Magnetic Field Evolution in Neutron Star Crusts: Beyond the Hall Effect

Neutron stars host the strongest magnetic fields that we know of in the Universe. Their magnetic fields are the main means of generating their radiation, either magnetospheric or through the crust. Moreover, the evolution of the magnetic field has been intimately related to explosive events of magnetars, which host strong magnetic fields, and their persistent thermal emission. The evolution of the magnetic field in the crusts of neutron stars has been described within the framework of the Hall effect and Ohmic dissipation. Yet, this description is limited by the fact that the Maxwell stresses exerted on the crusts of strongly magnetised neutron stars may lead to failure and temperature variations. In the former case, a failed crust does not completely fulfil the necessary conditions for the Hall effect. In the latter, the variations of temperature are strongly related to the magnetic field evolution. Finally, sharp gradients of the star’s temperature may activate battery terms and alter the magnetic field structure, especially in weakly magnetised neutron stars. In this review, we discuss the recent progress made on these effects. We argue that these phenomena are likely to provide novel insight into our understanding of neutron stars and their observable properties.

An Electromechanical Model for Electrowetting With Finite Droplet Size

We present an electromechanical model for the analysis of electrowetting by considering the balance between an electric force and a surface tension force acting on the contact line of three phases, namely the droplet (D) phase, the substrate (S) phase, and the ambiance (A) phase. We show that the Maxwell stresses at the ambiance–substrate (A–S) interface, the droplet–substrate (D–S) interface, and the droplet–ambiance (D–A) interface induce an electric force on the three-phase contact line which is responsible for the modification of the apparent contact angle in electrowetting. For a classical electrowetting configuration with a flat substrate, we show that the electric force on the contact line (or the electrowetting number) is mainly due to the Maxwell stresses at the D–A interface. The model is validated by its excellent agreement with the classical Young-Lippmann (Y-L) model for sufficiently large droplets and comparable electric permittivities between A and S phases. Interestingly, our new model reveals that the finite size of droplet produces profound effects on the electrowetting that the electrowetting number becomes dependent on the permittivity of A phase and the equilibrium contact angle, which is in stark contrast to the Y-L model. The reasons for these remarkable effects are elaborated and clarified. The findings in the current study are complementary to the classical Y-L model and provide new insights into the electrowetting phenomenon.

Breakup and non-coalescence mechanism of aqueous droplets suspended in castor oil under electric field

The effect of an electric field on the coalescence of two water droplets suspended in an insulating oil (castor oil) in the non-coalescence regime is investigated. Unlike the immediate breakup of the bridge, as reported in earlier studies, e.g. Ristenpart et al. (Nature, vol. 461 (7262), 2009, pp. 377–380), the non-coalescence observed in our experiments indicate that at strong fields the droplets exhibit a tendency to coalesce, the intervening bridge thickens whereafter the bridge dramatically begins to thin, initiating non-coalescence. Numerical simulations using the boundary integral method are able to explain the physical mechanism of thickening of this bridge followed by thinning and non-coalescence. The underlying reason is the competing meridional and azimuthal curvatures which affect the pressure inside the bridge to become either positive or negative under the effect of electric field induced Maxwell stresses. Velocity and pressure profiles confirm this hypothesis and we are able to predict this behaviour of transitory coalescence followed by non-coalescence.

An Electromechanical Model for Electrowetting

We present an electromechanical model for analysis of electrowetting by considering the balance between an electric force and a surface tension force acting on the contact line of three phases, namely the droplet (D) phase the substrate (S) phase and the ambiance (A) phase. We show that the electric force acting on the three-phase contact line generally is contributed by the Maxwell stresses at the ambiance-substrate (A-S) interface, the droplet-substrate (D-S) interface, and the droplet-ambiance (D-A) interface. It was identified that the change of contact angle in electrowetting is essentially a consequence of the modification of the electric force on the contact line. For a classical electrowetting configuration, we show that the electric force on the contact line is mainly due to the Maxwell stresses at the D-A interface. Then we examine comprehensively how the electric force on the contact line varies with the permittivity difference between A and S phases, the contact angle and size. It was found that our model agrees excellently with the classical Yong-Lippmann (Y-L) model when the permittivities of A and S phases are equal, while the difference between the two increases as the permittivity difference between A and S phases increases. The electric force increases with the increase of the contact angle for a given droplet size. Our model approaches the Y-L model with the increasing droplet size. The findings are complementary to the classical Y-L model and provide new insights into the electrowetting.

Machine learning reveals systematic accumulation of electric current in lead-up to solar flares

Solar flares—bursts of high-energy radiation responsible for severe space weather effects—are a consequence of the occasional destabilization of magnetic fields rooted in active regions (ARs). The complexity of AR evolution is a barrier to a comprehensive understanding of flaring processes and accurate prediction. Although machine learning (ML) has been used to improve flare predictions, the potential for revealing precursors and associated physics has been underexploited. Here, we train ML algorithms to classify between vector–magnetic-field observations from flaring ARs, producing at least one M-/X-class flare, and nonflaring ARs. Analysis of magnetic-field observations accurately classified by the machine presents statistical evidence for (i) ARs persisting in flare-productive states—characterized by AR area—for days, before and after M- and X-class flare events; (ii) systematic preflare buildup of free energy in the form of electric currents, suggesting that the associated subsurface magnetic field is twisted; and (iii) intensification of Maxwell stresses in the corona above newly emerging ARs, days before first flares. These results provide insights into flare physics and improving flare forecasting.

Magnetic and rotational quenching of the Λ effect

Context. Differential rotation in stars is driven by the turbulent transport of angular momentum.Aims. Our aim is to measure and parameterize the non-diffusive contribution to the total (Reynolds plus Maxwell) turbulent stress, known as the Λ effect, and its quenching as a function of rotation and magnetic field.Methods. Simulations of homogeneous, anisotropically forced turbulence in fully periodic cubes are used to extract their associated turbulent Reynolds and Maxwell stresses. The forcing is set up such that the vertical velocity component dominates over the horizontal ones, as in turbulent stellar convection. This choice of the forcing defines the vertical direction. Additional preferred directions are introduced by the imposed rotation and magnetic field vectors. The angle between the rotation vector and the vertical direction is varied such that the latitude range from the north pole to the equator is covered. Magnetic fields are introduced by imposing a uniform large-scale field on the system. Turbulent transport coefficients pertaining to the Λ effect are obtained by fitting. The results are compared with analytic studies.Results. The numerical and analytic results agree qualitatively at slow rotation and low Reynolds numbers. This means that vertical (horizontal) transport is downward (equatorward). At rapid rotation the latitude dependence of the stress is more complex than predicted by theory. The existence of a significant meridional Λ effect is confirmed. Large-scale vorticity generation is found at rapid rotation when the Reynolds number exceeds a threshold value. The Λ effect is severely quenched by large-scale magnetic fields due to the tendency of the Reynolds and Maxwell stresses to cancel each other. Rotational (magnetic) quenching of Λ occurs at more rapid rotation (at lower field strength) in the simulations than in the analytic studies.Conclusions. The current results largely confirm the earlier theoretical results, and also offer new insights: the non-negligible meridional Λ effect possibly plays a role in the maintenance of meridional circulation in stars, and the appearance of large-scale vortices raises the question of their effect on the angular momentum transport in rapidly rotating stellar convective envelopes. The results regarding magnetic quenching are consistent with the strong decrease in differential rotation in recent semi-global simulations and highlight the importance of including magnetic effects in differential rotation models.