Stellar Populations Models
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 SpectroPhotometric Model Fitting
 Emission Line Kinematics
 Principal Component Analysis (PCA) Method
SpectroPhotometric Model Fitting
The stellar population models of Maraston (2005) and Maraston et al. (2009) are used to perform a bestfit to the observed ugriz magnitudes of BOSS galaxies with the spectroscopic redshift determined by the BOSS pipeline, using an adaptation of the publicly available HyperZ code of Bolzonella, Miralles & Pelló (2000). The fit is carried out on extinction corrected model magnitudes that are scaled to the iband cmodel magnitude, i.e.:
mag_x = modelmag_x  extinction_x + (cmodelmag_i  modelmag_i),
where x denotes the photometric band (ugriz).
Two sets of template spectra are used (see Maraston et al. 2012 for details):
 a passively evolving galaxy with a twocomponent metallicity of same age and no ongoing star formation or reddening, as in Maraston et al. (2009),
 an ensemble of canonical star formation modes, including exponentiallydeclining, constant with truncation, and constant, star formation, for various timescales and various metallicities, as in Maraston et al. (2006). In order to minimize the event of lowage, highdust fake solutions, reddening is not included (Pforr, Maraston & Tonini 2012 [submitted to MNRAS]). Both template sets are available for Salpeter and Kroupa initial mass functions.
The output of the fit for each galaxy includes: age, star formation mode, metallicity, kcorrected absolute magnitudes in ugriz, plus the reduced χ^{2}. Additionally, the best fit model spectrum as well as the probability distribution function (PDF) for the stellar mass are provided.
Stellar masses and star formation rates are computed from the bestfit SED as in Maraston et al. (2006). Furthermore the stellar mass at the median PDF and 68% confidence levels are provided. Mass loss due to stellar evolution and the account of mass in stellar remnants is included.
The algorithm assumes a ΛCDM cosmology with H_{0} = 71.9, Ω_{m} = 0.258, and Ω_{Λ} = 0.742.
Emission Line Kinematics
An adaptation of the publicly available Gas AND Absorption Line Fitting (GANDALF, Sarzi et al. 2006) and penalised PiXel Fitting (pPXF, Cappellari & Emsellem 2004) codes are used to fit the stellar population synthesis models of Maraston & Strömbäck (2011) and Thomas, Maraston & Johansson (2011) to observed BOSS galaxy spectra. We chose these codes as GANDALF simultaneously fits stellar templates and Gaussian emissionline models.
The stellar population synthesis models used were all at fixed solar metallicity to limit computing time, utilised the MILES stellar library and had age ranges from 6.5 Myr to 11 Gyr. Since we were not using this fit to extract stellar population metallicities and ages, considering only solar metallicity did not impact on our results and agemetallicity degeneracy effects were unimportant. We adopted the MILES resolution calculated in Beifiori et al. (2011).
Outputs from this fitting process that we are providing include the emissionline fluxes (both observed and dereddened) and equivalent widths, the gas kinematics, the stellar kinematics, an E(BV) value and derived BPT classifications. Our reddening values can be obtained by plugging the E(BV) value for each object into the dust attenuation equation of Calzetti et al. (2000).
Outputs from this fitting process that we are providing include the emissionline fluxes (both observed and dereddened) and equivalent widths, the gas kinematics, the stellar kinematics, two E(BV) values (explained below), absorption line indices and derived BPT classifications.
A reduced χ^{2} value is also provided for the fit, as well as AmplitudeoverNoise (AoN) values for each of the emission lines.
Principal Component Analysis (PCA) Method
Chen et al. (2012) model physical galaxy parameters based on a library of model spectra for which principal components (PCs) have been identified. The method is applied in the following steps.
Create library of model spectra
The library of model spectra is based on Bruzual & Charlot (2003) stellar population synthesis models. The model is parameterized by the following characteristics.
 Star formation histories (SFHs)

Each SFH consists of three parts: an underlying continuous model + a series of superimposed stochastic bursts + a random probability for star formation to stop exponentially (i.e. truncation). Figure 1 shows three examples of SFHs. The top panel is a continuous model, middle panel shows a continuous model with two random bursts, a truncation can be found in the bottom panel.
Figure 1: Three different examples of SFHs.  Metallicity

95% of the model galaxies in the library are distributed uniformly in metallicity from 0.2  2.5 Z_{☉}; 5% of the model galaxies are distributed uniformly between 0.02 and 0.2 Z_{☉}.
 Dust extinction

Dust extinction is modelled using the twocomponent model described in Charlot & Fall (2000). The Vband optical depth has a Gaussian distribution over the range 0 < τ_{V} < 6. with a peak at 1.2 and 68% of the total probability distribution distributed over the range 0~2. This prior distribution of τ_{V} values is motivated by the observed distribution of Balmer decrements in SDSS spectra (Brinchmann et al. 2004). The fraction of the optical depth that affects stellar populations older than 0.01 Gyr is parametrized as μ, which is again modeled as a Gaussian with a peak at μ = 0.3, and a 68 percentile range of 0.1~1.
 Velocity dispersion

Each of the model spectra is convolved to a velocity that is uniformly distributed over the range of values from 75 to 400 km/s.
Principal components (PCs) are identified from the model library
The regions around nebular emission lines are masked in the model spectra. We mask 500 km/s around the [OII]3726.03, [OII]3728.82, Hζ3889.05, [NeIII]3869.06, Hδ4101.73, Hγ4340.46, Hβ4861.33, [OIII]4959.91, and [OIII]5007.84 Å lines. Each spectrum in the masked library is normalized to its mean flux between 37005500 Å (this is the range we use for analysis). The mean spectrum of the masked library is calculated and subtracted from each of the model spectra.
Figure 2: From top to bottom: the mean spectrum of the model library followed by the first to seventh eigenspectra. 
PCA code is run on the "residual" spectra. Figure 2 presents the mean spectrum and the top seven PCs for the input model library.
Project BOSS data and models onto PCs
Figure 3 shows an example of projection. The black is the BOSS spectrum. The red is the PCA fit, it is a linear combination of the mean spectrum and the PCs, namely, fit = mean + C_{1} × PC_{1} + C_{2} × PC_{2} + … + C_{7} × PC_{7}, where C_{α} (α = 1–7) are the coefficients of the projection.
Figure 3: An example of projection. The black is the BOSS spectrum. The red is the PCA fit. 
Estimate galaxy physical parameters for BOSS
For an observed galaxy at redshift z, we select only models that have an age smaller than the age of the universe at that redshift. We step through the models one at a time, calculating the χ^{2} as follows:
Figure 4: χ^{2} formula. 
where C_{α} (α = 1–7) represents the projection coefficients. The superscript "m" and "d" refer to model and data. i represents the ith model. P_{α,α′} is the inverse of the covariance matrix of C_{α}. The covariance matrix of C_{α} is calculated in the projection process.