Stability of power-law discs — II. The global spiral modes

This paper reports on the in-plane normal modes in the self-consistent and the cut-out power-law discs. Although the cut-out discs are remarkably stable to bisymmetric perturbations, they are very susceptible to one-armed modes. For this harmonic, there is no inner Lindblad resonance, thus removing a powerful stabilizing influence. A physical mechanism for the generation of the one-armed instabilities is put forward. Incoming trailing waves are reflected as leading waves at the inner cut-out, thus completing the feedback for the swing-amplifier. Growing three-armed and four-armed modes occur only at very low temperatures. However, neutral m  = 3 and m  = 4 modes are possible at higher temperatures for some discs. The rotation curve index β has a marked effect on stability. For all azimuthal wavenumbers, any unstable modes persist to higher temperatures and grow more vigorously if the rotation curve is rising (β < 0) than if the rotation curve is falling (β > 0). If the central regions or outer parts of the disc are carved out more abruptly, any instabilities become more virulent. The self-consistent power-law discs possess a number of unusual stability properties. There is no natural time-scale in the self-consistent disc. If a mode is admitted at some pattern speed and growth rate, then it must be present at all pattern speeds and growth rates. Our analysis — although falling short of a complete proof — suggests that such a two-dimensional continuum of non-axisymmetric modes does not occur and that the self-consistent power-law discs admit no global non-axisymmetric normal modes whatsoever. Without reflecting boundaries or cut-outs, there is no resonant cavity and no possibility of unstable growing modes. The self-consistent power-law discs certainly admit equi-angular spirals as neutral modes, together with a one-dimensional continuum of growing axisymmetric modes.     

On the observability of spiral structures in cataclysmic variable accretion discs

We use the grid of hydrodynamic accretion disc calculations of Stehle to construct orbital phase‐dependent emission‐line profiles of thin discs carrying spiral density waves. The observational signatures of spiral waves are explored to establish the feasibility of detecting spiral waves in cataclysmic variable discs using prominent emission lines in the visible range of the spectrum. For high Mach number accretion discs ( M v _φ c _s≃ 15 – 30), we find that the spiral shock arms are so tightly wound that they leave few obvious fingerprints in the emission lines. Only a minor variation of the double peak separation in the line profile at a level of ∼8 per cent is produced. For accretion discs in outburst ( M ≃ 5 – 20) however, the lines are dominated by the emission from an m =2 spiral pattern in the disc. We show that reliable Doppler tomograms of spiral shock patterns can be reconstructed provided that a signal‐to‐noise ratio of at least 15, a wavelength resolution of ∼80 km s⁻¹ and a time resolution of ∼50 spectra per binary orbit are achieved. We confirm that the observed spiral pattern in the disc of IP Pegasi can be reproduced by tidal density waves in the accretion disc and demands the presence of a large, hot disc, at least in the early outburst stages.     

Turbulence and its parameterization in accretion discs

Accretion disc turbulence is investigated in the framework of the shearing box approximation. The turbulence is either driven by the magneto‐rotational instability or, in the non‐magnetic case, by an explicit and artificial forcing term in the momentum equation. Unlike the magnetic case, where most of the dissipation occurs in the disc corona, in the forced hydrodynamic case most of the dissipation occurs near the midplane. In the hydrodynamic case evidence is presented for the stochastic excitation of epicycles. When the vertical and radial epicyclic frequencies are different (modeling the properties around rotating black holes), the beat frequency between these two frequencies appear to show up as a peak in the temporal power spectrum in some cases. Finally, the full turbulent resistivity tensor is determined and it is found that, if the turbulence is driven by a forcing term, the signs of its off‐diagonal components are such that this effect would not be capable of dynamo action by the shear–current effect. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bars and the symmetry of star formation patterns in the discs of spiral galaxies

We present a test for the degree of symmetry in the distribution of the Hα brightness along the arms of a sample of spiral galaxies. The test consists of deriving the cross-correlation function of the Hα brightness as a function of curvilinear distance along pairs of opposed arms, after unfolding the arms geometrically. Our results reveal a significantly greater degree of symmetry in the non-barred population than in the barred. We derive parameters for both bar strength and bar ellipticity, and compare these with the derived cross-correlations to strengthen this conclusion. We suggest that density waves are a probable cause for the appearance of global, i.e. disc-wide, two-fold symmetry in spiral discs. Comparison with published work on abundance gradients in the discs of barred and non-barred galaxies indicates that, as for the abundances, mixing in the spiral disc as a result of the bar potential may well be responsible for our observation that stronger bars are related to reduced two-fold symmetry in the distribution of star-forming regions along the spiral arms.     

The structure of spiral galaxies — I. Near-infrared properties of bulges, discs and bars

We present data for a sample of 45 spiral galaxies over a range of Hubble types, imaged in the near-IR J K bands. Parameters are calculated describing the bulge, disc and bar K -band light distributions, and we look for correlations showing the interrelation between these components. We find that bulge profiles are not well-fitted by the classic de Vaucouleurs profile, and that exponential or R ^1/2 fits are preferred. The bulge-to-disc ratio correlates only weakly with Hubble type. Many of the galaxies show central reddening of their J  −  K colours, which we interpret as due to nuclear starbursts or dusty AGN. We define a new method for measuring the strength of bars, which we call 'equivalent angle'. We stress that this is better than the traditional bar–interbar contrast, as it is not subject to seeing and resolution effects. Bars are found in 40 of the 45 galaxies, nine of which had been previously classified as unbarred. Bar strengths are found not to correlate with disc surface brightness or the presence of near neighbours, but a tendency is found for the most strongly barred galaxies to lie within a restricted, intermediate range of bulge-to-disc ratio. Bar light profiles are found to be either flat or exponentially decreasing along their long axes, with profile type not correlating strongly with Hubble type. Bar short axis profiles are significantly asymmetric, with the steeper profile being generally on the leading edge, assuming trailing arms. In the K band we find bars with higher axial ratios than have been found previously in optical studies.     

Chemo-spectrophotometric evolution of spiral galaxies – III. Abundance and colour gradients in discs

We study the relations between luminosity and chemical-abundance profiles of spiral galaxies, using detailed models for the chemical and spectrophotometric evolution of galactic discs. The models are 'calibrated' on the Milky Way disc and are successfully extended to other discs with the help of simple 'scaling' relations, obtained in the framework of semi-analytic models of galaxy formation. We find that our models exhibit oxygen abundance gradients that increase in absolute value with decreasing disc luminosity (when expressed in dex kpc⁻¹) and are independent of disc luminosity (when expressed in dex scalelength⁻¹), both in agreement with observations. We notice an important strong correlation between abundance gradient and disc scalelength. These results support the idea of 'homologous evolution' of galactic discs.     

The excitation of spiral density waves through turbulent fluctuations in accretion discs – I. WKBJ theory

We study and elucidate the mechanism of spiral density wave excitation in a differentially rotating flow with turbulence which could result from the magneto-rotational instability. We formulate a set of wave equations with sources that are only non-zero in the presence of turbulent fluctuations. We solve these in a shearing box domain, subject to the boundary conditions of periodicity in shearing coordinates, using a WKBJ method. It is found that, for a particular azimuthal wavelength, the wave excitation occurs through a sequence of regularly spaced swings during which the wave changes from leading to trailing form. This is a generic process that is expected to occur in shearing discs with turbulence. Trailing waves of equal amplitude propagating in opposite directions are produced, both of which produce an outward angular momentum flux that we give expressions for as functions of the disc parameters and azimuthal wavelength.
By solving the wave amplitude equations numerically, we justify the WKBJ approach for a Keplerian rotation law for all parameter regimes of interest. In order to quantify the wave excitation completely, the important wave source terms need to be specified. Assuming conditions of weak non-linearity, these can be identified and are associated with a quantity related to the potential vorticity, being the only survivors in the linear regime. Under the additional assumption that the source has a flat power spectrum at long azimuthal wavelengths, the optimal azimuthal wavelength produced is found to be determined solely by the WKBJ response and is estimated to be  2π H   , with H being the nominal disc scaleheight. In a following paper by Heinemann & Papaloizou, we perform direct three-dimensional simulations and compare results manifesting the wave excitation process and its source with the assumptions made and the theory developed here in detail, finding excellent agreement.     

The formation of galaxy discs

Galaxy disc formation must incorporate the multiphase nature of the interstellar medium. The resulting two-phase structure is generated and maintained by gravitational instability and supernova energy input, which yield a source of turbulent viscosity that is able to compete effectively in the protodisc phase with early angular momentum loss of the baryonic component via dynamical friction in the dark halo. Provided that star formation occurs on the viscous drag time-scale, this mechanism provides a means of accounting for disc sizes and radial profiles. The star formation feedback is self-regulated by turbulent gas pressure limited percolation of the supernova remnant heated hot phase, but can run away in gas-rich protodiscs to generate compact starbursts. A simple analytic model is derived for a Schmidt-like global star formation law in terms of the cold gas volume density.     

The evolution of galactic discs

We use recent observations of high-redshift galaxies to study the evolution of galactic discs over the redshift range 0 <  z ≲1. The data are inconsistent with models in which discs were already assembled at z  = 1 and have evolved only in luminosity since that time. Assuming that disc properties change with redshift as powers of 1 +   z and analysing the observations assuming an Einstein–de Sitter universe, we find that for given rotation speed, disc scalelength decreases with z as ∼ (1 +  z )⁻¹, total B -band mass-to-light ratio decreases with z as ∼ (1 +  z )⁻¹, and disc luminosity (again in B ) depends only weakly on z . These scalings are consistent with current data on the evolution of disc galaxy abundance as a function of size and luminosity. Both the scalings and the abundance evolution are close to the predictions of hierarchical models for galaxy formation. If different cosmogonies are compared, the observed evolution in disc size and disc abundance favours a flat low-Ω₀ universe over an Einstein–de Sitter universe.     

Chemo-spectrophotometric evolution of spiral galaxies – V. Properties of galactic discs at high redshift

We explore the implications for the high-redshift universe of 'state-of-the-art' models for the chemical and spectrophotometric evolution of spiral galaxies. The models are based on simple 'scaling relations' for discs, obtained in the framework of cold dark matter models for galaxy formation, and were 'calibrated' so as to reproduce the properties of the Milky Way and of nearby discs (at redshift z ∼0) . In this paper, we compare the predictions of our 'hybrid' approach to galaxy evolution to observations at moderate and high redshift. We find that the models are in fairly good agreement with observations up to z ∼1 , while some problems appear at higher redshift (provided there is no selection bias in the data); these discrepancies may suggest that galaxy mergers (not considered in this work) played a non-negligible role at z >1 . We also predict the existence of a 'universal' correlation between abundance gradients and disc scalelengths, independent of redshift.     

The migration and growth of protoplanets in protostellar discs

We investigate the gravitational interaction of a Jovian-mass protoplanet with a gaseous disc with aspect ratio and kinematic viscosity expected for the protoplanetary disc from which it formed. Different disc surface density distributions are investigated. We focus on the tidal interaction with the disc with the consequent gap formation and orbital migration of the protoplanet. Non-linear two-dimensional hydrodynamic simulations are employed using three independent numerical codes.
A principal result is that the direction of the orbital migration is always inwards and such that the protoplanet reaches the central star in a near-circular orbit after a characteristic viscous time‐scale of ∼10⁴ initial orbital periods. This is found to be independent of whether the protoplanet is allowed to accrete mass or not. Inward migration is helped by the disappearance of the inner disc, and therefore the positive torque it would exert, because of accretion on to the central star. Maximally accreting protoplanets reach about 4 Jovian masses on reaching the neighbourhood of the central star. Our results indicate that a realistic upper limit for the masses of closely orbiting giant planets is ∼5 Jupiter masses, if they originate in protoplanetary discs similar to the minimum-mass solar nebula. This is because of the reduced accretion rates obtained for planets of increasing mass.
Assuming that some process such as termination of the inner disc through a magnetospheric cavity stops the migration, the range of masses estimated for a number of close orbiting giant planets as well as their inward orbital migration can be accounted for by consideration of disc–protoplanet interactions during the late stages of giant planet formation.