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Register a new userFeathering Instability of Spiral Arms. I: Formulation of the Problem
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Wing-Kit Lee UCSD
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In this paper we study the feathering substructures along spiral arms by considering the perturbational gas response to a spiral shock. Feathers are density fluctuations that jut out from the spiral arm to the inter-arm region at pitch angles given by the quantum numbers of the doubly-periodic structure. In a localized asymptotic approximation, related to the shearing sheet except that the inhomogeneities occur in space rather than in time, we derive the linearized perturbation equations for a razor-thin disk with turbulent interstellar gas, frozen-in magnetic field, and gaseous self-gravity. Apart from the modal quantum numbers, the individual normal modes of the system depend on seven dimensionless quantities that characterize the underlying time-independent axisymmetric state plus its steady, nonlinear, two-armed spiral-shock (TASS) response to a hypothesized background density-wave supported by the disk stars of the galaxy. We show that some of these normal modes have positive growth rates. Their over-density contours in the post-shock region are very reminiscent of observed feathering substructures in full magnetohydrodynamic (MHD) simulations. The feathering substructures are parasitic instabilities intrinsic to the system; thus, their study not only provides potential diagnostics for important parameters that characterize the interstellar medium of external galaxies, but also yields a deeper understanding of the basic mechanism that drives the formation of the giant molecular clouds (GMCs) and the OB stars that outline observed grand-design spirals.
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We investigate dynamical states of grand-design spiral arms in three local galaxies: M51, NGC3627 and NGC628. Based on linear perturbation analysis considering multiple components in the galaxies, we compute instability parameters of the spiral arms using their observational data and argue whether the arms will fragment by their self-gravity. Our analysis utilises observations of carbon monoxide (CO), 21-centimetre line emission and multi-band photometric images for molecular gas, atomic gas and stellar components in the arms, respectively. We find that the grand-design arms of these galaxies indicate marginally stable states, and hence they are not on the way to fragment. We consider this to be consistent with the commonness of spiral galaxies and the relative rarity of fragmented discs at low redshifts. In the analysis, molecular gas is the dominant component to determine the (in)stability of the arms, whereas atomic gas and stars are far less important. Therefore, the results of our analysis are sensitive to an assumed CO-to-H$_{rm 2}$ conversion factor. If we assume a typical scatter of the measurements and admit nearly twice as large a conversion factor as our fiducial value, our analysis results in predicting the instability for the spiral arms. More sophisticated determination of the conversion factor is required for more accurate analysis for the (in)stability of spiral arms.
In spiral galaxies, the pitch angle, $alpha$, of the spiral arms is often proposed as a discriminator between theories for the formation of the spiral structure. In Lin-Shu density wave theory, $alpha$ stays constant in time, being simply a property of the underlying galaxy. In other theories (e.g tidal interaction, self-gravity) it is expected that the arms wind up in time, so that to a first approximation $cot alpha propto t$. For these theories, it would be expected that a sample of galaxies observed at random times should show a uniform distribution of $cot alpha$. We show that a recent set of measurements of spiral pitch angles (Yu & Ho 2018) is broadly consistent with this expectation.
We present high-resolution (30 mas or 130 au at 4.2 kpc) Atacama Large Millimeter/submillimeter Array observations at 1.2 mm of the disc around the forming O-type star AFGL 4176 mm1. The disc (AFGL 4176 mm1-main) has a radius of ~1000 au and contains significant structure, most notably a spiral arm on its redshifted side. We fitted the observed spiral with logarithmic and Archimedean spiral models. We find that both models can describe its structure, but the Archimedean spiral with a varying pitch angle fits its morphology marginally better. As well as signatures of rotation across the disc, we observe gas arcs in CH$_3$CN that connect to other millimetre continuum sources in the field, supporting the picture of interactions within a small cluster around AFGL 4176 mm1-main. Using local thermodynamic equilibrium modelling of the CH$_3$CN K-ladder, we determine the temperature and velocity field across the disc, and thus produce a map of the Toomre stability parameter. Our results indicate that the outer disc is gravitationally unstable and has already fragmented or is likely to fragment in the future, possibly producing further companions. These observations provide evidence that disc fragmentation is one possible pathway towards explaining the high fraction of multiple systems around high-mass stars.
Since the discovery that the majority of low-redshift galaxies exhibit some level of spiral structure, a number of theories have been proposed as to why these patterns exist. A popular explanation is a process known as swing amplification, yet there is no observational evidence to prove that such a mechanism is at play. By using a number of measured properties of galaxies, and scaling relations where there are no direct measurements, we model samples of SDSS and S$^4$G spiral galaxies in terms of their relative halo, bulge and disc mass and size. Using these models, we test predictions of swing amplification theory with respect to directly measured spiral arm numbers from Galaxy Zoo 2. We find that neither a universal cored or cuspy inner dark matter profile can correctly predict observed numbers of arms in galaxies. However, by invoking a halo contraction/expansion model, a clear bimodality in the spiral galaxy population emerges. Approximately 40 per cent of unbarred spiral galaxies at $z lesssim 0.1$ and $mathrm{M_*} gtrsim 10^{10} mathrm{M_odot}$ have spiral arms that can be modelled by swing amplification. This population display a significant correlation between predicted and observed spiral arm numbers, evidence that they are swing amplified modes. The remainder are dominated by two-arm systems for which the model predicts significantly higher arm numbers. These are likely driven by tidal interactions or other mechanisms.
It has been believed that spirals in pure stellar disks, especially the ones spontaneously formed, decay in several galactic rotations due to the increase of stellar velocity dispersions. Therefore, some cooling mechanism, for example dissipational effects of the interstellar medium, was assumed to be necessary to keep the spiral arms. Here we show that stellar disks can maintain spiral features for several tens of rotations without the help of cooling, using a series of high-resolution three-dimensional $N$-body simulations of pure stellar disks. We found that if the number of particles is sufficiently large, e.g., $3times 10^6$, multi-arm spirals developed in an isolated disk can survive for more than 10 Gyrs. We confirmed that there is a self-regulating mechanism that maintains the amplitude of the spiral arms. Spiral arms increase Toomres $Q$ of the disk, and the heating rate correlates with the squared amplitude of the spirals. Since the amplitude itself is limited by the value of $Q$, this makes the dynamical heating less effective in the later phase of evolution. A simple analytical argument suggests that the heating is caused by gravitational scattering of stars by spiral arms, and that the self-regulating mechanism in pure-stellar disks can effectively maintain spiral arms on a cosmological timescale. In the case of a smaller number of particles, e.g., $3times 10^5$, spiral arms grow faster in the beginning of the simulation (while $Q$ is small) and they cause a rapid increase of $Q$. As a result, the spiral arms become faint in several Gyrs.
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