We present a galaxy classification system for 238 (E1–Sdm) CALIFA (Calar
Alto Legacy Integral Field Area) galaxies based on the shapes and
amplitudes of their circular velocity curves (CVCs). We infer the CVCs
from the de-projected surface brightness of the galaxies, after scaling
by a constant mass-to-light ratio based on stellar dynamics – solving
axisymmetric Jeans equations via fitting the second velocity moment

of the stellar kinematics. We use principal component analysis (PCA)
applied to the CVC shapes to find characteristic features and use a k-means
classifier to separate circular curves into classes. This objective
classification method identifies four different classes, which we name
slow-rising (SR), flat (FL), round-peaked (RP) and sharp-peaked (SP)
circular curves. SR are typical for low-mass, late-type (Sb–Sdm), young,
faint, metal-poor and disc-dominated galaxies. SP are typical for
high-mass, early-type (E1–E7), old, bright, metal-rich and
bulge-dominated galaxies. FL and RP appear presented by galaxies with
intermediate mass, age, luminosity, metallicity, bulge-to-disc ratio and
morphologies (E4–S0a, Sa–Sbc). The discrepancy mass factor, f_d = 1 − M_*/M_dyn,
have the largest value for SR and SP classes (∼ 74 per cent
and ∼ 71 per cent, respectively) in contrast to the FL and RP classes
(with ∼ 59 per cent and ∼ 61 per cent, respectively). Circular curve
classification presents an alternative to typical morphological
classification and appears more tightly linked to galaxy evolution.