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<!-- DOI: 10.1051/0004-6361/200810878 -->

<h2 class="sec">Online Material</h2>

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<h2 class="sec"><a name="SECTION000100000000000000000"></a>
Appendix A: Fit of the deprojected gas density profiles
</h2>
We show the electron density profiles, obtained from the deprojection of the 
surface brightness, of the objects in our high-<I>z</I> sample. We overplot the best-fitted function form in Eq.&nbsp;(<a href="/articles/aa/full_html/2009/25/aa10878-08/aa10878-08.html#eq:ngas">5</a>) fitted over the radial range 
<!-- MATH: $0-R_{\rm spat}$ -->
<IMG
 WIDTH="45" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img299.png"
 ALT="$0{-}R_{\rm spat}$">.
Both the best-fit parameters and 
<!-- MATH: $R_{\rm spat}$ -->
<IMG
 WIDTH="29" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img1.png"
 ALT="$R_{\rm spat}$">
are quoted in Table&nbsp;<a href="/articles/aa/full_html/2009/25/aa10878-08/aa10878-08.html#tab:highz">1</a>.

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<div class="inset-old">
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<tr><td><!-- init Label --><A NAME="fig:profiles">&#160;</A><!-- end Label--><A NAME="1617"></A><A NAME="figure1368"
 HREF="img561.png"><IMG
 WIDTH="155" HEIGHT="231" SRC="Timg561.png"
 ALT="\begin{figure}
\par\vspace*{-0.0cm} \hbox{
\includegraphics[width=7cm]{ngas/MS1...
...s.ps}\includegraphics[width=7cm]{ngas/MACS-J1720.2+3536_ngas.ps} }\end{figure}"></A><!-- HTML Figure number: 13 --></td>
<td class="img-txt"><span class="bold">Figure A.1:</span><p>
Plots of the deprojected electron density profiles with the
best-fit model in Eq.&nbsp;(<a href="/articles/aa/full_html/2009/25/aa10878-08/aa10878-08.html#eq:ngas">5</a>) overplotted and the residuals 
<!-- MATH: $\sigma_i = (d_i-m_i)/\epsilon_i$ -->
<IMG
 WIDTH="96" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img28.png"
 ALT="$\sigma _i = (d_i-m_i)/\epsilon _i$">
shown in the bottom panel, where <I>d</I><SUB><I>i</I></SUB>, <I>m</I><SUB><I>i</I></SUB> and 
<!-- MATH: $\epsilon_i$ -->
<IMG
 WIDTH="13" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img29.png"
 ALT="$\epsilon _i$">
are the values of the data, model and error on the data at a given radius, respectively. Together with the 
<!-- MATH: $\chi^2 = \sum (d_i-m_i)^2/\epsilon_i^2 = \sum \sigma_i^2$ -->
<IMG
 WIDTH="161" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img30.png"
 ALT="$\chi ^2 = \sum (d_i-m_i)^2/\epsilon _i^2 = \sum \sigma _i^2$">
value, the <I>R</I> factor represents a measure of the overall residuals and is given by 
<!-- MATH: $R=\sum {\rm abs} (d_i-m_i) / \sum d_i$ -->
<IMG
 WIDTH="142" HEIGHT="26" ALIGN="MIDDLE" BORDER="0"
 SRC="img31.png"
 ALT="$R=\sum {\rm abs} (d_i-m_i) / \sum d_i$">.
In 81&nbsp;per&nbsp;cent of the cases, <I>R</I> &lt; 0.2.</p></td>
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<tr><td><!-- init Label --><!-- end Label--><A NAME="1402"></A><A NAME="figure1388"
 HREF="img562.png"><IMG
 WIDTH="166" HEIGHT="248" SRC="Timg562.png"
 ALT="\begin{figure}
\par\vspace*{-0.0cm} \hbox{\includegraphics[width=7.5cm]{ngas/Zw0...
...s} \includegraphics[width=7.5cm]{ngas/MACS-J1206.2-0847_ngas.ps} }\end{figure}"></A><!-- HTML Figure number: 14 --></td>
<td class="img-txt"><span class="bold">Figure A.1:</span><p>
continued.</p></td>
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<tr><td><!-- init Label --><!-- end Label--><A NAME="1420"></A><A NAME="figure1406"
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<td class="img-txt"><span class="bold">Figure A.1:</span><p>
continued.</p></td>
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<td class="img-txt"><span class="bold">Figure A.1:</span><p>
continued.</p></td>
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<td class="img-txt"><span class="bold">Figure A.1:</span><p>
continued.</p></td>
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...as.ps} \includegraphics[width=7.5cm]{ngas/CL1415.1+3612_ngas.ps} }\end{figure}"></A><!-- HTML Figure number: 18 --></td>
<td class="img-txt"><span class="bold">Figure A.1:</span><p>
continued.</p></td>
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<td class="img-txt"><span class="bold">Figure A.1:</span><p>
continued.</p></td>
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