Gravitationally unstable gaseous disks of flat galaxies

Abstract

Context. The dynamics of a self-gravitating gaseous subsystem of a disk galaxy is considered analytically, using a local WKB approximation in the radial direction. The simplified model of a galaxy is used in which stars (and a dark matter, if it exists at all) do not participate in the disk collective oscillations and just form a background charge. Aims. For the first time in galactic dynamics, an equation is derived to describe the torque that results from the buildup of gravitational Jeans-type instability of nonaxisymmetric gravity perturbations (e.g., those produced by a spontaneous disturbance or, in rare cases, a satellite system). Methods. The torque serves to redistribute the angular momentum of the inhomogeneous disk by growing (that is, unstable) nonaxisymmetric density waves in such a way that a fraction of the mass (eventually residing in the central parts) retains only a minor fraction of the angular momentum, most of the latter being deposited in extended outer regions of the system. Results. The outward transfer of angular momentum (and the "heating") bring the disk toward stability against all small perturbations, including the most unstable nonaxisymmetric ones.

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

“…Morozov, Torgashin & Fridman (1985) additionally considered dissipative effects. Our dispersion relation () reduces to those of Lin & Lau (1979), Morozov (1985), Morozov et al (1985), Montenegro et al (1999), Griv et al (1999, 2002, 2008), Lou et al (2001), and Griv (2006) when the finite thickness, ‘out‐of‐phase,’ radial inhomogeneity, dissipation, magnetic field, and wave‐fluid contributions vanish, so it seems as correct as their result. To emphasize it again, in the low‐frequency () and local WKB () approximations we are indeed explored in , the terms that describe both finite arm‐inclination and finite‐thickness effects are assumed to be small in comparison with other terms.…”

“…The resultant equations of motion are cyclic in the variables t and ϕ, hence by applying the widely used horizontally local short wavelength, or WKB method, one may determine solutions in the form of normal modes by expanding where is a real amplitude, ω=ℜω+ i ℑω is the complex frequency of excited waves, the spiral arms rotate around the centre with constant angular velocity Ω p =ℜω/ m , t is the elapsed time from the onset of the perturbation, r is a distance from the centre of the galaxy, k r is the radial wavenumber, and | k r | r > 1. The meaning of a localized WKB solution has been discussed (Lin & Lau 1979; Bertin 1980; Fridman 1989; Griv et al 1999, 2002; Griv, Gedalin & Yuan 2003; Griv et al 2006; Griv 2006). This is accurate for short‐wave perturbations only, but qualitatively correct even for perturbations with a longer wavelength, on the order of disc radius.…”

“…This is nothing but the second‐order approximation in the Lin–Shu asymptotic theory of tightly wound spirals. The condition m 2 ( k r r ) −2 ≪ 1 is equivalent to the requirement where is the pitch angle (the angle between the direction of the wave front and the tangent to the circular orbit of the fluid), with ‘≲’ in place of ‘≪’ in contrast to the first approximation of the Lin–Shu theory (Lin & Lau 1979; Bertin 1980; Morozov 1980, 1985; Griv et al 1999, 2000, 2002, 2006; Montenegro et al 1999; Lou et al 2001; Griv 2006; Griv, Liverts & Mond 2008). In the vacuum ( z > + h and z < − h ), is reduced to the Laplace equation The solutions of the Laplace equation are In the regions z > + h , z < − h , and − h < z < + h , therefore, a solution may be sought as In , the constants A , B , C and D are determined by four boundary conditions that both Φ 1 and ∂Φ 1 /∂ z to be continuous at z =+ h and z =− h : (The potential Φ must be a continuous function for all z and, in particular, when z =± h , as otherwise the z ‐component of the force would be infinite.)…”

“…indicates that non‐axisymmetric m ≠ 0 instabilities in a differentially rotating (2Ω/κ > 1), two‐dimensional ( h = 0) disc are more difficult to stabilize than the axisymmetric m = 0 ones; stability is achieved only for sufficiently large sound speed (although still on the order of c T ), or Toomre’s Q ≡ c s / c T ‐value, (Lin & Lau 1979; Bertin 1980, 2000; Morozov 1980, 1985; Griv et al 1999, 2002, 2006; Griv 2006). In galaxies, 2Ω/κ=1.5–1.8, therefore and the critical sound speed (velocity dispersion) required to stabilize non‐axisymmetric disturbances in a differentially rotating disc Comparing equations () and () (or () and ()), we conclude that non‐axisymmetric instabilities could still grow in a non‐uniformly rotating disc (d Ω/d r ≠ 0, that is, 2Ω/κ > 1) that is axisymmetrically Safronov–Toomre‐stable.…”

Clumpy galaxies at z∼0.6: kinematics, stability and comparison with analogues at other redshifts

“…For a gravitational disc to fragment into clumps, it is required that Q < 1, which means that the system is unstable to both radial and axisymmetric perturbations (e.g. Polyachenko, Polyachenko & Strel’Nikov 1997; Griv 2006).…”