\begin{table}%t1
\caption{\label{tab:highz}Properties of the $z>0.3$ cluster sample described in Balestra et~al. (\cite{Balestra2007}).}
%\centerline
 {\tiny 
\begin{tabular}{lccccccccc}
\hline \hline \noalign{\smallskip}
Cluster & $z$ & $kT_{\rm gas}$ & $(a_0,a_1,a_2/10^{-3},a_3,a_4,a_6)$ & $R_{\rm spat}$ & $R_{\rm spec}$ & $R_{500}$  &  $f_{\rm gas}$  &  $\hat{R}_{500}$  &  $\hat{f}_{\rm gas}$  \\ 
  &  & keV &  & kpc & kpc & kpc & ($<$$R_{500})$ & kpc & ($<$$R_{500})$ \\
\hline 
MS$1008.1-1224$ & 0.306 & $6.90\pm0.35$ & $(0.928,0.028,3.9,0.39,1.13,0.44)$ & 688 & 490 & $1176\pm116$ & $0.135\pm0.045$ & $1303\pm179$ & $0.112\pm0.044$ \\
MS$2137.3-2353$ & 0.313 & $5.05\pm0.11$ & $(0.028,0.204,93.3,0.37,0.53,0.47)$ & 698 & 362 & $940\pm26$ & $0.152\pm0.016$ & $997\pm35$ & $0.135\pm0.016$ \\
A1995 & 0.320 & $8.61\pm0.35$ & $(0.142,0.290,7.3,0.32,0.30,1.56)$ & 855 & 479 & $1317\pm46$ & $0.091\pm0.011$ & $1429\pm60$ & $0.076\pm0.010$ \\
MACS-J$0308.9+2645$ & 0.324 & $12.73\pm1.02$ & $(0.104,0.230,11.2,0.30,0.30,0.96)$ & 1039 & 577 & $1423\pm68$ & $0.131\pm0.020$ & $1491\pm77$ & $0.120\pm0.017$ \\
ZW$1358.1+6245$ & 0.328 & $6.78\pm0.28$ & $(0.006,0.400,143.5,0.00,0.35,1.40)$ & 869 & 419 & $1157\pm73$ & $0.106\pm0.021$ & $1256\pm100$ & $0.090\pm0.019$ \\
MACS-J$0404.6+1109$ & 0.355 & $7.38\pm0.90$ & $(0.105,0.125,4.6,0.00,0.30,0.19)$ & 1398 & 782 & $887\pm63$ & $0.205\pm0.039$ & $850\pm68$ & $0.215\pm0.038$ \\
RXJ$0027.6+2616$ & 0.367 & $8.76\pm1.69$ & $(0.676,0.163,2.0,0.35,0.89,0.62)$ & 642 & 550 & $1299\pm269$ & $0.067\pm0.054$ & $1421\pm351$ & $0.055\pm0.048$ \\
MACS-J$1720.2+3536$ & 0.391 & $6.46\pm0.33$ & $(0.010,0.533,161.4,0.00,0.40,2.03)$ & 974 & 546 & $1200\pm104$ & $0.103\pm0.034$ & $1345\pm143$ & $0.078\pm0.028$ \\
ZW$0024.0+1652$ & 0.395 & $4.32\pm0.32$ & $(0.375,0.010,13.2,0.17,0.66,0.60)$ & 672 & 341 & $879\pm100$ & $0.098\pm0.035$ & $957\pm144$ & $0.083\pm0.031$ \\
V$1416+4446$ & 0.400 & $3.43\pm0.20$ & $(0.008,0.544,72.5,0.00,0.36,2.19)$ & 677 & 397 & $797\pm100$ & $0.135\pm0.058$ & $894\pm148$ & $0.110\pm0.058$ \\
MACS-J$0159.8-0849$ & 0.405 & $9.43\pm0.61$ & $(0.011,0.302,167.0,0.09,0.40,0.86)$ & 994 & 639 & $1214\pm62$ & $0.139\pm0.025$ & $1286\pm81$ & $0.125\pm0.022$ \\
MACS-J$2228.5+2036$ & 0.412 & $8.25\pm0.59$ & $(0.240,0.079,6.4,0.42,0.48,0.23)$ & 1211 & 753 & $1052\pm61$ & $0.217\pm0.033$ & $1091\pm82$ & $0.205\pm0.032$ \\
MS$0302.7+1658$ & 0.424 & $4.78\pm0.60$ & $(0.015,0.361,50.7,0.00,0.37,2.50)$ & 369 & 328 & $1041\pm92$ & $0.055\pm0.023$ & $1167\pm104$ & $0.041\pm0.016$ \\
MS$1621.5+2640$ & 0.426 & $7.22\pm0.75$ & $(0.248,0.212,3.9,0.12,0.30,0.96)$ & 1003 & 658 & $977\pm79$ & $0.153\pm0.040$ & $1006\pm106$ & $0.146\pm0.039$ \\
MACS-J$0417.5-1154$ & 0.440 & $10.84\pm0.98$ & $(0.015,1.000,137.1,0.00,0.40,1.58)$ & 1259 & 785 & $1340\pm105$ & $0.201\pm0.043$ & $1465\pm141$ & $0.171\pm0.036$ \\
MACS-J$1206.2-0847$ & 0.440 & $11.98\pm0.85$ & $(0.012,0.316,82.9,0.00,0.30,1.11)$ & 1259 & 785 & $1336\pm75$ & $0.161\pm0.028$ & $1416\pm95$ & $0.144\pm0.025$ \\
V$1701+6414$ & 0.453 & $4.36\pm0.28$ & $(0.011,0.842,66.4,0.00,0.39,2.50)$ & 729 & 370 & $826\pm98$ & $0.146\pm0.051$ & $910\pm150$ & $0.123\pm0.050$ \\
CL$1641+4001$ & 0.464 & $4.74\pm0.54$ & $(1.000,0.135,1.7,0.44,0.30,1.34)$ & 341 & 287 & $848\pm139$ & $0.079\pm0.059$ & $902\pm189$ & $0.070\pm0.055$ \\
MACS-J$1621.4+3810$ & 0.465 & $6.62\pm0.74$ & $(0.301,0.010,139.1,0.00,0.30,1.14)$ & 893 & 458 & $980\pm102$ & $0.152\pm0.041$ & $1037\pm146$ & $0.137\pm0.037$ \\
MACS-J$1824.3+4309$ & 0.487 & $9.69\pm2.82$ & $(0.034,0.343,7.6,1.50,0.30,0.00)$ & 765 & 506 & $930\pm189$ & $0.136\pm0.072$ & $873\pm223$ & $0.145\pm0.069$ \\
MACS-J$1311.0-0311$ & 0.492 & $8.17\pm0.86$ & $(0.086,0.029,39.8,0.00,0.44,0.59)$ & 631 & 478 & $1055\pm72$ & $0.106\pm0.026$ & $1112\pm85$ & $0.096\pm0.023$ \\
V$1525+0958$ & 0.516 & $5.54\pm0.40$ & $(0.740,0.092,4.2,0.00,1.20,0.59)$ & 834 & 490 & $901\pm113$ & $0.137\pm0.050$ & $1002\pm168$ & $0.115\pm0.048$ \\
MS$0451.6-0305$ & 0.540 & $9.11\pm0.45$ & $(0.481,0.082,14.4,0.02,0.82,0.71)$ & 1167 & 625 & $1292\pm86$ & $0.129\pm0.025$ & $1446\pm124$ & $0.099\pm0.020$ \\
MS$0015.9+1609$ & 0.541 & $9.59\pm0.43$ & $(1.000,0.256,3.5,0.38,0.54,1.18)$ & 1408 & 626 & $1177\pm54$ & $0.180\pm0.020$ & $1279\pm78$ & $0.155\pm0.018$ \\
MACS-J$1149.5+2223$ & 0.544 & $13.10\pm1.12$ & $(0.769,0.225,5.0,0.00,1.20,0.46)$ & 1147 & 944 & $1536\pm150$ & $0.103\pm0.031$ & $1734\pm201$ & $0.079\pm0.025$ \\
MACS-J$1423.8+2404$ & 0.545 & $7.55\pm0.59$ & $(0.019,0.875,164.6,0.00,0.52,2.50)$ & 805 & 504 & $1176\pm138$ & $0.091\pm0.041$ & $1343\pm187$ & $0.067\pm0.033$ \\
V$1121+2327$ & 0.562 & $5.24\pm0.37$ & $(0.811,0.590,1.4,0.36,1.20,2.50)$ & 647 & 447 & $1053\pm167$ & $0.071\pm0.043$ & $1217\pm225$ & $0.050\pm0.031$ \\
SC$1120-1202$ & 0.562 & $6.35\pm1.15$ & $(0.039,0.037,12.9,0.00,0.30,0.47)$ & 297 & 318 & $795\pm132$ & $0.083\pm0.057$ & $795\pm163$ & $0.082\pm0.058$ \\
RXJ$0848.7+4456$ & 0.570 & $3.42\pm0.35$ & $(0.150,0.119,2.8,0.44,0.30,0.90)$ & 380 & 196 & $648\pm91$ & $0.074\pm0.039$ & $679\pm127$ & $0.068\pm0.039$ \\
MACS-J$2129.4-0741$ & 0.570 & $9.17\pm0.90$ & $(0.105,0.830,14.4,0.32,0.48,2.50)$ & 1199 & 639 & $1339\pm81$ & $0.089\pm0.014$ & $1526\pm92$ & $0.066\pm0.009$ \\
MS$2053.7-0449$ & 0.583 & $5.77\pm0.51$ & $(1.000,0.191,1.0,0.71,0.30,1.21)$ & 568 & 357 & $903\pm132$ & $0.075\pm0.036$ & $975\pm183$ & $0.065\pm0.033$ \\
MACS-J$0647.7+7015$ & 0.584 & $12.79\pm1.59$ & $(1.000,0.311,2.7,0.57,0.30,1.92)$ & 832 & 584 & $1440\pm149$ & $0.077\pm0.027$ & $1586\pm192$ & $0.061\pm0.021$ \\
RXJ$0956.0+4107$ & 0.587 & $7.59\pm2.00$ & $(1.000,0.138,3.5,0.00,1.18,0.91)$ & 450 & 424 & $1046\pm332$ & $0.088\pm0.130$ & $1152\pm457$ & $0.072\pm0.122$ \\
CL$0542.8-4100$ & 0.634 & $8.36\pm1.09$ & $(1.000,0.168,2.2,0.41,0.30,1.03)$ & 714 & 539 & $946\pm116$ & $0.126\pm0.045$ & $984\pm164$ & $0.119\pm0.043$ \\
RCS-J$1419.2+5326$ & 0.640 & $4.35\pm0.74$ & $(0.053,0.043,29.0,0.00,0.30,0.72)$ & 276 & 303 & $685\pm140$ & $0.157\pm0.114$ & $709\pm192$ & $0.148\pm0.107$ \\
MACS-J$0744.9+3927$ & 0.686 & $9.58\pm0.67$ & $(0.010,0.217,159.7,0.00,0.36,0.59)$ & 1079 & 695 & $963\pm43$ & $0.192\pm0.026$ & $995\pm53$ & $0.183\pm0.024$ \\
RXJ$1221.4+4918$ & 0.700 & $8.37\pm0.82$ & $(1.000,0.308,2.1,0.28,0.30,1.63)$ & 901 & 562 & $990\pm81$ & $0.114\pm0.026$ & $1064\pm103$ & $0.101\pm0.022$ \\
RXJ$1113.1-2615$ & 0.730 & $5.92\pm0.76$ & $(0.327,0.035,12.9,0.00,1.15,0.79)$ & 290 & 286 & $934\pm177$ & $0.039\pm0.058$ & $1046\pm238$ & $0.030\pm0.049$ \\
RXJ$2302.8+0844$ & 0.734 & $8.39\pm1.35$ & $(0.116,0.103,7.0,0.00,0.30,0.78)$ & 930 & 393 & $856\pm84$ & $0.090\pm0.028$ & $876\pm95$ & $0.087\pm0.026$ \\
MS$1137.5+6624$ & 0.782 & $6.87\pm0.52$ & $(0.067,0.427,20.4,0.00,0.47,2.18)$ & 590 & 367 & $893\pm123$ & $0.089\pm0.040$ & $968\pm172$ & $0.075\pm0.037$ \\
RXJ$1317.4+2911$ & 0.805 & $4.51\pm1.17$ & $(0.110,1.000,3.6,0.45,0.60,1.20)$ & 202 & 184 & $693\pm112$ & $0.042\pm0.026$ & $751\pm130$ & $0.037\pm0.021$ \\
RXJ$1350.0+6007$ & 0.810 & $4.44\pm0.67$ & $(1.000,0.538,0.6,0.78,0.30,2.50)$ & 526 & 483 & $615\pm146$ & $0.151\pm0.102$ & $660\pm219$ & $0.140\pm0.121$ \\
RXJ$1716.4+6708$ & 0.813 & $7.04\pm0.81$ & $(1.000,0.254,1.5,0.67,0.30,1.79)$ & 565 & 408 & $844\pm124$ & $0.110\pm0.055$ & $904\pm166$ & $0.097\pm0.051$ \\
RXJ$0152.7-1357$S & 0.828 & $9.43\pm2.35$ & $(0.367,0.533,3.6,0.35,1.20,1.20)$ & 420 & 400 & $1162\pm248$ & $0.030\pm0.037$ & $1326\pm309$ & $0.022\pm0.026$ \\
MS$1054.4-0321$ & 0.832 & $7.91\pm0.48$ & $(1.000,0.323,5.6,0.00,0.30,2.39)$ & 848 & 599 & $962\pm92$ & $0.147\pm0.038$ & $1067\pm128$ & $0.120\pm0.031$ \\
RXJ$0152.7-1357$N & 0.835 & $6.74\pm1.03$ & $(0.073,0.642,7.8,0.00,0.30,2.50)$ & 582 & 442 & $866\pm179$ & $0.117\pm0.094$ & $975\pm265$ & $0.095\pm0.094$ \\
1WGA-J$1226.9+3332$ & 0.890 & $12.14\pm1.38$ & $(0.077,0.257,29.1,0.00,0.46,0.87)$ & 677 & 497 & $1126\pm166$ & $0.085\pm0.040$ & $1222\pm226$ & $0.071\pm0.035$ \\
CL$1415.1+3612$ & 1.030 & $6.93\pm0.74$ & $(0.040,0.316,18.2,1.02,0.30,2.50)$ & 425 & 318 & $857\pm93$ & $0.059\pm0.026$ & $960\pm121$ & $0.045\pm0.020$ \\
RDCS-J$0910+5422$ & 1.106 & $6.43\pm1.41$ & $(0.147,1.000,3.4,0.58,0.36,1.20)$ & 230 & 201 & $576\pm144$ & $0.117\pm0.092$ & $570\pm208$ & $0.116\pm0.096$ \\
RDCS-J$1252-2927$ & 1.235 & $7.57\pm1.18$ & $(1.000,0.089,4.0,0.32,0.30,1.20)$ & 329 & 287 & $636\pm123$ & $0.079\pm0.061$ & $662\pm172$ & $0.073\pm0.061$ \\
RDCS-J$0849+4452$ & 1.261 & $5.21\pm1.31$ & $(0.046,1.000,10.3,0.00,0.36,1.20)$ & 222 & 197 & $504\pm152$ & $0.103\pm0.100$ & $512\pm216$ & $0.099\pm0.103$ \\
RDCS-J$0848+4453$ & 1.273 & $3.75\pm1.86$ & $(0.069,1.000,6.8,0.00,0.60,1.20)$ & 112 & 165 & $432\pm151$ & $0.052\pm0.295$ & $456\pm192$ & $0.047\pm0.436$ \\
\hline 
\end{tabular}}
\medskip
Column~(1): name; Col.~(2): adopted redshift; Col.~(3): best-fit gas temperature within $R_{\rm spec}$; Col.~(4): best-fit parameters of the gas density profile in Eq.~(\ref{eq:ngas}) fitted over the radial range $0{-}R_{\rm spat}$; Col.~(5): outer radius $R_{\rm spat}$ where the signal-to-noise ratio is above~2; Col.~(6): radius $R_{\rm spec}$ of the circular region adopted in the spectral fit; Cols.~(7--8): $R_{500}$ and $f_{\rm gas}$ estimated by assuming the temperature profile in Eq.~(\ref{eq:tr}); Cols.~(9--10): $R_{500}$ and $f_{\rm gas}$ estimated by assuming a constant temperature equal to $kT_{\rm gas}$. A cosmology of $(H_0, \Omega_{\rm m}, \Omega_{\Lambda}) = (70$~km~s$^{-1}$~Mpc$^{-1}, 0.3, 0.7)$ is adopted here.
\end{table}