A variance analysis of galaxy spectra Zahra Sharbaf 1, Ignacio Ferreras 1,2,3 1 Instituto de Astrofísica de Canarias, Calle Vía Láctea s/n, E38205, Tenerife, Spain 2 Departamento de Astrofísica, Universidad de La Laguna (ULL), E-38206 La Laguna, Tenerife, Spain 3 Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK 3 Galaxy formation transition through the PCA Figure 1: Galaxy spectra projected on the first three principal components (corresponding to the highest variance). The red, blue and green dots represent the results for the spectra of quiescent, star-forming, and active nuclei galaxies, respectively. The spectra are classified with the standard BPT diagram regarding nebular emission (Baldwin et al. 1981, PASP, 93, 5). The covariance analysis is performed independently for each type. We apply PCA to a homogenous sample of galaxy spectra from the Sloan Digital Sky Survey (SDSS) in the velocity dispersion range 100-150km/s, including all three types of galaxies concerning nebular emission – namely star-forming, AGN, and quiescent – according to the standard BPT classification, to assess the properties of the spectra in a model- independent way. We perform PCA separately in each of the three groups across the 3800–4200Å wavelength range. The galaxy spectra are de-redshifted, continuum subtracted and normalized, and we mask out the intervals containing strong emission lines to focus on the stellar population content. This way of performing PCA allows us to assess in more detail the variations in each group of galaxies. If applied to the whole sample, i.e. from a single covariance matrix, PCA will pick a larger signal between galaxies of different types, whereas our approach allows us to focus on variations within each group, and then among the three classes. The first three principal components carry ~95 percent of information (here understood as variance). We adopt only those first three components and the galaxy spectra are projected to produce a distribution of data points on a 3D space. Fig. 1 shows the projection of the spectra of all galaxies in our sample on components 1, 2, and 3, shown as a 3D plot. Fig.2 shows the equivalnt 2D projections in Cartesian space. The projections of the third component (PC3, whose corresponding parameter in spherical coordinates is roughly the Theta polar angle) show the separation between three groups of galaxies, so we try to study this component and find a physical interpretation of the projection. Neighbourhood galaxies in Theta space Figure 3: Correlation of the galaxy projections (using the PCA-derived parameter Theta) with respect to a few physical observables for the three spectral classes (quiescent: red, star-forming:blue and AGN:green). Each point represents the binned average of 500 galaxies, and error bars give the binned variance. Figure 4: This figure illustrates the features of spectra corresponding to extreme values of the Theta parameter in the three classes, as labelled. The stacked spectra comprise the 500 galaxies with the highest and lowest Theta in each class. Fig. 3 compares the projection of the principal components with a set of physical observables such as redshift, stellar mass, etc. The figure illustrates the transition from the blue cloud to the red sequence, in a model-independent way (i.e. no stellar population observables have been used to define the three classes). It is quite remarkable to find such a trend for continuum-subtracted spectra, where the colour information has been removed, and the interval of emission lines has been omitted, when presenting the spectra to PCA. To put the physics in context of the Theta parameter, we look for the properties of galaxies with high and low Theta within each group of galaxies. What do their spectra look like, and what do they have in common? Fig 4. shows the comparison of the stacked spectra of 500 galaxies with high and low Theta. The most apparent differences are