The rotation of the solar atmosphere

A model of the solar atmosphere is presented in which we discuss the conservation of angular momentum for the two basic states in which the solar gas can be: namely, either confined by closed field lines or outflowing along open magnetic field lines. It can be shown that the boundary conditions are in general different for these two cases. From this we obtain the results that in the closed configuration the gas can corotate at the solar surface with the magnetic field lines and its angular velocity will then increase with height, whereas for a gas flowing along an open field line the angular velocity will decrease. An exception to the latter case can be found where the open magnetic field lines are strongly nonradial and where the density is a slowly varying function of radius. In such regions the angular velocity may initially increase with height, reach a maximum and then decrease.Kitt Peak National Observatory Contribution No. 439.Operated by The Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

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 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 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 influence of direct solar radiation pressure on the nodal period of artificial earth satellites

Approximate formulae for the evaluation of the effect of direct solar radiation pressure (neglecting the POYNTING -ROBERTSON effect and shadow effect) on the nodal period of artificial Earth satellites with quasi-circular orbits are derived. The cases of osculating elements considered in the ascending node and of circular orbits are studied.     

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.     

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.     

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 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 %.     

Effects of solar variations on the upper atmosphere

Several semi-empirical models of the terrestrial upper atmosphere are presently available. These models take into account solar activity effects by using the solar decimetric flux as an index. Such a procedure is a consequence of the lack of continuous determinations of the solar spectrum directly responsible for the physical structure of the upper atmosphere. Variations of the thermopause temperature are discussed. Using five sets of solar irradiances measured in the ultraviolet and in the extreme ultraviolet, the penetration of solar radiation is analyzed as a function of solar activity. Several examples of absorption profiles and ion production rates are discussed for variable conditions. Various energetic effects are also described. All computations are made for physical conditions above Scheveningen (52.08° N) where the 14th ESLAB symposium was held.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

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.     

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.     

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 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.     

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.     

Velocity fields in the solar atmosphere

Observations of velocity fields in the solar atmosphere made with the Mount Wilson solar magnetograph are analyzed. These observations, which were made with very high velocity sensitivity, cover nearly 250 hours and were made with apertures of several sizes and at various parts of the solar disk, and in strong and weak magnetic fields. The amplitudes of the 300-sec oscillations are about 25% weaker in regions where the magnetic field is greater than 80 gauss than where the field is less than 10 gauss. No difference in the frequencies of the oscillations could be found between strong-field and field-free regions. It is suggested that the oscillations occur only where the field is absent and the lower amplitude in a strong field represents the fraction of the magnetograph aperture occupied by a magnetic field. The element sizes for the 300-sec oscillations are probably at least 5–10 arc seconds.Observations made simultaneously with two lines formed at different depths in the solar atmosphere showed small phase differences in the 5-min oscillations. The upper level showed shorter period oscillations when the lower level oscillations underwent phase changes.A short period oscillation is found superposed on the 300-sec oscillation. These SPOs come in bursts that last for a minute or two and have average amplitudes that fall in the range 0.05–0.10 km/sec peak to peak. All attempts to explain them as instrumental or seeing effects have failed. Their periods fall in the range 1–5 seconds. The horizontal scale of these oscillations is smaller than that of the 300-sec oscillations, and the SPOs are more nearly isotropic oscillations than are these around 300 seconds. They do not represent a high-frequency tail of the latter. These observations did not have a digitizing interval short enough to analyze the SPOs for power spectra, but it is clear from the tracings that they are not a nearly monochromatic oscillation as are the longer waves. The amplitudes of the SPOs in the solar atmosphere must be very large and they contribute greatly to the non-radiative energy flux. It is suggested that they represent a large microturbulence line-broadening effect.     

Lithium depletion in the solar atmosphere

Using a complete non-local convection theory, we carried out the theoretical calculations of ⁷Li depletion of the solar convective envelope models with different convective parameters c₁ and c₂, and got a model of the solar convection zone consistent with the observed ⁷Li abundance and the depth of the solar convection zone determined by helioseismic techniques. The overshooting distance of effective non-local convective mixing of ⁷Li is very extensive, which is about 1.07H_P or 0.09R. However, the super-radiative temperature zone is much narrower, and it is only 0.20H_P or 0.016R.     

Ion-acoustic waves in the solar atmosphere

A model for ion-acoustic waves in the solar atmosphere is presented. In the limit of strongly magnetized plasma this model leads to the Zakharov-Kuznetsov equation which possesses a flat solitary wave solution. An initial-value problem for this equation is solved numerically to show a transition of the flat solitary waves into spherical solitary waves. The paper suggests further developments of an ion-acoustic wave theory that may improve our knowledge of ion-acoustic waves and lead to the possibility of their being detected in the solar atmosphere.     

Wave reflections in the solar atmosphere

The small phase-lag between velocities observed at different chromospheric levels is interpreted as being due to acoustic waves reflected by the very hot atmospheric layers of the chromosphere-corona transition zone. We consider first an isothermal slab, then a realistic solar atmospheric model and calculate weighting functions for velocities in Ca ii lines. It is shown that taking into account these functions and integrating over horizontal wave numbers leads to a good agreement with previous observations (Mein, 1977) in the case of 8498 and 8542 Ca ii lines. For the K line, the less good agreement shows that magnetoacoustic waves become important in the upper chromospheric layers.