Differential rotation and meridional flow in the solar convection zone and beneath

The influence of the basic rotation on anisotropic and inhomogeneous turbulence is discussed in the context of differential rotation theory. An improved representation for the original turbulence leads to a Λ‐effect which complies with the results of 3D numerical simulations. The resulting rotation law and meridional flow agree well with both the surface observations (∂Ω/∂r < 0 and meridional flow towards the poles) and with the findings of helioseismology. The computed equatorward flow at the bottom of convection zone has an amplitude of about 10 m/s and may be significant for the solar dynamo. The depth of the meridional flow penetration into the radiative zone is proportional to ν^0.5_core, where ν_core is the viscosity beneath the convection zone. The penetration is very small if the tachocline is laminar. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Meridional flow profile measurements with SOHO/MDI

We present meridional flow measurements of the Sun using a novel helioseismic approach for analyzing SOHO/MDI data in order to push the current limits in radial depth. Analyzing three consecutive months of data during solar minimum, we find that the meridional flow is as expected poleward in the upper convection zone, turns equatorward at a depth of around 40 Mm (∼ 0.95 R_⊙), and possibly changes direction again in the lower convection zone. This may indicate two meridional circulation cells in each hemisphere, one beneath the other. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effects of convection electric field on the distribution of ring current type protons

The topology of the boundaries of penetration (or inversely the boundaries of the forbidden regions) of 90° pitch angle equatorial protons with energies less than 100 keV are explored for an equatorial convection E-field which is directed in general from dawn to dusk. Due to the dependence of drift path on energy (or magnetic moment) complex structural features are expected in the proton energy spectra detected on satellites since the penetration distance of a proton is not a monotonically increasing or decreasing function of energy. During a storm when the convection E is enhanced, model calculations predict elongations of the forbidden regions analogous to plasmatail extensions of the plasmasphere. Following a reduction in the convection field, spiral-structured forbidden regions can occur. Structural features inherent to large scale convection field changes may be seen in the noselike proton spectrograms observed near dusk by instrumentation on the satellite Explorer 45 (S³) (Smith and Hoffman, 1974). These nose events are modelled by using an electric field model developed originally by Volland (1973). The strength of the field is related to K_p through night-time equatorial plasmapause measurements.     

Convective flux in the solar photosphere as determined from fluctuations

The fractional convective flux πF _c (x _c /πF) is computed for the effective level x _c = logτ _c = 0.125, using bi-dimensional co-spectra for relative continuum-brightness fluctuations ΔI and radial velocity fluctuations ΔV measured for the C _i 5052.16 spectral line. A more uncertain flux for x _Fe ≈ - 0.9 is obtained for the Fe _i 5049.83 line. Since the results (Figure 1) incorporate current uncertainties in RMS _ΔI , RMS _ΔV and RMS _ΔT (x), where ΔT are photospheric temperature fluctuations, they must be considered qualitative until these uncertainties are appreciably reduced. The requirement that the fractional convective flux < 1, places restrictions on these uncertainties which suggest that current RMS _ΔT (x)'s are too large. The results confirm the importance of overshoot at the top of the solar hydrogen convection zone and suggest a non-negligible fractional convective flux throughout the lower photosphere. Qualitatively, they do not agree with the predictions of the generally-used, local, mixing-length theory or those of Parsons' (1969) modified mixing-length theory. However, qualitative agreement with the predictions of the non-local, generalized mixing-length theory of Spiegel (1963) and with the non-local theory of Ulrich (1970) cannot be considered as observational confirmation of these theories.     

On the origin and initial temperature of Jupiter and Saturn

A two-stage growth of the giant planets, Jupiter and Saturn, is considered, which is different from the model of contraction of large gaseous protoplanets. In the first stage, within a time of ～3 × 10⁷ years in Jupiter's zone and ～2 × 10⁸ years in Saturn's zone, a nucleus forms from condensed (solid) material having the mass, ～10²⁸ g, necessary for the beginning of acceleration. The second stage may gravitating body, and a relatively slow accretion begins until the mass of the planet reaches ～10 m_⊕. Then a rapid accretion begins with the critical radius less than the radius of the Hill lobe, so that the classical formulae for the rate of accretion may be applied. At a mass m > m₁ ≈ 50 m_⊕ accretion proceeds slower than it would according to these formulae. When the planet sweeps out all the gas from its nearest zone of feeding (m = m₂ ≈ 130 m_⊕), the width of the exhausted zone being $\text{～}\text{built1}\text{3}$ of the whole zone of the planet) growth is provided the slow diffusion of gas from the rest of the zone (time scale increases to 10⁵?10⁶ years and more). The process is terminated by the dissipation of the remnants of gas. In Saturn's zone m₁ > m₂ ≈ 30 m_⊕. The initial mass of the gas in Jupiter's zone is estimated. Before the beginning of the rapid accretion about 90% of the gas should have been lost from the solar system, and in the planet's zone less than two Jupiter masses remain. The highest temperature of Jupiter's surface, ≈5000°K, is reached at the stage of rapid accretion, m < 100 m_⊕, when the luminosity of the planet reaches 3 × 10^?3 L_⊙. This favors an effective heating of the inner parts of the accretionary disk and the dissipation of gas from the disk. The accretion of Saturn produced a temperature rise up to 2000?2400° K (at m ≈ 20?25 m_⊕) and a luminosity up to 10^?4 L_⊙.     

Solar dynamo models with α ‐effect and turbulent pumping from local 3D convection calculations

Results from kinematic solar dynamo models employing α ‐effect and turbulent pumping from local convection calculations are presented. We estimate the magnitude of these effects to be around 2–3 m s^–1, having scaled the local quantities with the convective velocity at the bottom of the convection zone from a solar mixing‐length model. Rotation profile of the Sun as obtained from helioseismology is applied in the models; we also investigate the effects of the observed surface shear layer on the dynamo solutions. With these choices of the small‐ and large‐scale velocity fields, we obtain estimate of the ratio of the two induction effects, C _α /C _Ω ≈ 10^–3, which we keep fixed in all models. We also include a one‐cell meridional circulation pattern having a magnitude of 10–20 m s^–1 near the surface and 1–2 m s^–1 at the bottom of the convection zone. The model essentially represents a distributed turbulent dynamo, as the α ‐effect is nonzero throughout the convection zone, although it concentrates near the bottom of the convection zone obtaining a maximum around 30° of latitude. Turbulent pumping of the mean fields is predominantly down‐ and equatorward. The anisotropies in the turbulent diffusivity are neglected apart from the fact that the diffusivity is significantly reduced in the overshoot region. We find that, when all these effects are included in the model, it is possible to correctly reproduce many features of the solar activity cycle, namely the correct equatorward migration at low latitudes and the polar branch at high latitudes, and the observed negative sign of B _r B _ϕ . Although the activity clearly shifts towards the equator in comparison to previous models due to the combined action of the α ‐effect peaking at midlatitudes, meridional circulation and latitudinal pumping, most of the activity still occurs at too high latitudes (between 5° … 60°). Other problems include the relatively narrow parameter space within which the preferred solution is dipolar (A0), and the somewhat too short cycle lengths of the solar‐type solutions. The role of the surface shear layer is found to be important only in the case where the α ‐effect has an appreciable magnitude near the surface. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A comparison of the interiors of Jupiter and Saturn

Interior models of Jupiter and Saturn are calculated and compared in the framework of the three-layer assumption, which rely on the perception that both planets consist of three globally homogeneous regions: a dense core, a metallic hydrogen envelope, and a molecular hydrogen envelope. Within this framework, constraints on the core mass and abundance of heavy elements (i.e. elements other than hydrogen and helium) are given by accounting for uncertainties on the measured gravitational moments, surface temperature, surface helium abundance, and on the inferred protosolar helium abundance, equations of state, temperature profile and solid/differential interior rotation. Results obtained solely from static models matching the measured gravitational fields indicate that the mass of Jupiter’s dense core is less than 14 M_⊕ (Earth masses), but that models with no core are possible given the current uncertainties on the hydrogen–helium equation of state. Similarly, Saturn’s core mass is less than 22 M_⊕ but no lower limit can be inferred. The total mass of heavy elements (including that in the core) is constrained to lie between 11 and 42 M_⊕ in Jupiter, and between 19 and 31 M_⊕ in Saturn. The enrichment in heavy elements of their molecular envelopes is 1–6.5, and 0.5–12 times the solar value, respectively. Additional constraints from evolution models accounting for the progressive differentiation of helium (Hubbard WB, Guillot T, Marley MS, Burrows A, Lunine JI, Saumon D, 1999. Comparative evolution of Jupiter and Saturn. Planet. Space Sci. 47, 1175–1182) are used to obtain tighter, albeit less robust, constraints. The resulting core masses are then expected to be in the range 0–10 M_⊕, and 6–17 M_⊕ for Jupiter and Saturn, respectively. Furthermore, it is shown that Saturn’s atmospheric helium mass mixing ratio, as derived from Voyager, Y=0.06±0.05, is probably too low. Static and evolution models favor a value of Y=0.11−0.25. Using, Y=0.16±0.05, Saturn’s molecular region is found to be enriched in heavy elements by 3.5 to 10 times the solar value, in relatively good agreement with the measured methane abundance. Finally, in all cases, the gravitational moment J₆ of models matching all the constraints are found to lie between 0.35 and 0.38×10⁻⁴ for Jupiter, and between 0.90 and 0.98×10⁻⁴ for Saturn, assuming solid rotation. For comparison, the uncertainties on the measured J₆ are about 10 times larger. More accurate measurements of J₆ (as expected from the Cassini orbiter for Saturn) will therefore permit to test the validity of interior models calculations and the magnitude of differential rotation in the planetary interior.     

The gas composition of jupiter derived from 5-μm airborne spectroscopic observations

The atmospheric transmission window between 1850 and 2250 cm⁻¹ in Jupiter's atmosphere was observed at a spectral resolution of 0.5 cm⁻¹ from the Kuiper Airborne Observatory. The mole fractions of NH₃, PH₃, CH₄, CH₃D, CO, and GeH₄ were derived for the 1- to 6-bar portion of Jupiter's troposphere using a spectrum synthesis program. Knowledge of the abundances of these gases below the visible clouds is necessary to calculate the global inventory of nitrogen, phosphorus, carbon, and deuterium, which, in turn, may constrain models of Jupiter's formation. The N/H ratio is 1.5 ± 0.2 times the value for the Sun's photosphere. The P/H ratio for the 5-bar level is between 1.0 and 1.6 times the solar abundance. The weak ν₃−ν₄ hot band of CH₄ was detected for the first time on Jupiter, thus providing a deep atmospheric value for C/H of 3.6 ± 1.2 times solar. The Jovian deuterium abundance is comparable to that measured in the interstellar medium (D/H = 1.2 ± 0.5) × 10⁻⁵. CO appears to be well mixed with a mole fraction of (1.0 ± 0.3) × 10⁻⁹. Multiple absorption features confirm that GeH₄ is present on Jupiter with a mole fraction of (7.0_−2.0^+4.0) × 10⁻¹⁰. The observed abundances of CO, GeH₄, and PH₃ are consistent with models of convective transport from Jupiter's deep atmosphere.     

Mercury: Internal structure and thermal evolution

Astronomical observations and cosmochemical calculations suggest that the planet Mercury may be composed of materials which condensed at relatively high temperatures in the primitive solar nebula and may have a basaltic crust similar to parts of the moon. These findings, plus the long standing inference that Mercury is much richer in metallic iron than the other terrestrial planets, provide important constraints which we apply to models of the thermal evolution and density structure of the planet. The thermal history calculations include explicitly the differing thermal properties of iron and silicates and account for core segregation, melting and differentiation of heat sources, and simulated convection during melting. If the U and Th abundances of Mercury are taken from the cosmochemical model of Lewis, then the planet would have fully differentiated a metal core from the silicate mantle for all likely initial temperature distributions and heat transfer properties. Density distributions for the planet are calculated from the mean density and estimates of the present-day temperature. For the fully differentiated model, the moment of inertia C/MR² is 0.325 (J₂=0.302×10^?6). For models with lower heat source abundances, the planet may not yet have differentiated. The density profiles for such models give C/MR²=0.394 (J₂=0.487×10^?6). These results should be useful for preliminary interpretation of the Mariner 10 measurements of Mercury's gravitational field.     

SABRE observation of the morning sector convection reversal

Observation of the convection flows associated with the morning discontinuity indicate that under highly disturbed conditions (K_p = 8 +, Dst = ?300 nT, B_ty > 0), the polar cusp may be shifted equatorwards to the latitudes covered by the SABRE radar (61–65° N geomagnetic). The convection reversal occurred over a narrow range of local time ( < 30 min) and was preceded by a region of westward convection flow poleward of the ambient eastward flow. These observations are consistent with the flows associated with the DPY current system for B_y > 0.     

Germane in the atmosphere of Jupiter

High-altitude spectra of Jupiter obtained from the Kuiper Airborne Observatory are analyzed for the presence of germane (GeH₄) in Jupiter's atmosphere. Comparison with laboratory spectra shows that the strong Q branch of the ν₃ band of germane at 2111 cm^?1 is prominent in the Jovian spectra. The abundance of germane in Jupiter's atmosphere is 0.006 (±0.003) cm-am corresponding to a mixing ratio of 0.6 ppb. This trace amount of germane is consistent with chemical equilibrium calculations if the germane present at ～1000°K is carried up by convection to the spectroscopically observable region at ～300°K.     

Differential rotation and meridional flow of Arcturus

The spectroscopic variability of Arcturus hints at cyclic activity cycle and differential rotation. This could provide a test of current theoretical models of solar and stellar dynamos. To examine the applicability of current models of the flux transport dynamo to Arcturus, we compute a mean‐field model for its internal rotation, meridional flow, and convective heat transport in the convective envelope. We then compare the conditions for dynamo action with those on the Sun. We find solar‐type surface rotation with about 1/10th of the shear found on the solar surface. The rotation rate increases monotonically with depth at all latitudes throughout the whole convection zone. In the lower part of the convection zone the horizontal shear vanishes and there is a strong radial gradient. The surface meridional flow has maximum speed of 170 m/s and is directed towards the equator at high and towards the poles at low latitudes. Turbulent magnetic diffusivity is of the order 10¹⁵–10¹⁶ cm²/s. The conditions on Arcturus are not favorable for a circulation‐dominated dynamo (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computation of Jupiter interior models from gravitational inversion theory

A method for deriving a planetary interior model which exactly satisfies a set of N gravitational constraints is implemented. For Jupiter, recent spacecraft measurements provide the mass, radius at a standard pressure level, rotation law, multipole moments of the internal mass distribution, and constraints on the internal composition and temperature distribution. By appropriate iterations, interior models are found which exactly satisfy these constraints. The models are assumed to have constant chemical composition and constant specific entropy in the hydrogenic envelope. The derived pressure-density relation in the outer envelope depends sensitively on the observational uncertainty in the mass multipole moment J₄. Models are not forced to fit the more indirectly derived constraints, which are instead used as consistency checks. For a helium mass fraction in the envelope (Y) equal to 0.20, the inferred pressure at a mass density ≈ 0.2 g/cm³ is about a factor of 2 higher than would be indicated by experimental hydrogen shock compression data in the relevant pressure range of 10⁵ to 10⁶ bar. The inferred pressure distribution is in much better agreement with the shock data for a nominal Y = 0.30 ± 0.05. This value of Y is interpreted in terms of an enhancement in the envelope, by a factor of order 5 over solar abundance, of species primarily consisting of CH₄, NH₃, and possibly H₂O. The same method is applied to Saturn, but existing uncertainties in Saturn's gravitational parameters are still too large to allow useful conclusions about the composition of its envelope.     

Subsurface Meridional Flow from HMI Using the Ring-Diagram Pipeline

We have determined the meridional flows in subsurface layers for 18 Carrington rotations (CR 2097 to 2114) analyzing high-resolution Dopplergrams obtained with the Helioseismic and Magnetic Imager (HMI) instrument onboard the Solar Dynamics Observatory (SDO). We are especially interested in flows at high latitudes up to 75^° in order to address the question whether the meridional flow remains poleward or reverses direction (so-called counter cells). The flows have been determined in depth from near-surface layers to about 16 Mm using the HMI ring-diagram pipeline. The measured meridional flows show systematic effects, such as a variation with the B ₀-angle and a variation with central meridian distance (CMD). These variations have been taken into account to lead to more reliable flow estimates at high latitudes. The corrected average meridional flow is poleward at most depths and latitudes with a maximum amplitude of about $20~\mathrm{m\,s}^{-1}$ near 37.5^° latitude. The flows are more poleward on the equatorward side of the mean latitude of magnetic activity at 22^° and less poleward on the poleward side, which can be interpreted as convergent flows near the mean latitude of activity. The corrected meridional flow is poleward at all depths within ±?67.5^° latitude. The corrected flow is equatorward only at 75^° latitude in the southern hemisphere at depths between about 4 and 8 Mm and at 75^° latitude in the northern hemisphere only when the B ₀ angle is barely large enough to measure flows at this latitude. These counter cells are most likely the remains of an insufficiently corrected B ₀-angle variation and not of solar origin. Flow measurements and B ₀-angle corrections are difficult at the highest latitude because these flows are only determined during limited periods when the B ₀ angle is sufficiently large.     

Convection in a rotating deep compressible spherical shell: Application to the Sun

In this paper we study the interaction of rotation with convection in a deep compressible spherical shell as the Sun's convection zone. We examine how the energy transport and the large scale motions can be affected by rotation. In particular we study how a large scale meridional circulation can give rise to variations of angular velocity with latitude and depth.It is assumed that the energy transport is only due to convection and that the mixing-length theory gives an adequate representation of it. Furthermore we assume that rotation acts as a perturbation of the turbulent convective flux through its transport coefficient.The equations involved in the model are integrated numerically in the limit of large viscosity and slow rotation. After having expanded all physical quantities to the first order in terms of Legendre polynomials, the fitting with the observed solar differential rotation gives the expansion parameter, which represents the coupling constant between rotation and convection.The results show a three-cell circulation extending from the poles to the equator. The first one is located in the lower half of the convection zone with the fluid rising at the equator and sinking at the poles. In the second one the direction of the motion is reversed while the third one, located in a thin upper layer, shows the same characteristics of the first one. The meridional velocities at the surface are directed towards the poles and are about 20 cm s^-1. In the other cells the meridional velocities are typically of a few cm s^-1 while the radial velocities are of the order of a few tenths of cm s^-1.The heat flux relative variation at the surface is about 10^-4 (3 × 10^-3 at the bottom) with a polar excess. The temperature variation at the surface is of the same order, with an equatorial excess however. The convection seems to be stabilized stronger at the equator. The angular velocity increases inwards and varies about 6% between the surface and the bottom of the convection zone.An attempt is made for explaining the picture which emerges. In particular the negligible flux and temperature variations at the surface are explained in terms of equalization by the particular structure of the latitudinal flow. This configuration of large scale circulation is attributed to the high stratification of the convection zone with depth.     

Long-term changes in Saturn's troposphere

We report the results of monitoring Saturn's H₂ quadrupole and CH₄ band absorptions outside of the equatorial zone over one-half of Saturn's year. This interval covers most of the perihelion half of Saturn's elliptical orbit, which happens to be approximately bounded by the equinoxes. Marked long-term changes occur in the CH₄ absorption accompanied by weakly opposite changes in the H₂ absorption. Around the 1980 equinox, the H₂ and CH₄ absorptions in the northern hemisphere appear to be discontinuous with those in the southern hemisphere. This discontinuity and the temporal variation of the absorptions are evidence for seasonal changes. The absorption variations can be attributed to a variable haze in Saturn's troposphere, responding to changes in temperature and insolation through the processes of sublimation and freezing. Condensed or frozen CH₄ is very unlikely to contribute any haze. The temporal variation of the absorption in the strong CH₄ bands at south temperate latitudes is consistent with a theoretically expected phase lag of 60° between the tropopause temperature and the seasonally variable insolation. We model the vertical haze distribution of Saturn's south temperature latitudes during 1971–1977 in terms of a distribution having a particle scale height equal to a fraction of the atmospheric scale height. The results are a CH₄/H₂ mixing ratio of (4.2 ± 0.4) × 10^?3, a haze particle albedo of $\text{ω}\text{= 0.995 ± 0.003}$, and a range of variation in the particle to gas scale-height ratio of 0.6 ± 0.2. The haze was lowest near the time of maximum temperature. We also report spatial measurements of the absorption in the 6450 Å NH₃ band made annually since the 1980 equinox. A 20 ± 4% increase in the NH₃ absorption at south temperate latitudes has occurred since 1973–1976 and the NH₃ absorption at high northern latitudes has increased during spring. Increasing insolation, and the resulting net sublimation of NH₃ crystals, is probably the cause. Significant long-term changes apparently extend to the deepest visible parts of Saturn's atmosphere. An apparently anomalous ortho-para H₂ ratio in 1978 suggests that the southern temperate latitudes experienced an unusual upwelling during that time. This may have signaled a rise in the radiative-convective boundary from deep levels following maximum tropospheric temperature and the associated maximum radiative stability. This would be further evidence that the deep, visible atmosphere is governed by processes such as dynamics and the thermodynamics of phase changes, which have response times much shorter than the radiative time constant.     

Disk models for cataclysmic variables

This paper presents disk models for cataclysmic variables in which convection in the central layers has been included. The calculation of the vertical structure at different points is presented. The models have a central mass of 1M _⊙ and matter fluxes of 10^?9, 10^?8, and 10^?7 M _⊙ yr^?1. The corresponding luminosities are 1.86, 1.86×10 and 1.86×10² L _⊙.     

Comparing Simulations of Rising Flux Tubes Through the Solar Convection Zone with Observations of Solar Active Regions: Constraining the Dynamo Field Strength

We study how active-region-scale flux tubes rise buoyantly from the base of the convection zone to near the solar surface by embedding a thin flux tube model in a rotating spherical shell of solar-like turbulent convection. These toroidal flux tubes that we simulate range in magnetic field strength from 15 kG to 100 kG at initial latitudes of 1^° to 40^° in both hemispheres. This article expands upon Weber, Fan, and Miesch (Astrophys. J. 741, 11, 2011) (Article 1) with the inclusion of tubes with magnetic flux of 10²⁰ Mx and 10²¹ Mx, and more simulations of the previously investigated case of 10²² Mx, sampling more convective flows than the previous article, greatly improving statistics. Observed properties of active regions are compared to properties of the simulated emerging flux tubes, including: the tilt of active regions in accordance with Joy’s Law as in Article 1, and in addition the scatter of tilt angles about the Joy’s Law trend, the most commonly occurring tilt angle, the rotation rate of the emerging loops with respect to the surrounding plasma, and the nature of the magnetic field at the flux tube apex. We discuss how these diagnostic properties constrain the initial field strength of the active-region flux tubes at the bottom of the solar convection zone, and suggest that flux tubes of initial magnetic field strengths of ≥?40 kG are good candidates for the progenitors of large (10²¹ Mx to 10²² Mx) solar active regions, which agrees with the results from Article 1 for flux tubes of 10²² Mx. With the addition of more magnetic flux values and more simulations, we find that for all magnetic field strengths, the emerging tubes show a positive Joy’s Law trend, and that this trend does not show a statistically significant dependence on the magnetic flux.     

Solar Dynamo Model with Diamagnetic Pumping and Nonlocal α-Effect

A combination of diamagnetic pumping and a nonlocal α-effect of the Babcock–Leighton type in a solar dynamo model is shown to reproduce observations of solar magnetic activity. The period of the solar cycle can be reproduced without reducing magnetic diffusivity in the bulk of the convection zone below the standard mixing-length value of 10¹³?cm²?s^?1. The simulated global fields are antisymmetric about the equator, and the toroidal-to-poloidal field ratio is about one thousand. However, the time–latitude diagrams of magnetic fields in the model without meridional flow differ from observations. Only when the meridional flow is included and the α-effect profile peaking at mid-latitudes is applied, can the observed butterfly diagrams be reproduced.     

Long term variations in solar flare activity

A statistical analysis of the contemporary (1954-1975) solar flare particle events has been made for the parametersF (integrated, proton fluence in cm^-2 in an event with kinetic energy above 10 MeV) andR ₀ (the characteristic rigidity). These data are compared with the long-term averaged values determined from stable- and radio-nuclide measurements of lunar samples. The analysis shows that the ancient solar flare proton spectrum was harder (higher R₀ values) compared to that observed in contemporary flares. A similar analysis can not be made for the mean long-term averaged flux (ˉJ, cm^-2 S^-1), since the contemporary averages suffer from an uncertainty due to the statistics of a single event. However, the average flux estimates for time durations 〈T〉 exceeding 10³ yr, are free from such uncertainties. The long-term averaged ˉJ values obtained over different time scales (10⁴ - 10⁶ yr) suggest a possible periodic variation in solar flare activity, with enhanced flux level during the last 10⁵ yr. The available data rule out the occurrence of giant flares, with proton fluence exceeding 10¹⁵ cm^-2 during the last million years.