A Theoretical Framework for Interpreting Principal Component Analysis of the Properties of Galaxies.

Mathematics – Logic

Scientific paper

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Scientific paper

We perform a Principal Component Analysis (PCA) of the observable properties of disk galaxies as predicted by semi-analytic models of galaxy formation, considering several cosmological settings and different ``recipes'' for gas dynamics and cooling, reheating by supernova feedback, population synthesis and chemical evolution. This work takes as its starting point the disk scaling relations developed by Mo, Mao & White (1997). However, while Mo et al. focused on the predictions of specific cosmological models, we instead consider a broad range of input assumptions and examine the relation between the observable properties of disk galaxies (luminosities, scale lengths, colors, morphologies, velocity widths, spectroscopic signatures of star formation, etc.) and the physical parameters that describe galaxies in the theoretical framework (e.g., halo masses, halo density profiles, baryon fractions, initial angular momenta, collapse redshifts, star formation histories, merger histories). An ideal sample for such a comparison will be the Sloan Digital Sky Survey (SDSS). One of the SDSS major scientific contributions will be to produce a sample suitable for PCA orders of magnitude larger than those that exist today under well understood selection biases and excellent photometric properties. Our goal is to develop the theoretical framework for interpreting the results of this analysis thereby gaining useful insights on the process of galaxy formation.

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