Solar coronal heating by magnetic cancellation – III. Thermodynamics

We present two-dimensional numerical magnetohydrodynamics simulations of a coronal X-ray bright point (XBP) caused by a cancelling magnetic feature (CMF). Cancellation is driven by converging motions of two magnetic bipolar sources. These sources are initially disconnected from each other so that both, the CMF and the associated reconnection/heating event (i.e. the XBP), are modelled in a self-consistent way. In the initial state, there is no X-point but two separatrices are present. Hence, the reconnection/heating and the cancellation phases have not yet started. Our numerical experiments end shortly after the converging magnetic bipole has fully cancelled. By this time, reconnection in the inner domain has ceased and occurs only at the base. Solving the energy equation with various heating and cooling terms included, and considering different bottom boundary conditions, reveals that the unrealistically high temperatures produced by Ohmic heating are reduced to more moderate temperatures of 1.5–2 MK consistent with observations of XBPs, if thermal conduction is included and density and temperature are fixed at the base.     

Solar coronal heating by magnetic cancellation – II. Disconnected and unequal bipoles

Two-dimensional numerical magnetohydrodynamic simulations of a cancelling magnetic feature (CMF) and the associated coronal X-ray bright point (XBP) are presented. Coronal magnetic reconnection is found to produce the Ohmic heating required for a coronal XBP. During the BP phase where reconnection occurs above the base, about 90–95 per cent of the magnetic flux of the converging magnetic bipole cancels at the base. The last ≈5 to 10 per cent of the base magnetic flux is cancelled when reconnection occurs at the base. Reconnection happens in a time-dependent way in response to the imposed converging footpoint motions. A potential field model gives a good first approximation to the qualitative behaviour of the system, but the magnetohydrodynamics (MHD) experiments reveal several quantitative differences: for example, the effects of plasma inertia and a pressure build-up in-between the converging bipole are to delay the onset of coronal reconnection above the base and to lower the maximum X -point height.     

MHD waves in the solar north polar coronal hole

The effects, hitherto not treated, of the temperature and the number density gradients, both in the parallel and the perpendicular direction to the magnetic field, of O VI ions, on the MHD wave propagation characteristics in the solar North Polar Coronal Hole are investigated. We investigate the magnetosonic wave propagation in a resistive MHD regime where only the thermal conduction is taken into account. Heat conduction across the magnetic field is treated in a non‐classical approach wherein the heat is assumed to be conducted by the plasma waves emitted by ions and absorbed at a distance from the source by other ions. Anisotropic temperature and the number density distributions of O VI ions revealed the chaotic nature of MHD standing wave, especially near the plume/interplume lane borders. Attenuation length scales of the fast mode is shown not to be smoothly varying function of the radial distance from the Sun (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

MHD waves at a spherical interface modelling EIT waves

Eruptive events such as flares and coronal mass ejections (CMEs) are known to generate global waves propagating over distances comparable to the solar radius in different layers of the solar atmosphere. Here we investigate the propagation of coronal EIT waves, modelled as fast magnetoacoustic modes propagating at a spherical interface in the presence of a purely radial magnetic field. Based on a simplified equilibrium we derive the dispersion relation of the waves. The generation and propagation of EIT waves at the spherical interface is studied numerically for different values of spherical degree and preliminary conclusions are reached regarding the properties of EIT waves. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

High-frequency oscillations in a solar active region coronal loop

The Solar Eclipse Corona Imaging System (SECIS) was used to record high-cadence observations of the solar corona during the total solar eclipse of 1999 August 11. During the 2 min 23.5 s of totality, 6364 images were recorded simultaneously in each of the two channels: a white light channel, and the Fe  xiv (5303 Å) 'green line' channel ( T ∼2 MK) . Here we report initial results from the SECIS experiment, including the discovery of a 6-s intensity oscillation in an active region coronal loop.     

The heating of the solar corona

The heating of the solar corona has been a fundamental astrophysical issue for over sixty years. Over the last decade in particular, space-based solar observatories (Yohkoh, SOHO and TRACE) have revealed the complex and often subtle magnetic-field and plasma interactions throughout the solar atmosphere in unprecedented detail. It is now established that any energy release mechanism is magnetic in origin - the challenge posed is to determine what specific heat input is dominating in a given coronal feature throughout the solar cycle. This review outlines a range of possible magnetohydrodynamic (MHD) coronal heating theories, including MHD wave dissipation and MHD reconnection as well as the accumulating observational evidence for quasi-periodic oscillations and small-scale energy bursts occurring in the corona. Also, we describe current attempts to interpret plasma temperature, density and velocity diagnostics in the light of specific localised energy release. The progress in these investigations expected from future solar missions (Solar-B, STEREO, SDO and Solar Orbiter) is also assessed.Received: 6 February 2003, Published online: 14 November 2003 Correspondence to: R. W. Walsh     

The effect of density stratification on the resonant absorption of MHD waves in coronal loops

The standing quasi-modes of the ideal magnetohydrodynamics (MHD) in a zero-β cylindrical magnetic flux tube that undergoes a longitudinal density stratification and radial density structuring are considered. The radial structuring is assumed to be a linearly varying density profile. Using the relevant connection formulae of the resonant absorption, the dispersion relation for the fast MHD body waves is derived and solved numerically to obtain both the frequencies and damping rates of the fundamental and first-overtone,   k = 1, 2  , modes of both the kink  ( m = 1)  and fluting  ( m = 2)  waves, where k and m are the longitudinal and azimuthal mode numbers, respectively.     

The problem of phase mixed shear Alfvén waves in the solar corona revisited

The problem of phase mixing of shear Alfvén waves is revisited taking into account dissipative phenomena specific for the solar corona. In regions of space plasmas where the dynamics is controlled by the magnetic field, transport coefficients become anisotropic with transport mechanism having different behavior and magnitude depending on the orientation with respect to the ambient magnetic field. Taking into account realistic values for dissipative coefficients we obtain that the previous results derived in context of torsional Alfvén wave phase mixing are actually heavily underestimated so phase mixing cannot be used to explain the damping of torsional Alfvén waves and heating of open coronal structures. The presented results indicate that in order for phase mixing to still be a viable mechanism to explain heating or wave damping unrealistic assumptions have to be made. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The interfringe intensity in coronal interferograms

The paper discusses the low contrast of the Fabry-Perot (FP) fringes observed in the interferograms of the solar corona. The various factors which affect the interfringe intensity of Fabry-Pérot line profiles are considered. The effect of continuum radiation on the interfringe intensity of Fabry-Pérot line profiles is calculated by assuming a coronal model. For the given FP, it was found that unless the ratio of line to continuum intensity (integrated line intensity to continuum per angström) is less than 10, continuum contribution has no significant effect on the fringe contrast. The analysis may be pertinent in the design aspects of a FP interferometer for astronomical observations. The excess interfringe intensity found in the coronal line profiles is interpreted as due to the presence of fast moving plasma components in corona along the line of sight. A detailed analysis qualitatively shows that the line excitation conditions existing in ambient corona and coronal loops are different in active regions while they are more similar in polar regions.     

Evidence for interchange reconnection between a coronal hole and an adjacent emerging flux region

Coronal holes are regions of dominantly monopolar magnetic field on the Sun where the field is considered to be ‘open’ towards interplanetary space. Magnetic bipoles emerging in proximity to a coronal hole boundary naturally interact with this surrounding open magnetic field. In the case of oppositely aligned polarities between the active region and the coronal hole, we expect interchange reconnection to take place, driven by the coronal expansion of the emerging bipole as well as occasional eruptive events. Using SOHO/EIT and SOHO/MDI data, we present observational evidence of such interchange reconnection by studying AR 10869 which emerged close to a coronal hole. We find closed loops forming between the active region and the coronal hole leading to the retreat of the hole. At the same time, on the far side of the active region, we see dimming of the corona which we interpret as a signature of field line ‘opening’ there, as a consequence of a topological displacement of the ‘open’ field lines of the coronal hole. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

What SDO tells us about structure and evolution of coronal bright points

Using magnetograms and coronal images from two instruments on board the Solar Dynamics Observatory (SDO), we study structure and evolution of a limited number of coronal bright points (CBPs). Our results show that the relation between CBPs and their magnetic footpoints is not simple. In some cases, CBP may appear as a bright portion of a larger loop (with clearly identifiable footpoints), and in some cases, an isolated CBP may develop between magnetic poles, which might not be the closest ones to each other or which might not be involved in the magnetic flux cancellation. We suggest that the magnetic connectivity responsible for formation of isolated coronal bright points is governed by the orientation of the large‐scale magnetic field. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effects of density stratification on standing fast body oscillations in coronal loops and dissipation

The standing magnetohydrodynamic (MHD) quasi-linear modes in a zero-β cylindrical magnetic flux tube that undergoes a longitudinal density stratification and radial density structuring are considered. The radial structuring is assumed to have a step-like density profile. The dispersion relation for the fast MHD body waves is derived and solved numerically to obtain the frequencies of the fundamental, first-overtone and second-overtone   k = 1, 2, 3  modes of both kink  ( m = 1)  and fluting  ( m = 2)  waves, where k and m are the longitudinal and azimuthal mode numbers, respectively. Damping rates due to both viscous and resistive dissipations in the presence of the density stratification are derived and solved numerically for the first three modes of both kink and fluting waves.     

To the problem of solar coronal heating

We consider the adequacy of various solar coronal heating models. We show that the correlation between the intensity of the coronal Fe XIV 530.5 nm green line and the calculated magnetic field strength in the solar corona can be a useful tool for this purpose. We have established this correlation for coronal structures and magnetic fields of large spatial and temporal scales. The correlation found exhibits a strong dependence on both solar cycle phase and heliolatitude. The efficiency of a particular coronal heating mechanism is probably determined by the relative area occupied by low and high loops (including open structures). The direct current models based on slow field dissipation (DC) and the wave models based on Alfvén and magnetosonic wave dissipation (AC) are more efficient in the equatorial and polar zones, respectively.