A New Algorithm to Quantify Maximum Discs in Galaxies
  Maximum disc decompositions of rotation curves place a dynamical upper limit
to the mass attributable to stars in galaxies. The precise definition of this
term, however, can be vague and varies in usage. We develop an algorithm to
robustly quantify maximum-disc mass models and apply it to 153 galaxies from
the SPARC database. Our automatic procedure recovers classic results from
manual decompositions. High-mass, high-surface-brightness galaxies have mean
maximum-disc mass-to-light ratios of $\sim 0.7
\;{\mathrm{M}_\odot}/{\mathrm{L}_\odot}$ in the Spitzer 3.6 $\mu$m band, which
are close to the expectations from stellar population models, suggesting that
these galaxies are nearly maximal. Low-mass, low-surface-brightness galaxies
have very high maximum-disc mass-to-light ratios (up to 10
$\mathrm{M}_\odot/\mathrm{L}_\odot$), which are unphysical for standard stellar
population models, confirming they are sub-maximal. The maximum-disc
mass-to-light ratios are more closely correlated with surface brightness than
luminosity. The mean ratio between baryonic and observed velocity at the peak
of the baryonic contribution is
$\mathrm{V}_{\mathrm{bar}}/{\mathrm{V}_\mathrm{p}} \approx 0.88$, but
correlates with surface brightness, so it is unwise to use this mean value to
define the maximum disc concept. Our algorithm requires no manual intervention
and could be applied to large galaxy samples from future HI surveys with
Apertif, Askap, and SKA.
