Scaling relations of metallicity, stellar mass, and star formation rate
  in metal-poor starbursts: I. A fundamental plane
  Most galaxies follow well-defined scaling relations of metallicity (O/H),
star formation rate (SFR), and stellar mass. However, low-metallicity
starbursts, rare in the Local Universe but more common at high redshift,
deviate significantly from these scaling relations. On the "main sequence" of
star formation, these galaxies have high SFR for a given M*; and on the
mass-metallicity relation, they have excess M* for their low metallicity. In
this paper, we characterize O/H, M*, and SFR for these deviant "low-metallicity
starbursts", selected from a sample of ~1100 galaxies, spanning almost two
orders of magnitude in metal abundance, a factor of ~10^6 in SFR, and of ~10^5
in stellar mass. Our sample includes quiescent star-forming galaxies and blue
compact dwarfs at redshift 0, luminous compact galaxies at redshift 0.3, and
Lyman Break galaxies at redshifts 1-3.4. Applying a Principal Component
Analysis (PCA) to the galaxies in our sample with M*<10^{10} Msun gives a
Fundamental Plane (FP) of scaling relations; SFR and stellar mass define the
plane itself, and O/H its thickness. The dispersion for our sample in the
edge-on view of the plane is 0.17 dex, independently of redshift and including
the metal-poor starbursts. The same FP is followed by 55100 galaxies selected
from the Sloan Digital Sky Survey, with a dispersion of 0.06dex. In a companion
paper, we develop multi-phase chemical evolution models that successfully
predict the observed scaling relations and the FP; the deviations from the main
scaling relations are caused by a different (starburst or "active") mode of
star formation. These scaling relations do not truly evolve, but rather are
defined by the different galaxy populations dominant at different cosmological
epochs.
