4.2. Disk evolution
The sizes of disks in the hierarchical scenario decrease significantly with redshift (Mao, Mo et al. 1998; Giallongo et al. 1999; Avila-Reese & Firmani 2001). Interpretation of data regarding disk size and SB evolution is controversial. Roche et al. (1998) using HST data concluded that since z 1, spirals suffered both size and luminosity evolution, while Simard et al. (1999) concluded that data show no size evolution. Bouwens & Silk (2002) show that the SB distribution of disk galaxies evolves strongly. They re-analyzed the data of Simard et al. introducing new corrections for SB selection bias and found size evolution in the data. The question is open.
The SF history of disk models is driven by both the gas accretion rate determined by the MAH, and the disk surface density determined by (Avila-Reese & Firmani 2001). Merging could also play a relevant role (Kauffmann et al. 2001). The increase of the SF rate (and B-band luminosity) with z inferred from observations of normal spirals (e.g., Lilly et al. 1997; Abraham et al. 1999) is slightly steeper than our model predictions. The integral colors of the models become bluer toward the past, in agreement with observations.
The evolution of the TFR is a highly debated topic and apparently it depends on whether the studied sample is dominated by small or normal spirals. Model predictions show that the slope of the B-band TFR decreases and the zero point becomes brighter at higher z's (Fig. 3; see also Avila-Reese & Firmani 2001). Comparing with the observed sample of Vogt et al. (1997) at < z > = 0.54, the agreement in the zero point is reasonable (for the CDM cosmology). On the other hand models show that the zero-point of TFR in the near infrared band evolves in an opposite way: at z = 1 it is fainter than at z = 0. (see Fig. 3) This can be understood taking into account that galaxy evolution traces halo evolution: the halo mass (scaling with the disk mass traced by the infrared luminosity) decreases significantly from z = 0 to z = 1, while Vmax decreases only moderately. In the case of the B-band, since the accretion rate peaks at z ~ 1 - 2, the star formation rate, and therefore LB, are (slightly) higher at these reshifts. The evolution of the comoving number density of halos is connected with the TFR; a deficit of bright (massive) galaxies at larger redshifts translates into a dimming of the zero-point of the infrared TFR (Bullock et al. 2001a). The evolution of the TFR up to high redshifts (z ~ 3) can be a potentially powerful discriminator of galaxy formation models (Buchalter, Jiménez & Kamionkowski 2001).
Figure 3. Evolution of the model TFR in the bands B and K. The slopes at different redshifts were fixed to the corresponing ones at z = 0. The zero-point becomes brighter at higher redshifts in the band B, while in the band K the behaviour is opposite (see text). The arrow indicates the lower limit inferred from observations by Vogt et al. (1997); we have passed their data to the CDM cosmology used here.