Energy balance of the corona and the origin of quasi-stationary high-speed solar wind streams

The energy balance of open-field regions of the corona and solar wind and the influence of the flow geometry in the corona upon the density and temperature, are analyzed. It is found that the energy flux arriving at the corona is constant for the corona's open regions with different flow geometries. For the waves heating the corona and solar wind, the dependence of the absorption coefficient on the corona's plasma density is found to be within the range of distances r=1.05–1.5R . It is shown that the wave absorption is more dependent on electron density than the coronal emission. It is this difference that causes lower-density coronal holes to be colder than quiet regions. It is found that the additional energy flux necessary for providing energy balance of the corona and for producing solar wind is a flux of Alfvén waves, which can provide the energy needed for producing quasi-stationary high-speed solar wind streams. Theoretical models of coronal holes and the question of why the high-speed solar wind streams are precisely flowing out of coronal holes, are discussed.     

Coronal heating and solar wind acceleration; gyrotropic electron-proton solar wind

In coronal holes the electron (proton) density is low, and heating of the proton gas produces a rapidly increasing proton temperature in the inner corona. In models with a reasonable electron density in the upper transition region the proton gas becomes collisionless some 0.2 to 0.3 solar radii into the corona. In the collisionless region the proton heat flux is outwards, along the temperature gradient. The thermal coupling to electrons is weak in coronal holes, so the heat flux into the transition region is too small to supply the energy needed to heat the solar wind plasma to coronal temperatures. Our model studies indicate that in models with proton heating the inward heat conduction may be so inefficient that some of the energy flux must be deposited in the transition region to produce the proton fluxes that are observed in the solar wind. If we allow for coronal electron heating, the energy that is needed in the transition region to heat the solar wind to coronal temperatures, may be supplied by heat conduction from the corona.     

Energy budget in coronal holes

It is shown that the constancy of the ratio between conductive flux and pressure squared as one goes from quiet regions to holes (regions of exceptionally low density and temperature) in the solar corona, observed in the case of the first well-studied coronal hole, implies that a strong solar wind is likely to originate in coronal holes.On leave of absence from Osservatorio Astrofisico di Arcetri, Florence, Italy.     

Damping of slow magnetoacoustic waves in an inhomogeneous coronal plasma

We study the propagation and dissipation of slow magnetoacoustic waves in an inhomogeneous viscous coronal loop plasma permeated by uniform magnetic field. Only viscosity and thermal conductivity are taken into account as dissipative processes in the coronal loop. The damping length of slow-mode waves exhibit varying behaviour depending upon the physical parameters of the loop in an active region AR8270 observed by TRACE. The wave energy flux associated with slow magnetoacoustic waves turns out to be of the order of 10⁶ erg cm^?2 s^?1 which is high enough to replace the energy lost through optically thin coronal emission and the thermal conduction below to the transition region. It is also found that only those slow-mode waves which have periods more than 240s provide the required heating rate to balance the energy losses in the solar corona. Our calculated wave periods for slow-mode waves nearly match with the oscillation periods of loop observed by TRACE.     

Long-lived coronal structures and recurrent geomagnetic patterns in 1974

Daily measurements of the intensity distribution of the Sun's white-light corona over the height range $\text{1.1–2.7. R}{}_{\mathrm{?}}$ show that the global structure became quite stable (constant over periods of several months) in late 1973 and throughout 1974, as flares, ascending prominences and other transient activity became less frequent with the decline of the solar activity cycle. A highly persistent pattern of geomagnetic activity prevailed for much of this time. Bright coronal structures in the ecliptic plane were associated with geomagnetically quiet conditions, and faint coronal regions (“holes”) with geomagnetic disturbance, after a delay of about three days. These results confirm the “cone-of-avoidance” model for M-regions and reinforce the postulate that high-speed streams in the solar wind originate from coronal holes. Identification of coronal holes from ground-based K-coronal observations corresponds well with those made from spacecraft EUV and X-ray experiments on OSO-7 and Skylab.     

Coronal holes

Coronal holes are extensive regions of extremely low density in the solar corona within 60° of latitude from the equator. (They are not to be confused with the well-known coronal cavities which surround quiescent prominences beneath helmet streamers.) We have superposed maps of the calculated current-free (potential) coronal magnetic field with maps of the coronal electron density for the period of November 1966, and find that coronal holes are generally characterized by weak and diverging magnetic field lines. The chromosphere underlying the holes is extremely quiet, being free of weak plages and filaments. The existence of coronal holes clearly has important implications for the energy balance in the transition region and the solar wind.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

宁静日冕和冕洞研究现状

主要论述宁静日冕洞，以及日冕加热问题的研究现状。讨论了宁静日冕的理论模型、观测模型和混合模型，以及冕洞区大气模型和太阳风加热问题。最后对计划中的日冕空间探测作了简要介绍。     

A survey of coronal holes and their solar wind associations throughout sunspot cycle 20

To gain insight into the relationships between solar activity, the occurrence and variability of coronal holes, and the association of such holes with solar wind features such as high-velocity streams, a study of the period 1963–1974 was made. This period corresponds approximately with sunspot cycle 20. The primary data used for this work consisted of X-ray and XUV solar images obtained from rockets. The investigation revealed that:

1. The polar coronal holes prominent at solar minimum, decreased in area as solar activity increased and were small or absent at maximum phase. This evolution exhibited the same phase difference between the two hemispheres that was observed in other indicators of activity.
2. During maximum, coronal holes occurred poleward of the sunspot belts and in the equatorial region between them. The observed equatorial holes were small and persisted for one or two solar rotations only; some high latitude holes had lifetimes exceeding two solar rotations.
3. During 1963–74 whenever XUV or X-ray images were available, nearly all recurrent solar wind streams of speed ?500 km s^?1 were found associated with coronal holes at less than 40° latitude; however some coronal holes appeared to have no associated wind streams at the Earth.

     

Transition region and coronal plasmas: instrumentation and spectral analysis

The plasma conditions in the solar atmosphere and, in particular, in coronal holes are summarized, before space-borne instrumentation for observing these regions in vacuum-ultraviolet light is briefly introduced with the Solar Ultraviolet Measurements of Emitted Radiation (SUMER) spectrometer on the Solar and Heliospheric Observatory (SOHO) as example. Spectroscopic measurements of small plasma jets are then analyzed in detail. Magnetic reconnection is thought to be responsible for heating the corona of the Sun as well as accelerating the solar wind by converting magnetic energy into thermal and kinetic energies. The continuous outflow of the fast solar wind from coronal holes on ‘open’ field lines, which reach out into interplanetary space, then requires many reconnection events of very small scale sizes – most of them probably below the resolution capabilities of present-day instruments. Our observations of such an event have been obtained with the Solar and Heliospheric Observatory (SOHO) providing both high-resolution imaging and spectral information for structural and dynamical studies. We find whirling or rotating motions as well as jets with acceleration along their propagation paths in close spatial and temporal vicinity to the coronal jet. This revised version was published online in July 2006 with corrections to the Cover Date.     

An Interpretation of the Coronal Holes’ Visibility in the Millimeter Wavelength Range

Various observations indicate that coronal holes generally appear as low brightness temperature regions (LTRs) in the centimeter and millimeter wavelength ranges. However, within their borders local enhancements of radiation, that is, high brightness temperature regions (HTRs), often occur. The theory behind the described behavior is not fully understood and therefore we analyze full-disk solar images obtained at a wavelength of 8 mm at Metsähovi Radio Observatory and compare them with data simultaneously taken in other wavelength ranges. The observational finding that the average brightness temperature of coronal holes is not much different from the quiet-Sun level (with localized deviations toward higher and lower intensities on the order of a few percent) is compared with theoretical models of the thermal bremsstrahlung radiation originating in the solar chromosphere, transition region, and corona. Special attention is devoted to the interpretation of the localized enhancements of radiation observed inside coronal holes at millimeter wavelengths. The main conclusion is that the most important contribution to the brightness temperature comes from an increased density in the transition region and low corona (i.e., at the heights where the temperature is below 10⁶ K). This can explain both the LTRs and HTRs associated with coronal holes.     

On an efficient shock wave generation mechanism in the quiet solar transition region

Two competing fundamental hypotheses are usually postulated in the solar coronal heating problem: heating by nanoflares and heating by waves. In the latter it is assumed that acoustic and magnetohydrodynamic disturbances whose amplitude grows as they propagate in a medium with a decreasing density come from the convection zone. The shock waves forming in the process heat up the corona. In this paper we draw attention to yet another very efficient shock wave generation process that can be realized under certain conditions typical for quiet regions on the Sun. In the approximation of stationary dissipative hydrodynamics we show that a shock wave can be generated in the quiet solar chromosphere–corona transition region by the fall of plasma from the corona into the chromosphere. This shock wave is directed upward, and its dissipation in the corona returns part of the kinetic energy of the falling plasma to the thermal energy of the corona. We discuss the prospects for developing a quantitative nonstationary model of the phenomenon.     

The solar wind during the Maunder minimum

It is presently believed that the high speed solar wind originates almost entirely in coronal holes. Theory suggests that the origin of the high speeds is extended energy deposition in proportion to the magnetic field intensity in the holes and at 1.5–3.0 solar radii heliocentric distance. Evidence from the time of the Maunder Minimum, together with the above results, allows a hypothesis to be made for the state of the solar wind at that time. Firstly, carbon-14 data indicate an enhanced cosmic ray intensity, with the conclusion that the interplanetary magnetic field (IMF) was smooth and perhaps of low intensity. Secondly, the apparent absence of a corona during eclipses requires low coronal density, suggesting an absence of closed magnetic loops. Thirdly, the absence of sunspots eliminates the possibility of a solar maximum type of corona of low emission intensity and implies a low large-scale photospheric field intensity. Finally, the absence of mid-latitude aurorae implies either that the solar wind speed or the IMF intensity or both, were low and not irregular.A resulting self-consistent hypothesis is that the solar wind was of the simplest variety, analogous to that described in models of the so-called “quiet solar wind”. All closed coronal field regions would have been absent and extended energy deposition in the corona would have been far less important than today. At 1 a.u., the density and speed would have been less than 5 cm^?3 and 300 km^?1s, respectively. At the same time, there would have been a very low level of fluctuation all the way from the microscale up to the contrast between high and low speed solar wind streams. Also, if the IMF is the source of the 22 yr and magnetic sector associated modulations in the present terrestrial climate, these modulations may have been suppressed during the Maunder Minimum. Recently, it has been discovered that the 22 yr modulation in fact was suppressed during the Maunder Minimum (C. Stockton and M. Mitchell, personal communication), in support of the above suggestion.     

Constraints on the solar coronal temperature in regions of open magnetic field

It is shown that the simultaneous consideration of observed values of the solar wind proton flux density at 1 AU and of the electron pressure at the base of the solar corona leads to relatively strong constraints on the coronal temperature in the region of subsonic solar wind flow. The extreme upper limit on the mean coronal temperature in the subsonic region is found to be about 2.6 × 10⁶ K, but this upper limit is reduced to about 2.0 × 10⁶ K if reasonable, rather than extreme, assumptions are made; the limit on the maximum temperature is about 0.5 × 10⁶ K greater than the limit on the mean. It is also found that the same two observations limit the rate of momentum addition possible in the region of subsonic solar wind flow.On leave from The Auroral Observatory, Institute of Mathematical and Physical Sciences, University of Troms0, N-9001 Tromsø, Norway.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Solar coronal heating by magnetosonic waves

Solar coronal heating by magnetohydrodynamic (MHD) waves is investigated. ultraviolet (UV) and X-ray emission lines of the corona show non-thermal broadenings. The wave rms velocities inferred from these observations are of the order of 25–60 km s⁻¹ . Assuming that these values are not negligible, we solved MHD equations in a quasi-linear approximation, by retaining the lowest order non-linear term in rms velocity. Plasma density distribution in the solar corona is assumed to be inhomogeneous. This plasma is also assumed to be permeated by dipole-like magnetic loops. Wave propagation is considered along the magnetic field lines. As dissipative processes, only the viscosity and parallel (to the local magnetic field lines) heat conduction are assumed to be important. Two wave modes emerged from the solution of the dispersion relation. The fast mode magneto-acoustic wave, if originated from the coronal base can propagate upwards into the corona and dissipate its mechanical energy as heat. The damping length-scale of the fast mode is of the order of 500 km. The wave energy flux associated with these waves turned out to be of the order of 2.5×10⁵ ergs cm⁻² s⁻¹ which is high enough to replace the energy lost by thermal conduction to the transition region and by optically thin coronal emission. The fast magneto-acoustic waves prove to be a likely candidate to heat the solar corona. The slow mode is absent, in other words cannot propagate in the solar corona.     

Role of magnetic carpet in coronal heating

One of the fundamental questions in solar physics is how the solar corona maintains its high temperature of several million Kelvin above photosphere with a temperature of 6000 K. Observations show that solar coronal heating problem is highly complex with many different facts. It is likely that different heating mechanisms are at work in the solar corona. The separate kinds of coronal loops may also be heated by different mechanisms. Using data from instruments onboard the Solar and Heliospheric Observatory (SOHO) and from the more recent Transition Region and Coronal Explorer (TRACE) scientists have identified small regions of mixed polarity, termed magnetic carpet contributing to solar activity on a short time scale. Magnetic loops of all sizes rise into the solar corona, arising from regions of opposite magnetic polarity in the photosphere. Energy released when oppositely directed magnetic fields meet in the corona is one likely cause for coronal heating. There is enough energy coming up from the loops of the “magnetic carpet” to heat the corona to its known temperature.     

Dynamics of coronal hole regions

The hydrodynamic properties of a steadily expanding corona are explored for situations in which departures from spherically symmetric outflow are large, in the sense that the geometrical cross section of a given flow tube increases outward from the Sun faster than r ² in some regions. Assuming polytropic flow, it is shown that in certain cases the flow may contain more than one critical point. We derive the criterion for determining which of these critical points is actually crossed by the transonic solution which begins at the Sun and extends continuously outward. Next, we apply the theory to geometries which exhibit rapid spreading of the flow tubes in the inner corona, followed by more-or-less radial divergence at large distances. This is believed to be the type of geometry found in coronal hole regions. The results show that, if this initial divergence is sufficiently large, the outflow becomes supersonic at a critical point encountered low in the corona in the region of high divergence, and it remains supersonic at all greater heights in the corona. This feature strongly suggests that coronal hole regions differ from other open-field regions of the corona in that they are in a fast, low density expansion state over much of their extent. Such a dynamical configuration makes it possible to reconcile the low values of electron density observed in coronal holes with the large particle fluxes in the associated high speed streams seen in the solar wind.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Thermally conductive flows in coronal holes

Polytropic solar wind flows in flow tubes whose cross-sectional area increases faster with radius than for a radial expansion have been studied by Kopp and Holzer (1976). Their use of a faster-than-radial expansion proved promising in analytically associating the high-speed streams observed near 1 AU with the relatively low values of electron densities observed in the lower corona. They could not, however, obtain quantitative agreement with observations. We have extended their work to include thermal conduction and have compared thermally conductive and polytropic flows in the lower corona for given high-speed conditions at 1 AU. The thermally conductive flows (calculated using the Spitzer (1962) thermal conductivity) do yield closer agreement with observations, although the predicted electron density is still too low and the predicted temperature is too high. We also considered a modified thermal conductivity which decreases more rapidly with increasing radius than does the Spitzer value. Again the results were improved, but the agreement could not be termed quantitative. We conclude that thermal conduction alone will not explain solar wind flows originating in coronal holes and that some other mechanism (such as wave pressure) is necessary.     

Expansion of chromospheric matter in the gradual phase of solar flares

Interferometric radio observations together with soft X-ray observations are presented here to show that during the growth phase of soft X-ray flares, a large mass increase occurs simultaneously with the creation of an X-ray hot region in the corona. The lack of an increase of radio flux from pre-flare active regions absolutely excludes the possibility of the coronal accumulation of low-temperature matter just prior to flare onset. Therefore we suggest a hypothesis that a large amount of hot matter, which contains almost the entire energy in the flare, is supplied from the chromosphere into the corona during each flare. Since even small flares produce coronal hot regions radiating thermal soft X-rays and microwaves, the formation of the hot region may be a basic process in most flares. Energy, created by some instability in the corona, travels by thermal conduction to the chromosphere where the dense matter is heated and subsequently expands into the corona, producing the observed hot region. Impulsive heating of the chromosphere by nonthermal electrons which simultaneously emit hard X-rays is not sufficient to be the energy source in our model. Slower heating, which supplies the flare more energy than that supplied in the impulsive phase, is required. If the temperature of the energy source in the corona exceeds 2 × 10⁷ K, the conductive energy flux becomes sufficient to exceed the radiation loss from the chromosphere-corona transition region. This excess energy may cause the chromospheric gas expansion.     

Oblique propagation and dissipation of Alfvén waves in coronal holes

We investigate the effect of viscosity and magnetic diffusivity on the oblique propagation and dissipation of Alfvén waves with respect to the normal outward direction, making use of MHD equations, density, temperature and magnetic field structure in coronal holes and underlying magnetic funnels. We find reduction in the damping length scale, group velocity and energy flux density as the propagation angle of Alfvén waves increases inside the coronal holes. For any propagation angle, the energy flux density and damping length scale also show a decrement in the source region of the solar wind (< 1.05 R_⊙) where these may be one of the primary energy sources, which can convert the inflow of the solar wind into the outflow. In the outer region (> 1.21 R_⊙), for any propagation angle, the energy flux density peaks match with the peaks of MgX 609.78 Å and 624.78 Å linewidths observed from the Coronal Diagnostic Spectrometer (CDS) on SOHO and the non-thermal velocity derived from these observations, justify the observed spectroscopic signature of the Alfvén wave dissipation.     

Observability of coronal heating processes

The mechanisms that could possibly heat the corona are briefly reviewed with emphasis on their observability. Observing enhanced wave flux at footpoints of active regions would confirm wave heating. Observation of nonthermal electrons in tiny coronal events (nanoflares) would confirm dissipation of current sheets. Presence of large scale flows in coronal arcades would underline the importance of turbulent resistivity for coronal heating. A comparison of HeI absorption in quiet and active regions demonstrates the difficulty of interpreting data that connect chromospheric dynamics with coronal heating. Finally, the implications of the search for observations of coronal heating processes are mentioned.