Stability of galactic discs: finite arm-inclination and finite-thickness effects★

Abstract

A modified theory of the Lin–Shu density waves, studied in connection with the problem of spiral pattern of rapidly and differentially rotating disc galaxies, is presented for both the axisymmetric and non‐axisymmetric structures in highly flattened galaxies resulted from the classical Jeans instability of small gravity perturbations (e.g. those produced by a spontaneous disturbance). A new method is provided for the analytical solution of the self‐consistent system of the gas‐dynamic equations and the Poisson equation describing the stability of a three‐dimensional galactic disc composed of stars or gaseous clouds. In order to apply the method, the modifications introduced for the properties of the gravitationally unstable, that is to say, amplitude‐growing density waves are considered by removing the often used assumptions that the gravity perturbations are axisymmetric and the disc is infinitesimally thin. In contrast to previous studies, in this paper these two effects – the non‐axial symmetry effect and the finite thickness effect – are simultaneously taken into account. We show that non‐axisymmetric perturbations developing in a differentially rotating disc are more unstable than the axisymmetric ones. We also show that destabilizing self‐gravity is far more ‘dangerous’ in thin discs than in thick discs. The primary effect of small but finite thickness is a reduction of the growth rate of the gravitational Jeans instability and a shift in the threshold of instability towards a longer wavelength (and larger wavelength will include more mass). The results of this paper are in qualitative agreement with previous analytical and numerical estimations of the effects. The extent to which our results on the disc’s stability can have a bearing on observable spiral galaxies, including the Milky Way, is also discussed.

Two-component gravitational instability in spiral galaxies

“…The gravitational instability criterion for nonaxisymmetric perturbations contains a factor α, which for the one-fluid case range from ≈ 1/3 (Hunter et al 1998) to ≈ 1/2 (Kennicutt 1989;Martin & Kennicutt 2001). The corresponding star formation threshold Q g < 2 − 3 also follows from the theoretical (Morozov 1985;Griv & Gedalin 2012) and numerical (Li et al 2005) investigations. Also there are some evidences of even a higher level of instability (Q g < 2 − 4 in Zasov & Zaitseva 2017 and Q RW ≈ 1 − 4 in star-forming spirals from THINGS, see figure 5 in Romeo & Wiegert 2011).…”

From massive spirals to dwarf irregulars: a new set of tight scaling relations for cold gas and stars driven by disc gravitational instability

“…Note that Qcrit is higher than unity, but its precise value is still questioned (Romeo & Fathi 2015). In fact, Qcrit is influenced by complex phenomena such as non-axisymmetric perturbations (e.g., Griv & Gedalin 2012) and gas dissipation (Elmegreen 2011), whose effects are difficult to evaluate. Now that we have clarified how self-regulated galaxy discs are, let us analyse how the Toomre parameter of component i, Qi = κσi/πGΣi, varies from galaxy to galaxy.…”

What powers the starburst activity of NGC 1068? Star-driven gravitational instabilities caught in the act

“…Unfortunately, there is still no general consensus about the value of Qcrit. For example, Griv & Gedalin (2012) found that the classical estimate Qcrit ≈ 2 is an absolute upper limit on the critical stability level. Elmegreen (2011) showed that gas dissipation has a similar destabilizing effect, and estimated that Qcrit ≈ 2-3.…”