Data Analysis Lab Report

\section{Reduction of \textit{Chandra} Data} \label{sec::chandra}
To confirm the existence of a galaxy cluster, \textit{Chandra} X-ray observation is important as it provides an evidence for extremely hot intracluster medium (ICM), which is expected from such a deep potential well of a cluster. In particular, high spatial resolution X-ray images can be used to determine different properties of this hot ICM, such as gas temperature profile, gas density profile, and total hydrostatic mass. In this section, we describe how we reduce the data from a raw X-ray image taken by \textit{Chandra} to various ICM's properties.

\subsection{Data Preparation}
PKS1353-341 (OBSID 17214) was observed with \textit{Chandra} ACIS-I for 31 ks. The cluster has

The spacing for the radial bins is equally separated in the logarithmic scale for 30 bins with the minimum spacing of 1", excluding the central bin. The maximum radius is roughly 400"-450" from the center. This criterion assures that we have enough counts to get good constraints on cluster density for each annulus. The simulated point source profile was subtracted from the surface brightness profile, as described in the previous section, to remove the brightness contribution from the central AGN, (see

\corr{The entropy is a useful observable for studying the feedback on the cluster because it provides us with the insight on the gas properties and its thermal history of a cluster as it is influenced solely from heat gains and losses~\citep{2009Cavagnolo, 2013Panagoulia, 2000Lloyd-Davies}. We expect to find a power law at large radii and near constant at small radii because of a buoyancy of high-entropy gas and a sinkage of low entropy gas~\citep{2005Voitb,2009Cavagnolo}.}

Lastly, the cooling time represents the amount of time that the ICM needs to radiate all of the excess heat via thermal bremsstrahlung emission. This is calculated using $t_{cooling}=\frac{kT(r)}{n(r)\Lambda(T)}$
%\begin{equation} \label{eqn::coolingtime}
%t_{cooling}=\frac{kT(r)}{n(r)\Lambda(T)},
%\end{equation} where $T(r)$ is the temperature profile, $n_e(r)$ is the electron density profile and $\Lambda(T)$ is the cooling function~\citep{1993Sutherland}. The cooling time is also an important property to calculate because the central cooling time (the cooling time within $0.5\%$ of $R_{500}$) is often used to distinguish between cool core and non-cool core