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The Kormendy Relation of HDF Ellipticals

We present the results of the detailed surface photometry of a sample of elliptical galaxies in the Hubble Deep Field. In the (surface_brightness-effective_radius) plane, the elliptical galaxies of the HDF turn out to follow a `rest frame' Kormendy relation, once the appropriate K+E corrections are applied. This evidence, linked to the dynamical information gathered by Steidel et al. (1996), indicates that these galaxies, even at z ~ 2-3, lie in the Fundamental Plane, in a virial equilibrium condition. At the same redshifts a statistically signifcant lack of large galaxies [i.e. with log r_e(kpc)>0.2] is observed.


Data and techniques
The present sample of early-type galaxies has been extracted from the second release of the W F P C2 − HDF frames, in the V 606 band. The selection is based on the photometry carried out by the ESO − ST ECF − HDF Group (Clements and Couch 1996) with the automated SExtractor algorithm (Bertin and Arnouts 1996).
A preliminary list of candidate ellipticals was defined, including all the galaxies satisfying the following criteria: a) Kron STMAG magnitude in the V 606 band ≤ 26.5; b) number of pixels above the threshold limit of 1.3σ of the background noise ≥ 200; c) star/galaxy classifier (s/g) ≤ 0.6 (s/g=1 means 'star'). The ∼400 objects matching the above limits were examined to produce a first screening against late-type objects. The preliminary morphological classification was also compared with the ones by Van den Bergh et al. (1996) and Statler (1996), finding a general good agreement. Detailed surface photometry (luminosity and geometrical profiles) was carried out on the resulting list of 162 early-type candidates. As a consequence, 99 objects were left in the final sample of 'bona-fide' early-type galaxies. We derived the near infrared (J,H,K) total magnitudes of these galaxies by applying the SExtractor algorithm to the deep images provided by Dickinson (1997).
We have restricted our analysis to the galaxies for which a spectroscopic redshift is available (24), or a reliable redshift estimate is possible (24), on the basis of multi-band (optical and infrared) photometry.
Many galaxies in the present sample show a luminosity profile close to the instrumental PSF. Therefore, in order to extract useful morphological information, we used the 'Multi-Gaussian Expansion' deconvolution technique (Bendinelli 1991) to restore the profiles. Actually, Fasano et al. (1997a) have shown that this technique gives good results in recovering the 'true' equivalent half-light radius r e and the corresponding average surface brightness < µ e > down to r true e ≃ F W HM .

The Kormendy relation of HDF ellipticals
The relation between the effective radius r e and the corresponding average surface brightness < µ e > (Kormendy 1985) is just a projection of the Fundamental Plane of elliptical galaxies (Djorgovski and Davis (1987)). The zero point of < µ e > in the Kormendy relation (hereafter KR) has been recently used in galaxy clusters at different redshifts, as a standard candle to perform the classical Tolman test for the expansion of the Universe and for testing the evolutionary models of elliptical galaxies (Pahre et al. 1996, Fasano et al. (1997a). In the HDF we are dealing with a completely different situation, since the galaxies have very different redshifts. Still, putting the elliptical galaxies in the (< µ e >r e ) plane is an interesting exercise. Fig. 1. The < µe >-re plane for HDF ellipticals with spectroscopic redshift. In the left panel we plot the < µe > as derived from the deconvolved profiles. The average error bars in both coordinates are reported in the upper-right part of the plot. In the right panel we have applied to < µe > the standard correction for the cosmological dimming, (1+z) 4 . The solid line represents the local KR in the V606 band. The triangles represent the galaxies showing an inward flattening of the luminosity profiles (with respect to the de Vaucouleurs' law) which cannot be ascribed to the effect of the P SF (see Filippi et al. 1997 andFasano et al. 1997b for details). The size of the symbols decreases with increasing redshift. Figure 1 shows the < µ e >-r e plane for the 24 HDF ellipticals in our sample with spectroscopic redshift. By applying only the (1 + z) 4 cosmological dimming correction (right panel) we obtain two distinct sequences for high redshift and low redshift galaxies in the < µ e > -r e plane. Both sequences are roughly parallel to the local KR, with a small negative shift in the zero point at low-redshift and a large positive shift at high redshift. We also note the tendency of high redshift galaxies (z > 2) to be intrinsically smaller with respect to galaxies with z < 1.
In order to derive more realistic corrections for the observed surface brightness of the HDF ellipticals, we need to model their evolution. We have used the chemical-spectrophotometric models of population synthesis produced by Bressan et al. (1994) ('closed-box' models, BCF ) and Tantalo et al. (1996) (models governed by the infall scheme, T CBF ) to estimate the K+evolutionarycorrections (K+E) for elliptical galaxies of different mass, age and evolutionary history.
In order to verify which subset of the models is able to best describe the elliptical galaxies observed in HDF we have compared the observed colors as a function of the (spectroscopic) redshifts with the model predictions. We found that a BCF model with an 'active' star formation until the age of 11 Gyr with a redshift of formation z f orm = 5 in a universe with q o = 0.5 provides a reasonable 'global' description of the observed colors. The passive closed-box model and the models governed by the infall are not able to reproduce the color-z diagrams with a unique redshift of formation. Fig. 2. The Kormendy relation for HDF ellipticals in our sample. The filled and empty symbols refer to galaxies with spectroscopic and photometric redshift, respectively. The symbols and the symbol sizes are the same as in fig.1. The regions below the dotted, dashed and dot-dashed lines represent, in the framework of the BCF active models, the forbidden regions of the Kormendy plane for z = 1, 2 and 3, respectively (see text).
To improve the statistics, we have estimated the photometric redshifts of the 24 galaxies in the present sample having sufficient and reliable infrared information (i.e. detection in J, H and K, no deblending problems), besides the optical magnitudes.
The Figure 2 indicates that, if we apply to the observed < µ e > the K+Ecorrection deduced from the galaxy models that properly reproduce the observed colors (BCF active model with q o = 0.5 and z f orm = 5), the elliptical galaxies in the HDF follow the local Kormendy relation at any redshift. In particular, for spectroscopic redshifts (filled symbols), the agreement with the local KR is fairly good. On the other hand, the KR is well known to be a projection of the Fundamental Plane which roughly represents the virial equilibrium condition of galaxies. Steidel et al. (1996) measured the line widths of compact spheroidal galaxies at z > 3 which, if interpreted as due to gravitational motions, imply velocity dispersions of the order 180 ≤ σ ≤ 320 km s −1 . Such values would place the high-z galaxies of the present sample in the typical region of the Fundamental Plane corresponding to ellipticals, showing that, even at z > 2, elliptical galaxies obey an average, rest-frame, virial equilibrium condition. On the other hand, the fact that the galaxies in our sample follow the Kormendy relation is highly suggestive that a significant fraction of the compact, high-surface brightness, high-z objects spectroscopically observed by Steidel et al. (1996) have their lines widths due to gravitational motions. Fig.2 also shows that, high redshift galaxies are confined in the high surface brightness, small effective radius region of the KR plane. Is this tendency due to the fact that large ellipticals have a faint surface brightness (according to the Kormendy relation itself) ? Large galaxies at high redshifts could lie below the detection limit. We have checked at various redshifts what regions of the Kormendy plane result "forbidden" because of the adopted selection criteria. The regions of Fig.2 below the dotted, dashed and dot-dashed lines represent, in the framework of the BCF active models, the forbidden regions of the Kormendy plane for z = 1, 2 and 3, respectively. We conclude that, had there been large galaxies at high redshifts in the HDF , they would have been included in our sample. In other words, at z > 1.5 a scarcity of large r e elliptical galaxies is observed with respect to the local universe.