Alexander J. B. Russell

Effects of M dwarf magnetic fields on potentially habitable planets

We investigate the e ect of the magnetic fields of M dwarf (dM) stars on potentially habitable Earth-like planets. These fields can reduce the size of planetary magnetospheres to such an extent that a significant fraction of the planet’s atmosphere may be exposed to erosion by the stellar wind. We used a sample of 15 active dM stars, for which surface magnetic-field maps were reconstructed, to determine the magnetic pressure at the planet orbit and hence the largest size of its magnetosphere, which would only be decreased by considering the stellar wind. Our method provides a fast means to assess which planets are most a ected by the stellar magnetic field, which can be used as a first study to be followed by more sophisticated models. We show that hypothetical Earth-like planets with similar terrestrial magnetisation ( 1 G) orbiting at the inner (outer) edge of the habitable zone of these stars would present magnetospheres that extend at most up to 6 (11:7) planetary radii. To be able to sustain an Earth-sized magnetosphere, with the exception of only a few cases, the terrestrial planet would either (1) need to orbit significantly farther out than the traditional limits of the habitable zone; or else, (2) if it were orbiting within the habitable zone, it would require at least a magnetic field ranging from a few G to up to a few thousand G. By assuming a magnetospheric size that is more appropriate for the young-Earth (3:4 Gyr ago), the required planetary magnetic fields are one order of magnitude weaker. However, in this case, the polar-cap area of the planet, which is unprotected from transport of particles to/from interplanetary space, is twice as large. At present, we do not know how small the smallest area of the planetary surface is that could be exposed and would still not a ect the potential for formation and development of life in a planet. As the star becomes older and, therefore, its rotation rate and magnetic field reduce, the interplanetary magnetic pressure decreases and the magnetosphere of planets probably expands. Using an empirically derived rotation-activity/magnetism relation, we provide an analytical expression for estimating the shortest stellar rotation period for which an Earth-analogue in the habitable zone could sustain an Earth-sized magnetosphere. We find that the required rotation rate of the early- and mid-dM stars (with periods &37‐202 days) is slower than the solar one, and even slower for the late-dM stars (&63‐263 days). Planets orbiting in the habitable zone of dM stars that rotate faster than this have smaller magnetospheric sizes than that of the Earth magnetosphere. Because many late-dM stars are fast rotators, conditions for terrestrial planets to harbour Earth-sized magnetospheres are more easily achieved for planets orbiting slowly rotating early- and mid-dM stars.

Propagation of Alfvénic Waves from Corona to Chromosphere and Consequences for Solar Flares

How do magnetohydrodynamic waves travel from the fully ionized corona, into and through the underlying partially ionized chromosphere, and what are the consequences for solar flares? To address these questions, we have developed a two-fluid model (of plasma and neutrals) and used it to perform one-dimensional simulations of Alfven waves in a solar atmosphere with realistic density and temperature structure. Studies of a range of solar features (faculae, plage, penumbra, and umbra) show that energy transmission from corona to chromosphere can exceed 20% of incident energy for wave periods of 1 s or less. Damping of waves in the chromosphere depends strongly on wave frequency: waves with periods 10 s or longer pass through the chromosphere with relatively little damping, however, for periods of 1 s or less, a substantial fraction (37%-100%) of wave energy entering the chromosphere is damped by ion-neutral friction in the mid- and upper chromosphere, with electron resistivity playing some role in the lower chromosphere and in umbras. We therefore conclude that Alfvenic waves with periods of a few seconds or less are capable of heating the chromosphere during solar flares, and speculate that they could also contribute to electron acceleration or exciting sunquakes.

Implosion of Coronal Loops during the Impulsive Phase of a Solar Flare

We study the relationship between implosive motions in a solar flare, and the energy redistribution in the form of oscillatory structures and particle acceleration. The flare SOL2012-03-09T03:53 (M6.4) shows clear evidence for an irreversible (stepwise) coronal implosion. Extreme-ultraviolet (EUV) images show at least four groups of coronal loops at different heights overlying the flaring core undergoing fast contraction during the impulsive phase of the flare. These contractions start around a minute after the flare onset, and the rate of contraction is closely associated with the intensity of the hard X-ray and microwave emissions. They also seem to have a close relationship with the dimming associated with the formation of the coronal mass ejection and a global EUV wave. Several studies now have detected contracting motions in the corona during solar flares that can be interpreted as the implosion necessary to release energy. Our results confirm this, and tighten the association with the flare impulsive phase. We add to the phenomenology by noting the presence of oscillatory variations revealed by Geostationary Operational Environmental Satellite soft X-rays (SXR) and spatially integrated EUV emission at 94 and 335 A. We identify pulsations of ≈60 s in SXR and EUV data, which we interpret as persistent, semi-regular compressions of the flaring core region which modulate the plasma temperature and emission measure. The loop oscillations, observed over a large region, also allow us to provide rough estimates of the energy temporarily stored in the eigenmodes of the active-region structure as it approaches its new equilibrium.

Resonant absorption with 2D variation of field line eigenfrequencies

Context. Resonant absorption, also known as field line resonance, can be used to describe coupling between fast and Alfven waves in non-uniform plasmas. Since the conditions for resonant absorption occur widely in astrophysics, it is applicable in many different contexts, all of which are united by their common physics. For example, resonant absorption is known to play a major role in the excitation of ultra-low frequency pulsations in the terrestrial magnetosphere and is also a leading explanation for the decay of fast kink oscillations of coronal loops. The occurrence of non-axisymmetric conditions in the magnetosphere, and observational evidence that coronal loops may possess fine transverse structure, highlight a need to consider equilibria that vary in two dimensions across the background magnetic field. Aims. We investigate the properties of resonant absorption when field line eigenfrequencies vary in two dimensions across the background magnetic field. We aim to place the theory on a firm mathematical footing and explore some of its key features. Methods. Using cold, linear, ideal MHD with a straight, uniform background magnetic field, we systematically obtain a complete analytic solution for behaviour at late times. This provides a framework from which the features of resonant absorption may be understood. The time-dependent problem is solved numerically, reproducing key features of the analytic solution. Results. Energy is deposited from a monochromatic fast wave as a phase mixing Alfven wave, in the vicinity of the resonant surface, at which the local field line eigenfrequency matches the frequency of the driver. A generalisation of the one dimensional phase mixing length to higher dimensions is suggested, and shown to successfully estimate the finest lengthscales in time-dependent simulations. The resonant Alfven wave is driven by gradients of the field aligned magnetic field perturbation, which is associated with the fast wave pressure. This leads to amplitude variations of the Alfven wave that can be used to reveal the spatial form of the fast wave.

Simulations of the Mg II k and Ca II 8542 lines from an Alfvén wave-heated flare chromosphere

We use radiation hydrodynamic simulations to examine two models of solar flare chromospheric heating: Alfven wave dissipation and electron beam collisional losses. Both mechanisms are capable of strong chromospheric heating, and we show that the distinctive atmospheric evolution in the mid-to-upper chromosphere results in Mg ii k-line emission that should be observably different between wave-heated and beam-heated simulations. We also present Ca ii 8542 A profiles that are formed slightly deeper in the chromosphere. The Mg ii k-line profiles from our wave-heated simulation are quite different from those from a beam-heated model and are more consistent with Interface Region Imaging Spectrograph observations. The predicted differences between the Ca ii 8542 A in the two models are small. We conclude that careful observational and theoretical study of lines formed in the mid-to-upper chromosphere holds genuine promise for distinguishing between competing models for chromospheric heating in flares.

Production of small-scale Alfvén waves by ionospheric depletion, nonlinear magnetosphere-ionosphere coupling and phase mixing

The authors acknowledge the International Space Science Institute (Switzerland) for funding the program that inspired this work. AJBR is grateful to the Royal Commission for the Exhibition of 1851 for present support and acknowledges an STFC studentship that funded part of this work.

A unified view of coronal loop contraction and oscillation in flares

Context: Transverse loop oscillations and loop contractions are commonly associated with solar flares, but the two types of motion have traditionally been regarded as separate phenomena. Aims: We present an observation of coronal loops contracting and oscillating following onset of a flare. We aim to explain why both behaviours are seen together and why only some of the loops oscillate. Methods: A time sequence of SDO/AIA 171 \r{A} images is analysed to identify positions of coronal loops following the onset of M6.4 flare SOL2012-03-09T03:53. We focus on five loops in particular, all of which contract during the flare, with three of them oscillating as well. A simple model is then developed for contraction and oscillation of a coronal loop. Results: We propose that coronal loop contractions and oscillations can occur in a single response to removal of magnetic energy from the corona. Our model reproduces the various types of loop motion observed and explains why the highest loops oscillate during their contraction while no oscillation is detected for the shortest contracting loops. The proposed framework suggests that loop motions can be used as a diagnostic for the removal of coronal magnetic energy by flares, while rapid decrease of coronal magnetic energy is a newly-identified excitation mechanism for transverse loop oscillations.

Evolution of field line helicity during magnetic reconnection.

We investigate the evolution of field line helicity for magnetic fields that connect two boundaries without null points, with emphasis on localized finite-B magnetic reconnection. Total (relative) magnetic helicity is already recognized as an important topological constraint on magnetohydrodynamic processes. Field line helicity offers further advantages because it preserves all topological information and can distinguish between different magnetic fields with the same total helicity. Magnetic reconnection changes field connectivity and field line helicity reflects these changes; the goal of this paper is to characterize that evolution. We start by deriving the evolution equation for field line helicity and examining its terms, also obtaining a simplified form for cases where dynamics are localized within the domain. The main result, which we support using kinematic examples, is that during localized reconnection in a complex magnetic field, the evolution of field line helicity is dominated by a work-like term that is evaluated at the field line endpoints, namely the scalar product of the generalized field line velocity and the vector potential. Furthermore, the flux integral of this term over certain areas is very small compared to the integral of the unsigned quantity, which indicates that changes of field line helicity happen in a well-organized pairwise manner. It follows that reconnection is very efficient at redistributing helicity in complex magnetic fields despite having little effect on the total helicity.

Physical role of topological constraints in localized magnetic relaxation

Predicting the final state of turbulent plasma relaxation is an important challenge, both in astro-physical plasmas such as the Suns corona and in controlled thermonuclear fusion. Recent numerical simulations of plasma relaxation with braided magnetic fields identified the possibility of a novel constraint, arising from the topological degree of the magnetic field-line mapping. This constraint implies that the final relaxed state is drastically different for an initial configuration with topological degree 1 (which allows a Taylor relaxation) and one with degree 2 (which does not reach a Taylor state). Here, we test this transition in numerical resistive-magnetohydrodynamic simulations, by embedding a braided magnetic field in a linear force-free background. Varying the background force-free field parameter generates a sequence of initial conditions with a transition between topological degree 1 and 2. For degree 1, the relaxation produces a single twisted flux tube, whereas for degree 2 we obtain two flux tubes. For predicting the exact point of transition, it is not the topological degree of the whole domain that is relevant, but only that of the turbulent region.

Solar flares and focused energy transport by MHD waves

Context. Transport of flare energy from the corona to the chromosphere has traditionally been assigned to electron beams; however, interest has recently been renewed in magnetohydrodynamic (MHD) waves as a complementary or alternative mechanism. Aims. We determine whether, and under what conditions, MHD waves deliver spatially localised energy to the chromosphere, as required if MHD waves are to contribute to emission from flare ribbons and kernels. This paper also highlights several properties of MHD waves that are relevant to solar flares and demonstrates their application to the flare problem. Methods. Transport is investigated using a magnetic arcade model and 2.5D MHD simulations. Di! erent wave polarisations are considered and the e! ect of fine structuring transverse to the magnetic field is also examined. Ray tracing provides additional insight into the evolution of waveguided fast waves. Results. Alfven waves are very e! ective at delivering energy fluxes to small areas of chromosphere, localisation being enhanced by magnetic field convergence and phase mixing. Fast waves, in the absence of fine coronal structure, are more suited to powering emission from di! use rather than compact sources; however, fast waves can be strongly localised by coronal waveguides, in which case focused energy is best transported to the chromosphere when waveguides are directly excited by the energy release. Conclusions. MHD waves pass an important test for inclusion in future flare models.