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Paola Oliva-Altamirano added subsection_Stellar_Population_Models_label__.tex
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\subsection{Stellar Population Models}\label{sec:miles}
We use the stellar population models of \citet{VAZDEKIS10}, based on the MILES stellar library \citep{MILES}, to estimate the ages and metallicities of galaxies in our sample. The \citet{VAZDEKIS10} models use the Padova 2000 \citep[][]{GIRARDI00} isochrones which cover a metallicity range of [Fe/H]~\footnote{[Fe/H] = log$_{10}$ (Z/Z$_{\odot}$), and Z$_{\odot} = 0.0189$ \citep{ANDERS89}} = [-1.7, 0.4] and ages [$2.1\times 10^7,1.7\times 10^{10}$] yr. After testing our spectra with the whole age range, we restrict our analysis to single stellar population sequences of [$1\times 10^9,1.7\times10^{10}$] yr, divided into 40 age bins.
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We also considered the stellar population models of PEGASE-HR \citep{LEBORGNE04} coupled to the ELODIE \citep{ELODIE} stellar library. These models are known for their high spectral resolution (0.55~\AA) and for allowing the user to choose the initial mass function along with other physical ingredients. Its wavelength coverage is consistent with our data, ($\lambda>3900$~\AA). Furthermore, the stellar library has the same age range as MILES. We find both libraries to give similar results. Both metallicities and ages are consistent within 1$\sigma$ uncertainties. However,
the flux calibration of the MILES library over a wide spectral range is more appropriate for our spectral fitting of unresolved stellar populations. The average spectral resolution of MILES ($2.3$~\AA) is also closer to that of the VIMOS observations ($2.1$~\AA). This minimises information loss when broadening the library spectra. We therefore use the \citet{VAZDEKIS10} models in the results presented here.
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\subsection{Full Spectrum Fitting}\label{sec:steckmap}
To estimate the stellar population parameters we used the full spectrum fitting technique \citep[e.g.][]{KOLEVA08}. This technique features some advantages over classical methods, i.e. the Lick/IDS system \citep[e.g.][]{WORTHEY97}, as it exploits all the information contained in the spectra, pixel by pixel, independently of the spectrum shape. It also allows analysis at medium spectral resolutions ($<3$~\AA), in contrast to the Lick/IDS system which has a low spectral resolution, ($>8$~\AA). We use the STEllar Content and Kinematics via Maximum A Posteriori algorithm \citep[STECKMAP;][]{STECKMAP,STECMAP} to extract the ages and metallicities from our spectra.
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STECKMAP uses Bayesian statistics to estimate the stellar content of the spectra. It is based on a non-parametric formalism. The code returns a luminosity-weighted age and metallicity distribution. This comes from flux-normalising the stellar library (rather than mass normalisation). The results are a proxy to the star formation history of the galaxy. The method is regularised by a Laplacian kernel in order to avoid chaotic oscillations. To prevent systematic errors from poor flux calibration, the code produces a non-parametric transmission curve which represents the instrumental response multiplied by the interstellar extinction. We further mask the spectral region around the weak emission lines so that they do not interfere with the stellar population model fitting (e.g, [NeIII] 3868.71, [OIII] 4959, 5007, [NI] 5198, 5200).
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In order to obtain accurate, robust results we first test the spectrum by measuring the stellar population parameters using two different age initial conditions: (a) a flat stellar age distribution. (b) a random Gaussian distribution of ages \citep[see][]{OCVIRK11}. We then compare the results from both runs expecting them to be consistent. If this test is successful, we proceed to calculate the final value of the stellar population parameters. The final estimated luminosity-weighted age and metallicity are the median values from 150 Monte Carlo realisations. In each Monte Carlo realisation the initial condition is a random Gaussian age distribution that is later refined through iterations until it reaches the best fit. The measurement uncertainties are the standard deviations of the 150 Monte Carlo realisations. In Fig \ref{fig:spectrum} we show the spectrum of the central annulus of 2039. The black line is our data, the red line represents the best fit to the data, the vertical dotted lines indicate the significant lines.
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Unfortunately, STECKMAP, in conjunction with the MILES/ELODIE stellar libraries, has the disadvantage of being tied to solar abundance ratios ($[\alpha$/Fe$]=0$). This means that were not include very high metallicities and $\alpha$-element [$\alpha$/Fe] abundance in this model. BCGs are known to have high metallicities and super solar [$\alpha$/Fe] ratios \citep[e.g.][]{LINDEN07}. We therefore explore the impact of this on our fits using a Lick index analysis.
