snack at 10.30am. Dinner is at midday.
They sit with their friends to enjoy stimulating meal times that are made special by a strong family atmosphere.
To encourage children to have their 5 a day, children are offered snacks at 10.30 am and 2pm. Drinks are available in all rooms at all times.


text:
Sign up – Norgesskolen
Registration part 2
Photos from Norgesskolen
About Norgesskolen
Working at Norgesskolen
Our school facilities
Books, film & TV
Education and Work
All about May 17
17. mai-sanghefter / May 17 Song Booklets
Chapters and Representatives
How to become a Representative or start a Chapter
Let there be light..in Rjukan!
Rjukan in Telemark presents a unique installation, which will finally give light to the village's inhabitants. It's today a 100 years ago the idea of a solar mirrors was born, when Oscar Kittelsen wrote in the Rjukan newspaper. The mountains surrounding the city are so high that they obscure the sun all winter, but now the world's largest solar mirrors will bring the sun down to the valley. The sun will hit three huge mirrors, and thus reflected down to the town square. Hydro–founder Sam Eyde (1866-1940) was the first who tried to realize the idea. He wanted to bring the sunlight down to his workers, but had to give up, and instead built a cable car that could carry the workers up to the sunlight. The artist Martin Andersen brought the idea to life again in 2003 and initiated large-scale planning and research.
There have already been over 250 media stories about these mirrors, including in the New York Times, BBC, Canadian Television, CBS, and Chinese TV. On the occasion of the opening day, a local optometrist have sponsored the local school kids with 600 pairs of sunglasses.
The Solar Mirror.
Solar mirror or heliostat state, consists of a pillar of steel, sunshade and a washing system. The mirror must be kept clean for optimum effect.
It must be anchored in a concrete foundation, and the mirrors are rotated.
The mirrors are mounted on a surface which can be moved over a horizontal and a vertical axis.
Rotation and elevation of the mirror surface is done by using solar energy.
It must withstand wind forces and snow. It must remain still and be robust in order to avoid that a vibrating light hits the square.
Ref: Teknisk ukeblad
Telephone: (+47) 23 35 71 70
Email: info@nww.no
Email: skolen@nww.no
Board and Advisory Council