  The structure of dust spirals in the nuclei of the SAab-type Liner galaxies
NGC 4450 and NGC 4736 is studied using archival HST PC images. The spirals are
typically only several hundredths of a magnitude fainter than the neighboring
disks, so unsharp mask techniques are used to highlight them. The ambient
extinction is estimated to be less than 0.1 mag from the intensity decrements
of the dust features and from the spiral surface filling factor, which is about
constant for all radii and sizes. The nuclear dust spirals differ from
main-disk spirals in several respects: the nuclear spirals have no associated
star formation, they are very irregular with both trailing and leading
components that often cross, they become darker as they approach the center,
they completely fill the inner disks with a constant areal density, making the
number of distinct spirals (the azimuthal wavenumber m) increase linearly with
radius, and their number decreases with increasing arm width as a power law.
Fourier transform power spectra of the spirals, taken in the azimuthal
direction, show a power law behavior with a slope of -5/3 over the range of
frequencies where the power stands above the pixel noise. This is the same
slope as that found for the one-dimensional power spectra of HI emission in the
Large Magellanic Cloud, and also the slope expected for a thin turbulent disk.
All of these properties suggest that the dust spirals are a manifestation of
acoustic turbulence in the inner gas disks of these galaxies. Such turbulence
should dissipate orbital energy and transfer angular momentum outward, leading
to a steady accretion of gas toward the nucleus.
