MHD Waves and Heating in Coronal Holes

Coronal holes have been identified as source regions of the fast solar wind, and MHD wave activity has been detected in coronal holes by remote sensing, and in situ in fast solar wind streams. I review some of the most suggestive wave observations, and discuss the theoretical aspects of MHD wave heating and solar wind acceleration in coronal holes. I review the results of single fluid 2.5D MHD, as well as multi-fluid 2.5D MHD models of waves in coronal holes, the heating, and the acceleration of the solar wind be these waves.     

Short Quasi-Periodic MHD Waves in Coronal Structures

The possibility of remote diagnostics of coronal structures with impulsively-generated short-period fast magnetoacoustic wave trains is demonstrated. An initially broad-band, aperiodic fast magnetoacoustic perturbation guided by a 1D plasma inhomogeneity develops into a quasi-periodic wave train with a well-pronounced frequency and amplitude modulation. The quasi-periodicity results from the geometrical dispersion of the modes, determined by the transverse profile of the loop, and hence contains information about the profile. Wavelet images of the wave train demonstrate that their typical spectral signature is of a “crazy tadpole’’ shape: a narrow spectrum tail precedes a broad-band head. The instantaneous period of the oscillations in the wave train decreases gradually with time, with a mean value of several seconds for typical coronal values. The period and the spectral amplitude evolution are determined by the steepness of the transverse density profile and the density contrast ratio in the loop, which offers a tool for estimation of the sub-resolution structuring of the corona.     

Longitudinal Waves in Coronal Loops

Outwardly propagating intensity disturbances are a common feature in large, quiescent coronal loop structures. In this paper, an overview is given of the observed properties and the theoretical modelling. As a large number of events have been observed and analysed, good statistical results on the estimated parameters have now been obtained. The theoretical modelling mainly focuses on two distinct aspects, namely the observed rapid damping of the perturbations, thought to be due to thermal conduction and the origin of the driver. Leakage of the solar surface p-modes is the main candidate to explain the observed periodicity, due to the strong correlation between loop position and period and the filamentary nature of the observed coronal intensity perturbations. Recent observational results appear to confirm the leakage and subsequent upward propagation of the solar surface 5 minute oscillations into the overlying atmospheric layers.     

EUV Observations Above Polar Coronal Holes

We derive electron temperature and density as a function of height up to 0.2 R_⊙ above the limb in polar coronal holes, using five EUV data sets recorded by the SOHO Coronal Diagnostic Spectrometer between July 1997 and February 1998. Radial T and N distributions, averaged in a 2° to 10° range of position angles, are the same above the North and South coronal holes. They do not show any time variability over a period of seven months. Polar plumes are found to have lower electron temperature and higher density than the interplume lanes. The electron density slope suggests that the proton temperatures are twice as high as the electron temperatures. This revised version was published online in June 2006 with corrections to the Cover Date.     

Coronal Holes and Open Magnetic Flux

Coronal holes are low-density regions of the corona which appear dark in X-rays and which contain “open” magnetic flux, along which plasma escapes into the heliosphere. Like the rest of the Sun’s large-scale field, the open flux originates in active regions but is subsequently redistributed over the solar surface by transport processes, eventually forming the polar coronal holes. The total open flux and radial interplanetary field component vary roughly as the Sun’s total dipole strength, which tends to peak a few years after sunspot maximum. An inverse correlation exists between the rate of flux-tube expansion in coronal holes and the solar wind speed at 1 AU. In the rapidly diverging fields present at the polar hole boundaries and near active regions, the bulk of the heating occurs at low heights, leading to an increase in the mass flux density at the Sun and a decrease in the asymptotic wind speed. The quasi-rigid rotation of coronal holes is maintained by continual footpoint exchanges between open and closed field lines, with the reconnection taking place at the streamer cusps. At much lower heights within the hole interiors, “interchange reconnection” between small bipoles and the overlying open flux also gives rise to coronal jets and polar plumes.     

Two-fluid 2.5D MHD Simulations of the Fast Solar Wind in Coronal Holes and the Relation to UVCS Observations

Recent SOHO/UVCS observations indicate that the perpendicular proton and ion temperatures are much larger than electron temperatures. In the present study we simulate numerically the solar wind flow in a coronal hole with the two-fluid approach. We investigate the effects of electron and proton temperatures on the solar wind acceleration by nonlinear waves. In the model the nonlinear waves are generated by Alfvén waves with frequencies in the 10^-3 Hz range, driven at the base of the coronal hole. The resulting electron and proton flow profile exhibits density and velocity fluctuations. The fluctuations may steepen into shocks as they propagate away from the sun. We calculate the effective proton temperature by combining the thermal and wave velocity of the protons, and find qualitative agreement with the proton kinetic temperature increase with height deduced from the UVCS Ly-α observations by Kohl et al. (1998). This revised version was published online in June 2006 with corrections to the Cover Date.     

Soho Observations of Density Fluctuations in Coronal Holes

In recent UVCS/SOHO White Light Channel (WLC) observations we found quasi-periodic variations in the polarized brightness (pB) in the polar coronal holes at heliocentric distances of 1.9 to 2.45 solar radii. The motivation for the observation is the 2.5D MHD model of solar wind acceleration by nonlinear waves, that predicts compressive fluctuations in coronal holes. In February 1998 we performed new observations using the UVCS/WLC in the coronal hole and obtained additional data. The new data corroborate our earlier findings with higher statistical significance. The new longer observations show that the power spectrum peaks in the 10–12 minute range. These timescales agree with EIT observations of brightness fluctuations in polar plumes. We performed preliminary LASCO/C2 observations in an effort to further establish the coronal origin of the fluctuations. This revised version was published online in June 2006 with corrections to the Cover Date.     

Coronal Holes and the High-Speed Solar Wind

Coronal holes are the lowest density plasma components of the Sun's outer atmosphere, and are associated with rapidly expanding magnetic fields and the acceleration of the high-speed solar wind. Spectroscopic and polarimetric observations of the extended corona, coupled with interplanetary particle and radio sounding measurements going back several decades, have put strong constraints on possible explanations for how the plasma in coronal holes receives its extreme kinetic properties. The Ultraviolet Coronagraph Spectrometer (UVCS) aboard the Solar and Heliospheric Observatory (SOHO) spacecraft has revealed surprisingly large temperatures, outflow speeds, and velocity distribution anisotropies for positive ions in coronal holes. We review recent observations, modeling techniques, and proposed heating and acceleration processes for protons, electrons, and heavy ions. We emphasize that an understanding of the acceleration region of the wind (in the nearly collisionless extended corona) is indispensable for building a complete picture of the physics of coronal holes.     

Heating Diagnostics with MHD Waves

The heating of the solar atmosphere is a fundamental problem of modern solar and astrophysics. A review of the seismological aspects of magnetohydrodynamic (MHD) waves with an emphasis on standing longitudinal waves in the context of coronal heating is presented. Efforts made recently may be split into two categories: forward modelling and data inversion. Forward modelling can be applied to predict the observational footprints of various heating scenarios. A new diagnostic method based on the analysis of Doppler shift time series is outlined with specific application to solar coronal conditions. The power of the method is demonstrated and tested using synthetic data and comparing them with actual high-resolution (e.g. SoHO/SUMER) observations. Further, related recent examples of standing longitudinal oscillations in coronal loop structures observed with the new Hinode/EIS instrument are also presented. These latter observations provide an advanced ground for MHD seismology as a tool for plasma heating diagnostics in the atmosphere of the Sun.     

Resonant MHD Waves in the Solar Atmosphere

The linear theory of MHD resonant waves in inhomogeneous plasmas is reviewed. The review starts from discussing the properties of driven resonant MHD waves. The dissipative solutions in Alfvén and slow dissipative layers are presented. The important concept of connection formulae is introduced. Next, we proceed on to non-stationary resonant MHD waves. The relation between quasi-modes of ideal MHD and eigenmodes of dissipative MHD are discussed. The solution describing the wave motion in non-stationary dissipative layers is given. It is shown that the connection formulae remain valid for non-stationary resonant MHD waves. The initial-value problem for resonant MHD waves is considered. The application of theory of resonant MHD waves to solar physics is discussed.     

A Cosmic Ray Signature of Equatorial Coronal Holes

The evolution of open field regions on the Sun over the last cycle is illustrated by observations of coronal holes in SOHO EIT images. The development of a large equatorial coronal hole near solar minimum is discussed, indicating the processes which led to the appearance of open field regions at low latitude. The observed cosmic ray signature is presented and interpreted in terms of the passage of the Earth through the streamer belt, which at this time had become distorted by the coronal hole and associated active region. The times when such equatorial coronal holes might be expected to directly influence cosmic ray counts in this way are seen to be limited to the approach to solar minimum, around minimum and the approach to maximum. This revised version was published online in August 2006 with corrections to the Cover Date.     

Solar MHD Waves and Solar Neutrinos

We analyze here how solar neutrino experiments could detect time fluctuations of the solar neutrino flux due to magnetohydrodynamics (MHD) perturbations of the solar plasma. We state that if such time fluctuations are detected, this would provide a unique signature of the Resonant Spin-Flavor Precession (RSFP) mechanism as a solution to the Solar Neutrino Problem. This revised version was published online in August 2006 with corrections to the Cover Date.     

Acceleration of the High Speed Solar Wind in Coronal Holes

We outline a theory for the origin and acceleration of the fast solar wind as a consequence of network microflares releasing a spectrum of high frequency Alfvén waves which heat (by cyclotron absorption) the corona close to the Sun. The significant features of our model of the fast wind are that the acceleration is rapid with the sonic point at around two solar radii, the proton temperatures are high (~ 5 million degrees) and the minor ions are correspondingly hotter, roughly in proportion to their mass. Moreover we argue that since the energy flux needed to power the quiet corona in closed field regions is about the same as that needed to drive the fast solar wind, and also because at deeper levels (< 2 × 10⁵ K) there is no great difference in the properties of supergranules and network in closed and open field regions, the heating process (i.e., dissipation of high frequency waves) must be the same in both cases. This revised version was published online in June 2006 with corrections to the Cover Date.     

UVCS Observations of Temperature and Velocity Profiles in Coronal Holes

The spectroscopic observations of the Ultraviolet Coronagraph Spectrometer (UVCS), on board the SOHO observatory, allow the study and the full characterization of the expansion of the solar atmosphere by means of measurements of the outflow speeds and the physical properties of the wind, directly in the region where the solar plasma is heated and accelerated: the extended corona. During solar minimum, when the magnetic configuration of the corona is rather simple, the open magnetic fields emerging from the wide polar coronal holes channel toward the heliosphere both the fast and the slow wind. The fast wind flows along flux tubes with lower areal divergence than the slow wind which is guided by flux tubes characterized by non-monotonic areal expansion functions. Differences in the physical properties, such as kinetic temperature, electron density, composition and density fluctuations, of the fast and slow wind in the corona are discussed.     

The Composition of the Solar Wind in Polar Coronal Holes

The solar wind charge state and elemental compositions have been measured with the Solar Wind Ion Composition Spectrometers (SWICS) on Ulysses and ACE for a combined period of about 25 years. This most extensive data set includes all varieties of solar wind flows and extends over more than one solar cycle. With SWICS the abundances of all charge states of He, C, N, O, Ne, Mg, Si, S, Ar and Fe can be reliably determined (when averaged over sufficiently long time periods) under any solar wind flow conditions. Here we report on results of our detailed analysis of the elemental composition and ionization states of the most unbiased solar wind from the polar coronal holes during solar minimum in 1994–1996, which includes new values for the abundance S, Ca and Ar and a more accurate determination of the ²⁰Ne abundance. We find that in the solar minimum polar coronal hole solar wind the average freezing-in temperature is ∼1.1×10⁶ K, increasing slightly with the mass of the ion. Using an extrapolation method we derive photospheric abundances from solar wind composition measurements. We suggest that our solar-wind-derived values should be used for the photospheric ratios of Ne/Fe=1.26±0.28 and Ar/Fe=0.030±0.007.     

MHD Waves and Instabilities in Space Plasma Flows

Shear flow instabilities are an important aspect of hydrodynamic studies. The present review article discusses the role of an ambient magnetic field which both modifies the Kelvin-Helmholtz instability and may introduce new types of magnetohydrodynamic waves and instabilities. A brief overview of magnetospheric pulsations is presented with an emphasis on the long-period resonant Alfv??n waves associated with the high speed solar wind. The spatio-temporal evolution of magnetically modified shear flow instabilities in various space plasma structures is addressed. A distinction between convective and absolute instabilities is necessary for proper understanding of theory and correct interpretation of the observations. Finally, it is shown how incompressible Alfv??nic disturbances may become unstable in a compressible flow in the absence of any shear. An application to coronal loops is presented.     

Standing Slow-Mode Waves in Hot Coronal Loops: Observations, Modeling, and Coronal Seismology

Strongly damped Doppler shift oscillations are observed frequently associated with flarelike events in hot coronal loops. In this paper, a review of the observed properties and the theoretical modeling is presented. Statistical measurements of physical parameters (period, decay time, and amplitude) have been obtained based on a large number of events observed by SOHO/SUMER and Yohkoh/BCS. Several pieces of evidence are found to support their interpretation in terms of the fundamental standing longitudinal slow mode. The high excitation rate of these oscillations in small- or micro-flares suggest that the slow mode waves are a natural response of the coronal plasma to impulsive heating in closed magnetic structure. The strong damping and the rapid excitation of the observed waves are two major aspects of the waves that are poorly understood, and are the main subject of theoretical modelling. The slow waves are found mainly damped by thermal conduction and viscosity in hot coronal loops. The mode coupling seems to play an important role in rapid excitation of the standing slow mode. Several seismology applications such as determination of the magnetic field, temperature, and density in coronal loops are demonstrated. Further, some open issues are discussed.     

Cosmic Ray Transport in a Heliospheric Magnetic Field with Non-Polar Coronal Holes

The simple tilted dipole picture of Corotating Interaction Regions which prevailed during the first polar pass of Ulysses no longer applies since the Sun entered a more active phase. Recent observations show that CIRs still persist, though the large polar coronal holes of solar minimum shrink to smaller areas and move to lower latitudes. We present 3-D simulations for the cosmic-ray intensity variations in a model with non-polar high speed streams. Latitudinal and recurrent time-variations are discussed, but more detailed and realistic simulations are required before quantitative comparisons with observations can be made. This revised version was published online in August 2006 with corrections to the Cover Date.     

UVCS/SOHO Observations of Spectral Line Profiles in Polar Coronal Holes

Ultraviolet emission line profiles have been measured on 15-29 September 1997 for H I 1216 Å, O VI 1032, 1037 Å and Mg X 625 Å in a polar coronal hole, at heliographic heights ? (in solar radii) between 1.34 and 2.0. Observations of H I 1216 Å and the O VI doublet from January 1997 for ? = 1.5 to 3.0 are provided for comparison. Mg X 625 Å is observed to have a narrow component at ? = 1.34 which accounts for only a small fraction of the observed spectral radiance, and a broad component that exists at all observed heights. The widths of O VI broad components are only slightly larger than those for H I at ? = 1.34, but are significantly larger at ? = 1.5 and much larger for ? > 1.75. In contrast, the Mg X values are less than those of H I up to 1.75 and then increase rapidly up to at least ? = 2.0, but never reach the values of O VI.     

Review Article: MHD Wave Propagation Near Coronal Null Points of Magnetic Fields

We present a comprehensive review of MHD wave behaviour in the neighbourhood of coronal null points: locations where the magnetic field, and hence the local Alfvén speed, is zero. The behaviour of all three MHD wave modes, i.e. the Alfvén wave and the fast and slow magnetoacoustic waves, has been investigated in the neighbourhood of 2D, 2.5D and (to a certain extent) 3D magnetic null points, for a variety of assumptions, configurations and geometries. In general, it is found that the fast magnetoacoustic wave behaviour is dictated by the Alfvén-speed profile. In a ??=0 plasma, the fast wave is focused towards the null point by a refraction effect and all the wave energy, and thus current density, accumulates close to the null point. Thus, null points will be locations for preferential heating by fast waves. Independently, the Alfvén wave is found to propagate along magnetic fieldlines and is confined to the fieldlines it is generated on. As the wave approaches the null point, it spreads out due to the diverging fieldlines. Eventually, the Alfvén wave accumulates along the separatrices (in 2D) or along the spine or fan-plane (in 3D). Hence, Alfvén wave energy will be preferentially dissipated at these locations. It is clear that the magnetic field plays a fundamental role in the propagation and properties of MHD waves in the neighbourhood of coronal null points. This topic is a fundamental plasma process and results so far have also lead to critical insights into reconnection, mode-coupling, quasi-periodic pulsations and phase-mixing.