3.3. The number density and evolution of large disk galaxies at high redshift
The 2-dimensional fitting approach (Schade et al. 1995, 1996) introduces a quantitative parameter, size, to the analysis of the galaxy population. It also offers the possibility of isolating different components within galaxies (e.g., spheroid and disk) that are likely to have different evolutionary histories, and also of isolating particular subsets of the galaxy population (e.g., "large-disk" galaxies). Accordingly multi-parameter bulge-plus-disk models have been fit to all of the sources that have been observed with HST.
Lilly et al. (1997, hereafter Paper 2) have examined the properties of those galaxies in the sample that appear to be disk dominated (i.e., with bulge-to-total ratio less than 0.5), with particular emphasis on the large disks that have fitted exponential scale lengths greater than 3-4h-150 kpc). The bulge and disk decomposition of these relatively large galaxies is more straightforward than for the smaller galaxies since their morphologies are better defined. Furthermore, a magnitude-limited sample will be most complete at a given redshift for these large and luminous galaxies. The distribution of disk ellipticities (i.e., of implied inclination angles) suggest that we are dealing with true two-dimensional disks.
Fig. 2 shows the size function for these large disks in the interval 0.5 < z < 1.0 computed for two different cosmologies and compared with the local estimate of de Jong (1996b). There is little evidence in these data for a change in the size function to redshifts approaching unity, suggesting that disks have roughly constant size and number density to these redshifts. Internal to the CFRS sample, the average scale length at constant number density has likely increased by no more than 30% since z ~ 0.8, and a tighter constraint is obtained by including the de Jong (1996b) local size function. If disks have grown on average by more than this, then their number density must have fallen with time, presumably through the effect of merging.
Figure 2. The size function of galactic disks in the CFRS sample in three redshift bins (data points), compared with the local size function derived by de Jong et al. (1996b) (histogram representation).
In addition to a roughly constant number density, other properties of the large-disk galaxies such as the distribution of bulge-to-total B/T ratios are consistent with their being a single "identifiable" population seen at a range of epochs. It is thus reasonable to suppose that changes in the average properties of these galaxies with redshift will reflect evolutionary changes in individual members of the population, although care must be taken to address biases introduced by the selection criteria of the original redshift surveys.
Figure 3. Montage of disk galaxies with 0.5 < z < 0.75 in the CFRS and LDSS samples. The galaxies have B/T < 0.5 and disk scale lengths -1 > 4h-150 kpc.
We find that the average properties of the large disk galaxies (with -1 > 4h-150 kpc) have indeed changed with time (Figs. 4a-d). In comparison with the local disks studied by de Jong (1996a), the high redshift disks show an elevated rest-B surface brightness (by 0.5-0.8 mag at z = 0.7), bluer rest-frame (U - V) colors, later type morphologies and somewhat elevated rest-frame equivalent widths of [O II] 3727. The change in B-band surface brightness is consistent with other recent estimates (Forbes et al. 1996, Vogt et al. 1996), and also with the original estimate of Schade et al. (1995) when it is realized that the latter was an average based on a luminosity limited sample rather than a size limited one as here.
In Paper 2, it is shown that these changes are all consistent with a model in which the star-formation rate in the disks has declined with an e-folding time of around 5 Gyr, equivalent to a factor of 4 since z ~ 1, and are inconsistent with a scenario in which the star-formation rate in the disks has been constant with time. The Milky Way Galaxy would be a member of the high redshift sample (unless H0 < 50 km s-1 Mpc-1 and the modest change in scale length and the declining star-formation history that is implied by our observations of high redshift galaxies are entirely consistent with models for the evolution of the Milky Way disk (see e.g., Twarog 1980, Prantzos & Aubert 1995).
The B-band luminosity of the large disks is evidently increasing roughly as (1 + z)1.4. This is smaller than the change observed in the galaxy population as a whole, (1 + z)2.7±0.5 for q0 ~ 0.5. This suggests that other, presumably smaller, galaxies are making a larger contribution to the overall change in the galaxy population. However, it should be noted that this shortfall is narrowed significantly if q0 ~ 0, since the disk brightening is essentially independent of q0 but the luminosity density decreases as (1 + z)0.5.
Figure 4. (a-top left) The disk central surface brightness of disks with -1 > 4h-150 kpc as a function of redshift. Data is CFRS+LDSS sample (z > 0.2) and the local sample of de Jong et al. (with a stretched redshift scale for the latter). The dashed lines represent various aspects of selection effects and are discussed in detail in Paper 2. (b-top right) As for a, the overall rest-frame (U - V)0,AB color of large disk galaxies is plotted as a function of redshift. (c-bottom left) The distribution of [O II] 3727 rest-frame equivalent widths in the large disk galaxies in the CFRS (solid) and LDSS (hatched) samples, in three redshift bins. (d-bottom right) As for c, the visual morphological classification of large disk galaxies in the CFRS and LDSS samples, in three redshift bins.