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Volume 524, December 2010
Article Number A6
Number of page(s) 33
Section Extragalactic astronomy
Published online 19 November 2010

Online material

6. table

Table 1

The FP parameters of cluster galaxies.

Table 2

The FP parameters of field galaxies.

Table 3

The structural parameters of galaxies with measured velocity dispersions and HST photometry derived from Sersic fits to HST images and bulge+disk fits to VLT images.

Appendix A: Circularized half-luminosity radii

GIM2D delivers bulge ae and disk ah scale lengths along the major axis, bulge apparent flattening (b/a)B and disk inclination angles i (corresponding to an apparent flattening (b/a)D = 1 − cosi), and bulge-to-total ratios B/T. When fitting Sersic profiles, GIM2D delivers the n Sersic index, the major axis , and the flattening (b/a)Ser. We compute the circularized half-luminosity radius Re of the resulting galaxy model as follows. We determine the flux inside a circular aperture of radius R (the so-called curve of growth) of a model of apparent flattening b/a and surface density distribution constant on ellipses as (A.1)Using , we derive (A.2)We perform the angular integration numerically, using , where z = 7.67(r/ReB)1/4, and , and x = R/h for the normalized de Vaucouleurs and exponential density laws, respectively. For a Sersic profile of given n, we use , where P is the incomplete Γ function and X = k(r/ReSer)1/n and k = 1.9992n − 0.3271 (Simard et al. 2002). We determine Re by solving the equation (A.3)for the bulge-plus-disk models, and (A.4)for the Sersic fits numerically. In general, the resulting Re agree within 1% with the half-luminosity radii derived by measuring the curves of growth directly from (ACS HST like) images generated by GIM2D with the fit parameters and no PSF convolution, but the image-based method overestimates Re by up to 10% when it is smaller than 4 pixels (0.2 arcsec).

Figure A.1 illustrates that a more accurate approximation of the circularized radius Re(Ser) of Sersic profiles, more accurate than 2%, is obtained by taking the simple mean Rave = (ae + be)/2 of the major and minor axis scale lengths ae and be instead of the harmonic mean . This is surprising only at a first sight, since Rhar goes to zero as the flattening increases, while Rave does not. Therefore Rave should provide a closer approximation of the half-luminosity radius derived from circular curves of growth at high ellipticities. On the other hand, the effective surface brightness within the ellipse of semi-major and minor axis ae and be is constant regardless of the flattening, while this is not true for the surface brightness within the circle of radius Re(Ser). Since in this exercise the total luminosity L is kept constant, we have , with and . This is almost orthogonal to the FP (see Eq. (1)), making the choice of method unimportant, as long as not too many disks seen edge-one (i.e. of very high flattening) are present in the sample (see Fig. 5 and discussion in Sect. 2.2).

thumbnail Fig. A.1

The circularized half-luminosity radius Re(Ser) of the sample of EDisCS galaxies with HST photometry and velocity dispersions computed according to Eqs. (A.2) and (A.4) compared to the simple mean Rave = 0.5(ae + be) (top) and harmonic mean (bottom) as a function of the ellipticity 1 − be/ae. The simple mean approximates more accurately Re(Ser).

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