Effects of errors in the solar radius on helioseismic inferences

Frequencies of intermediate-degree f modes of the Sun seem to indicate that the solar radius is smaller than what is normally used in constructing solar models. We investigate the possible consequences of an error in radius on results for solar structure obtained using helioseismic inversions. It is shown that solar sound speed will be overestimated if oscillation frequencies are inverted using reference models with a larger radius. Using solar models with a radius of 695.78 Mm and new data sets, the base of the solar convection zone is estimated to be at a radial distance of 0.7135 ± 0.0005 of the solar radius. The helium abundance in the convection zone as determined using models with an OPAL equation of state is 0.248 ± 0.001, where the errors reflect the estimated systematic errors in the calculation, the statistical errors being much smaller. Assuming that the OPAL opacities used in the construction of the solar models are correct, the surface Z / X is estimated to be 0.0245 ± 0.0006.     

Secular increase of astronomical unit from analysis of the major planet motions, and its interpretation

From the analysis of all available radiometric measurements of distances between the Earth and the major planets (including observations of martian landers and orbiters over 1971–2003 with the errors of few meters) the positive secular trend in the Astronomical Unit AU is estimated as . The given uncertainty is the 10 times enlarged formal error of the least-squares estimate and so accounts for possible systematic errors of measurements and deficiencies of the mathematical model. The reliability of this estimate as well as its physical meaning are discussed. A priori most plausible attribution of this effect to the cosmological expansion of the Universe turns out inadequate. A model of the observables developed in the frame of the relativistic background metric of the uniform isotropic Universe shows that the corresponding dynamical perturbations in the major planet motions are completely canceled out by the Einstein effect of dependence of the rate of the observer’s clock (that keeps the proper time) on the gravitational field, though separately values of these two effects are quite large and attainable with the accuracy achieved. Another tentative source of the secular rate of AU is the loss of the solar mass due to the solar wind and electromagnetic radiation but it amounts in only to 0.3 m/cy. Excluding other explanations that seem exotic (such as secular decrease of the gravitational constant) at present there is no satisfactory explanation of the detected secular increase of AU, at least in the frame of the considered uniform models of the Universe.     

Contraction of the solar nebula

The concept of Roche limit is applied to the Laplacian theory of the origin of the solar system to study the contraction of a spherical gas cloud (solar nebula). In the process of contraction of the solar nebula, it is assumed that the phenomenon of supersonic turbulent convection described by Prentice (1978) is operative and brings about the halt at various stages of contraction. It is found that the radius of the contracting solar nebula follows Titius-Bode law R _p = Ra^p, where R is the radius of the present Sun and a = 1.442. We call a the Roche's constant. The consequences of the relation are also discussed. The aim, here, is an attempt to explain, on the basis of the concept of Roche limit, the distribution of planets in the solar system and try to understand the physics underlying it.     

Magnetic clouds: Voyager observations between 2 and 4 AU

Magnetic clouds were observed in the solar wind between 2–4 AU by Voyagers 1 and 2, indicating that they are stable enough to persist without major changes out to such distances. The average size in radial extent of the clouds observed at these distances was 0.47 AU, compared to 0.25 for clouds observed at 1 AU. Assuming that these numbers are representative, we estimate that the clouds were expanding at a speed of the order of 45 km s^-1. This is consistent with the expansion speed derived from the difference of the speeds of the front and rear boundaries of the clouds, 33 km s^-1. The average Alfvén speed at the front and rear boundaries was 104 km s^-1, so our estimated expansion speed is nearly half of the Alfvén speed, consistent with an earlier estimate of the expansion speed of clouds between the Sun and 1 AU. The magnetic field configuration cannot be determined uniquely, but it is highly ordered and consistent with the passage of some kind of loop. The simple model of a magnetic tongue with magnetic field lines in planes, e.g., meridian planes, is not consistent with the data.     

On the solar tsunami

Some problems of qualitative theory of solar tsunami caused by rapid magnetic disturbances are discussed. The energy of tsunami is found sufficient to produce oscillations of quiescent prominences, facular brightenings after flares and also some flares and also some flares of moderate intensity. Coronal plasma satisfied the condition of incompressibility, but in the chromosphere the effects of incompressibility, but in the chromosphere the effects of compressibility generally must be taken into account. Long gravity waves with the wave-length of 10⁵ km can propagate on distances comparable with solar radius without sensible damping and dissipation. The solution of tsunami problem for a model of two-component ocean consists of two long gravity waves moving with different velocity in the chromosphere and corona. The effect of encounter of tsunami with magnetic fields are discussed.     

On the heliographic latitude dependence of the solar wind velocity

Plasma data from Pioneers 6–7 and from a variety of satellites operating near the Earth are used to investigate the heliographic latitude dependence of the solar wind bulk speed near the sunspot maximum. No evidence is found for a latitude effect: the latitudinal gradient, if any, turns out to be 2 km (sec degree)^–1, to be compared with the gradient of 10 km (sec degree)^–1 observed in periods of low or moderate solar activity.     

Solar Radius at Subterahertz Frequencies and Its Relation to Solar Activity

The Sun emits radiation at several wavelengths of the electromagnetic spectrum. In the optical band, the solar radius is 695?700 km, and this defines the photosphere, which is the visible surface of the Sun. However, as the altitude increases, the electromagnetic radiation is produced at other frequencies, causing the solar radius to change as a function of wavelength. These measurements enable a better understanding of the solar atmosphere, and the radius dependence on the solar cycle is a good indicator of the changes that occur in the atmospheric structure. We measure the solar radius at the subterahertz frequencies of 0.212 and 0.405 THz, which is the altitude at which these emissions are primarily generated, and also analyze the radius variation over the 11-year solar activity cycle. For this, we used radio maps of the solar disk for the period between 1999 and 2017, reconstructed from daily scans made by the Solar Submillimeter-wave Telescope (SST), installed at El Leoncito Astronomical Complex (CASLEO) in the Argentinean Andes. Our measurements yield radii of \(966.5'' \pm2.8''\) for 0.2 THz and \(966.5'' \pm2.7''\) for 0.4 THz. This implies a height of \(5.0 \pm2.0 \times10^{6}\) m above the photosphere. Furthermore, we also observed a strong anticorrelation between the radius variation and the solar activity at both frequencies.     

The geometrical height-scale and the pressure equilibrium in the sunspot umbra

Spectra of spots very near to the solar limb (limb distance 8) are used to determine the height difference between the levels of formation of the continuum and the line cores of 60 medium-strong Fraunhofer lines. For all lines (with Rowland Intensity < 10), this difference is < 1 (= 725 km) and well correlated with the Rowland intensity. The line absorption coefficient is calculated for some lines with known oscillator strength. This gives a possibility to deduce a value for the scale height of the umbra, which is found to be about 100 km, thus being equal to the photospheric scale height. Pure hydrostatic equilibrium exists, therefore, in the umbra, and vertical magnetic forces are negligible. Other methods for determining the scale height are discussed for comparison.The horizontal pressure equilibrium is discussed by taking into account the Wilson effect, and by neglecting dynamic terms (flow of matter). The magnetic field is confirmed to be force-free in higher layers (chromosphere). The pressure difference umbra-photosphere increases towards deeper layers, having a maximum at ^* - 1 which corresponds to about two times the magnetic pressure H ²/8. If rotational symmetry of the field is assumed, this can be explained by a minimum radius of curvature of the field lines of 1/4 spot radius.Mitteilungen aus dem Fraunhofer Institut Nr. 90.     

The formation of Mg i 4571 Å in the solar atmosphere

An analysis of the 4571 Å line of neutral magnesium is presented in which one-dimensional macroscopic velocity fields are included. It is shown that gradients over restricted heights in the vertical and horizontal components of the velocity field of order -0.005 s^–1 and -0.004 s^–1 (such that velocity towards the observer decreases as height increases), respectively, result in asymmetries in the computed line profile similar to those observed. The heights in the solar atmosphere at which these velocity gradients exist are shown to be very critical in reproducing the observations. It was found that the best results were obtained when the gradients existed in the height range from 200 km to 300 km below the temperature minimum. The results indicate that for the Mg i 4571 Å line model calculations that do not include one-dimensional flow velocities may safely be compared with frequency-averaged observations.     

Synoptic Maps of Solar Wind: Comparison of IPS Data and the NOAA/SEC Version of the Wang and Sheeley Model

Since the 1970s, the Solar-Terrestrial Environment Laboratory, Japan, has been publishing synoptic maps of solar wind velocity prepared using the technique of interplanetary scintillation. These maps, known as V-maps, are useful to study the global distribution of solar wind in the heliosphere. As the Earth-orbiting satellites are unable to probe regions outside the ecliptic, it is important to exploit the scope of interplanetary scintillation to study the solar wind properties at these regions and their relation with coronal features. It has been shown by Wang and Sheeley that there exists an inverse correlation between rate of magnetic flux expansion and the solar wind velocity. The NOAA/Space Environment Center daily updated version of the Wang and Sheeley model has been used to produce synoptic maps of solar wind velocity and magnetic field polarity for individual Carrington rotations. The predictions of the model at 1 AU have been found to be in good agreement with the observed values of the same. The present work is a comparison of the synoptic maps on the source surface using the interplanetary scintillation measurements from Japan and the NOAA/SEC version of the Wang and Sheeley model. The two results agree near the equatorial regions and the slow solar wind locations are consistent most of the times. However, at higher latitudes within ±60°, the wind velocities differ considerably. In the Wang and Sheeley model the highest speed obtained is 600 km s^–1 whereas in the IPS results velocities as high as 800 km s^–1 have been detected. The paper discusses the possible causes for this discrepancy and suggestion to improve the agreement between the two results.     

Kinematics of Stars from the TGAS (Gaia DR1) Catalogue

Based on the stellar proper motions of the TGAS (Gaia DR1) catalogue, we have analyzed the velocity field of main-sequence stars and red giants from the TGAS catalogue with heliocentric distances up to 1.5 kpc. We have obtained four variants of kinematic parameters corresponding to different methods of calculating the distances from the parallaxes of stars measured with large relative errors. We have established that within the Ogorodnikov–Milne model changing the variant of distances affects significantly only the solar velocity components relative to the chosen centroid of stars, provided that the solution is obtained in narrow ranges of distances (0.1 kpc). The estimates of all the remaining kinematic parameters change little. This allows the Oort coefficients and related Galactic rotation parameters as well as all the remaining Ogorodnikov–Milne model parameters (except for the solar terms) to be reliably estimated irrespective of the parallax measurement accuracy. The main results obtained from main-sequence stars in the range of distances from 0.1 to 1.5 kpc are: A = 16.29 ± 0.06 km s^?1 kpc^?1, B = ?11.90 ± 0.05 km s^?1 kpc^?1, C = ?2.99 ± 0.06 km s^?1 kpc^?1, K = ?4.04 ± 0.16 km s^?1 kpc^?1, and the Galactic rotation period P = 217.41 ± 0.60 Myr. The analogous results obtained from red giants in the range from 0.2 to 1.6 kpc are: the Oort constants A = 13.32 ± 0.09 km s^?1 kpc^?1, B = ?12.71 ± 0.06 km s^?1 kpc^?1, C = ?2.04 ± 0.08 km s^?1 kpc^?1, K = ?2.72 ± 0.19 km s^?1 kpc^?1, and the Galactic rotation period P = 236.03 ± 0.98 Myr. The Galactic rotation velocity gradient along the radius vector (the slope of the Galactic rotation curve) is ?4.32 ± 0.08 km s^?1 kpc^?1 for main-sequence stars and ?0.61 ± 0.11 km s^?1 kpc^?1 for red giants. This suggests that the Galactic rotation velocity determined from main-sequence stars decreases with increasing distance from the Galactic center faster than it does for red giants.     

Limb observations of the 12.32-micron Mg I emission line during the 1994 annular eclipse

We determined the limb profile of the extremely Zeeman-sensitive emission line of Mg i at 12.32 m (811.58 cm–1) during the May 1994 annular eclipse, using the 3.5-m ARC telescope at the Apache Point site on Sacramento Peak, New Mexico. Spectra were recorded at 0.1 cm–1 spectral resolution and 1 s time resolution using a cryogenic grating spectrometer. The time derivatives of the observed line energy and continuum intensity were used to infer high-resolution profiles of the solar limb. Data were obtained at second contact only, since clouds prevented observations at third contact. We find that the emission line energy peaks very close to the 12 m continuum limb. This agrees with our result from the 1991 total eclipse over Mauna Kea, and also with non-LTE radiative transfer theory for this line, which predicts an upper-photospheric origin. However, in 1991, line emission remained observable as high as 2000 km above the continuum limb, whereas the 1994 data show observable emission to only 500 km. This difference greatly exceeds any applicable errors, or sensitivity differences in either data set, and must be attributed to spatial and/or temporal inhomogeneities in the solar limb emission of this line. We discuss possible causes of these inhomogeneities, and implications for observations at far-IR and submillimeter wavelengths.     

Solar flares and the cosmic ray intensity

The relationship between the cosmic ray intensity and solar activity during solar cycle 20 is discussed. A model is developed whereby it is possible to simulate the observed cosmic ray intensity from the observed number of solar flares of importance 1. This model leads to a radius for the modulation region of 60–70 AU. It is suggested that high speed solar streams also made a small contribution to the modulation of cosmic rays during solar cycle 20.     

A model of the sunspot umbra

Equations governing the structure of the umbra of a single spot have been integrated on the spot-axis. It is shown that a consistent umbral model can be obtained only for a narrow range of the electron pressures at the spot surface. The spot center is found to be at a depth of about 400 km below the normal solar surface. The reduced energy flux observed at the surface is assumed to be due to the effect of the spot-magnetic field on subphotospheric convection and an empirical factor is introduced to take into account the reduction in the convective energy flux. With an inferred expression for as a function of the internal and magnetic-energy density it is shown that in a consistent model the physical variables in the spot approach their ambient values at about 2330 km below the undisturbed solar surface and at the same depth the energy flux approaches the normal solar value and the magnetic interference with convection vanishes. The present investigation is a refinement of an earlier paper by Chitre (1963).Supported in part by the Office of Naval Research [Nonr-220(47)] and the National Science Foundation [GP-5391].     

Fabry-Pérot line profiles in the λ5303 å and λ6374 å coronal lines obtained during the 1983 Indonesian eclipse

During the total solar eclipse of 11 June, 1983, an imaging dual-channel Fabry-Pérot interferometer was used to obtain line profiles simultaneously in the green 5303 Å [Fe xiv] and the red 6374 Å [Fe x] coronal lines at various positions in the corona. Extensive microdensitometry followed by multi-Gaussian curve-fitting analysis has resulted in the determination of coronal temperatures and velocity separations between different pockets of coronal gas in the line of sight over a large extent of the corona. Fewer high temperature zones are to be found in the corona of 1983 compared with our similar green-line measurements of the solar maximum corona of 1980. The data are consistent with a temperature maximum occurring at 1.2 R , as found at the 1980 eclipse, but our new data are insufficient to observe farther out than this radius and so determine the position of a maximum. The velocity field in the corona at the 1983 eclipse is less structured compared with that at the 1980 eclipse and is mainly confined to the zone 20–30km s^–1.     

A comment on the suspected solar neutrino-solar activity connection

Recently, it has been proposed that there exists a highly statistically significant (at 98% level of confidence) relationship between³⁷Ar production rate (viz., solar neutrinos) and the Ap geomagnetic index (viz., solar particles), based on the _X -square goodness-of-fit test and correlation analysis, for the interval 1970–1990. While a relationship between the two parameters, indeed, seems to be discernible, the strength of the relationship has been overstated. Instead of being significant at the afore-mentioned level of confidence, the relationship is found to be significant at only 95% level of confidence, based on Yates' modification to the _X -square test for 2 × 2 contingency tables. Likewise, while correlation analysis yields a value ofr = 0.2691, it is important to note that such a value suggests that only about 7% of the variance can be explained by the inferred correlation and that the remaining 93% of the variance must be attributed to other sources.     

Time variations of the Heliospheric Termination Shock Radius

In this work we study the temporal variation of the heliospheric termination shock radius using in-ecliptic combined measurements from different spacecraft at 1 AU near the Earth. The results show that the radius of the heliospheric termination shock varies in time with a period of 11 years. During some 11-year time periods the shock radius anti-correlates with the solar cycle activity, specifically with the sunspot number. The average radius is approximately 115 AU with minimum value 80 AU and maximum value 150 AU. These values are the upper limits since we do not take into account the charge exchange effects of solar wind with the interstellar neutrals. We also compare the results with those from other spacecraft (Helios 1 and Voyager 2). We find that Helios 1 measurements give almost the same result as the one obtained from measurements at 1 AU while Voyager 2 measurements give a heliospheric termination shock radius approximately 15 AU lower.     

Differential rotation,meridional and random motions of the solar Ca+ network

From high precision computer controlled tracings of bright Ca⁺-mottles we investigated differential rotation, meridional and random motions of these chromospheric fine structures. The equatorial angular velocity of the Ca⁺-mottles agrees well with that of sunspots (14°.50 per day, sidereal) and is 5 % higher than for the photosphere. The slowing down with increasing latitude is larger than for sunspots. Hence in higher latitudes Ca⁺-mottles rotate as fast as the photospheric plasma. A systematic meridional motion of about 0.1 km s^–1 for latitudes around 10° was found. The Ca⁺-mottles show horizontal random motions due to the supergranular flow pattern with an rms velocity of about 0.15 km s^–1. We finally investigated the correctness of the solar rotation elements i and derived by Carrington (1863).     

Statistical and computational uncertainties in atmospheric profiles from radio occultation: Mariner 10 at Venus

Radio occultation studies of planetary atmospheres and ionospheres are based on measurements of the frequency and amplitude of the received radio signal. These measurements have random errors due to noise in the receiving system and linearly mapped into atmospheric profiles to give uncertainties can be estimated from the data and linearly mapped into atmospheric profiles to give uncertainties in temperature, T, pressure, p, and absorption profiles. For Mariner 10 occultation immersion at Venus, the standard deviations of T and p due to receiver noise are less than 2° K and 2 mbar over the range of radii from 6087 to 6140 km, based on our reduction from analog, “ open-loop” data. The temperature has a systematic error due to boundary uncertainty, estimated to be 50°K at 6140 km, that decays rapidly with depth; below 6117 km, it is less than 0.5°K. For the attenuation profile, systematic errors incurred during our calculations are more important than statistical errors. We estimate an upper bound to the uncertainty which is 32% at the peak value of absorption, which is about 0.01 db/km and occurs at a radius of 6096 km. A calculation of the 95% confidence limits for T profiles indicates that the local deviations are statistically significant to about 1°K or less. We have also analyzed “closed-loop” data to give temperature profiles which deviate from the open-loop results by less than 0.2°K below 6110 km but by as much as 2°K in the upper atmosphere. For the same occultation and the same boundary conditions, our closed-loop T-p profile is within 2°K of that of P. D. Nicholson and D. O. Muhleman but differs from those derived by A. J. Kliore by as much as 10°K. We cannot account for deviations as large as the latter by minor differences in trajectory information or computational methods.