Instability of sheared density interfaces

Of the canonical flow instabilities (Kelvin–Helmholtz, Holmboe-wave and Taylor–Caulfield) of stratified shear flow, the Taylor–Caulfield instability (TCI) has received relatively little attention, and forms the focus of the current study. First, a diagnostic of the linear instability dynamics is developed that exploits the net pseudomomentum to distinguish TCI from the other two instabilities for any given flow profile. Second, the nonlinear dynamics of TCI is studied across its range of unstable horizontal wavenumbers and bulk Richardson numbers using numerical simulation. At small bulk Richardson numbers, a cascade of billow structures of sequentially smaller size may form. For large bulk Richardson numbers, the primary nonlinear travelling waves formed by the linear instability break down via a small-scale, Kelvin–Helmholtz-like roll-up mechanism with an associated large amount of mixing. In all cases, secondary parasitic nonlinear Holmboe waves appear at late times for high Prandtl number. Third, a nonlinear diagnostic is proposed to distinguish between the saturated states of the three canonical instabilities based on their distinctive density–streamfunction and generalised vorticity–streamfunction relations

Instabilities in a staircase stratified shear flow

We study stratified shear flow instability where the density profile takes the form of a staircase of interfaces separating uniform layers. Internal gravity waves riding on density interfaces can resonantly interact due to a background shear flow, resulting in the Taylor-Caulfield instability. The many steps of the density profile permit a multitude of interactions between different interfaces, and a rich variety of Taylor-Caulfield instabilities. We analyse the linear instability of a staircase with piecewise-constant density profile embedded in a background linear shear flow, locating all the unstable modes and identifying the strongest. The interaction between nearest-neighbour interfaces leads to the most unstable modes. The nonlinear dynamics of the instabilities are explored in the long-wavelength, weakly stratified limit (the defect approximation). Unstable modes on adjacent interfaces saturate by rolling up the intervening layer into a distinctive billow. These nonlinear structures coexist when stacked vertically and are bordered by the sharp density gradients that are the remnants of the steps of the original staircase. Horizontal averages remain layer-like

Probing Solar Convection

In the solar convection zone acoustic waves are scattered by turbulent sound speed fluctuations. In this paper the scattering of waves by convective cells is treated using Rytov's technique. Particular care is taken to include diffraction effects which are important especially for high-degree modes that are confined to the surface layers of the Sun. The scattering leads to damping of the waves and causes a phase shift. Damping manifests itself in the width of the spectral peak of p-mode eigenfrequencies. The contribution of scattering to the line widths is estimated and the sensitivity of the results on the assumed spectrum of the turbulence is studied. Finally the theoretical predictions are compared with recently measured line widths of high-degree modes.Comment: 26 pages, 7 figures, accepted by MNRA

Modelling the Autocovariance of the Power Spectrum of a Solar-Type Oscillator

Asteroseismology is able to conduct studies on the interiors of solar-type stars from the analysis of stellar acoustic spectra. However, such an analysis process often has to rely upon subjective choices made throughout. A recurring problem is to determine whether a signal in the acoustic spectrum originates from a radial or a dipolar oscillation mode. In order to overcome this problem, we present a procedure for modelling and fitting the autocovariance of the power spectrum which can be used to obtain global seismic parameters of solar-type stars, doing so in an automated fashion without the need to make subjective choices. From the set of retrievable global seismic parameters we emphasize the mean small frequency separation and, depending on the intrinsic characteristics of the power spectrum, the mean rotational frequency splitting. Since this procedure is automated, it can serve as a useful tool in the analysis of the more than one thousand solar-type stars expected to be observed as part of the Kepler Asteroseismic Investigation (KAI). We apply the aforementioned procedure to simulations of the Sun. Assuming different apparent magnitudes, we address the issues of how accurately and how precisely we can retrieve the several global seismic parameters were the Sun to be observed as part of the KAI.Comment: 10 pages, 8 figures, accepted for publication in MNRA

Stellar turbulence and mode physics

An overview of selected topical problems on modelling oscillation properties in solar-like stars is presented. High-quality oscillation data from both space-borne intensity observations and ground-based spectroscopic measurements provide first tests of the still-ill-understood, superficial layers in distant stars. Emphasis will be given to modelling the pulsation dynamics of the stellar surface layers, the stochastic excitation processes and the associated dynamics of the turbulent fluxes of heat and momentum.Comment: Proc. HELAS Workshop on 'Synergies between solar and stellar modelling', eds M. Marconi, D. Cardini, M. P. Di Mauro, Astrophys. Space Sci., in the pres

Stochastic excitation of acoustic modes in stars

For more than ten years, solar-like oscillations have been detected and frequencies measured for a growing number of stars with various characteristics (e.g. different evolutionary stages, effective temperatures, gravities, metal abundances ...). Excitation of such oscillations is attributed to turbulent convection and takes place in the uppermost part of the convective envelope. Since the pioneering work of Goldreich & Keely (1977), more sophisticated theoretical models of stochastic excitation were developed, which differ from each other both by the way turbulent convection is modeled and by the assumed sources of excitation. We review here these different models and their underlying approximations and assumptions. We emphasize how the computed mode excitation rates crucially depend on the way turbulent convection is described but also on the stratification and the metal abundance of the upper layers of the star. In turn we will show how the seismic measurements collected so far allow us to infer properties of turbulent convection in stars.Comment: Notes associated with a lecture given during the fall school organized by the CNRS and held in St-Flour (France) 20-24 October 2008 ; 39 pages ; 11 figure

Stellar Model Analysis of the Oscillation Spectrum of eta Bootis Obtained from MOST

Eight consecutive low-frequency radial p-modes are identified in the G0 IV star eta Bootis based on 27 days of ultraprecise rapid photometry obtained by the MOST (Microvariability & Oscillations of Stars) satellite. The MOST data extend smoothly to lower overtones the sequence of radial p-modes reported in earlier groundbased spectroscopy by other groups. The lower-overtone modes from the MOST data constrain the interior structure of the model of eta Boo. With the interior fit anchored by the lower-overtone modes seen by MOST, standard models are not able to fit the higher-overtone modes with the same level of accuracy. The discrepancy is similar to the discrepancy that exists between the Sun's observed p-mode frequencies and the p-mode frequencies of the standard solar model. This discrepancy promises to be a powerful constraint on models of 3D convection.Comment: 30 pages with 14 figures. Accepted for publication in Ap

Low-mass planets in nearly inviscid disks: Numerical treatment

Embedded planets disturb the density structure of the ambient disk and gravitational back-reaction will induce possibly a change in the planet's orbital elements. The accurate determination of the forces acting on the planet requires careful numerical analysis. Recently, the validity of the often used fast orbital advection algorithm (FARGO) has been put into question, and special numerical resolution and stability requirements have been suggested. In this paper we study the process of planet-disk interaction for small mass planets of a few Earth masses, and reanalyze the numerical requirements to obtain converged and stable results. One focus lies on the applicability of the FARGO-algorithm. Additionally, we study the difference of two and three-dimensional simulations, compare global with local setups, as well as isothermal and adiabatic conditions. We study the influence of the planet on the disk through two- and three-dimensional hydrodynamical simulations. To strengthen our conclusions we perform a detailed numerical comparison where several upwind and Riemann-solver based codes are used with and without the FARGO-algorithm. With respect to the wake structure and the torque density acting on the planet we demonstrate that the FARGO-algorithm yields correct results, and that at a fraction of the regular cpu-time. We find that the resolution requirements for achieving convergent results in unshocked regions are rather modest and depend on the pressure scale height of the disk. By comparing the torque densities of 2D and 3D simulations we show that a suitable vertical averaging procedure for the force gives an excellent agreement between the two. We show that isothermal and adiabatic runs can differ considerably, even for adiabatic indices very close to unity.Comment: accepted by Astronomy & Astrophysic

The first evidence for multiple pulsation axes: a new roAp star in the Kepler field, KIC 10195926

We have discovered a new rapidly oscillating Ap star among the Kepler Mission target stars, KIC 10195926. This star shows two pulsation modes with periods that are amongst the longest known for roAp stars at 17.1 min and 18.1 min, indicating that the star is near the terminal age main sequence. The principal pulsation mode is an oblique dipole mode that shows a rotationally split frequency septuplet that provides information on the geometry of the mode. The secondary mode also appears to be a dipole mode with a rotationally split triplet, but we are able to show within the improved oblique pulsator model that these two modes cannot have the same axis of pulsation. This is the first time for any pulsating star that evidence has been found for separate pulsation axes for different modes. The two modes are separated in frequency by 55 microHz, which we model as the large separation. The star is an alpha^2 CVn spotted magnetic variable that shows a complex rotational light variation with a period of Prot = 5.68459 d. For the first time for any spotted magnetic star of the upper main sequence, we find clear evidence of light variation with a period of twice the rotation period; i.e. a subharmonic frequency of $\nu_{\rm rot}/2$. We propose that this and other subharmonics are the first observed manifestation of torsional modes in an roAp star. From high resolution spectra we determine Teff = 7400 K, log g = 3.6 and v sin i = 21 km/s. We have found a magnetic pulsation model with fundamental parameters close to these values that reproduces the rotational variations of the two obliquely pulsating modes with different pulsation axes. The star shows overabundances of the rare earth elements, but these are not as extreme as most other roAp stars. The spectrum is variable with rotation, indicating surface abundance patches.Comment: 17 pages; 16 figures; MNRA

Mutually Penetrating Motion of Self-Organized 2D Patterns of Soliton-Like Structures

Results of numerical simulations of a recently derived most general dissipative-dispersive PDE describing evolution of a film flowing down an inclined plane are presented. They indicate that a novel complex type of spatiotemporal patterns can exist for strange attractors of nonequilibrium systems. It is suggested that real-life experiments satisfying the validity conditions of the theory are possible: the required sufficiently viscous liquids are readily available.Comment: minor corrections, 4 pages, LaTeX, 6 figures, mpeg simulations available upon or reques