A modelling study of satellite beacon measurements of protonospheric replenishment

Recent satellite beacon derived measurements of the recovery of protonospheric ionization following periods of increased geomagnetic activity show that the recovery takes longer than is indicated by whistler measurements. Realistic plasmasphere models have been used to determine whether satellite beacon measurements are reliable indicators of this recovery. It is found that the recovery time of the protonospheric content is similar to that of the minimum L-value flux tube intersected by the slant raypaths. Satellite beacon results are therefore useful indicators of protonospheric recovery after a storm provided any unrepresentative diurnal variations are eliminated.     

A new look at pulsar statistics — Birthrate and evidence for injection

We make a statistical analysis of the periodsP and period-derivativesP of pulsars using a model independent theory of pulsar flow in theP-P diagram. Using the available sample ofP andP values, we estimate the current of pulsars flowing unidirectionally along theP-axis, which is related to the pulsar birthrate. Because of radio luminosity selection effects, the observed pulsar sample is biased towards lowP and highP. We allow for this by weighting each pulsar by a suitable scale factor. We obtain the number of pulsars in our galaxy to be 6.05_−2.80 ^+3.32 × 10⁵ and the birthrate to be 0.048_−0.011 ^+0.014 pulsars yr⁻¹ galaxy⁻¹. The quoted errors refer to 95 per cent confidence limits corresponding to fluctuations arising from sampling, but make no allowance for other systematic and random errors which could be substantial. The birthrate estimated here is consistent with the supernova rate. We further conclude that a large majority of pulsars make their first appearance at periods greater than 0.5 s. This ‘injection’, which runs counter to present thinking, is probably connected with the physics of pulsar radio emission. Using a variant of our theory, where we compute the current as a function of pulsar ‘age’ (1/2P/P), we find support for the dipole braking model of pulsar evolution upto 6 × 10⁶ yr of age. We estimate the mean pulsar braking index to be 3.7_−0.8 ^+0.8.     

The optical continuum of solar and stellar flares

A further development of the Kostyuk-Pikelner's model is presented. The response of the chromosphere heated by non-thermal electrons of the power-law energy spectrum has been studied on the basis of the numerical solution of the one-dimensional time-dependent equations of gravitational gas dynamics. The ionization and energy loss for the emissions in the Lyman and Balmer lines have been determined separately for the optically thin and thick L-line layers. Due to the initial heating, a higher-pressure region is formed. From this region, disturbances propagate upwards (a shock wave with a velocity of more than 1000 km s^-1) and downwards. A temperature jump propagates downwards, and a shock is formed in front of the thermal wave. During a period of several seconds after the beginning of this process, the temperature jump intensifies the downward shock wave and the large radiative loss gives rise to the high density jump ( ₂/ ₁ 100). The numerical solution has been analyzed in detail for the case heating of the ionized and neutral plasma, and a value of this heating is close to the upper limit of the admissible values. In this case, the condensation located between the temperature jump and the shock wave front, may emit in the observed optical continuum.In their essential features, the gas dynamic processes during the flares in red dwarf atmospheres are the same as those in the solar atmosphere. However, the high atmospheric densities, smaller height scale in red dwarf atmospheres, and greater energy of this processes in stellar flares, give rise, in practice, to the regular generation of optical continuum. The photometric parameters of a source with n 0¹⁵ cm^-3, T 9000 K, and _z 10 km are in a good agreement with observations.     

The eruption of active region filaments and its relation to the triggering of a solar flare

The formation and eruption of active region filaments is supposed to be caused by the increase of a concentrated current embedded in the active region background magnetic field of an active region according to the theory of Van Tend and Kuperus (1978).The onset of a filament eruption is due to either changes in the background magnetic field or the increase of the filament current intensity. Both processes can be caused by the emergence of new magnetic flux as well as by the motion of the photospheric footpoints of the magnetic field lines. It is shown that if the background field evolves from a potential field to a nearly force-free field the vertical equilibrium of the current filament is not affected, but large forces are generated along the filament axis. This is identified as the cause of filament activation and the increase in filament turbulence during the flare build-up phase. Depending on the evolution of the background field and the current filament, two different scenarios for flare build-up and filament eruption are distinguished.This work was done while one of the authors (M.K.) was participating in the CECAM workshop on Physics of Solar Flares held at Orsay, France, in June 1979.     

Average nocturnal and seasonal variations of sodium nightglow at 23°S, 46°W

The seasonal variation of the nocturnal average intensity, and the typical variation of the sodium airglow intensity during the night have been deduced, using a data set that has been accumulated over a period of 5 years. The maximum intensity, which occurs at the equinoxes, is about 2–3 times as large as the intensity during winter, when the intensity of the D₂ line is about 30 R. The nocturnal variation is symmetrical about midnight, where the intensity is some 30% less than just after (before) dusk (dawn) values.     

Electron content modelling: The significance of protonospheric contents

The principal advance of the ATS-6 satellite beacon experiment was the ability to deduce continuously the electron content along the entire slant path from ground-based measurements of the signal group delay. This feature has been exploited in conjunction with the more usual Faraday rotation technique to separate the total electron content into ionospheric and protonospheric components. The physical validity of the deduced quantities is investigated using a mathematical model of the plasmasphere in which integration of the time-dependent continuity and momentum equations for oxygen and hydrogen ions along selected L shells yields the ion concentrations and field-aligned fluxes. The ion concentrations are then integrated along the propagation path to various ground stations from ATS-6 to give computed values for comparison with observations. The mathematical model is used with different sets of atmospheric parameters to investigate the significance of ionospheric and protonospheric contents as derived from beacon data.The calculated electron concentrations are able to reproduce mid-latitude equinoctial electron content observations. The shape parameters τ and F can also be simulated by day, but night-time values do not match the observations well, a greater protonospheric content being required. The calculations show that the quantity N_p, which is readily derived from ATS-6 observations, may be interpreted as the slant H⁺ content above some fixed height in the case of some stations (but not others) if the plasmasphere is reasonably full. The total slant content of H⁺ is approx. twice the value of N_p, though it appears that for the Lancaster raypath a closer relationship exists between N_p and the H⁺ tube content at L = 1.8. In general,N_p is most closely related to the tube content for an L value slightly greater than the minimum L intersected along the raypath.     

User's guide to REDUCE subroutines for algebraic computations in general relativity

We describe the use of a package of subroutines for general-relativistic algebraic computations written in the LISP-based algebraic programming system REDUCE developed by Anthony Hearn. The first group of routines calculates concomitants of the metric tensor such as the Riemann tensor, Ricci tensor, Ricci scalar, Einstein tensor and Weyl tensor from given covariant or covariant and contravariant metric tensor components. One of these procedures includes the evaluation of the Maxwell equations and invariants as well as the Maxwell energy momentum tensor. A second group of routines takes the components of a null tetrad as input and evaluates the null frame projections of the Riemann tensor, the Einstein tensor as well as – if required – the 14 local invariants of the Riemann tensor. It also includes a determination of the Petrov type. Perturbation calculations may be performed and run effectively. The output can be presented in a flexible format chosen according to the needs of the user. A number of further special-purpose programs are available on request. The article should enable a reader familar with General Relativity but unfamilar with formula manipulating system, to employ the package.     

A Comparison of Wolf's Reconstructed Record of Annual Sunspot Number with Schwabe's Observed Record of ‘Clusters of Spots’ for the Interval of 1826–1868

Samuel Heinrich Schwabe, the discoverer of the sunspot cycle, observed the Sun routinely from Dessau, Germany during the interval of 1826–1868, averaging about 290 observing days per year. His yearly counts of ‘clusters of spots’ (or, more correctly, the yearly number of newly appearing sunspot groups) provided a simple means for describing the overt features of the sunspot cycle (i.e., the timing and relative strengths of cycle minimum and maximum). In 1848, Rudolf Wolf, a Swiss astronomer, having become aware of Schwabe's discovery, introduced his now familiar ‘relative sunspot number’ and established an international cadre of observers for monitoring the future behavior of the sunspot cycle and for reconstructing its past behavior (backwards in time to 1818, based on daily sunspot number estimates). While Wolf's reconstruction is complete (without gaps) only from 1849 (hence, the beginning of the modern era), the immediately preceding interval of 1818–1848 is incomplete, being based on an average of 260 observing days per year. In this investigation, Wolf's reconstructed record of annual sunspot number is compared against Schwabe's actual observing record of yearly counts of clusters of spots. The comparison suggests that Wolf may have misplaced (by about 1–2 yr) and underestimated (by about 16 units of sunspot number) the maximum amplitude for cycle 7. If true, then, cycle 7's ascent and descent durations should measure about 5 years each instead of 7 and 3 years, respectively, the extremes of the distributions, and its maximum amplitude should measure about 86 instead of 70. This study also indicates that cycle 9's maximum amplitude is more reliably determined than cycle 8's and that both appear to be of comparable size (about 130 units of sunspot number) rather than being significantly different. Therefore, caution is urged against the indiscriminate use of the pre-modern era sunspot numbers in long-term studies of the sunspot cycle, since such use may lead to specious results.     

Using Strong Solar Coronal Emission Lines as Coronal Flux Proxies

We investigate the possibility that strong EUV lines observed with the Goddard Solar EUV Rocket Telescope and Spectrograph (SERTS) provide good proxies for estimating the total coronal flux over shorter wavelength ranges. We use coordinated SERTS and Yohkoh observations to obtain both polynomial and power-law fits relating the broad-band soft X-ray fluxes to the intensities of Fexvi 335 Ú and 361 Ú, Fexv 284 Ú and 417 Ú, and Mgix 368 Ú measured with SERTS. We found that the power-law fits best cover the full range of solar conditions from quiet Sun through active region, though not surprisingly the cooler Mgix 368 Ú line proves to be a poor proxy. The quadratic polynomial fits yield fair agreement over a large range for all but the Mgix line. However, the linear fits fail conspicuously when extrapolated into the quiet-Sun regime. The implications of this work for the Heii 304 Ú line formation problem are also briefly considered.