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A. Resolved Color Modelling

Consider the central equation of population synthesis [6], commonly used to model spectral evolution in galaxies:

Equation 1 (1)

In this formulation the emergent flux from a galaxy, Flambda, at time T is described by the convolution of the spectrum of an evolving instantaneous starburst, flambda(t), with an assumed star-formation rate (SFR) function Psi(t). The flambda(t) term is in principle known for various choices of initial mass function (IMF) and metallicity, using libraries of template stellar spectra and isochrones. Hierarchical formation scenarios suggest that stellar populations become built up over time, so in reality the age T of a galaxy is not a constant, and the distribution of internal colors is a partial record of the formation timescale(s) of the system. This age information for a given stellar population is diluted by the convolution with Psi(t), whose form is usually unknown. But in regions where the resolution is high enough to resolve the sites of current star-formation, or where mixing of multiple generations of stars has not occured, Psi (t) can be approximated by a delta-function, breaking the convolution degeneracy in Equation 1, and allowing direct measurement the age distribution and form of flambda(t). Consider, for example, the canonical picture of a late-type spiral galaxy, where the bulk Psi(t) can be well-approximated by a constant star-formation rate. This "constant" overall star formation rate is physically simply a time-average over the appearance and disappearance of spatially distinct HII regions and star-formation complexes, each of which individually can be considered to be a bursting simple stellar population with a lifetime (before disruption or gas depletion) that is short compared to the dynamical timescale of the galaxy. Therefore the distribution of colors for individual resolved young stellar associations on a color-color diagram directly maps out the shape of flambda(t) for a set of young ages, giving direct access to the integrand of Equation~1 without first filtering by a convolution. As these stellar associations age and disappear the convolution with Psi(t) in Equation 1 becomes important, as young stars become assimilated into older galactic components (ie. the disk and bulge) and are spatially averaged with earlier generations of stars. The distribution of colors for older stellar populations (gtapprox 1 Gyr) are therefore expected to trace out a continuous age track on the color-color diagram. The shape of this track for older stellar populations is in effect a measurement of the form of the star-formation law Psi(t), while the distribution of colors along this track is a record of the uniformity with which episodes of star formation have added to the stellar population (e.g., via numerous small bursts, or a smaller number of larger bursts).

Figure 4

Figure 4. Morphophotometric color-color diagrams for two "canonical" galaxies in the Hubble Deep Field. The panels on the left show I-band images of the galaxies, "segmented" from the background sky by isophotal thresholding. The right hand panels show the color-color diagrams for individual pixels in the galaxy. The data points have been subdivided into high signal-to-noise (SNR) pixels [circles] and low signal-to-noise pixels [dots]. The mean error bars for the high SNR and low SNR points are shown by the dark and light error bars. Model tracks are also shown on the right, and are calibrated to age in Gyr [keyed to the color bar]. Arrows on the color bar indicate the age of the Universe in the rest frame of the galaxy, for H0 = 70 km/s/Mpc and Omega = 0.1 and Omega = 1. The dust vectors (for LMC and SMC extinction laws) shown correspond to an extinction of AB = 0.2 mag in the rest frame of the galaxy. The colored points shown on the color-color diagram for the spiral galaxy correspond to pixels inside the colored polygons shown on the left hand panel.

Figure 4 shows the resolved color-color diagram for two rather typical spiral and elliptical galaxies in the HDF. These exhibit star-formation characteristics that are in reasonable agreement with our expectations based on studies of stellar populations in local galaxies. For example, the spiral galaxy is well described by a roughly constant star formation history. The bulge is the oldest component of this system, has a small dispersion in color, and is several Gyr older than the disk. By contrast the elliptical system shown is well described by an exponential star-formation history with a short e-folding timescale (around tau = 1 Gyr.) This system is apparently rather old and (from the small dispersion in color), all parts of the galaxy are well mixed and roughly coeval. The majority of spirals and ellipticals in the Hubble Deep Field exhibit morphophotometric diagrams qualitatively similar to those shown in Figure 4.

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