Tearing mode instability in the atmosphere above a sunspot

We derived the energy balance equation in steady state and made numerical calculations for 37 sets of parameter values for three layers of the atmosphere. The main results are: 1) The energy density released by tearing mode instability rapidly falls with rising temperature. It is much greater in the colmnar pinch than in the thin plate pinch. 2) The critical temperature increases with the intensity of the sheared magnetic field and decreases with its width. It is higher in the columnar pinch, and the rise time is shorter, than in the thin plate pinch. 3) At the surface of the photosphere, the energy released by tearing mode instability raises the local temperature by less than 1 K. 4) When the sheared width of the magnetic field is below a certain threshold, the local temperature is raised sharply to over (+6) K. This threshold is an increasing function of the strength of the sheared field. Our calculated results fit the observations to within one order of magnitude.     

Median ionospheric height variations over a sunspot cycle in the Australian-Japanese longitudinal sector

The monthly median virtual height (h′F) of the F-region was studied for a period of 6 years (1980–1985) from sunspot maximum to minimum, using data from 11 ionosonde stations in the Japanese-Australian longitudinal sector, in an invariant latitude range: 37°N to 54°S. The night-time maximum in the median height progressively decreases equatorwards, particularly in the local winter and spring, while a reverse weak tendency is observed in summer. The median height reaches peak in both hemispheres from 1 to 2 years after sunspot maximum then decreases towards sunspot minimum. A second diurnal maximum in h′F, preceded by a well-defined minimum, was consistently observed over the solar cycle close to the sunrise time at the F-region, mainly at low invariant latitudes (9–20°). The second maximum has a distinct seasonal variation, being most pronounced in winter and diminishing in summer. It is envisaged that the second peak in h′F is associated with the wave disturbance generated by the supersonic motion of the sunrise terminator. Possible effects of the background height variations on the propagation of the magnetic storm-induced travelling ionospheric disturbances are discussed.     

A new method to calculate the resonant response of a sunspot model atmosphere to magneto-atmospheric waves

In order to understand the observed oscillations in sunspots we present a new method for calculating the resonant response of a realistic semi-empirical model of the sunspot umbral atmosphere and subphotosphere to magneto-atmospheric waves in a vertical magnetic field. The depth dependence of both the adiabatic coefficient and the turbulent pressure is taken into account. This requires an extension of the wave equations by Ferraro & Plumpton (1958). We compare the coefficients of wave transmission, re flection, and conversion between fast mode and slow mode waves for different assumptions, compare the results with those from earlier modelling efforts, and point out possible sources of mistakes. The depth dependence of the adiabatic coefficient strongly influences the resulting spectrum of resonance frequencies. The condition of a conservation of wave flux is violated if the depth dependence of the turbulent pressure is not properly considered.     

On physical conditions in the chromosphere above sunspot umbrae

By means of an inversion of H and K Ca ii line profiles the temperature and electron density in the chromosphere above the umbrae of two sunspots have been estimated. The temperature gradient 5 K km^–1 exceeds the corresponding values in both quiet regions and plages. At a height of about 1500 km the umbra becomes hotter than the quiet region. At a temperature of about 10000 K the temperature gradient increases sharply. The electron density at 1500 km is approximately the same as that in the quiet chromosphere at the same height.     

The shape of the sunspot cycle

The temporal behavior of a sunspot cycle, as described by the International sunspot numbers, can be represented by a simple function with four parameters: starting time, amplitude, rise time, and asymmetry. Of these, the parameter that governs the asymmetry between the rise to maximum and the fall to minimum is found to vary little from cycle to cycle and can be fixed at a single value for all cycles. A close relationship is found between rise time and amplitude which allows for a representation of each cycle by a function containing only two parameters: the starting time and the amplitude. These parameters are determined for the previous 22 sunspot cycles and examined for any predictable behavior. A weak correlation is found between the amplitude of a cycle and the length of the previous cycle. This allows for an estimate of the amplitude accurate to within about 30% right at the start of the cycle. As the cycle progresses, the amplitude can be better determined to within 20% at 30 months and to within 10% at 42 months into the cycle, thereby providing a good prediction both for the timing and size of sunspot maximum and for the behavior of the remaining 7–12 years of the cycle. The U.S. Government right to retain a non-exclusive, royalty free licence in and to any copyright is acknowledged.     

Mathematical modelling of the sunspot cycle

The sunspot record for the time interval 1749–1977 can be represented conveniently by an harmonic model comprising a relatively large number of lines. Solar activity can otherwise be considered as a sequence of partly overlapping events, triggered periodically at intervals of the order of 11 years. Each individual cycle is approximated by a function of the Maxwell distribution type; the resulting impulse model consists of the superposition of the independent pulses. Application of these two models for the prediction of annual values of the Wolf sunspot numbers leads to controversial results. Mathematical modelling of the sunspot time series does not give an unambiguous result.     

On long-term periodicities in the sunspot cycle

Occurrences of interplanetary shock waves near the Earth after the powerful isolated flares of 1957–1978 are investigated. The close connection between the occurrences of shock waves and the positions of magnetic axes of bipolar groups of sunspots is suggested on the basis of a statistical study. The shock waves are principally observed when the Earth finds itself near the planes that are projected through the flares in parallel to the appropriate magnetic axes of the nearest bipolar groups. This regularity is interpreted as an indirect argument for a three-dimensional geometry for the interplanetary shock waves which, when projected on these flattened to corresponding planes, are traces of large circular arcs. The typical angular scales of isolated interplanetary shock waves are estimated as 150° and 30° parallel and perpendicular, respectively, to the magnetic axes correspondingly.     

A numerical response of the middle atmosphere to the 11-year solar cycle

A two-dimensional numerical model with coupled photochemistry and dynamics has been used to investigate the response of the middle atmosphere (16–116 km) to changes in solar activity over the 11-year solar cycle. Model inputs that vary with solar cycle include solar radiation, cosmic ray and auroral ionization rates and the flux of NO_x at the model's upper boundary.In this study, the results of model runs for solar cycle minimum and maximum conditions are compared. In the stratosphere, using currently accepted estimates of changes in solar radiation at wavelengths longer than 180 nm, only small responses in ozone, temperature and zonal winds are obtained. On the other hand, changes at shorter wavelengths, and the effects of particle precipitation, lead to large variations in the abundances of trace species in the thermosphere and upper mesosphere. In particular, very large abundances of NO_x are produced above 90 km by auroral particle precipitation. Considerable amounts of NO_x are transported subsequently to the stratosphere by the global mean meridional circulation. It is shown that this excess NO_x can lead to significant decreases in ozone concentrations at high latitudes and that it may explain observations of nitrate deposition in Antarctic snow.     

Polar coronal holes and the sunspot cycle. A new method to predict sunspot numbers

Twenty years ago, Ohl (1966, 1968) found a correlation between geomagnetic activity around the minimum of the solar cycle and the Wolf sunspot number in the maximum of the following solar cycle. In this paper we shall show that such a relation means indeed a relation between the polar coronal holes area around the minimum of the solar cycle and the sunspot number in the maximum of the next. In fact, a very high positive correlation exists between the temporal evolution of the size of polar coronal holes and the Wolf sunspot number 6.3. years later.     

The viability with respect to temperature,of micro-organisms incident on the Earth's atmosphere

Using laboratory measurements of the resistance of E. coli to flash-heating, it is shown that a large fraction of interplanetary micro-organisms in prograde orbits could be added to the Earth without losing viability due to heating by the atmospheric gases.     

On the average rate of growth in sunspot number and the size of the sunspot cycle

The average rate of growth during the ascending portion of the sunspot cycle, defined here as the difference in smoothed sunspot number values between elapsed time (in months) t and sunspot minimum divided by t, is shown to correlate (r 0.78) with the size of the sunspot cycle, especially for t 18 months. Also, the maximum value of the average rate of growth is shown to highly correlate (r = 0.98) with the size of the cycle. Based on the first 18 months of the cycle, cycle 22 is projected to have an R(M) = 186.0 ± 27.2 (at the ± 1 level), and based on the first 24 months of the cycle, it is projected to have an R(M) = 201.0 ± 20.1 (at the ± 1 level). Presently, the average rate of growth is continuing to rise, having a value of about 4.5 at 24 months into the cycle, a value second only to that of cycle 19 (4.8 at t = 24 and a maximum value of 5.26 at t = 27). Using 4.5 as the maximum value of the average rate of growth for cycle 22, a lower limit can be estimated for R(M); namely R(M) for cycle 22 is estimated to be 164.0 (at the 97.5% level of confidence). Thus, these findings are consistent with the previous single variate predictions that project R(M) for cycle 22 to be one of the greatest on record, probably larger than cycle 21 (164.5) and near that of cycle 19 (201.3).     

Predicting the maximum amplitude for the sunspot cycle from the rate of rise in sunspot number

Examined are associational aspects as they relate the maximum amplitude R _M for the sunspot cycle to the rate of rise R _t during the ascending phase, where R _M is the smoothed sunspot number at cycle maximum and R _t is the sum of the monthly mean sunspot numbers for selected 6-month intervals (t) measured from cycle onset. One finds that, prior to about 2 yr into the cycle, the rate of rise is not a reliable predictor for maximum amplitude. Only during the latter half of the ascent do the fits display strong linearity, having a coefficient of correlation r 0.9 and a standard error S _yx 20. During the first four intervals, the expected R _M and the observed R _M were found to differ by no more than 20 units of smoothed sunspot number only 25, 42, 50, and 58 % of the time; during the latter four intervals, they differed by no more than 20 units 67, 83, 92, and 100% of the time.     

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.     

Interpretation of oscillations in UV lines observed above sunspot umbrae

Our theory of a resonator for slow magneto-atmospheric waves in the chromosphere of a sunspot umbra has been used to check different models of the structure of the chromosphere and transition region. Oscillations of velocity and intensity in Civ, Siiv, and Oiv lines observed by Gurman et al. (1982) on the SMM spacecraft have been compared with the calculated oscillations. The observed spectrum of resonant peaks could well be explained by a gradient model of the umbral chromosphere. Different assumptions concerning the structure of the transition region do not influence the calculated resonance periods, but the amplitudes and phases of oscillations are modified. There is strong evidence for a concentration of the observed oscillations in cold fine structure elements of the transition region, even if the filling factor of such elements is very small (some few percent). Isothermal rather than adiabatic oscillations in the cold elements should be assumed in order to explain the observed fluctuations of line intensity; the relative amplitudes of pressure oscillations in the hot main component with a steep gradient of temperature are too small to explain the observed intensity fluctuations.     

Extreme ultra-violet absorption cross-sections in the Earth's upper atmosphere

Relative absorption cross-sections between 180 Å and 304 Å, and between 584 Å and 304 Å are obtained for atomic oxygen in the upper atmosphere, by observing the attentuation of solar radiation using a satellite instrument.     

On the maximum rate of change in sunspot number growth and the size of the sunspot cycle

Statistically significant correlations exist between the size (maximum amplitude) of the sunspot cycle and, especially, the maximum value of the rate of rise during the ascending portion of the sunspot cycle, where the rate of rise is computed either as the difference in the month-to-month smoothed sunspot number values or as the average rate of growth in smoothed sunspot number from sunspot minimum. Based on the observed values of these quantities (equal to 10.6 and 4.63, respectively) as of early 1989, one infers that cycle 22's maximum amplitude will be about 175 ± 30 or 185 ± 10, respectively, where the error bars represent approximately twice the average error found during cycles 10–21 from the two fits.     

Comparison of the microwave and soft X-ray emission above a sunspot

The Westerbork Synthesis Radio Telescope (WSRT) 6 cm radio observations of the active region HL 16864 large spot (Strong, Alissandrakis, and Kundu, 1984) are compared with X-ray data obtained from the Flat Crystal Spectrometer (FCS) onboard the Solar Maximum Mission satellite on May 25, 1980. The X-ray data confirm the presence of a temperature depression above the spot umbra in agreement with suggestions obtained from radio data analysis. Significant differences in the spatial distribution of both kinds of emission observed in the corona above this spot are attributed mainly to the strong resonant character of the cyclotron radio radiation. Some differences are also caused by both the relatively low efficiency and the low spatial resolution of the FCS. Deconvolution of X-ray images allows to see the new structures and enhances the mutual correlation between X-ray and radio pictures.     

On the inhomogeneous structure of the chromosphere-corona transition region above sunspot umbrae

Multiple wavelength observations of sunspot umbrae can only be expalined by an inhomogeneous, two-component model for the structure of the umbral transition region and lower corona. The ‘Wroclaw-Ondrejov sunspot model’ was a first step in this direction. This working model has now been improved using analytic expressions for the atmospheric structure in each component and fitting the free parameters to recent sunspot observations, particularly in EUV lines. The main component has a shallow transition region and a deep-set corona. The second, ‘active’ component has a vast transition region in relatively cool fine structure elements embedded in the coronal main component. The spatial filling factor of this active component amounts to 5–10% in sunspots with bright EUV plumes, but is is more than ten times smaller in sunspot without such plumes. Observations with high spatial and temporal resolutions are necessary to understand in more detail the basic physical processes.     

Interannual sea level variability in the South China Sea and its response to ENSO

Sea level observed by altimeter during the 1993–2004 period, thermosteric sea level from 1945 through 2004, and tide gauge records are analyzed to investigate the interannual variability of sea level in the South China Sea (SCS) and its relationship with ENSO (El Niño and Southern Oscillation). Both the interannual variations of the observed sea level and the thermosteric sea level are closely related to ENSO. An ‘enigma’ that the SST and sea level in the SCS have inverse response to ENSO is revealed. It is found that the thermosteric sea level has an excellent correspondence to seawater temperature at 100 m depth, and their variations are unsynchronized to SST. Detailed analysis denotes that the warming of seawater occurs only in the upper 75 m during and after the mature phase of El Niño, while the cooling appears in the layers deeper than 75 m during El Niño years. The volume transports between the SCS and the adjacent oceans and the anomalous Ekman pumping contribute a lot for the sea level fall in the developing stage of El Niño, while the mass exchange, which is dominated by precipitation, plays a more significant role in the following continuous negative sea level anomalies.