NOEMA Observations of the Center of M33: A Parsec-scale Molecular Filament and an Ordered Gas-Star-Formation Sequence

We present NOEMA CO(1-0) observations of the inner $\sim$500 pc of M33 at a resolution of $0.91''\times0.37''$ ($3.7\times1.5$ pc), resolving the compact molecular gas structures and revealing their relation to recent massive star formation. The most prominent structure is a southeastern molecular filament (SE filament) that extends 76 pc along its principal axis, is 23 pc wide, and contains three CO-bright knots. Across eight independent transverse cuts, the adjacent H$α$ ridge is displaced preferentially to one side of the principal CO ridge by a median $10.0^{+0.9}_{-1.4}$ pc. Young OB candidates are more closely associated with H$α$ than with compact CO. The filament shows little velocity change along its length but a resolved gradient across its minor axis. Its elongated morphology, transverse kinematics, and ordered CO-H$α$ distribution are consistent with locally asymmetric molecular-gas compression and subsequent massive star formation. Across the wider field, 23 well-measured compact clumps have a median radius of 2.67 pc and a median velocity dispersion of 2.15 km s$^{-1}$. Their linewidth and apparent virial-parameter distributions show no clear difference between the SE filament and the rest of the field. Although the local spiral potential and pattern speed remain unconstrained, the observations provide a resolved view of a compression-compatible molecular-to-ionized-gas sequence in the center of M33.