The post-terminator ionosphere of Venus

We have modeled the near and post-terminator thermosphere/ionosphere of Venus with a view toward understanding the relative importance of EUV solar fluxes and downward fluxes of atomic ions transported from the dayside in producing the mean ionosphere. We have constructed one-dimensional thermosphere/ionosphere models for high solar activity for seven solar zenith angles (SZAs) in the dusk sector: 90°, 95°, 100°, 105°, 110°, 115° and 125°. For the first 4 SZAs, we determine the optical depths for solar fluxes from 3 Å to 1900 Å by integrating the neutral densities numerically along the slant path through the atmosphere. For SZAs of 90°, 95°, and 100°, we first model the ionospheres produced by absorption of the solar fluxes alone; for 95°, 100°, and 105° SZAs, we then model the ion density profiles that result from both the solar source and from imposing downward fluxes of atomic ions, including O⁺, Ar⁺, C⁺, N⁺, H⁺, and He⁺, at the top of the ionospheric model in the ratios determined for the upward fluxes in a previous study of the morphology of the dayside (60° SZA) Venus ionosphere. For SZAs of 110°, 115° and 125°, which are characterized by shadow heights above about 300 km, the models include only downward fluxes of ions. The magnitudes of the downward ion fluxes are constrained by the requirement that the model O⁺ peak density be equal to the average O⁺ peak density for each SZA bin as measured by the Pioneer Venus Orbiter Ion Mass Spectrometer. We find that the 90° and 95° SZA model ionospheres are robust for the solar source alone, but the O⁺ peak density in the “solar-only” 95° SZA model is somewhat smaller than the average value indicated by the data. A small downward flux of ions is therefore required to reproduce the measured average peak density of O⁺. We find that, on the nightside, the major ion density peaks do not occur at the altitudes of peak production, and diffusion plays a substantial role in determining the ion density profiles. The average downward atomic ion flux for the SZA range of 90–125° is determined to be about 1.2 × 10⁸ cm⁻² s⁻¹.     

Solar Magnetic Activity and Total Irradiance Since the Maunder Minimum

We develop a model for estimating solar total irradiance since 1600 AD using the sunspot number record as input, since this is the only intrinsic record of solar activity extending back far enough in time. Sunspot number is strongly correlated, albeit nonlinearly with the 10.7-cm radio flux (F _10.7), which forms a continuous record back to 1947. This enables the nonlinear relationship to be estimated with usable accuracy and shows that relationship to be consistent over multiple solar activity cycles. From the sunspot number record we estimate F _10.7 values back to 1600 AD. F _10.7 is linearly correlated with the total amount of magnetic flux in active regions, and we use it as input to a simple cascade model for the other magnetic flux components. The irradiance record is estimated by using these magnetic flux components plus a very rudimentary model for the modulation of energy flow to the photosphere by the subphotospheric magnetic flux reservoir feeding the photospheric magnetic structures. Including a Monte Carlo analysis of the consequences of measurement and fitting errors, the model indicates the mean irradiance during the Maunder Minimum was about 1 ± 0.4 W m⁻² lower than the mean irradiance over the last solar activity cycle.     

Solar radio burst and in situ determination of interplanetary electron density

We review and discuss a few interplanetary electron density scales which have been derived from the analysis of interplanetary solar radio bursts, and we compare them to a model derived from 1974–1980 Helios 1 and 2 in situ density observations made in the 0.3–1.0 AU range. The Helios densities were normalized to 1976 with the aid of IMP and ISEE data at 1 AU, and were then sorted into 0.1 AU bins and logarithmically averaged within each bin. The best fit to these 1976-normalized, bin averages is N(R _AU) = 6.1R ^-2.10 cm^-3. This model is in rather good agreement with the solar burst determination if the radiation is assumed to be on the second harmonic of the plasma frequency. This analysis also suggests that the radio emissions tend to be produced in regions denser than the average where the density gradient decreases faster with distance than the observed R ^-2.10.NAS/NRC Postdoctoral Research Associate on leave from Laboratory Associated with CNRS No. 264, Paris Observatory, France.     

Radio interferometric observations of solar bursts at 3.7 and 11.1 cm wavelengths

Several solar active regions were observed during the 1976 vernal equinox with the 3-element interferometer of the National Radio Astronomy Observatory. The element spacings for these observations were 600, 2100, and 2700 m, resulting in maximum angular resolutions of about 3 arc sec at 3.7 cm and 8.5 arc sec at 11.1 cm. We fitted the fringe visibility for each baseline pair as a function of projected baseline with a single gaussian component, and calculated the extrapolated flux at zero baseline, F ₀, the FWHM source size, a, and the peak brightness temperature T _b. We present physical parameters derived for the observed bursts.     

Slow and Fast Rotating Coronal Holes from Geomagnetic Indices

The evolution of the 27-day recurrence in the series of two solar indices (Wolf number WN and 10.7 cm radio flux F) and two geomagnetic indices (Dst and ζ, variance of the geomagnetic field recorded at a magnetic observatory) have been studied over the 1957 – 2007 time span. Spectral energies contained in two period domains (25 – 27.3 and 27.3 – 31 days), designated as E ₁ and E ₂, have been computed. Whereas the evolution of E ₁ is the same for the four indices, that of E ₂ is essentially different for WN and F on the one hand, Dst and ζ on the other hand. Some general conclusions on the dynamics of the solar outer layers are inferred from these results. First the solar activity, as measured by WN, and when averaged over a few years, evolves in the same way whatever the latitude. Second, two families of coronal holes (CHs) are identified; the rapidly and the slowly rotating CHs evolve quite differently.     

Predicting Solar Cycle 24 Using a Geomagnetic Precursor Pair

We describe using Ap and F_10.7 as a geomagnetic-precursor pair to predict the amplitude of Solar Cycle 24. The precursor is created by using F_10.7 to remove the direct solar-activity component of Ap. Four peaks are seen in the precursor function during the decline of Solar Cycle 23. A recurrence index that is generated by a local correlation of Ap is then used to determine which peak is the correct precursor. The earliest peak is the most prominent but coincides with high levels of non-recurrent solar activity associated with the intense solar activity of October and November 2003. The second and third peaks coincide with some recurrent activity on the Sun and show that a weak cycle precursor closely following a period of strong solar activity may be difficult to resolve. A fourth peak, which appears in early 2008 and has recurrent activity similar to precursors of earlier solar cycles, appears to be the “true” precursor peak for Solar Cycle 24 and predicts the smallest amplitude for Solar Cycle 24. To determine the timing of peak activity it is noted that the average time between the precursor peak and the following maximum is ≈?6.4 years. Hence, Solar Cycle 24 would peak during 2014. Several effects contribute to the smaller prediction when compared with other geomagnetic-precursor predictions. During Solar Cycle 23 the correlation between sunspot number and F_10.7 shows that F_10.7 is higher than the equivalent sunspot number over most of the cycle, implying that the sunspot number underestimates the solar-activity component described by F_10.7. During 2003 the correlation between aa and Ap shows that aa is 10 % higher than the value predicted from Ap, leading to an overestimate of the aa precursor for that year. However, the most important difference is the lack of recurrent activity in the first three peaks and the presence of significant recurrent activity in the fourth. While the prediction is for an amplitude of Solar Cycle 24 of 65±20 in smoothed sunspot number, a below-average amplitude for Solar Cycle 24, with maximum at 2014.5±0.5, we conclude that Solar Cycle 24 will be no stronger than average and could be much weaker than average.     

Two Unusual Episodes of ≈13-Day Variations II. Implications for the Solar Radio Flux Density, <Emphasis Type="Italic">F</Emphasis><Subscript>10.7 cm</Subscript>

Additional analysis of the behavior of the international sunspot number (R) series and the solar radio flux density (F_{10.7 cm}) series during two long (250–500 days) and distinct episodes of persistent ≈13-day variations (Crane, Solar Phys. 1998, 253, 177) is reported. The conclusion is that while the center-to-limb behavior of R does not change between solar minimum and solar maximum, F_{10.7 cm} exhibits significantly less limb brightening at solar maximum than at solar minimum.     

Changed Relation between Solar 10.7-cm Radio Flux and some Activity Indices which describe the Radiation at Different Altitudes of Atmosphere during Cycles 21–23

The correlation coefficients of the linear regression of six solar indices versus 10.7 cm radio flux F _10.7 were analysed in solar cycles 21, 22 and 23. We also analysed the interconnection between these indices and F _10.7 with help of approximation by polynomials of second order. The indices we have studied in this paper are: the relative sunspot numbers – SSN, 530.3 nm coronal line flux – F ₅₃₀, the total solar irradiance – TSI, Mg II 280 nm core-to-wing ratio UV-index, the Flare Index – FI and the counts of flares. In most cases the regressions of these solar indices vs. F _10.7 are close to the linear regression except the moments of time near the minimums and maximums of the 11-year activity. For the linear regressions, we found that correlation coefficients K _corr(t) for the solar indices vs. F _10.7 and SSN dropped to their minimum values twice during each 11-year cycle.     

The 156-day quasi-periodicity in solar indices

This paper investigates a series of daily solar indices: the sunspot number W (1900–2008), solar flux at 2800 MHz F _10.7 (1947–2008), and a number of X-ray flares N _x (1981–2008). The methods of Fourier and wavelet analysis are used to reveal the so-called 156-day Rieger-type periodicity (RTP). The W index is observed to have a statistically significant RTP amplitude in the neighborhood of the solar maxima in most of the solar cycles under study, except for cycles 14, 15, and 23. The 156-day peak is observed to have its largest power during the declining phase of cycle 16, at the maximum of cycle 21, and during the increasing phase of cycles 20 and 23. Statistically significant RTPs are also observed at the minima of cycles 17, 18 and 19. We conclude that there is no stable dependence between RTP and the solar cycle. The wavelet analysis shows that the pattern of the RTP time dependence for the F _10.7 index is almost identical to that of the W index. The correlation coefficient between the RTP curves is 0.95. The correlation coefficients for the pairs of indices W-N _x and F _10.7-N _x are 0.36 and 0.32, respectively. No time lags are found between the RTP starting points for different indices. Thus, the 156-day quasi-periodicity involves, almost simultaneously, events that occur in active regions of the solar atmosphere at different heights. This paper discusses the possible nature of RTP.     

Influence of the hot oxygen corona on the satellite drag in the Earth’s upper atmosphere

Calculation results on the possible influence of the hot oxygen fraction on the satellite drag in the Earth’s upper atmosphere on the basis of the previously developed theoretical model of the hot oxygen geocorona are presented. Calculations have shown that for satellites with orbits above 500 km, the contribution from the corona is extremely important. Even for the energy flux Q ₀ = 1 erg cm⁻² s⁻¹, the contribution of the hot oxygen can reach tens of percent; and considering that real energy fluxes are usually higher, one can suggest that for extreme solar events, the contribution of hot oxygen to the atmospheric drag of the satellite will be dominant. For lower altitudes, the contribution of hot oxygen is, to a considerable degree, defined by the solar activity level. The calculations imply that for the daytime polar atmosphere, the change of the solar activity level from F _10.7 ∼ 200 to F _10.7 ∼ 70 leads to an increase in the ratio of the hot oxygen partial pressure to the thermal oxygen partial pressure by a factor of almost 30, from 0.85 to 25%. The transition from daytime conditions to nighttime conditions almost does not change the contribution from suprathermal particles. The decrease of the characteristic energy of precipitating particles, i.e., for the case of charged particles with a softer energy spectrum, leads to a noticeable increase of the contribution of the suprathermal fraction, by a factor of 1.5–2. It has been ascertained that electrons make the main contribution to the formation of the suprathermal fraction; and with the increase of the energy of precipitating electrons, the contribution of hot oxygen to the satellite drag also increases proportionally. Thus, for a typical burst, the contribution of the suprathermal fraction is 30% even at relatively high solar activity F _10.7 = 135.     

DO SOLAR FLARES EXHIBIT AN INTERVAL–SIZE RELATIONSHIP?

Some models for flare statistics predict or assume that there is a relationship between the times between flares and the energy of flares. This question is examined observationally using the WATCH solar X-ray burst catalogue. A rank correlation test applied to the data finds strong evidence for a correlation between the time since the last event, t _b, and the size (peak count rate) of an event, and for a correlation between the time to the next event, t _a, and the size of an event. A more sophisticated statistical test, taking into account a probable bias in event selection, does not support the hypothesis that event size depends on t _b or t _a.     

Satellite theory

In this paper dynamical characteristics of satellites are outlined by classifying the satellites into three categories according to the values of the solar tidal factor (n/n)² which is the disturbing factor due to the sun and the oblateness factor of the primary planetJ ₂/a ². For inner satellites (n/n)² is much smaller thanJ ₂/a ² and there are several pairs among them, for which the mean motions are commensurable to each other, and for some of them secular accelerations in the mean longitudes have been detected. For outer satellites (n/n)² is much larger and the solar perturbations are dominant. For intermediary satellites the motion of the pole of the orbital plane is not so simple as those of the satellites of the other categories.     

Periodicities in the occurrence rate of solar proton events

Power spectral analyses of the time series of solar proton events during the past three solar cycles reveal a periodicity around 154 days. This feature is prominent in all of the cycles combined, cycles 19 and 21 individually but is only weak in cycle 20. These results are consistent with the presence of similar periodicities between 152 and 155 days in the occurrence rate of major solar flares, the sunspot blocking function (P _s ), the 10.7 cm radio flux (F _10.7) and the sunspot number (R _z ). This suggests that the circa 154-days periodicity may be a fundamental characteristic of the Sun. Periods around 50–52 days are also found in the combined data set and in the three individual cycles in general agreement with the detection of this periodicity in major flares in cycle 19 and inP _s ,F _10.7, andR _z in cycle 21. The cause of the 155 day period remains unknown. The spectra contain lines (or show power at frequencies) consistent with a model in which the periodicity is caused by differential rotation of active zones and a model in which it is related to beat frequencies between solar oscillations, as proposed by Wolff.     

Green's theorem and Green's functions for the steady-state cosmic-ray equation of transport

Green's Theorem is developed for the spherically-symmetric steady-state cosmic-ray equation of transport in interplanetary space. By means of it the momentum distribution functionF _o(r,p), (r=heliocentric distance,p=momentum) can be determined in a regionr _arr_bwhen a source is specified throughout the region and the momentum spectrum is specified on the boundaries atr _a andr _b . Evaluation requires a knowledge of the Green's function which corresponds to the solution for monoenergetic particles released at heliocentric radiusr _o , Examples of Green's functions are given for the caser _a =0,r _b = and derived for the cases of finiter _a andr _b . The diffusion coefficient is assumed of the form = _o(p)r ^b . The treatment systematizes the development of all analytic solutions for steady-state solar and galactic cosmic-ray propagation and previous solutions form a subset of the present solutions.     

Comparative Analysis of Super-Kamiokande and SNO Solar-Neutrino Data and the Photospheric Magnetic Field

We carry out a comparative analysis of Super-Kamiokande, SNO, and photospheric magnetic-field data for the interval in which these datasets overlap. This proves to be the interval of operation of the D₂O phase of the SNO experiment. Concerning solar-rotational modulation, we find that the magnetic-field power spectrum shows the strongest peaks at the second and sixth harmonics of the solar synodic rotation frequency [i.e., at 3ν _rot and 7ν _rot]. We find that the restricted Super-Kamiokande dataset has a strong modulation at the second harmonic, as we found to be the case for the complete Super-Kamiokande dataset. The SNO D₂O dataset exhibits weak modulation at that frequency, but shows strong modulation in the band corresponding to the sixth harmonic (too high a frequency to be detectable in the Super-Kamiokande dataset, which is available only in five-day bins, whereas SNO data is available in one-day bins). We estimate the significance level of the correspondence of the Super-Kamiokande second-harmonic peak with the corresponding magnetic-field peak to be 0.0004, and the significance level of the correspondence of the SNO D₂O sixth-harmonic peak with the corresponding magnetic-field peak to be 0.009. By estimating the amplitude of the modulation of the solar-neutrino flux at the second harmonic from the restricted Super-Kamiokande dataset, we find that the weak power at that frequency in the SNO D₂O power spectrum is not particularly surprising. We also examine power spectra in the neighborhood of 9.43 year⁻¹, which is the frequency of a particularly strong modulation in the entire Super-Kamiokande dataset. There is no peak at this frequency in the power spectrum formed from the restricted Super-Kamiokande dataset. It is therefore not surprising that we find (in agreement with the recent analysis by the SNO collaboration) that this peak does not show up in the SNO D₂O dataset either.     

Identifying the quasi-regular and stochastic components of solar cyclicity and their properties

We have averaged over every Carrington semi-rotation (C.s.-r.), the daily Wolf numbers (RW), total areas of sunspot groups (SA), the 10.7-cm radio flux (F _10.7), and the modulus of the mean magnetic field (|SMMF|). The fractal method of scaling the variance of time series was used to separate the regular and stochastic components. The manifestation of chaotic and stochastic properties of these components was investigated by testing with the methods of chaotic dynamics, as well as with two new methods: (1) close return maps; and (2) multivariate scaling analysis. Results: (1) by separating time series of global indices of solar activity, it is possible to identify the quasi-regular (the quasi-regularity is caused not by the absolute smoothness of the function) component on time scales longer than two years, and the irregular component on time scales shorter than two years; (2) the regular component has the properties of a nonlinear quasi-periodic oscillator; (3) the irregular component is a random one and has the properties of chromatic noise; and (4) by investigating the nonlinear connection of the solar activity indices under consideration it was found that such a connection is strong between F _10.7and RW. A nonlinear correlation between the attractors RW–|SMMF| and F _10.7–|SMMF| was also revealed.     

Response of peak electron densities in the martian ionosphere to day-to-day changes in solar flux due to solar rotation

Photochemical Chapman theory predicts that the square of peak electron density, N_m, in the dayside ionosphere of Mars is proportional to the cosine of solar zenith angle. We use Mars Global Surveyor Radio Science profiles of electron density to demonstrate that this relationship is generally satisfied and that positive or negative residuals between observed and predicted values of are caused by periods of relatively high or low solar flux, respectively.Understanding the response of the martian ionosphere to changes in solar flux requires simultaneous observations of the martian ionosphere and of solar flux at Mars, but solar flux measurements are only available at Earth. Since the Sun's output varies both in time and with solar latitude and longitude, solar flux at Mars is not simply related to solar flux at Earth by an inverse-square law. We hypothesize that, when corrected for differing distances from the Sun, solar fluxes at Mars and Earth are identical when shifted in time by the interval necessary for the Sun to rotate through the Earth–Sun–Mars angle.We perform four case studies that quantitatively compare time series of N_m at Mars to time series of solar flux at Earth and find that our hypothesis is satisfied in the three of them that used ionospheric data from the northern hemisphere. We define a solar flux proxy at Mars based upon the E_10.7 proxy for solar flux at Earth and use our best case study to derive an equation that relates N_m to this proxy. We discuss how the ionosphere of Mars can be used to infer the presence of solar active regions not facing the Earth.Our fourth case study uses ionospheric observations from the southern hemisphere at latitudes where there are strong crustal magnetic anomalies. These profiles do not have Chapman-like shapes, unlike those of the other three case studies. We split this set of measurements into two subsets, corresponding to whether or not they were made at longitudes with strong crustal magnetic anomalies. Neither subset shows N_m responding to changes in solar flux in the manner that we observe in the three other case studies.We find many similarities in ionospheric responses to short-term and long-term changes in solar flux for Venus, Earth, and Mars. We consider the implications of our results for different parametric equations that have been published describing this response.     

Investigation of heliogeoactivity impact on the dynamics of orbital parameters of Earth’s artificial satellites. I

The influence of active processes on the Sun and their response on the dynamics of Earth’s artificial satellites has been investigated. The relationship between the characteristics of solar activity and variations of the periods P of the orbital motion of Earth’s artificial satellites has been found. These variations mainly indicate the variations in the Earth’s atmosphere density caused by solar activity (index F_10.7) and geomagnetic activity (ΣK_p index). High values of the correlation coefficients between P and ^F_10.7 (–0.77…–0.91) and between P and ΣK_p (–0.67…–0.89) exhibit significant effect of solar and geomagnetic activity on the orbital periods of satellites.     

On the relation of SPA measured at VLF to solar microwave burst energies

A surprisingly good correlation has been found for SPA measured at VLF propagation () and 7 GHz solar microwave burst energies (E ). The data are correlated in the form = a log E + b and include all kind of solar events, irrespectively from type, complexity or duration. Soft X-ray peak fluxes (I _x) have a known similar correlation to SPA, and a functional relationship of the form 479-01 can be established. As one practical application, the energies from solar events can be reasonably well inferred from SPA data, which are quite reliable and easily obtainable.     

Limits to the accuracy of the 10.7 cm flux

The 10.7 cm flux data, which are widely used as an index of solar activity, are actually spot measurements of the solar flux density at 10.7 cm wavelength, made three times each day, usually at 17:00, 20:00, and 23:00 UT. These values, or the 20:00 UT determination alone, are frequently used as the average flux for that day. Since each spot measurement takes about one hour to make, and the Sun's emissions at that wavelength can vary over time scales shorter than the intervals between the measurements, the data are unavoidably undersampled. Radio emissions from transient events, such as flares, are defined as contaminants of the flux, and largely-empirical procedures have evolved which are used to filter them from the data. The utility of theF _10.7 index over more than 40 years suggests that the consequences of the under-sampling and the use of largely-empirical data filters are not serious. However, as new applications of the flux data appear, and existing ones become more quantitative, we need to better understand the accuracy of data as estimates of the 10.7 cm flux index, and to know how much precision we can reasonably expect to attain. In this paper we describe part of a study aimed at estimating how good the spot measurements are as estimators of the ‘daily-average’ flux. By a combination of measurement and modelling, the contributions to the flux monitor output truly due to the Sun are separated from the non-solar signals. We then derive the daily average 10.7 cm flux values and compare them with the spot measurements. We find that in general, the spot measurements are usually within a percent or so of the daily-average fluxes.