Modern techniques of full spectral fitting allow comparison of observations and models on
a pixel by pixel basis, for example: GANDALF, Sarzi et al. (2006)), pPXF, Cappellari &
Emsellem (2004)), ULySS (Koleva et al., 2009) etc. ULySS is the package we used to fit
our observed spectra. As mentioned before in chapter 3 section 3.7.7, ULySS is not strictly
for an absolute flux calibrated spectra, as it is not sensitive to galactic extinction or any other cause affecting the shape of the spectrum. Besides, it gives options to visualize the degeneracies and validate the errors on the parameters. We fitted each LRG spectrum to single-age, single-metallicity population synthesis models. LRGs are believed to form most of their stars very early in the Universe, and as such, SSP models are generally found to be good
descriptions for their spectra (Jimenez et al., 2003; Liu et al., 2012; Moresco et al., 2012a;
Simon et al.,2005;Stern et al.,2010a;Zhang et al., 2012, , etc.). Although in our previous
work (Crawford et al., 2010a) we did find that LRGs may better be described by slightly
extended star formation histories, we have only fit the LRGs to SSPs in order to compare this work to previous studies.
4.5.1 LSF study
Prior to fitting our science spectra, we needed to match the resolution between the observed spectra and models. The spectral resolution matching is described by the LSF (more details
about LSF in chapter 3 section 3.7.7.3). In this study, we used the spectrum of a standard
star HD 14802 observed with SALT during the night of 2012/10/11 along with the target
SDSS J013403.82+004358.8. The atmospheric parameters (Teff, log (g) and [Fe/H]) of this
star are already known in SIMBAD database. They have been measured by several scientists
but we chose the recent ones by Ram´ırez et al. (2013). If those parameters are unknown,
they also can be determined by fitting the star spectrum with ULySS and used to calculate the relative LSF. Measuring the LSF means determining the broadening function (cz, σ and possibly h3, h4) in a sequence of small wavelength ranges. Here we used an overlapping
windows of 200 ˚A separated with 100 ˚A steps. After comparing different relative LSF using
different spectral object, the decrease instrumental velocity dispersion, σinstr is typically from
150 km s−1 (blue) to 110 km s−1 (red) which is the characteristic of the spectrograph and
grating. While the radial velocity, vrad changes from 0 to 31 km s−1, due to the uncertainty in
the wavelength calibration. The LSF relative to the Elodie.3.1 library obtained with ULySS
is shown in figure 4.8. This relative LSF was then injected to the models to generate the
resolution-matched models by the convolution function in ULySS. The injection of the LSF to the models is necessary in order to take into consideration the variation of the resolution with wavelength and to remove possible small uncertainties in the wavelength calibration. We used the resolution-matched models to perform the fitting process of the observed spectra.
4.5.2 SSP fitting
The SSP models that we used are based on the Pegase-HR (PE) models (Le Borgne et al.,
2004). These models were introduced in chapter3section3.7.7.2. The PE models were chosen
among the other models because their empirical libraries have a wide range and number of age and metallicity with high spectral resolution. After testing different fits using four models
described in chapter 3, these models provided the most stable SSP results. Since LRG are
supposed to be old, sometimes the oldest ages of these galaxies hit the upper limits of the models. To avoid this problem during the fitting, we used an age limit, which is the age of the Universe at each redshift. We take this into account especially during the Monte-Carlo simulation runs.
Figure 4.8: Relative LSF between the observed spectrum and the models as a function of wavelength. Radial velocity is at the top panel, the instrumental velocity dispersion is at the bottom panel. Blue points are the measured LSF, and red points are the smoothed version which are used to inject to the model spectra.
We derived ages and metallicities as well as the kinametics of the LRGs by fitting our observations to the SSP models. The full wavelength range of each galaxy spectrum was mostly used during the fitting process. The red end of some of the spectra was significantly affected by the fringing. Due to the presence of the fringes, removal of the sky emission lines became very difficult. Thus the residuals from the bright sky emission lines are very significant. For those spectra where the residuals of the sky emission lines removal are very
significant, we set the maximum wavelength range to be 5500˚A.
The errors on the parameters are the 1 sigma errors. These errors are computed from the covariance matrix by the ULySS calling function MPFIT (a fitting function) algorithm. MPFIT provides the optimal parameters from the best fit and the 1 sigma errors on each one of them. In addition, ULySS provides the possibility of exploring and visualising the parameter
space with χ2 maps, convergence maps and Monte-Carlo simulations to validate the errors on
the parameters. We performed Monte-Carlo simulations and χ2maps experiments to carefully
test the reliability of the fitting. A series of 500 Monte-Carlo simulations was performed. At each step of the simulation, a random noise equivalent to the observed noise was added. The outputs from this simulation are the mean values of the resulting distributions of all parameters: age, metallicity, velocity dispersion and their corresponding standard deviations.
To help assess the quality of the fits, χ2 maps and convergence maps were examined. We