1999ApJS..122..109T

The evolution of the structure of galaxies as a function of redshift is investigated using two parameters: the metric radius of the galaxy (R_η) and the power at high spatial frequencies in the disk of the galaxy (χ). A direct comparison is made between nearby (z∼0) and distant (0.2≲z≲1) galaxies by following a fixed range in rest frame wavelengths. The data of the nearby galaxies comprise 136 broadband images at ∼4500 Å observed with the 0.9 m telescope at Kitt Peak National Observatory (23 galaxies) and selected from the catalog of digital images of Frei et al. (113 galaxies). The high-redshift sample comprises 94 galaxies selected from the Hubble Deep Field (HDF) observations with the Hubble Space Telescope using the Wide Field Planetary Camera 2 in four broad bands that range between ∼3000 and ∼9000 Å (Williams et al.).

The radius is measured from the intensity profile of the galaxy using the formulation of Petrosian, and it is argued to be a metric radius that should not depend very strongly on the angular resolution and limiting surface brightness level of the imaging data. It is found that the metric radii of nearby and distant galaxies are comparable to each other. The median value of the radius of the local sample is <R_η≳5±1 kpc, and the median radius of the HDF sample is <R_η≳6±2 kpc for q₀=0.5, H₀=65 km.s^–1.Mpc^–1; however, for q₀=0.1, <R_η≳7 kpc and for q₀=1, <R_η≳5 kpc. In the HDF, galaxies with redshifts larger than z>0.6 have flatter R_η distributions than galaxies with redshifts smaller than z≤0.6. However, the median R_η values of high- and low-redshift galaxies are consistent with each other. This result is consistent with the simulations of galaxy images at redshifts z=0.35, z=0.5, and z=0.9, which show that the metric sizes can be recovered within ±2 kpc.

The flocculency or power at high spatial frequencies is quantified using a simple method that is based on surface photometry in one band and that depends on the size of the star-forming regions and on the intensity profile of the galaxy. In nearby galaxies, the flocculency is found to trace the star formation rate as χ is correlated with optical colors (B-V) and the strength of the hydrogen recombination lines (Hα).

In the HDF, galaxies at redshifts smaller than z∼1 and with fluxes brighter than B=25 have values of χ similar to what is measured in nearby galaxies and to what is expected from simulations of distant galaxy images. Among the HDF galaxies, I find that at most 4% can be identified as dwarf galaxies with rates of star formation similar to NGC 4449 and NGC 1569. Most HDF galaxies are giants with star formation rates similar to those in nearby giant galaxies.

In summary, in this study I have introduced a method to measure the metric sizes and flocculency of the two-dimensional light distribution of galaxies. As a result, I find that the high spatial frequency power is related to the star formation rate. Further, I find that the sizes and power at high spatial frequencies of HDF galaxies remain largely unchanged between the present epoch and redshifts lower than z∼1.