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Appendix A: Updated fundamental plane coefficients

The fundamental plane, which was first mentioned in Terlevich et al. (1981) and properly defined and discussed Dressler et al. (1987) and Djorgovski & Davis (1987), is an empirical relation between three global parameters of elliptical galaxies: the central velocity dispersion σ₀, the physical effective radius R₀, and the mean surface brightness μ₀ within the effective radius. The last parameter is usually expressed as I₀, which is a renormalized surface brightness μ₀: . The coefficients a, b, and c are obtained by fitting (A.1)We provide updated values of the fundamental plane coefficients presented in Saulder et al. (2013). The main improvements are that we now use SDSS DR10 (Ahn et al. 2014) instead of SDSS DR8 (Aihara et al. 2011) and that we do not use any constraints on or information about the SDSS u band, which we found to be quite problematic. Therefore, we have 133 107 galaxies instead of 100 427 for our basic sample (for definitions see Saulder et al. 2013), and after all filtering we end up with 119 085 galaxies instead of the 92 953 that are used for the final fit. This again makes it the largest sample ever used for calibrating the fundamental plane so far. In addition to improved fits, which are based on the de Vaucouleurs fit parameters directly from SDSS, we provide new fits for the g and r bands using the Sersic parameters from Simard et al. (2011). To this end, we use 121 443 galaxies selected after some 3σ clipping from the basic sample in this paper.

	Fig. A.1 Edge-on projections of the fundamental plane of elliptical galaxies for four different SDSS filters using the de Vaucouleurs fit parameters. The g band is shown in the top left panel and the r band in the top right panel. The bottom left panel displays the i band and the bottom right the z band. The dashed black lines indicate the fundamental plane fits in the corresponding filters.
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	Fig. A.2 Edge-on projections of the fundamental plane of elliptical galaxies for the SDSS g band (left panel) and r band (right panel) using Sersic fit parameters. The dashed black lines indicate the fundamental plane fits in the corresponding filters.
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Aside from the extended sample, there are a couple of other minor changes and improvements over the old paper (Saulder et al. 2013). First of all, we corrected a minor mistake in the calculation of the average distance error. This mistake caused the values of the error estimate in the old paper to be systematically lower by a couple of percentage points than they actually are. Even with the slightly larger error, it is still the best fit of the fundamental plane using a large sample at this wave-length range (Bernardi et al. 2003; Hyde & Bernardi 2009; La Barbera et al. 2010).

Another improvement on the fit is that the volume weights are now considering that the sample only covers a limited redshift from 0.01 to 0.2 (or from 0.05 to 0.4 for the Sersic fits based on the basic sample in this paper). In our previous analysis, the very luminous galaxies were slightly under-represented, because their volume weights assumed a larger volume (the one in which they are theoretically still visible) than the volume of sample (redshift cut at 0.2). We then also subtract the volume corresponding to a redshift of 0.01 from the volume weights, where all galaxies were removed from the sample. The saturation limit of SDSS spectroscopy is also measured and included in the new volume weights by removing the volume associated with it in the same fashion as for the Malmquest bias limitation. The negligence of these two corrections caused the volume weights of very faint galaxies to be underestimated. Both corrections are relatively tiny, and the new coefficients are only slightly different from the old ones. In particular, the a coefficient is moderately larger, hence closer to the values from the literature (see Table 1 in Saulder et al. 2013). The new coefficients are listed in Table A.1, edge-on projects of the fundamental plane for all four bands used for the de Vaucouleurs fit parameters in the calibration can be found in Fig. A.1, and the edge-on projects of the fundamental plane for the g and r SDSS bands using the Sersic fit parameters are displayed in Fig. A.2.

Appendix B: The Sersic fit sample

	Fig. B.1 Selection of the alternative candidates in the R0σ0 plane. The restrictions, which define our alternative candidates, are indicated by the dashed magenta lines. The black stars represent the 85 candidates for galaxies with similar properties in Sersic fit parameters as b19, and b19 itself is represented by a grey filled square in the plot.
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In addition to the candidate sample defined using the de Vaucouleurs fit parameters, we provide an alternative sample using the Sersic fit parameters from Simard et al. (2011).

The sample is defined in the same fashion as the main candidate sample, and we find 85 galaxies fulfilling the requirements (listed in Table B.1, together with b19, which was assigned the Sersic ID 1). The logarithm of the physical radius R₀ has to be smaller than the sample’s average by at least one standard deviation, which provides us with an upper limit for R₀ of ~2.65 kpc. The lower limit for the central velocity dispersion σ₀ of ~316.6 km s^-1 is obtained by requiring it to be at least two standard deviations higher than the mean of the logarithm of the central velocity dispersion. The last criterion ensures that all candidates are more than three standard deviations off from the log ₁₀(R₀) − log ₁₀(σ₀) relation, which was obtained by a linear fit to the data points. The selection criteria is illustrated in

Fig. B.1. We find that b19 fails to fulfil the radial size requirement in the case of the Sersic fit parameters (see Table B.2 for numbers), and it is not included in the 85 alternative candidates. However, we keep on providing its position in the plots and tables. As illustrated in Figs. B.2 to B.9, the alternative sample has generally speaking similar properties to the main candidate sample, but it is less cohesive and more scattered. We therefore prefer our main sample to this one. There are 51 galaxies, which the two candidate lists have in common (see Table C.1). We consider these galaxies as candidates with increased priority for any follow-up observations.

Fig. B.2 Location of the candidate galaxies on the fundamental plane using Sersic fit parameters. The candidates are indicated by black stars. The galaxies belonging to the Ta10 sample are represented using filled green triangles, and the Tr09 sample is marked by filled cyan diamonds. The starting point of our investigation, b19, is indicated by a filled grey square. The magenta dotted lines show the limiting physical radius used in the sample sample selection. The black dashed lines are the fundamental plane fits from Appendix A with their corresponding 3σ confidence intervals shown as red solid lines. The fit appears to be slightly offset owing to the volume weights used to correct the Malmquist bias in the fitting process.

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Fig. B.3 Stellar mass-size relation for our basic sample using the Sersic fit parameters. The alternative candidates are indicated by black stars. The galaxies belonging to the Ta10 sample are represented using filled green triangles, and the Tr09 sample is indicated by filled cyan diamonds. B19 is indicated by a filled grey square. The magenta dashed line denotes the limiting scaling radius for our sample selection.

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Fig. B.4 Dynamical mass-size relation for our basic sample using the Sersic fit parameters. The alternative candidates are indicated by black stars. The galaxies belonging to the Ta10 sample are represented using filled green triangles, and the Tr09 sample is indicated by filled cyan diamonds. B19 is indicated by a filled grey square. The magenta dashed line denotes the limiting scaling radius for our sample selection.

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	Fig. B.5 Distribution of the dynamical mass-to-light ratios ♈dyn using the Sersic fit parameters. The blue histogram corresponds to our basic sample, which only consists of early-type galaxies. The green histogram represents the Ta10 sample, while the cyan histogram corresponds to Tr09 sample. The red histogram denotes our 85 alternative candidates.
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	Fig. B.6 Distribution of the stellar mass-to-light ratios ♈∗ using the Sersic fit parameters. The blue histogram corresponds to our basic sample, which only consists of early-type galaxies. The green histogram represents the Ta10 sample, while the cyan histogram corresponds to Tr09 sample. The red histogram denotes our 85 alternative candidates.
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Fig. B.7 Dependence of the dynamical mass Mdyn to stellar mass M∗ ratio on central velocity dispersion σ0 using the Sersic fit parameters. The alternative candidates are indicated by black stars. The galaxies belonging to the Ta10 sample are represented using filled green triangles and the Tr09 sample is marked by filled cyan diamonds. B19 is indicated by a filled grey square. The magenta dashed line marks the limiting scaling central velocity dispersion for our sample selection. The area below the black dashed line is considered to be unphysical, because M∗ would exceed Mdyn.

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Fig. B.8 Distribution of the sample’s galaxies in the dynamical mass Mdyn vs. stellar mass M∗ plane using the Sersic fit parameters. The alternative candidates are indicated by black stars. The galaxies belonging to the Ta10 sample are represented using filled green triangles, and the Tr09 sample is indicated by filled cyan diamonds. B19 is indicated by a filled grey square.The magenta dashed line marks the limiting scaling central velocity dispersion for our sample selection. The black dashed line denotes the limit of the Mdyn to M∗ ratio, which is still considered to be physical, because M∗ would exceed Mdyn above it.

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Fig. B.9 Distribution of the Sersic indices of different samples of galaxies. The black histogram of the Sersic indices stands for all galaxies in SDSS DR7 for which Simard et al. (2011) did their refits. The blue histogram indicates the distribution of Sersic parameters for our basic sample, which only consists of early-type galaxies. The green histogram represents the Ta10 sample, while the cyan histogram corresponds to Tr09 sample. The red histogram denotes our 85 alternative candidates.

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Appendix C: The cross-match list and, the Ta10 and Tr09 samples

© ESO, 2015