Objective Identification of Informative Wavelength Regions in Galaxy
  Spectra
  Understanding the diversity in spectra is the key to determining the physical
parameters of galaxies. The optical spectra of galaxies are highly convoluted
with continuum and lines which are potentially sensitive to different physical
parameters. Defining the wavelength regions of interest is therefore an
important question. In this work, we identify informative wavelength regions in
a single-burst stellar populations model by using the CUR Matrix Decomposition.
Simulating the Lick/IDS spectrograph configuration, we recover the widely used
Dn(4000), Hbeta, and HdeltaA to be most informative. Simulating the SDSS
spectrograph configuration with a wavelength range 3450-8350 Angstrom and a
model-limited spectral resolution of 3 Angstrom, the most informative regions
are: first region-the 4000 Angstrom break and the Hdelta line; second
region-the Fe-like indices; third region-the Hbeta line; fourth region-the G
band and the Hgamma line. A Principal Component Analysis on the first region
shows that the first eigenspectrum tells primarily the stellar age, the second
eigenspectrum is related to the age-metallicity degeneracy, and the third
eigenspectrum shows an anti-correlation between the strengths of the Balmer and
the Ca K and H absorptions. The regions can be used to determine the stellar
age and metallicity in early-type galaxies which have solar abundance ratios,
no dust, and a single-burst star formation history. The region identification
method can be applied to any set of spectra of the user's interest, so that we
eliminate the need for a common, fixed-resolution index system. We discuss
future directions in extending the current analysis to late-type galaxies.
