Formation of filaments and feathers in disc galaxies: Is self-gravity enough?

Context. Dense filaments/feathers are kpc-scale dusty features present in nearby main sequence galaxies. Distinct from the spiral arms, filaments constitute a major portion of dense gas concentration. They are expected to play an important role in star formation and are known to harbour star-forming regions and H II regions. Aims. We explore the origin of filaments/feathers in disc galaxies via global gravitational instability. Methods. We conduct a parameter study using three-dimensional hydrodynamical simulations of isolated disc galaxies that are isothermal, self-gravitating and initialised in equilibrium. Our galaxies are uniquely characterised by two dimensionless parameters, the Toomre $Q$ and the rotational Mach number, ${\mathcal{M}}_{\mathrm{c}}=v_{\mathrm{c}}\mathrm{/}{c}_{\mathrm{s}}$ (ratio of circular velocity to sound speed). We carry out simulations covering a wide range in both. Results. We find that galaxies with $Q=1$ form filaments within a single rotation, while galaxies with $Q\ge 2$ do not. These filaments are kpc long and are semi-regularly spaced along the azimuth. Their morphology, density contrast and formation timescale vary with ${\mathcal{M}}_{\mathrm{c}}$, with filament spacing and instability onset time both inversely proportional to ${\mathcal{M}}_{\mathrm{c}}$ and the density contrast increasing with ${\mathcal{M}}_{\mathrm{c}}$. However, their growth rates in all $Q=1$ galaxies are $\sim 0.5\mathrm{\Omega }$, where $\mathrm{\Omega }$ is the angular frequency. We compare the filament spacing in our simulations with the ones from JWST/MIRI and HST observations of nearby galaxies and find them in agreement. Conclusions. Our study suggests that self-gravity and rotation are sufficient to form filaments, even in the absence of spiral arms or magnetic fields. Their morphologies are primarily determined by ${\mathcal{M}}_{\mathrm{c}}$, which parametrises the importance of thermal versus rotational support.