Westward winds have now been inferred for two hot Jupiters (HJs): HAT-P-7b and CoRoT-2b. Such observations could be the result of a number of physical phenomena such as cloud asymmetries, ...asynchronous rotation, or magnetic fields. For the hotter HJs magnetic fields are an obvious candidate, though the actual mechanism remains poorly understood. Here we show that a strong toroidal magnetic field causes the planetary-scale equatorial magneto-Kelvin wave to structurally shear as it travels, resulting in westward tilting eddies, which drive a reversal of the equatorial winds from their eastward hydrodynamic counterparts. Using our simplified model we estimate that the equatorial winds of HAT-P-7b would reverse for a planetary dipole field strength , a result that is consistent with three-dimensional magnetohydrodynamic simulations and lies below typical surface dipole estimates of inflated HJs. The same analysis suggests the minimum dipole field strength required to reverse the winds of CoRoT-2b is , which considerably exceeds estimates of the maximum surface dipole strength for HJs. We hence conclude that our magnetic wave-driven mechanism provides an explanation for wind reversals on HAT-P-7b; however, other physical phenomena provide more plausible explanations for wind reversals on CoRoT-2b.
Context. Convectively driven flows play a crucial role in the dynamo processes that are responsible for producing magnetic activity in stars and planets. It is still not fully understood why many ...astrophysical magnetic fields have a significant large-scale component. Aims. Our aim is to investigate the dynamo properties of compressible convection in a rapidly rotating Cartesian domain, focusing upon a parameter regime in which the underlying hydrodynamic flow is known to be unstable to a large-scale vortex instability. Methods. The governing equations of three-dimensional non-linear magnetohydrodynamics (MHD) are solved numerically. Different numerical schemes are compared and we propose a possible benchmark case for other similar codes. Results. In keeping with previous related studies, we find that convection in this parameter regime can drive a large-scale dynamo. The components of the mean horizontal magnetic field oscillate, leading to a continuous overall rotation of the mean field. Whilst the large-scale vortex instability dominates the early evolution of the system, the large-scale vortex is suppressed by the magnetic field and makes a negligible contribution to the mean electromotive force that is responsible for driving the large-scale dynamo. The cycle period of the dynamo is comparable to the ohmic decay time, with longer cycles for dynamos in convective systems that are closer to onset. In these particular simulations, large-scale dynamo action is found only when vertical magnetic field boundary conditions are adopted at the upper and lower boundaries. Strongly modulated large-scale dynamos are found at higher Rayleigh numbers, with periods of reduced activity (grand minima-like events) occurring during transient phases in which the large-scale vortex temporarily re-establishes itself, before being suppressed again by the magnetic field.
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The propagation of charged particles, including cosmic rays, in a partially ordered magnetic field is characterized by a diffusion tensor whose components depend on the particle's Larmor radius R
L ...and the degree of order in the magnetic field. Most studies of the particle diffusion presuppose a scale separation between the mean and random magnetic fields (e.g. there being a pronounced minimum in the magnetic power spectrum at intermediate scales). Scale separation is often a good approximation in laboratory plasmas, but not in most astrophysical environments such as the interstellar medium (ISM). Modern simulations of the ISM have numerical resolution of the order of 1 pc, so the Larmor radius of the cosmic rays that dominate in energy density is at least 106 times smaller than the resolved scales. Large-scale simulations of cosmic ray propagation in the ISM thus rely on oversimplified forms of the diffusion tensor. We take the first steps towards a more realistic description of cosmic ray diffusion for such simulations, obtaining direct estimates of the diffusion tensor from test particle simulations in random magnetic fields (with the Larmor radius scale being fully resolved), for a range of particle energies corresponding to 10−2 ≲ R
L/l
c ≲ 103, where l
c is the magnetic correlation length. We obtain explicit expressions for the cosmic ray diffusion tensor for R
L/l
c ≪ 1, that might be used in a sub-grid model of cosmic ray diffusion. The diffusion coefficients obtained are closely connected with existing transport theories that include the random walk of magnetic lines.
Mean-field dynamo theory suggests that turbulent convection in a rotating layer of electrically conducting fluid produces a significant
$\alpha $
-effect, which is one of the key ingredients in any ...mean-field dynamo model. Provided that this
$\alpha $
-effect operates more efficiently than (turbulent) magnetic diffusion, such a system should be capable of sustaining a large-scale dynamo. However, in the Boussinesq model that was considered by Cattaneo & Hughes (J. Fluid Mech., vol. 553, 2006, pp. 401–418) the dynamo produced small-scale, intermittent magnetic fields with no significant large-scale component. In this paper, we consider the compressible analogue of the rotating convective layer that was considered by Cattaneo & Hughes (2006). Varying the horizontal scale of the computational domain, we investigate the dependence of the dynamo upon the rotation rate. Our simulations indicate that these turbulent compressible flows can drive a small-scale dynamo but, even when the layer is rotating very rapidly (with a mid-layer Taylor number of
$Ta= 1{0}^{8} $
), we find no evidence for the generation of a significant large-scale component of the magnetic field on a dynamical time scale. Like Cattaneo & Hughes (2006), we measure a negligible (time-averaged)
$\alpha $
-effect when a uniform horizontal magnetic field is imposed across the computational domain. Although the total horizontal magnetic flux is a conserved quantity in these simulations, the (depth-dependent) horizontally averaged magnetic field always exhibits strong fluctuations. If these fluctuations are artificially suppressed within the code, we measure a significant mean electromotive force that is comparable to that found in related calculations in which the
$\alpha $
-effect is measured using the test-field method, even though we observe no large-scale dynamo action.
Abstract
Magnetically driven hotspot variations (which are tied to atmospheric wind variations) in hot Jupiters are studied using nonlinear numerical simulations of a shallow-water ...magnetohydrodynamic (SWMHD) system and a linear analysis of equatorial SWMHD waves. In hydrodynamic models, mid-to-high-latitude geostrophic circulations are known to cause a net west-to-east equatorial thermal energy transfer, which drives hotspot offsets eastward. We find that a strong toroidal magnetic field can obstruct these energy transporting circulations. This results in winds aligning with the magnetic field and generates westward Lorentz force accelerations in hotspot regions, ultimately causing westward hotspot offsets. In the subsequent linear analysis we find that this reversal mechanism has an equatorial wave analogy in terms of the planetary-scale equatorial magneto-Rossby waves. We compare our findings to three-dimensional MHD simulations, both quantitatively and qualitatively, identifying the link between the mechanics of magnetically driven hotspot and wind reversals. We use the developed theory to identify physically motivated reversal criteria, which can be used to place constraints on the magnetic fields of ultra-hot Jupiters with observed westward hotspots.
We study dynamo action in a convective layer of electrically conducting, compressible fluid, rotating about the vertical axis. At the upper and lower bounding surfaces, perfectly conducting boundary ...conditions are adopted for the magnetic field. Two different levels of thermal stratification are considered. If the magnetic diffusivity is sufficiently small, the convection acts as a small-scale dynamo. Using a definition for the magnetic Reynolds number ${R}_{M} $ that is based upon the horizontal integral scale and the horizontally averaged velocity at the mid-layer of the domain, we find that rotation tends to reduce the critical value of ${R}_{M} $ above which dynamo action is observed. Increasing the level of thermal stratification within the layer does not significantly alter the critical value of ${R}_{M} $ in the rotating calculations, but it does lead to a reduction in this critical value in the non-rotating cases. At the highest computationally accessible values of the magnetic Reynolds number, the saturation levels of the dynamo are similar in all cases, with the mean magnetic energy density somewhere between 4 and 9 % of the mean kinetic energy density. To gain further insights into the differences between rotating and non-rotating convection, we quantify the stretching properties of each flow by measuring Lyapunov exponents. Away from the boundaries, the rate of stretching due to the flow is much less dependent upon depth in the rotating cases than it is in the corresponding non-rotating calculations. It is also shown that the effects of rotation significantly reduce the magnetic energy dissipation in the lower part of the layer. We also investigate certain aspects of the saturation mechanism of the dynamo.
Observations of differential rotation within the solar convection zone have revealed a cyclic pattern of zonal shear flows. Given that the 11-yr periodicity of this flow pattern is approximately half ...that of the 22-yr solar activity cycle, it is likely that these flows are magnetically driven. In this paper, these zonal shear flows are investigated in the context of a parametrized mean-field solar dynamo model which incorporates the feedback of the large-scale magnetic fields upon an imposed differential rotation profile. This ‘interface-like’ model produces dynamo action and a pattern of zonal flows that is qualitatively consistent with solar observations. One of the key parameters in this model is the magnetic Prandtl number – when this parameter is small, it is possible to find time-dependent solutions that are characterized by prolonged phases of significantly reduced magnetic activity (so-called ‘grand minima’). Despite the presence of grand minima, it is still possible to find a solar-like pattern of zonal shear flows in this highly modulated, low magnetic Prandtl number regime.
THE PARKER INSTABILITY IN DISK GALAXIES Rodrigues, L. F. S.; Sarson, G. R.; Shukurov, A. ...
Astrophysical journal/The Astrophysical journal,
01/2016, Volume:
816, Issue:
1
Journal Article
Peer reviewed
Open access
ABSTRACT We examine the evolution of the Parker instability in galactic disks using 3D numerical simulations. We consider a local Cartesian box section of a galactic disk, where gas, magnetic fields, ...and cosmic rays are all initially in a magnetohydrostatic equilibrium. This is done for different choices of initial cosmic-ray density and magnetic field. The growth rates and characteristic scales obtained from the models, as well as their dependences on the density of cosmic rays and magnetic fields, are in broad agreement with previous (linearized, ideal) analytical work. However, this nonideal instability develops a multimodal 3D structure, which cannot be quantitatively predicted from the earlier linearized studies. This 3D signature of the instability will be of importance in interpreting observations. As a preliminary step toward such interpretations, we calculate synthetic polarized intensity and Faraday rotation measure (RM) maps, and the associated structure functions of the latter, from our simulations; these suggest that the correlation scales inferred from RM maps are a possible probe for the cosmic-ray content of a given galaxy. Our calculations highlight the importance of cosmic rays in these measures, making them an essential ingredient of realistic models of the interstellar medium.
Abstract
We use results of shallow-water magnetohydrodynamics to place estimates on the minimum magnetic field strengths required to cause atmospheric wind variations (and therefore ...westward-venturing hotspots) for a data set of hot Jupiters (HJs), including HAT-P-7b, CoRoT-2b, Kepler-76, WASP-12b, and WASP-33b, on which westward hotspots have been observationally inferred. For HAT-P-7b and CoRoT-2b our estimates agree with past results; for Kepler-76b we find that the critical dipolar magnetic field strength, over which the observed wind variations can be explained by magnetism, lies between 4 G and 19 G; for WASP-12b and WASP-33b westward hotspots can be explained by 1 G and 2 G dipolar fields, respectively. Additionally, to guide future observational missions, we identify 61 further HJs that are likely to exhibit magnetically driven atmospheric wind variations and predict these variations are highly likely in ∼40 of the hottest HJs.
Context. Regions of quiet Sun generally exhibit a complex distribution of small-scale magnetic field structures, which interact with the near-surface turbulent convective motions. Furthermore, it is ...probable that some of these magnetic fields are generated locally by a convective dynamo mechanism. In addition to the well-known granular and supergranular convective scales, various observations have indicated that there is an intermediate scale of convection, known as mesogranulation, with vertical magnetic flux concentrations accumulating preferentially at the boundaries of mesogranules. Aims. Our aim is to investigate the small-scale dynamo properties of a convective flow that exhibits both granulation and mesogranulation, comparing our findings with solar observations. Methods. Adopting an idealised model for a localised region of quiet Sun, we use numerical simulations of compressible magnetohydrodynamics, in a three-dimensional Cartesian domain, to investigate the parametric dependence of this system (focusing particularly upon the effects of varying the aspect ratio and the Reynolds number). Results. In purely hydrodynamic convection, we find that mesogranulation is a robust feature of this system provided that the domain is wide enough to accommodate these large-scale motions. The mesogranular peak in the kinetic energy spectrum is more pronounced in the higher Reynolds number simulations. We investigate the dynamo properties of this system in both the kinematic and the nonlinear regimes and we find that the dynamo is always more efficient in larger domains, when mesogranulation is present. Furthermore, we use a filtering technique in Fourier space to demonstrate that it is indeed the larger scales of motion that are primarily responsible for driving the dynamo. In the nonlinear regime, the magnetic field distribution compares very favourably to observations, both in terms of the spatial distribution and the measured field strengths.
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