Keywords

The periods of magnetic activity cycles in the Sun and solar-type stars do not exhibit a simple or even single trend with respect to rotation rate or luminosity. Dynamo models can be used to interpret this diversity and can ultimately help us understand why some solar-like stars do not exhibit a magnetic cycle, whereas some do, and for the latter what physical mechanisms set their magnetic cycle period. Three-dimensional nonlinear MHD simulations present the advantage of having only a small number of tunable parameters, and produce in a dynamically self-consistent manner the flows and the dynamo magnetic fields pervading stellar interiors. We conduct a series of such simulations within the EULAG-MHD framework, varying the rotation rate and luminosity of the modeled solar-like convective envelopes. We find decadal magnetic cycles when the Rossby number near the base of the convection zone is moderate (typically between 0.25 and 1). Secondary, shorter cycles located at the top of the convective envelope close to the equator are also observed in our numerical experiments, when the local Rossby number is lower than 1. The deep-seated dynamo sustained in these numerical experiments is fundamentally nonlinear, in that it is the feedback of the large-scale magnetic field on the large-scale differential rotation that sets the magnetic cycle period. The cycle period is found to decrease with the Rossby number, which offers an alternative theoretical explanation to the variety of activity cycles observed in solar-like stars.

Observations of surface magnetic fields are now within reach for many stellar types thanks to the development of Zeeman–Doppler Imaging. These observations are extremely useful for constraining rotational evolution models of stars, as well as for characterizing the generation of the magnetic field. We recently demonstrated that the impact of coronal magnetic field topology on the rotational braking of a star can be parameterized with a scalar parameter: the open magnetic flux. However, without running costly numerical simulations of the stellar wind, reconstructing the coronal structure of the large-scale magnetic field is not trivial. An alternative—broadly used in solar physics—is to extrapolate the surface magnetic field assuming a potential field in the corona, to describe the opening of the field lines by the magnetized wind. This technique relies on the definition of a so-called source surface radius, which is often fixed to the canonical value of $2.5{R}_{\odot }.$ However this value likely varies from star to star. To resolve this issue, we use our extended set of 2.5D wind simulations published in 2015 to provide a criterion for the opening of field lines as well as a simple tool to assess the source surface radius and the open magnetic flux. This allows us to derive the magnetic torque applied to the star by the wind from any spectropolarimetric observation. We conclude by discussing some estimations of spin-down timescales made using our technique and compare them to observational requirements.

Fundamental modes supported by a thin magnetic flux tube embedded in the solar atmosphere are typically classified as longitudinal, transverse, and torsional waves. If the tube is isothermal, then the propagation of longitudinal and transverse tube waves is restricted to frequencies that are higher than the corresponding global cutoff frequency for each wave. However, no such global cutoff frequency exists for torsional tube waves, which means that a thin and isothermal flux tube supports torsional tube waves of any frequency. In this paper, we consider a thin and non-isothermal magnetic flux tube and demonstrate that temperature gradients inside this tube are responsible for the origin of a cutoff frequency for torsional tube waves. The cutoff frequency is used to determine conditions for the wave propagation in the solar atmosphere, and the obtained results are compared to the recent observational data that support the existence of torsional tube waves in the Sun.

We study the properties of the turbulence driven by the magnetorotational instability in a stratified shearing box with outflow boundary conditions and an equation of state determined by self-consistent dissipation and radiation losses. A series of simulations with increasing resolution are performed within a fixed computational box. We achieve numerical convergence with respect to radial and azimuthal resolution. As vertical resolution is improved, the ratio of stress to pressure increases slowly, but the absolute levels of both the stress and the pressure increase noticeably. These results are in contrast with those of previous work on unstratified shearing boxes, in which improved resolution caused a diminution in the magnetic field strength. We argue that the persistence of strong magnetic field at higher resolution found in the stratified case is due to buoyancy. In addition, we find that the time-averaged vertical correlation length of the magnetic field near the disk midplane is ≃3 times larger than that found in previous unstratified simulations, decreasing slowly with improved vertical resolution. We further show that the undulatory Parker instability drives the magnetic field upwelling at several scale heights from the midplane that is characteristic of stratified magnetohydrodynamics-turbulent disks.

A model is presented for generation of fast solar wind in coronal holes, relying on heating that is dominated by turbulent dissipation of MHD fluctuations transported upward in the solar atmosphere. Scale-separated transport equations include large-scale fields, transverse Alfvénic fluctuations, and a small compressive dissipation due to parallel shears near the transition region. The model accounts for proton temperature, density, wind speed, and fluctuation amplitude as observed in remote sensing and in situ satellite data.

NGC 1275, the central galaxy in the Perseus cluster, is the host of gigantic hot bipolar bubbles inflated by active galactic nucleus (AGN) jets observed in the radio as Perseus A. It presents a spectacular Hα-emitting nebulosity surrounding NGC 1275, with loops and filaments of gas extending to over 50 kpc. The origin of the filaments is still unknown, but probably correlates with the mechanism responsible for the giant buoyant bubbles. We present 2.5 and three-dimensional magnetohydrodynamical (MHD) simulations of the central region of the cluster in which turbulent energy, possibly triggered by star formation and supernovae (SNe) explosions, is introduced. The simulations reveal that the turbulence injected by massive stars could be responsible for the nearly isotropic distribution of filaments and loops that drag magnetic fields upward as indicated by recent observations. Weak shell-like shock fronts propagating into the intracluster medium (ICM) with velocities of 100–500 km s⁻¹ are found, also resembling the observations. The isotropic outflow momentum of the turbulence slows the infall of the ICM, thus limiting further starburst activity in NGC 1275. As the turbulence is subsonic over most of the simulated volume, the turbulent kinetic energy is not efficiently converted into heat and additional heating is required to suppress the cooling flow at the core of the cluster. Simulations combining the MHD turbulence with the AGN outflow can reproduce the temperature radial profile observed around NGC 1275. While the AGN mechanism is the main heating source, the SNe are crucial to isotropize the energy distribution.

An electrical conductivity tensor is used in a 1.5D magnetohydrodynamic (MHD) simulation to describe how MHD shock waves may form, propagate, and heat the photosphere and chromosphere by compression and resistive dissipation. The spatial resolution is 1 km. A train of six shock waves is generated by a sinusoidal magnetic field driver in the photosphere with a period T = 30 s, mean of 500 G, and variation of 250 G. The duration of the simulation is 200 s. Waves generated in the photosphere evolve into shock waves at a height z ∼ 375 km above the photosphere. The transition of the atmosphere from weakly to strongly magnetized with increasing height causes the Pedersen resistivity η_P to increase to ∼2000 times the Spitzer resistivity. This transition occurs over a height range of a few hundred kilometers near the temperature minimum of the initial state at z ∼ 500 km. The initial state is a model atmosphere derived by Fontenla et al., plus a background magnetic field. The increase in η_P is associated with an increase in the resistive heating rate Q. Shock layer thicknesses are ∼10–20 km. They are nonzero due to the presence of resistive dissipation, so magnetization-induced resistivity plays a role in determining shock structure, and hence the compressive heating rate Q_c. At t = 200 s the solution has the following properties. Within shock layers, Q_maximum ∼ 1.4–7 erg cm⁻³ s⁻¹, and Q_c,maximum ∼ 10–10³ Q_maximum. Between shock waves, and at some points within shock layers, Q_c < 0, indicating cooling by rarefaction. The integrals of Q and Q_c over the shock wave train are F ∼ 4.6 × 10⁶ erg cm⁻² s⁻¹ and F_c ∼ 1.24 × 10⁹ erg cm⁻² s⁻¹. A method based on the thermal, mechanical, and electromagnetic energy conservation equations is presented for checking the accuracy of the numerical solution, and gaining insight into energy flow and transformation. The method can be applied to higher dimensional simulations. It is suggested that observations be performed to map out the transition region across which the transition from weakly ionized, weakly magnetized plasma to weakly ionized, strongly magnetized plasma occurs, and to correlate it with net radiative loss.

We analyze the physical mechanisms that form a three-dimensional coronal flux rope and later cause its eruption. This is achieved by a zero-β magnetohydrodynamic (MHD) simulation of an initially potential, asymmetric bipolar field, which evolves by means of simultaneous slow magnetic field diffusion and sub-Alfvénic, line-tied shearing motions in the photosphere. As in similar models, flux-cancellation-driven photospheric reconnection in a bald-patch (BP) separatrix transforms the sheared arcades into a slowly rising and stable flux rope. A bifurcation from a BP to a quasi-separatrix layer (QSL) topology occurs later on in the evolution, while the flux rope keeps growing and slowly rising, now due to shear-driven coronal slip-running reconnection, which is of tether-cutting type and takes place in the QSL. As the flux rope reaches the altitude at which the decay index −∂ln B/∂ln z of the potential field exceeds ∼3/2, it rapidly accelerates upward, while the overlying arcade eventually develops an inverse tear-drop shape, as observed in coronal mass ejections (CMEs). This transition to eruption is in accordance with the onset criterion of the torus instability. Thus, we find that photospheric flux-cancellation and tether-cutting coronal reconnection do not trigger CMEs in bipolar magnetic fields, but are key pre-eruptive mechanisms for flux ropes to build up and to rise to the critical height above the photosphere at which the torus instability causes the eruption. In order to interpret recent Hinode X-Ray Telescope observations of an erupting sigmoid, we produce simplified synthetic soft X-ray images from the distribution of the electric currents in the simulation. We find that a bright sigmoidal envelope is formed by pairs of $\textsf{J}$-shaped field lines in the pre-eruptive stage. These field lines form through the BP reconnection and merge later on into $\textsf{S}$-shaped loops through the tether-cutting reconnection. During the eruption, the central part of the sigmoid brightens due to the formation of a vertical current layer in the wake of the erupting flux rope. Slip-running reconnection in this layer yields the formation of flare loops. A rapid decrease of currents due to field line expansion, together with the increase of narrow currents in the reconnecting QSL, yields the sigmoid hooks to thin in the early stages of the eruption. Finally, a slightly rotating erupting loop-like feature (ELLF) detaches from the center of the sigmoid. Most of this ELLF is not associated with the erupting flux rope, but with a current shell that develops within expanding field lines above the rope. Only the short, curved end of the ELLF corresponds to a part of the flux rope. We argue that the features found in the simulation are generic for the formation and eruption of soft X-ray sigmoids.

We apply ionization balance and magnetohydrodynamical (MHD) calculations to investigate whether magnetic activity moderated by recombination on dust grains can account for the mass accretion rates and the mid-infrared spectra and variability of protostellar disks. The MHD calculations use the stratified shearing-box approach and include grain settling and the feedback from the changing dust abundance on the resistivity of the gas. The two-decade spread in accretion rates among solar-mass T Tauri stars is too large to result solely from variations in the grain size and stellar X-ray luminosity, but can plausibly be produced by varying these parameters together with the disk magnetic flux. The diverse shapes and strengths of the mid-infrared silicate bands can come from the coupling of grain settling to the distribution of the magnetorotational turbulence, through the following three effects. First, recombination on grains 1 μm or smaller yields a magnetically inactive dead zone extending more than two scale heights from the midplane, while turbulent motions in the magnetically active disk atmosphere overshoot the dead zone boundary by only about one scale height. Second, grains deep in the dead zone oscillate vertically in wave motions driven by the turbulent layer above, but on average settle at the rates found in laminar flow, so that the interior of the dead zone is a particle sink and the disk atmosphere will become dust-depleted unless resupplied from elsewhere. Third, with sufficient depletion, the dead zone is thinner and mixing dredges grains off the midplane. The last of these processes enables evolutionary signatures such as the degree of settling to sometimes decrease with age. The MHD results also show that the magnetic activity intermittently lifts clouds of small grains into the atmosphere. Consequently the photosphere height changes by up to one-third over timescales of a few orbits, while the extinction along lines of sight grazing the disk surface varies by factors of 2 over times down to a tenth of an orbit. We suggest that the changing shadows cast by the dust clouds on the outer disk are a cause of the daily to monthly mid-infrared variability found in many young stars.

We propose a model for diffusive shock acceleration (DSA) in which stochastic magnetic fields in the shock precursor are generated through purely fluid mechanisms of a so-called small-scale dynamo. This contrasts with previous DSA models that considered magnetic fields amplified through cosmic ray (CR) streaming instabilities, i.e., either by way of individual particles resonant scattering in the magnetic fields, or by macroscopic electric currents associated with large-scale CR streaming. Instead, in our picture, the solenoidal velocity perturbations that are required for the dynamo to work are produced through the interactions of the pressure gradient of the CR precursor and density perturbations in the inflowing fluid. Our estimates show that this mechanism provides fast growth of magnetic field and is very generic. We argue that for supernovae shocks the mechanism is capable of generating upstream magnetic fields that are sufficiently strong for accelerating CRs up to around 10¹⁶ eV. No action of any other mechanism is necessary.