F. Rincon

Weak magnetic fields in Ap/Bp stars: Evidence for a dipole field lower limit and a tentative interpretation of the magnetic dichotomy

Aims. We investigated a sample of 28 well-known spectroscopically-identified magnetic Ap/Bp stars, with weak, poorly-determined or previously undetected magnetic fields. The aim of this study is to explore the weak part of the magnetic field distribution of Ap/Bp stars. Methods. Using the MuSiCoS and NARVAL spectropolarimeters at Telescope Bernard Lyot (Observatoire du Pic du Midi, France) and the cross-correlation technique Least Squares Deconvolution (LSD), we obtained 282 LSD Stokes V signatures of our 28 sample stars, in order to detect the magnetic field and to infer its longitudinal component with high precision (median σ = 40 G). Results. For the 28 studied stars, we obtained 27 detections of StokesV Zeeman signatures from the MuSiCoS observations. Detection of the Stokes V signature of the 28th star (HD 32650) was obtained during science demonstration time of the new NARVAL spectropolarimeter at Pic du Midi. This result clearly shows that when observed with sufficient precision, all firmly classified Ap/Bp stars show detectable surface magnetic fields. Furthermore, all detected magnetic fields correspond to longitudinal fields which are significantly greater than some tens of G. To better characterise the surface magnetic field intensities and geometries of the sample, we phased the longitudinal field measurements of each star using new and previously-published rotational periods, and modeled them to infer the dipolar field intensity (Bd, measured at the magnetic pole) and the magnetic obliquity (β). The distribution of derived dipole strengths for these stars exhibits a plateau at about 1 kG, falling off to larger and smaller field strengths. Remarkably, in this sample of stars selected for their presumably weak magnetic fields, we find only 2 stars for which the derived dipole strength is weaker than 300 G. We interpret this “magnetic threshold” as a critical value necessary for the stability of large-scale magnetic fields, and develop a simple quantitative model that is able to approximately reproduce the observed threshold characteristics. This scenario leads to a natural explanation of the small fraction of intermediate-mass magnetic stars. It may also explain the near-absence of magnetic fields in more massive B and O-type stars.

The Sun’s Supergranulation

The Sun’s supergranulation refers to a physical pattern covering the surface of the quiet Sun with a typical horizontal scale of approximately 30,000 km and a lifetime of around 1.8 d. Its most noticeable observable signature is as a fluctuating velocity field of 360 m st-1 rms whose components are mostly horizontal. Supergranulation was discovered more than fifty years ago, however explaining why and how it originates still represents one of the main challenges of modern solar physics.A lot of work has been devoted to the subject over the years, but observational constraints, conceptual difficulties and numerical limitations have all concurred to prevent a detailed understanding of the supergranulation phenomenon so far. With the advent of 21st century supercomputing resources and the availability of unprecedented high-resolution observations of the Sun, a stage at which key progress can be made has now been reached. A unifying strategy between observations and modelling is more than ever required for this to be possible.The primary aim of this review is therefore to provide readers with a detailed interdisciplinary description of past and current research on the problem, from the most elaborate observational strategies to recent theoretical and numerical modelling efforts that have all taken up the challenge of uncovering the origins of supergranulation. Throughout the text, we attempt to pick up the most robust findings so far, but we also outline the difficulties, limitations and open questions that the community has been confronted with over the years.In the light of the current understanding of the multiscale dynamics of the quiet photosphere, we finally suggest a tentative picture of supergranulation as a dynamical feature of turbulent magnetohydrodynamic convection in an extended spatial domain, with the aim of stimulating future research and discussions.

Magnetofluid dynamics of magnetized cosmic plasma: firehose and gyrothermal instabilities

Both global dynamics and turbulence in magnetized weakly collisional cosmic plasmas are described by general magnetofluid equations that contain pressure anisotropies and heat fluxes that must be calculated from microscopic plasma kinetic theory. It is shown that even without a detailed calculation of the pressure anisotropy or the heat fluxes, one finds the macroscale dynamics to be generically unstable to microscale Alfv´ enically polarized fluctuations. Two instabilities that can be treated this way are considered in detail: the parallel firehose instability (including the finite Larmor radius effects that determine the growth rate and scale of the fastest growing mode) and the gyrothermal instability (GTI). The latter is a new result – it is shown that a parallel ion heat flux destabilizes Alfv´ enically polarized fluctuations even in the absence of the negative pressure anisotropy required for the firehose. The main physical conclusion is that both pressure anisotropies and heat fluxes associated with the macroscale dynamics trigger plasma microinstabilities and, therefore, their values will likely be set by the non-linear evolution of these instabilities. Ideas for understanding this non-linear evolution are discussed. It is argued that cosmic plasmas will generically be ‘three-scale systems’, comprising global dynamics, mesoscale turbulence and microscale plasma fluctuations. The astrophysical example of cool cores of galaxy clusters is considered quantitatively and it is noted that observations point to turbulence in clusters (velocity, magnetic and temperature fluctuations) being in a marginal state with respect to plasma microinstabilities and so it is the plasma microphysics that is likely to set the heating and conduction properties of the intracluster medium. In particular, a lower bound on the scale of temperature fluctuations implied by the GTI is derived.

A non-linear theory of the parallel firehose and gyrothermal instabilities in a weakly collisional plasma

Weakly collisional magnetized cosmic plasmas have a dynamical tendency to develop pressure anisotropies with respect to the local direction of the magnetic field. These anisotropies trigger plasma instabilities at scales just above the ion Larmor radius ρi and much below the mean free path λmfp. They have growth rates of a fraction of the ion cyclotron frequency, which is much faster than either the global dynamics or even local turbulence. Despite their microscopic nature, these instabilities dramatically modify the transport properties and, therefore, the macroscopic dynamics of the plasma. The non-linear evolution of these instabilities is expected to drive pressure anisotropies towards marginal stability values, controlled by the plasma beta βi. Here this non-linear evolution is worked out in an ab initio kinetic calculation for the simplest analytically tractable example – the parallel (k⊥= 0) firehose instability in a high-beta plasma. An asymptotic theory is constructed, based on a particular physical ordering and leading to a closed non-linear equation for the firehose turbulence. In the non-linear regime, both the analytical theory and the numerical solution predict secular (∝t) growth of magnetic fluctuations. The fluctuations develop a k−3∥ spectrum, extending from scales somewhat larger than ρi to the maximum scale that grows secularly with time (∝t1/2); the relative pressure anisotropy (p⊥−p∥)/p∥ tends to the marginal value −2/βi. The marginal state is achieved via changes in the magnetic field, not particle scattering. When a parallel ion heat flux is present, the parallel firehose mutates into the new gyrothermal instability (GTI), which continues to exist up to firehose-stable values of pressure anisotropy, which can be positive and are limited by the magnitude of the ion heat flux. The non-linear evolution of the GTI also features secular growth of magnetic fluctuations, but the fluctuation spectrum is eventually dominated by modes around a maximal scale ∼ρilT/λmfp, where lT is the scale of the parallel temperature variation. Implications for momentum and heat transport are speculated about. This study is motivated by our interest in the dynamics of galaxy cluster plasmas (which are used as the main astrophysical example), but its relevance to solar wind and accretion flow plasmas is also briefly discussed.

On the power spectrum of solar surface flows

Context. The surface of the Sun provides us with a unique and very detailed view of turbulent stellar convection. Studying its dynamics can therefore help us make significant progress in stellar convection modelling. Many features of solar surface turbulence like the supergranulation are still poorly understood. Aims. The aim of this work is to give new observational constraints on these flows by determining the horizontal scale dependence of the velocity and intensity fields, as represented by their power spectra, and to offer some theoretical guidelines to interpret these spectra. Methods. We use long time-series of images taken by the Solar Optical Telescope (SOT) on board the Hinode satellite; we reconstruct both horizontal (by granule tracking) and vertical (by Doppler effect) velocity fields in a field-of-view of ∼ 75×75 Mm 2 . The dynamics in the subgranulation range can be investigated with unprecedented precision thanks to the absence of seeing effects and the use of the modulation transfer function of SOT for correcting the spectra. Results. At small subgranulation scales down to 0.4 Mm the spectral density of kinetic energy associated with vertical motions exhibits a k −10/3 -like power law, while the intensity fluctuation spectrum follows either a k −17/3 or a k −3 -like power law at the two continuum levels investigated (525 and 450 nm respectively). We discuss the possible physical origin of these scalings and interpret the combined presence of k −17/3 and k −10/3 power laws for the intensity and vertical velocity as a signature of buoyancy-driven turbulent dynamics in a strongly thermally diffusive regime. In the mesogranulation range and up to a scale of 25 Mm, we find that the amplitude of the vertical velocity field decreases like λ −3/2 with the horizontal scale λ. This behaviour corresponds to a k 2 spectral power law. Still in the 2.5–10 Mm mesoscale range, we find that intensity fluctuations in the blue continuum also follow a k 2 power law. In passing we show that granule tracking cannot sample scales below 2.5 Mm. We finally further confirm the presence of a significant supergranulation energy peak at 30 Mm in the horizontal velocity power spectrum and show that the emergence of a pore erases this spectral peak. We tentatively estimate the scale height of the vertical velocity field in the supergranulation range and find 1 Mm; this value suggests that supergranulation flows are shallow.

Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow

Magnetorotational dynamo action in Keplerian shear flow is a three-dimensional, non-linear magnetohydrodynamic process whose study is relevant to the understanding of accretion processes and magnetic field generation in astrophysics. Transition to this form of dynamo action is subcritical and shares many characteristics of transition to turbulence in non-rotating hydrodynamic shear flows. This suggests that these different fluid systems become active through similar generic bifurcation mechanisms, which in both cases have eluded detailed understanding so far. In this paper, we build on recent work on the two problems to investigate numerically the bifurcation mechanisms at work in the incompressible Keplerian magnetorotational dynamo problem in the shearing box framework. Using numerical techniques imported from dynamical systems research, we show that the onset of chaotic dynamo action at magnetic Prandtl numbers larger than unity is primarily associated with global homoclinic and heteroclinic bifurcations of nonlinear magnetorotational dynamo cycles. These global bifurcations are found to be supplemented by local bifurcations of cycles marking the beginning of period-doubling cascades. The results suggest that nonlinear magnetorotational dynamo cycles provide the pathway to turbulent injection of both kinetic and magnetic energy in incompressible magnetohydrodynamic Keplerian shear flow in the absence of an externally imposed magnetic field. Studying the nonlinear physics and bifurcations of these cycles in different regimes and configurations may subsequently help to better understand the physical conditions of excitation of magnetohydrodynamic turbulence and instability-driven dynamos in a variety of astrophysical systems and laboratory experiments. The detailed characterization of global bifurcations provided for this three-dimensional subcritical fluid dynamics problem may also prove useful for the problem of transition to turbulence in hydrodynamic shear flows.

Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic-field generation in shear flows.

The nature of dynamo action in shear flows prone to magnetohydrodynamc instabilities is investigated using the magnetorotational dynamo in Keplerian shear flow as a prototype problem. Using direct numerical simulations and Newtons method, we compute an exact time-periodic magnetorotational dynamo solution to three-dimensional dissipative incompressible magnetohydrodynamic equations with rotation and shear. We discuss the physical mechanism behind the cycle and show that it results from a combination of linear and nonlinear interactions between a large-scale axisymmetric toroidal magnetic field and nonaxisymmetric perturbations amplified by the magnetorotational instability. We demonstrate that this large-scale dynamo mechanism is overall intrinsically nonlinear and not reducible to the standard mean-field dynamo formalism. Our results therefore provide clear evidence for a generic nonlinear generation mechanism of time-dependent coherent large-scale magnetic fields in shear flows and call for new theoretical dynamo models. These findings may offer important clues to understanding the transitional and statistical properties of subcritical magnetorotational turbulence.

Numerical experiments on dynamo action in sheared and rotating turbulence

Numerical simulations of forced turbulence in elongated shearing boxes are carried out to demonstrate that a nonhelical turbulence in conjunction with a linear shear can give rise to a mean-field dynamo. Exponential growth of magnetic field at scales larger than the outer (forcing) scale of the turbulence is found. Over a range of values of the shearing rate S spanning approximately two orders of magnitude, the growth rate of the magnetic field is proportional to the imposed shear, γ ∝ S, while the characteristic spatial scale of the field is lB ∝ S–1/2. The effect is quite general: earlier results for the nonrotating case by Yousef et al. (2008) are extended to shearing boxes with Keplerian rotation; it is also shown that the shear dynamo mechanism operates both below and above the threshold for the fluctuation dynamo. The apparently generic nature of the shear dynamo effect makes it an attractive object of study for the purpose of understanding the generation of magnetic fields in astrophysical systems. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

On self-sustaining processes in Rayleigh-stable rotating plane Couette flows and subcritical transition to turbulence in accretion disks

Context. Subcritical transition to turbulence in Keplerian accretion disks is still a controversial issue and some theoretical progress is required in order to determine whether or not this scenario provides a plausible explanation for the origin of angular momentum transport in non-magnetized accretion disks. Aims. Motivated by the recent discoveries of exact nonlinear steady self-sustaining solutions in linearly stable non-rotating shear flows, we attempt to compute similar solutions in Rayleigh-stable rotating plane Couette flows and to identify transition mechanisms in such flows. Methods. Numerical simulations (time-stepping approaches) have been employed in most recent studies of the problem. Here, we instead combine nonlinear continuation methods and asymptotic theory to study the nonlinear dynamics of plane Couette flows in Rayleigh-stable regimes. Results. We obtain exact nonlinear solutions for Rayleigh-stable cyclonic regimes using continuation techniques proposed by Waleffe and Nagata but show that it is not possible to compute solutions for Rayleigh-stable anticyclonic regimes, including Keplerian flow, using similar techniques. We also present asymptotic descriptions of these various problems at large Reynolds numbers that provide some insight into the differences between the non-rotating and Rayleigh-stable anticyclonic regimes and derive some necessary conditions for mechanisms analogous to the non-rotating self-sustaining process to be present in (constant angular momentum) flows on the Rayleigh line. Conclusions. Our results demonstrate that subcritical transition mechanisms cannot be identified in wall-bounded Rayleigh-stable anticyclonic shear flows by transposing directly the phenomenology of subcritical transition in cyclonic and non-rotating wall-bounded shear flows. Asymptotic developments, however, leave open the possibility that nonlinear self-sustaining solutions may exist in unbounded or periodic flows on the Rayleigh line. These could serve as a starting point to discover solutions in Rayleigh-stable flows, but the nonlinear stability of Keplerian accretion disks remains to be determined.

Dissipative effects on the sustainment of a magnetorotational dynamo in Keplerian shear flow

The magnetorotational (MRI) dynamo has long been considered one of the possible drivers of turbulent angular momentum transport in astrophysical accretion disks. However, various numerical results suggest that this dynamo may be difficult to excite in the astrophysically relevant regime of magnetic Prandtl number (Pm) significantly smaller than unity, for reasons currently not well understood. The aim of this article is to present the first results of an ongoing numerical investigation of the role of both linear and nonlinear dissipative effects in this problem. Combining a parametric exploration and an energy analysis of incompressible nonlinear MRI dynamo cycles representative of the transitional dynamics in large aspect ratio shearing boxes, we find that turbulent magnetic diffusion makes the excitation and sustainment of this dynamo at moderate magnetic Reynolds number (Rm) increasingly difficult for decreasing Pm. This results in an increase in the critical Rm of the dynamo for increasing kinematic Reynolds number (Re), in agreement with earlier numerical results. Given its very generic nature, we argue that turbulent magnetic diffusion could be an important determinant of MRI dynamo excitation in disks, and may also limit the efficiency of angular momentum transport by MRI turbulence in low Pm regimes.