Nuclear spirals in galaxies: gas response to an asymmetric potential - I. Linear theory

Nuclear spirals can provide a wealth of information about the nuclear potential in disc galaxies. They are unlikely to form in nuclei with solid-body rotation, yet they are present in a majority of galactic centres. Their morphology varies depending on whether a central massive black hole (MBH) is present in or absent from the galaxy. In this paper I consider predictions of the linear theory for waves induced in gas by an asymmetric gravitational potential, which are applicable to the nuclear spirals observed in galaxies. The generation and propagation of waves are governed by dynamical resonances, and inclusion of an MBH can move or even create resonances, greatly altering the extent and shape of the nuclear spiral. I will use predictions of the linear theory presented here as a guideline when interpreting hydrodynamical models in the second paper of this series. I also comment on modifications that self-gravity in gas imposes on the induced waves.