The rotation of magnetic loop systems in the solar atmosphere

Eclipse photographs indicate that large regions of the inner solar corona are confined in various types of closed magnetic configurations and, as a result, do not participate in the general solar wind expansion. In this paper, the rotation of initially poloidal loop configurations of this type, as influenced by differential rotation of the footpoints, is investigated. The analysis is restricted to axially symmetric fields and it is assumed that the toroidal magnetic field induced by differential rotation is small as compared to the initial poloidal field. This restricts the validity of the analysis to times less than about one month.The most interesting physical situation is that of flux tubes existing in one solar hemisphere only, one end of the tube being fixed in the photosphere at a higher latitude than the other. As a consequence, the lower end of the tube rotates at a faster rate than the upper end. Solution of the pertinent equations reveals that the angular velocity measured along a field line increases monotonically from its value at the poleward footpoint to that at the lower footpoint. The variation of angular velocity along the field depends upon the field geometry only and is not directly related to the variation of angular velocity along the solar surface between the footpoints. Depending upon the field configuration, both outward radial increases and decreases are possible. Using the Newton and Nunn model for the surface differential rotation rate, the angular velocity distribution on two particularly simple types of closed magnetic loop systems is determined analytically. It is shown that the angular velocity increases outward in the polar regions but decreases outward near the equator - leading to a decrease in differential rotation with height.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

On the differential rotation with height in the solar atmosphere

Spectroscopic measurements of solar rotation having good height discrimination show no change in angular velocity through the photosphere layers but an increase of 8% for the Hα chromosphere (epoch 1968.9). Spectroscopic results in general are compared with measures made with tracers, i.e. sunspots, filaments, etc., and it is seen that the spectroscopic method always shows increased differential rotation with height, while tracers indicate none. A westward flowing wind is proposed that increases in velocity with height, but produces negligible movement to magnetic regions associated with tracers. Kitt Peak National Observatory Contribution No. 450. Operated by The Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Differential rotation of the solar atmosphere as determined from millimeter data

Radiospectroheliograms obtained at millimeter wavelengths were used to determine the rotation of the solar atmosphere. Regions observed in both emission as well as absorption (associated with H dark filaments) were followed across the disk. The average sidereal rotation rate deduced from emissive regions is given by (deg day^-1)=14.152(±0.270)-4.194(±3.017)sin² B, where B is the heliographic latitude and the quoted errors are the standard deviations of a least squares fit to the data. The rate deduced from absorption regions is given by =14.729(±0.286)-1.050(±1.611)sin² B. This rate is larger than that of emissive regions at all latitudes and shows smaller differential rotation. This apparent difference in the rotation rates is probably due to the difference in the height of formation of the emissive and absorption regions. This difference could be used to estimate the difference in height between an emissive region and an absorption feature in millimeter radiation.     

The solar differential rotation from the eightteenth solar cycle

The sidereal daily rotation of the Sun, (), depends on the data used. From an appropriate selection of the data — sunspots with regular motion — it is found that ()=14.31–2.70 sin² , where denotes the heliographic latitude. Moreover, it seems that there is a variation, of the order of 3%, with the solar activity.     

The coarse structure of the solar atmosphere

Observations of the quiet sun at wavelengths from 3 Å to 75 cm show (with two exceptions: the Ovi line at 1032 Å and possibly the continuum at 1.2 mm) either no limb brightening or less than had been supposed. On the other hand, the brightness temperature is observed to increase with wavelength in the millimeter and centimeter range. If this increase is due to greater visibility of hot overlying material, that material ought to be evident at the limb at shorter wavelengths, resulting in limb brightening. The only possible explanation for the absence of limb brightening at almost all wavelengths is that the emitting surface is rough at all wavelengths, with a scale of roughness approximately equal to the scale height at each temperature. Contradictions with existing models, along with the additional observations required for an improved model are discussed.     

The magnetic field in the solar atmosphere

This publication provides an overview of magnetic fields in the solar atmosphere with the focus lying on the corona. The solar magnetic field couples the solar interior with the visible surface of the Sun and with its atmosphere. It is also responsible for all solar activity in its numerous manifestations. Thus, dynamic phenomena such as coronal mass ejections and flares are magnetically driven. In addition, the field also plays a crucial role in heating the solar chromosphere and corona as well as in accelerating the solar wind. Our main emphasis is the magnetic field in the upper solar atmosphere so that photospheric and chromospheric magnetic structures are mainly discussed where relevant for higher solar layers. Also, the discussion of the solar atmosphere and activity is limited to those topics of direct relevance to the magnetic field. After giving a brief overview about the solar magnetic field in general and its global structure, we discuss in more detail the magnetic field in active regions, the quiet Sun and coronal holes.     

The five-minute oscillations in the solar atmosphere

The acoustic overstability in a polytropic plane-parallel atmosphere with superadiabatic temperature gradient and radiative dissipation is demonstrated for optically thick disturbances. The periods of oscillation are found to be in the range 250–480 s and the associated wavelength of the order of 4000 km. The five-minute oscillations in the solar surface are attributed to self-excited sound waves in a layer in the subphotospheric convection zone of about 1000 km thickness.     

The abundance of cadmium in the solar atmosphere

The solar spectrum at 3261 Å has been studied using the spectrograph at the Oslo Solar Observatory. From analysis of this wavelength region and recent results at 5085 Å, a solar cadmium abundance log N _Cd = 1.86 ± 0.15 is obtained.     

The large-scale velocity fields of the solar atmosphere

Magnetograph velocity data are studied for evidence of large-scale velocity fields. It is established that there exist on the surface of the sun regions of more or less coherent downward motion with dimensions of the order of a solar radius. Velocity amplitudes in these regions are in the range 50–75 m/sec. Downward-moving large-scale features are observed to live for at least several days in general and to rotate at least approximately with the solar rotation rate. Horizontal east-west motions appears to have lifetimes of at least many months. The extent in longitude of these horizontal features is about 25°. There is no evidence for meridional motions from these data, with an upper limit to the line-of-sight velocity of about 30 m/sec. Active regions, as reported previously, are areas of generally downward motion. Some features in the autocorrelation of the rotational velocity of the sun remain unexplained.     

Differential rotation in the solar atmosphere inferred from optical,radio, and interplanetary data

Autocorrelation analysis of sunspot number, solar radio flux, and interplanetary field in the period 1967 to 1970 yields new information concerning solar atmospheric rotation. The upper chromosphere and the lower corona are rotating on the average about 5 to 8 % faster than is either the photosphere or the upper corona. In addition, short-lived features in the chromosphere and lower corona are found to rotate sometimes as much as 10% faster than relatively long-lived features at the same height. Coronal and photospheric features are found to rotate more or less synchronously. Analysis of yearly data has indicated a considerable change in rotation periods from one year to another.     

Seismology of the solar atmosphere

We describe a new instrument for seismically probing the properties of the Sun's lower atmosphere, and present some first results from an observational campaign carried out at the geographic South Pole during the austral summer of 2002/2003. A preliminary analysis of the data (simultaneous, high-cadence observations of the velocity signals from the photosphere and low chromosphere) shows that the well-known suppression of acoustic power in regions of strong magnetic field, and enhancement of high-frequency power around active regions (acoustic halos), are both consistent with a spreading out of the magnetic field lines with increasing height in the atmosphere. The data have also revealed some unexpected wave behavior. First, evanescent-like waves are found at frequencies substantially above the acoustic cut-off frequency in regions of intermediate magnetic field. Second, upward- and downward-propagating waves are detected in areas of strong magnetic field such as sunspots and plage: even at frequencies below the acoustic cut-off frequency. Third, the wave behavior in regions of strong magnetic field can change over periods of a few hours from propagating to evanescent. While we have no concrete explanation for the first two results, the latter result opens up the question of whether sound waves are involved in short-term events such as flares or CME's.     

The 4-day rotation of the upper atmosphere of venus

Near u.v. photographs of Venus have been analysed. Evidence is presented that so-called Y- and ψ-shaped markings accelerate from local sunrise to some time during local afternoon; mean horizontal velocities are 83 msec^?1 (morning) and 122 msec^?1 (afternoon). Possibly these configurations are more stable than a normal cloud system. ‘Irregular’ features do not seem to share this acceleration; they circulate at higher altitudes, sometimes covering or distorting the stable configurations.     

The peculiarities of rotation of the solar polar regions

The sidereal rotation rate of the high-latitude solar regions is examined using long-lived photospheric polar faculae. The observations were carried out with the photoheliograph of Kislovodsk Mountain Station of the Pulkovo Observatory from 1982 to 1986. The following facts have been established: (a) There is a differential rotation of the polar faculae close to the maximum of solar activity, while the amount of latitude gradient of solar rotation decreases towards the sunspot minimum; (b) small differences of rotation in the northern and southern hemispheres of the Sun are observed; (c) some deviations of differential rotation curves constructed for each Carrington rotation from the mean curve of differential rotation are revealed. The total amplitude of the maximum positive and negative excesses is about 40–50 m s^–1. The positive surplus velocities of solar rotation (the amplitude of which is about 20–25 m s^–1) move in the form of a wave from heliographic latitudes 40° with a velocity of 1.6 m s^–1. The latitude width of this flow is B 15°. This wave of abnormally high velocity starts in the year of minimum solar activity and reaches the pole 11 years later. The picture is symmetrical relative to the equator.     

The isotope ratio of europium in the solar atmosphere

Europium has two stable isotopes, Eu 151 and Eu 153. The high isotope shift and the different hyperfine splitting of the energy levels of the two isotopes make it possible to study the isotope ratio by an analysis of the spectral line profiles. From five spectral lines the solar isotope ratio is found to be equal to the terrestrial ratio within an error limit of about 10 %.     

The configuration of the loop-like structure of the solar atmosphere

An integral, governing steady flows in an isolated thin magnetic flux tube in the hydrostatic plane-stratified atmosphere, has been obtained. The integral, that we named as the shape integral, is expressed as (1 − M_A²)B cos θ = const. Here M_A² is the Alfven Mach number, B is the magnetic field strength and θ is the flux tube inclination to the horizontal. The shape integral should hold for most loop models because it represents just the momentum balance laws and has no relation to any energy balance mode. Its application to the isothermal and static cases is discussed and illustrated.     

Thallium in the solar atmosphere

Umbral spectra are shown to contain an absorption feature attributable to the Tl i transition 6p ² P°_3/2–7s ² S _1/2 at 5350 Å. Analysis of the umbral spectrum suggests a solar abundance in the 0.72< log N(Tl)T<1.10 on the standard scale log N(H) = 12.00. Unidentified blends limit the accuracy of the abundance determination.     

Models of the open solar atmosphere

McWhirter et al. (1975) have presented a standard model for the transition region and inner corona that matches with the Harvard Smithsonian Reference Atmosphere. They assume an open field line configuration and solve numerically the equations of energy and hydrostatic equilibrum. The purpose of the present paper is to generalise their model for the temperature and density as functions of height in several ways and, in particular, to determine the temperature maxium and its location. The effect of varying the following characteristics of the model is determined:

1. Boundary conditions on temperature and density;
2. magnitude of the heating;
3. form of the heating term;
4. divergence of the field lines;
5. presence of subsonic flows, either upward or downward.

If the heating is localised at great altitudes, it tends to produce a narrower and larger temperature maximum at a greater altitude than a uniform heating and even more so than a heating proportional to density. For fixed base conditions, an increase in heating or field line divergence or downflow decreases the coronal temperature and reduces the height of the temperature maximum, while a steady upflow has the opposite effects. A maximum possible upflow was found, beyond which a catastrophe occurs so that no steady hot solution exists.     

The rotation rate of the upper atmosphere: A non-linear effect

In order to study the apparent ‘super-rotation’ of the Earth's upper atmosphere, we examine a non-linear solution to the continuity, momentum conservation and state equations of gasdynamics for the steady state motion of a gravitationally stratified, cylindrical, inviscid atmosphere under the influence of a steady state, local time dependent temperature distribution. The resultant flow field can be understood in terms of angular momentum conservation of air masses: heated, rising air decreases its rotation rate and cooled, falling air increases its rotation rate. The local-time average of the differential rotation rate may given rise to an apparent altitude dependent ‘super-rotation’. Comparison with observations is presented.     

The induced electric field distribution in the solar atmosphere

A method of calculating the induced electric field is presented. The induced electric field in the solar atmosphere is derived by the time variation of the magnetic field when the accumulation of charged particles is neglected. In order to derive the spatial distribution of the magnetic field, several extrapolation methods are introduced. With observational data from the Helioseismic and Magnetic Imager aboard NASA’s Solar Dynamics Observatory taken on 2010 May 20, we extrapolate the magnetic field from the photosphere to the upper atmosphere. By calculating the time variation of the magnetic field, we can get the induced electric field. The derived induced electric field can reach a value of 102 V cm-1 and the average electric field has a maximum point at the layer 360 km above the photosphere. The Monte Carlo method is used to compute the triple integration of the induced electric field.     

Electric fields in the solar atmosphere

The gross-structure of the force-free currents in the solar atmosphere and their possible dynamics have been discussed as caused by quasi short-circuited electric fields, generated by the motion of the solar magnetic features.