Solar quadrupole moment and purely relativistic gravitation contributions to Mercury's perihelion advance

The perihelion advance of the orbit of Mercury has long been one of the observational cornerstones for testing General Relativity (G.R.).The main goal of this paper is to discuss how, presently, observational and theoretical constraints may challenge Einstein's theory of gravitation characterized by β=γ=1. To achieve this purpose, we will first recall the experimental constraints upon the Eddington-Robertson parameters γ,β and the observational bounds for the perihelion advance of Mercury, Δω_obs. A second point will address the values given, up to now, to the solar quadrupole moment by several authors. Then, we will briefly comment why we use a recent theoretical determination of the solar quadrupole moment, J ₂=(2.0 ± 0.4) 10^-7, which takes into account both surfacic and internal differential rotation, in order to compute the solar contribution to Mercury's perihelion advance. Further on, combining bounds on γ and J ₂ contributions, and taking into account the observational data range for Δω_obs,we will be able to give a range of values for β. Alternatively, taking into account the observed value of Δω_obs, one can deduce a dynamical estimation of J ₂ in the setting of G.R. This point is important as it provides a solar model independent estimation that can be confronted with other determinations of J ₂ based upon solar theory and solar observations (oscillation data, oblateness...). Finally, a glimpse at future satellite experiments will help us to understand how stronger constraints upon the parameter space (γω J ₂) as well as a separation of the two contributions (from the quadrupole moment, J ₂, or purely relativistic, 2α²+2αγ–β) might be expected in the future. This revised version was published online in July 2006 with corrections to the Cover Date.     

Long-Term Variations in the Growth and Decay Rates of Sunspot Groups

Using the combined Greenwich (1874 – 1976) and Solar Optical Observatories Network (1977 – 2009) data on sunspot groups, we study the long-term variations in the mean daily rates of growth and decay of sunspot groups. We find that the minimum and the maximum values of the annually averaged daily mean growth rates are ≈ 52% day⁻¹ and ≈ 183% day⁻¹, respectively, whereas the corresponding values of the annually averaged daily mean decay rates are ≈ 21% day⁻¹ and ≈ 44% day⁻¹, respectively. The average value (over the period 1874 – 2009) of the growth rate is about 70% more than that of the decay rate. The growth and the decay rates vary by about 35% and 13%, respectively, on a 60-year time scale. From the beginning of Cycle 23 the growth rate is substantially decreased and near the end (2007 – 2008) the growth rate is lowest in the past about 100 years. In the extended part of the declining phase of this cycle, the decay rate steeply increased and it is largest in the beginning of the current Cycle 24. These unusual properties of the growth and the decay rates during Cycle 23 may be related to cause of the very long declining phase of this cycle with the unusually deep and prolonged current minimum. A ≈ 11-year periodicity in the growth and the decay rates is found to be highly latitude and time dependent and seems to exist mainly in the 0° – 10° latitude interval of the southern hemisphere. The strength of the known approximate 33 – 44-year modulation in the solar activity seems to be related to the north-south asymmetry in the growth rate. Decreasing and increasing trends in the growth and the decay rates indicate that the next 2 – 3 solar cycles will be relatively weak.     

Power Spectrum Analysis of Physikalisch-Technische Bundesanstalt Decay-Rate Data: Evidence for Solar Rotational Modulation

Evidence for an anomalous annual periodicity in certain nuclear-decay data has led to speculation on a possible solar influence on nuclear processes. We have recently analyzed data concerning the decay rates of ³⁶Cl and ³²Si, acquired at the Brookhaven National Laboratory (BNL), to search for evidence that might be indicative of a process involving solar rotation. Smoothing of the power spectrum by weighted-running-mean analysis leads to a significant peak at frequency 11.18 year⁻¹, which is lower than the equatorial synodic rotation rates of the convection and radiative zones. This article concerns measurements of the decay rates of ²²⁶Ra acquired at the Physikalisch-Technische Bundesanstalt (PTB) in Germany. We find that a similar (but not identical) analysis yields a significant peak in the PTB dataset at frequency 11.21 year⁻¹, and a peak in the BNL dataset at 11.25 year⁻¹. The change in the BNL result is not significant, since the uncertainties in the BNL and PTB analyses are estimated to be 0.13 year⁻¹ and 0.07 year⁻¹, respectively. Combining the two running means by forming the joint power statistic leads to a highly significant peak at frequency 11.23 year⁻¹. We will briefly comment on the possible implications of these results for solar physics and for particle physics.     

Sunspot Group Decay

We examine daily records of sunspot group areas (measured in millionths of a solar hemisphere or μHem) for the last 130 years to determine the rate of decay of sunspot group areas. We exclude observations of groups when they are more than 60° in longitude from the central meridian and only include data when at least three days of observations are available following the date of maximum area for a group’s disk passage. This leaves data for over 18 000 measurements of sunspot group decay. We find that the decay rate increases linearly from 28 μHem day⁻¹ to about 140 μHem day⁻¹ for groups with areas increasing from 35 μHem to 1000 μHem. The decay rate tends to level off for groups with areas larger than 1000 μHem. This behavior is very similar to the increase in the number of sunspots per group as the area of the group increases. Calculating the decay rate per individual sunspot gives a decay rate of about 3.65 μHem day⁻¹ with little dependence upon the area of the group. This suggests that sunspots decay by a Fickian diffusion process with a diffusion coefficient of about 10 km² s⁻¹. Although the 18 000 decay rate measurements are lognormally distributed, this can be attributed to the lognormal distribution of sunspot group areas and the linear relationship between area and decay rate for the vast majority of groups. We find weak evidence for variations in decay rates from one solar cycle to another and for different phases of each sunspot cycle. However, the strongest evidence for variations is with latitude and the variations with cycle and phase of each cycle can be attributed to this variation. High latitude spots tend to decay faster than low latitude spots.     

A Statistical Study of Rhessi Flares

A statistical analysis of RHESSI X-ray flares in the 12–25 keV band during the period from February 2002 to June 2005 is presented. We found that a power-law with an index of 1.80± 0.02 can fit well the frequency distribution of the peak count rates. This power-law does not change significantly with time. However, the frequency distribution of the flare durations cannot be fitted well by a single power-law. There is a weak correlation between the peak count rates and the characteristic times like rise times, decay times, or durations. But the correlation between the rise times and decay times seems to be strong. We discuss the results obtained and compare them with previous works. The frequency distribution of rise times for the sub-group events with a similar magnitude of peak count rates is also shown. In particular, we propose a new parameter R _a , the growth factor of the count rate, defined as the peak count rate divided by the rise time, to reflect the characteristics of the rising phases of flares. The distribution of R _a is shown and discussed.     

Observations of the sodium tail of Mercury

Cross-sections of the sodium emission tail of Mercury were measured at various distances down the tail when Mercury was moving away from the Sun (true anomaly angles <180°), and again when Mercury was moving towards the Sun (true anomaly angles >180°). As predicted in early modeling studies, significant differences were expected between these two cases, as the result of Doppler shifts to higher solar intensity in the former case, and to lower solar intensity for the latter case. For observations with Mercury moving away from the Sun, the sodium tail was observed out to about 40,000 kilometers (16 Mercury radii, RM) downstream, expanding, on average, at a rate of 1.9±0.3 km/s. The source rates for sodium generation from Mercury into the tail were found to be in the range 2-5×¹⁰²³ atoms/s, corresponding to between 1 and 10% of the estimated total sodium production rate on the planet. The limiting value of radiation acceleration required to produce an observable sodium tail was estimated to be 112±24 cm/s². For observations where Mercury was moving towards the Sun, the emission intensity in the sodium tail decreased very rapidly with distance downstream, disappearing entirely beyond 12,000 (6 RM) kilometers for radiation accelerations of 128.7 and 135.4 cm/s². For smaller radiation accelerations, the sodium tail was not detectable at all, yielding a limiting value for tail generation of about 122±2 cm/s². Interpretation of the limiting radiation acceleration values suggests that the process that generates the sodium tail yields atoms with energies greater than 3 eV. Particle sputtering is the most reasonable source process.     

Some magnetized bulk viscous string cosmological models in?General Relativity

Some Bianchi type-I viscous fluid string cosmological models with magnetic field are investigated. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density ξ(t)=ξ ₀ ρ ^m , where ξ ₀ and m are constants. To get a determinate model, we assume conditions ρ=(1+ω)λ, where ρ is rest energy density, ω a positive constant and λ the string tension density and expansion θ is proportional to eigen value σ ₁¹ of the shear tensor σ _j ⁱ . The behaviour of the models from physical and geometrical aspects in presence and absence of magnetic field is discussed.      

Regularized Reconstruction of the Differential Emission Measure from Solar Flare Hard X-Ray Spectra

We address the problem of how to test whether an observed solar hard X-ray bremsstrahlung spectrum (I(∊)) is consistent with a purely thermal (locally Maxwellian) distribution of source electrons, and, if so, how to reconstruct the corresponding differential emission measure (ξ(T)). Unlike previous analysis based on the Kramers and Bethe-Heitler approximations to the bremsstrahlung cross-section, here we use an exact (solid-angle-averaged) cross-section. We show that the problem of determining ξ(T) from measurements of I(∊) invOlves two successive inverse problems: the first, to recover the mean source-electron flux spectrum ( [`(F)]\overline{F} (E)) from I(∊) and the second, to recover ξ(T) from [`(F)]\overline{F} (E). We discuss the highly pathological numerical properties of this second problem within the framework of the regularization theory for linear inverse problems. In particular, we show that an iterative scheme with a positivity constraint is effective in recovering δ-like forms of ξ(T) while first-order Tikhonov regularization with boundary conditions works well in the case of power-law-like forms. Therefore, we introduce a restoration approach whereby the low-energy part of [`(F)]\overline{F} (E), dominated by the thermal component, is inverted by using the iterative algorithm with positivity, while the high-energy part, dominated by the power-law component, is inverted by using first-order regularization. This approach is first tested by using simulated [`(F)]\overline{F} (E) derived from a priori known forms of ξ(T) and then applied to hard X-ray spectral data from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI).     

Sharp Changes of Solar Wind Ion Flux and Density Within and Outside Current Sheets

Analysis of the Interball-1 spacecraft data (1995 – 2000) has shown that the solar wind ion flux sometimes increases or decreases abruptly by more than 20% over a time period of several seconds or minutes. Typically, the amplitude of such sharp changes in the solar wind ion flux (SCIFs) is larger than 0.5×10⁸ cm⁻² s⁻¹. These sudden changes of the ion flux were also observed by the Solar Wind Experiment (SWE), on board the Wind spacecraft, as the solar wind density increases and decreases with negligible changes in the solar wind velocity. SCIFs occur irregularly at 1 AU, when plasma flows with specific properties come to the Earth’s orbit. SCIFs are usually observed in slow, turbulent solar wind with increased density and interplanetary magnetic field strength. The number of times SCIFs occur during a day is simulated using the solar wind density, magnetic field, and their standard deviations as input parameters for a period of five years. A correlation coefficient of ∼0.7 is obtained between the modelled and the experimental data. It is found that SCIFs are not associated with coronal mass ejections (CMEs), corotating interaction regions (CIRs), or interplanetary shocks; however, 85% of the sector boundaries are surrounded by SCIFs. The properties of the solar wind plasma for days with five or more SCIF observations are the same as those of the solar wind plasma at the sector boundaries. One possible explanation for the occurrence of SCIFs (near sector boundaries) is magnetic reconnection at the heliospheric current sheet or local current sheets. Other probable causes of SCIFs (inside sectors) are turbulent processes in the slow solar wind and at the crossings of flux tubes.     

The Variation of Solar Wind Correlation Lengths Over Three Solar Cycles

We present the results of a study of solar wind velocity and magnetic field correlation lengths over the last 35 years. The correlation length of the magnetic field magnitude λ _|B| increases on average by a factor of two at solar maxima compared to solar minima. The correlation lengths of the components of the magnetic field l_BXYZ\lambda_{B_{XYZ}} and of the velocity l_VYZ\lambda_{V_{YZ}} do not show this change and have similar values, indicating a continual turbulent correlation length of around 1.4×10⁶ km. We conclude that a linear relation between λ _|B|, VB ², and Kp suggests that the former is related to the total magnetic energy in the solar wind and an estimate of the average size of geoeffective structures, which is, in turn, proportional to VB ². By looking at the distribution of daily correlation lengths we show that the solar minimum values of λ _|B| correspond to the turbulent outer scale. A tail of larger λ _|B| values is present at solar maximum causing the increase in mean value.     

Combined Analysis of Solar Neutrino and Solar Irradiance Data: Further Evidence for Variability of the Solar Neutrino Flux and Its Implications Concerning the Solar Core

A search for any particular feature in any single solar neutrino dataset is unlikely to establish variability of the solar neutrino flux since the count rates are very low. It helps to combine datasets, and in this article we examine data from both the Homestake and GALLEX experiments. These show evidence of modulation with a frequency of 11.85 year⁻¹, which could be indicative of rotational modulation originating in the solar core. We find that precisely the same frequency is prominent in power spectrum analyses of the ACRIM irradiance data for both the Homestake and GALLEX time intervals. These results suggest that the solar core is inhomogeneous and rotates with a sidereal frequency of 12.85 year⁻¹. From Monte Carlo calculations, it is found that the probability that the neutrino data would by chance match the irradiance data in this way is only 2 parts in 10 000. This rotation rate is significantly lower than that of the inner radiative zone (13.97 year⁻¹) as recently inferred from analysis of Super-Kamiokande data, suggesting that there may be a second, inner tachocline separating the core from the radiative zone. This opens up the possibility that there may be an inner dynamo that could produce a strong internal magnetic field and a second solar cycle.     

Energetic protons from the solar flare of March 24, 1966

Ten to 100 meV protons from the solar flare of March 24, 1966 were observed on the University of California scintillation counter on OGO-I. The short rise and decay times observed in the count rates of the 32 channels of pulse-height analysis show that scattering of the protons by the interplanetary field was much less important in this event than in previously observed proton flares. A diffusion theory in which D = M _r is found to be inadequate to account for the time behavior of the count rates of this event. Small fluctuations of the otherwise smooth decay phase may be due to flare protons reflected from the back of a shock front, which passed the earth on March 23.     

Periodic Appearance of Coronal Holes and the Related Variation of Solar Wind Parameters

We compared the variability of coronal hole (CH) areas (determined from daily GOES/SXI images) with solar wind (daily ACE data) and geomagnetic parameters for the time span 25 January 2005 until 11 September 2005 (late declining phase of solar cycle 23). Applying wavelet spectral analysis, a clear 9-day period is found in the CH time series. The GOES/SXI image sequence suggests that this periodic variation is caused by a mutual triangular distribution of CHs ∼120° apart in longitude. From solar wind parameters a 9-day periodicity was obtained as well, simultaneously with the 9-day period in the CH area time series. These findings provide strong evidence that the 9-day period in solar wind parameters, showing up as higher harmonic of the solar rotation frequency, is caused by the “periodic” longitudinal distribution of CHs on the Sun recurring for several solar rotations. The shape of the wavelet spectrum from the Dst index matches only weakly with that from the CH areas and is more similar to the wavelet spectrum of the solar wind magnetic field magnitude. The distinct 9-day period does not show up in sunspot group areas which gives further evidence that the solar wind modulation is strongly related to CH areas but not to active region complexes. The wavelet power spectra for the whole ACE data range (∼1998 – 2006) suggest that the 9-day period is not a singular phenomenon occurring only during a specific time range close to solar minimum but is occasionally also present during the maximum and decay phase of solar cycle 23. The main periods correspond to the solar rotation (27^d) as well as to the second (13.5^d) and third (9^d) harmonic. Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users.     

On the homestake neutrino data

³⁷ Ar production rates from the Homestake experiment suggest a possible anticorrelation between solar neutrino flux and solar activity. In this paper we present results from linear correlation analyses between Homestake data and several solar activity parameters in the period 1970–1990. Our results support the hypothesis that Homestake neutrino fluxes exhibit a (positive or negative) correlation with those parameters, but they also suggest that the heliomagnetic field in the subphotosphere could be responsible for the observed flux modulation.     

A new class of bulk viscous universe with time dependent deceleration parameter and Λ-term

A new class of exact solutions of Einstein’s field equations with a bulk viscous fluid for an LRS Bianchi type-Ia obtained by using a time dependent deceleration parameter and cosmological term Λ. The coefficient of bulk viscosity is assumed to be a power function of mass density (ξ=ξ ₀ ρ ⁿ ). We have obtained a general solution of the field equations from which six models of the universe are derived: exponential, polynomial and sinusoidal form respectively. The behaviour of these models of the universe are also discussed in the frame of reference of recent supernovae Ia observations.      

The Non-Gravitational Perturbations impact on the BepiColombo Radio Science Experiment and the key rôle of the ISA accelerometer: direct solar radiation and albedo effects

The paper is focused on the estimate of the impact of the non-gravitational perturbations on the orbit of the Mercury Planetary Orbiter (MPO), one of the two spacecrafts that will be placed in orbit around the innermost planet of the solar system by the BepiColombo space mission. The key rôle of the Italian Spring Accelerometer (ISA), that has been selected by the European Space Agency (ESA) to fly on-board the MPO, is outlined. In the first part of the paper, through a numerical simulation and analysis we have estimated, over a time span of several years, the long-period behaviours of the disturbing accelerations produced by the incoming direct solar radiation pressure, and the indirect effects produced by Mercury’s albedo. The variations in the orbital parameters of the spacecraft, together with their spectral contents, have been estimated over the analysed period. The direct solar radiation pressure represents the strongest non-gravitational perturbation on the MPO in the very complex radiation environment of Mercury. The order-of-magnitude of this acceleration is quite high, about 10^?6 m/s², because of the proximity to the Sun and the large area-to-mass ratio of the spacecraft. In the second part of the paper, we concentrated upon the short-period effects of direct solar radiation pressure and Mercury’s albedo. In particular, the disturbing accelerations have been compared with the ISA measurement error and the advantages of an on-board accelerometer are highlighted with respect to the best modelling of the non-gravitational perturbations in the strong radiation environment of Mercury. The readings from ISA, with an intrinsic noise level of about $10^{-9}\,m/s^{2}/\sqrt{Hz}The paper is focused on the estimate of the impact of the non-gravitational perturbations on the orbit of the Mercury Planetary Orbiter (MPO), one of the two spacecrafts that will be placed in orbit around the innermost planet of the solar system by the BepiColombo space mission. The key r?le of the Italian Spring Accelerometer (ISA), that has been selected by the European Space Agency (ESA) to fly on-board the MPO, is outlined. In the first part of the paper, through a numerical simulation and analysis we have estimated, over a time span of several years, the long-period behaviours of the disturbing accelerations produced by the incoming direct solar radiation pressure, and the indirect effects produced by Mercury’s albedo. The variations in the orbital parameters of the spacecraft, together with their spectral contents, have been estimated over the analysed period. The direct solar radiation pressure represents the strongest non-gravitational perturbation on the MPO in the very complex radiation environment of Mercury. The order-of-magnitude of this acceleration is quite high, about 10⁻⁶ m/s², because of the proximity to the Sun and the large area-to-mass ratio of the spacecraft. In the second part of the paper, we concentrated upon the short-period effects of direct solar radiation pressure and Mercury’s albedo. In particular, the disturbing accelerations have been compared with the ISA measurement error and the advantages of an on-board accelerometer are highlighted with respect to the best modelling of the non-gravitational perturbations in the strong radiation environment of Mercury. The readings from ISA, with an intrinsic noise level of about in the frequency band of 3·10⁻⁵–10⁻¹ Hz, guarantees a very significant reduction of the non-gravitational accelerations impact on the space mission accuracy, especially of the dominant direct solar radiation pressure.     

Observations of the December 6, 2006 solar flare: Electron acceleration and plasma heating

The flare plasma temperature calculated from GOES-11 (1.5–12.4 and 3.1–24.8 keV) data is compared with the solar nonthermal fluxes in various energy ranges in the December 6, 2006 event. Particle acceleration and plasma heating episodes took place in the pre-flare and impulsive phases; a hard (ACS SPI > 150 keV) X-ray emission was observed 5 min before the onset of the GOES X-ray flare and was not accompanied by a temperature rise. A close correlation has been found between the flare plasma temperature and the hard X-ray intensity. The temperature delayed by 0.4 min turned out to be directly proportional to the logarithm of the ACS SPI count rate within the first 3 min of the impulsive phase. This shows that the accelerated electrons responsible for the X-ray emission were the main plasma heating source in the pre-flare and impulsive phases. The correlation between the temperature and the hard X-ray intensity disappears after the observation of a resonance peak at a frequency of 245 MHz. Significant electron fluxes may no longer be able to effectively heat the expanding plasma when its density in the interaction region reaches ∼10⁹ cm⁻³. The observations of the July 23, 2002 and December 5, 2006 events confirm the trends found.     

Simulating stochastically excited oscillations: The mode lifetime of ξ Hya

The discovery of solar-like oscillations in the giant star ξ Hya (G7 III) was reported by Frandsen et al. (2002). Their frequency analysis was very limited due to alias problems in the data set (caused by single-site observations). The extent to which the aliasing affected their analysis was unclear due to the unknown damping time of the stellar oscillation modes. In this paper we describe a simulator created to generate time series of stochastically excited oscillations, which takes as input an arbitrary window function and includes both white and non-white noise. We also outline a new method to compare a large number of simulated time series with an observed time series to determine the damping time, amplitude, and limited information on the degree of the stochastically excited modes. For ξ Hya we find the most likely amplitude to be ∼ 2 m s⁻¹, in good agreement with theory (Houdek and Gough, 2002), and the most likely damping time to be ∼ 2 days, which is much shorter than the theoretical value of 15–20 days calculated by Houdek and Gough (2002).     

Constraints on the176Lu cosmochronometer

In an endeavour to resolve reported discrepancies in the value of the branching ratio of¹⁷⁶Lu at astrophysical energies, a new determineation of the¹⁷⁵Lu (nγ)^176mLu capture cross section has been measured as 958 ± 58 mb. This gives a value of the branching ratio of 0.21 ±0.05. This result indicates that some reequilibration of the ground and isomeric states of¹⁷⁶Lu occurs in stellar environments undergoing s-process nucleosynthesis, and confirms that¹⁷⁶Lu is not a reliable cosmochronometer. However the very existence of¹⁷⁶Lu in the solar system implies that the ground state of¹⁷⁶Lu was not completely depopulated, and provides the possibility of using this nuclide as a sensitive thermometer for stellar processes.