  Observations indicate that the central gas discs are smoother in early-type
galaxies than their late-type counterparts, while recent simulations predict
that the dynamical suppression of star formation in spheroid-dominated galaxies
is preceded by the suppression of fragmentation of their interstellar media.
The mass surface density power spectrum is a powerful tool to constrain the
degree of structure within a gas reservoir. Specifically here, we focus on the
power spectrum slope and aim to constrain whether the shear induced by a
dominant spheroidal potential can induce sufficient turbulence to suppress
fragmentation, resulting in the smooth central gas discs observed. We compute
surface density power spectra for the nuclear gas reservoirs of fourteen
simulated isolated galaxies and twelve galaxies observed as part of the mm-Wave
Interferometric Survey of Dark Object Masses (WISDOM) project. Both simulated
and observed galaxies range from disc-dominated galaxies to spheroids, with
central stellar mass surface densities, a measure of bulge dominance, varying
by more than an order of magnitude. For the simulations, the power spectra
steepen with increasing central stellar mass surface density, thereby clearly
linking the suppression of fragmentation to the shear-driven turbulence induced
by the spheroid. The WISDOM observations show a different (but potentially
consistent) picture: while there is no correlation between the power spectrum
slopes and the central stellar mass surface densities, the slopes scatter
around a value of 2.6. This is similar to the behaviour of the slopes of the
simulated galaxies with high central stellar mass surface densities, and could
indicate that high shear eventually drives incompressible turbulence.
