The inner disc of the local group galaxy M33 appears to be in settled rotational balance , and near IR images reveal a mild , large-scale , two-arm spiral pattern with no strong bar .
We have constructed N -body models that match all the extensive observational data on the kinematics and surface density of stars and gas in the inner part of M33 .
We find that currently favoured models are unstable to the formation of a strong bar of semi-major axis 2 \la a _ { B } \la 3 kpc within 1 Gyr , which changes the dynamical properties of the models to become inconsistent with the current , apparently well-settled , state .
The formation of a bar is unaffected by how the gas component is modelled , by increasing the mass of the nuclear star cluster , or by making the dark matter halo counter-rotate , but it can be prevented by either reducing the mass-to-light ratio of the stars to \Upsilon _ { V } \sim 0.6 or \Upsilon _ { K } \sim 0.23 in solar units or by increasing the random motions of the stars .
Also a shorter and weaker bar results when the halo is rigid and unresponsive .
However , all three near-stable models support multi-arm spirals , and not the observed large-scale bi-symmetric spiral .
A two-arm spiral pattern could perhaps be tidally induced , but such a model would require an implausibly low mass disc to avoid a bar and there is no visible culprit .
Thus the survival of the current state of this exceptionally well-studied galaxy is not yet understood .
We also suspect that many other unbarred galaxies present a similar puzzle .