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Register a new userGalactic Spiral Shocks with Thermal Instability
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Using one-dimensional hydrodynamic simulations including interstellar heating, cooling, and thermal conduction, we investigate nonlinear evolution of gas flow across galactic spiral arms. We model the gas as a non-self-gravitating, unmagnetized fluid, and follow its interaction with a stellar spiral potential in a local frame comoving with the stellar pattern. Initially uniform gas rapidly separates into warm and cold phases as a result of thermal instability (TI), and also forms a quasi-steady shock that prompts phase transitions. After saturation, the flow follows a recurring cycle: warm and cold phases in the interarm region are shocked and immediately cool to become a denser cold medium in the arm; post-shock expansion reduces the mean density to the unstable regime in the transition zone and TI subsequently mediates evolution back into warm and cold interarm phases. For our standard model with n_0 = 2 cm^-3, the gas resides in the dense arm, thermally-unstable transition zone, and interarm region for 14%, 22%, 64% of the arm-to-arm crossing time. These regions occupy 1%, 16%, and 83% of the arm-to-arm distance, respectively. Gas at intermediate temperatures represents ~25-30% of the total mass, similar to the fractions estimated from HI observations. Despite transient features and multiphase structure, the time-averaged shock profiles can be matched to that of a diffusive isothermal medium with temperature 1,000 K and particle mean free path of l_0 = 100 pc. Finally, we quantify numerical conductivity associated with translational motion of phase-separated gas on the grid, and show that convergence of numerical results requires the numerical conductivity to be comparable to or smaller than the physical conductivity. (Abridged)
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Gas in disk galaxies interacts nonlinearly with an underlying stellar spiral potential to form galactic spiral shocks. While numerical simulations typically show that spiral shocks are unstable to wiggle instability (WI) even in the absence of magnetic fields and self-gravity, its physical nature has remained uncertain. To clarify the mechanism behind the WI, we conduct a normal-mode linear stability analysis as well as nonlinear simulations assuming that the disk is isothermal and infinitesimally thin. We find that the WI is physical, originating from the generation of potential vorticity at a deformed shock front, rather than Kelvin-Helmholtz instabilities as previously thought. Since gas in galaxy rotation periodically passes through the shocks multiple times, the potential vorticity can accumulate successively, setting up a normal mode that grows exponentially with time. Eigenfunctions of the WI decay exponentially downstream from the shock front. Both shock compression of acoustic waves and a discontinuity of shear across the shock stabilize the WI. The wavelength and growth time of the WI depend on the arm strength quite sensitively. When the stellar-arm forcing is moderate at 5%, the wavelength of the most unstable mode is about 0.07 times the arm-to-arm spacing, with the growth rate comparable to the orbital angular frequency, which is found to be in good agreement with the results of numerical simulations.
Spiral shocks are potentially a major source of turbulence in the interstellar medium. To address this problem quantitatively, we use numerical simulations to investigate gas flow across spiral arms in vertically stratified, self-gravitating, magnetized models of galactic disks. Our models are isothermal, quasi-axisymmetric, and local in the quasi-radial direction while global in the vertical direction. We find that a stellar spiral potential perturbation promptly induces a spiral shock in the gas flow. For vertically stratified gas disks, the shock front in the radial-vertical plane is in general curved, and never achieves a steady state. This behavior is in sharp contrast to spiral shocks in two-dimensional (thin) disks, which are generally stationary. The non-steady motions in our models include large-amplitude quasi-radial flapping of the shock front. This flapping feeds random gas motions on the scale of the vertical disk thickness, which then cascades to smaller scales. The induced gas velocity dispersion in quasi-steady state exceeds the sonic value for a range of shock strengths, suggesting that spiral shocks are indeed an important generator of turbulence in disk galaxies.
We found that loosely wound spiral shocks in an isothermal gas disk caused by a non-axisymmetric potential are hydrodynamically unstable, if the shocks are strong enough. High resolution, global hydrodynamical simulations using three different numerical schemes, i.e. AUSM, CIP, and SPH, show similarly that trailing spiral shocks with the pitch angle of larger than ~10 deg wiggle, and clumps are developed in the shock-compressed layer. The numerical simulations also show clear wave crests that are associated with ripples of the spiral shocks. The spiral shocks tend to be more unstable in a rigidly rotating disk than in a flat rotation. This instability could be an origin of the secondary structures of spiral arms, i.e. the spurs/fins, observed in spiral galaxies. In spite of this local instability, the global spiral morphology of the gas is maintained over many rotational periods. The Kelvin-Helmholtz (K-H) instability in a shear layer behind the shock is a possible mechanism for the wiggle instability. The Richardson criterion for the K-H stability is expressed as a function of the Mach number, the pitch angle, and strength of the background spiral potential. The criterion suggests that spiral shocks with smaller pitch angles and smaller Mach numbers would be more stable, and this is consistent with the numerical results.
Fragmentation of a spiral arm is thought to drive the formation of giant clumps in galaxies. Using linear perturbation analysis for self-gravitating spiral arms, we derive an instability parameter and define the conditions for clump formation. We extend our analysis to multi-component systems that consist of gas and stars in an external potential. We then perform numerical simulations of isolated disc galaxies with isothermal gas, and compare the results with the prediction of our analytic model. Our model describes accurately the evolution of the spiral arms in our simulations, even when spiral arms dynamically interact with one another. We show that most of the giant clumps formed in the simulated disc galaxies satisfy the instability condition. The clump masses predicted by our model are in agreement with the simulation results, but the growth time-scale of unstable perturbations is overestimated by a factor of a few. We also apply our instability analysis to derive scaling relations of clump properties. The expected scaling relation between the clump size, velocity dispersion, and circular velocity is slightly different from that given by the Toomre instability analysis, but neither is inconsistent with currently available observations. We argue that the spiral-arm instability is a viable formation mechanism of giant clumps in gas-rich disc galaxies.
Spiral density waves are known to exist in many astrophysical disks, potentially affecting disk structure and evolution. We conduct a numerical study of the effects produced by a density wave, evolving into a shock, on the characteristics of the underlying disk. We measure the deposition of angular momentum in the disk by spiral shocks of different strength and verify the analytical prediction of Rafikov (2016) for the behavior of this quantity, using shock amplitude (which is potentially observable) as the input variable. Good agreement between the theory and numerics is found as we vary shock amplitude (including highly nonlinear shocks), disk aspect ratio, equation of state, radial profiles of the background density and temperature, and pattern speed of the wave. We show that high numerical resolution is required to properly capture shock-driven transport, especially at low wave amplitudes. We also demonstrate that relating local mass accretion rate to shock dissipation in rapidly evolving disks requires accounting for the time-dependent contribution to the angular momentum budget, caused by the time dependence of the radial pressure support. We provide a simple analytical prescription for the behavior of this contribution and demonstrate its excellent agreement with the simulation results. Using these findings we formulate a theoretical framework for studying one-dimensional (in radius) evolution of the shock-mediated accretion disks, which can be applied to a variety of astrophysical systems.
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