Long Term Evolution of Solar Meridional Circulation and Phase Synchronization Viewed Through a Symmetrical Kuramoto Model

The solar-cycle oscillations of the toroidal and poloidal components of the solar magnetic field in the northern solar hemisphere have a persistent phase difference of about \(\pi \). We propose a symmetrical Kuramoto model with three coupled oscillators as a simple way to understand this anti-synchronization. We solve an inverse problem and reconstruct natural frequencies of the top and bottom oscillators under the conditions of a constant coupling strength and a non-delayed coupling. These natural frequencies are associated with angular velocities of the meridional flow circulation near the solar surface and in the deep layer of the solar convection zone. A relationship between our reconstructions of the shallow and the deep meridional flow speed during recent Solar Cycles 21?–?23 is in agreement with estimates obtained in helioseismology and flux-transport dynamo modeling. The reconstructed top oscillator speed presents significant solar-cycle like variations that agree with recent helioseismical reconstructions. The evolution of reconstructed natural frequencies strongly depends on the coupling strength. We find two stable regimes in the case of strong coupling with a change of regime during anomalous solar cycles. We see the onset of a new transition in Solar Cycle 24. We estimate the admitted range of coupling values and find evidence of cross-equatorial coupling between solar hemispheres not accounted for by the model.     

Electron Temperature in the Solar Wind From a Kinetic Collisionless Model: Application to High-Latitude Ulysses Observations

We use a kinetic collisionless model of the solar wind to calculate the radial variation of the electron temperature and obtain analytical expressions at large radial distances. In order to be compared with Ulysses observations, the model, which initially assumed a radial magnetic field, has been generalized to a spiral magnetic field. We present a preliminary comparison with Ulysses observations in the fast solar wind at high heliospheric latitudes. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Computationally Efficient,Time-Dependent Model of the Solar Wind for Use as a Surrogate to Three-Dimensional Numerical Magnetohydrodynamic Simulations

Solar radiation variability spans a wide range in time, ranging from seconds to decadal and longer. The nearly 40 years of measurements of solar irradiance from space established that the total solar irradiance varies by \(\approx 0.1\%\) in phase with the Sun’s magnetic cycle. Specific intervals of the solar spectrum, e.g., ultraviolet (UV), vary by orders of magnitude more. These variations can affect the Earth’s climate in a complex non-linear way. Specifically, some of the processes of interaction between solar UV radiation and the Earth’s atmosphere involve threshold processes and do not require a detailed reconstruction of the solar spectrum. For this reason a spectral UV index based on the (FUV-MUV) color has been recently introduced. This color is calculated using SORCE SOLSTICE integrated fluxes in the FUV and MUV bands. We present in this work the reconstructions of the solar (FUV-MUV) color and Ca ii K and Mg ii indices, from 1749–2015, using a semi-empirical approach based on the reconstruction of the area coverage of different solar magnetic features, i.e., sunspot, faculae and network. We remark that our results are in noteworthy agreement with latest solar UV proxy reconstructions that exploit more sophisticated techniques requiring historical full-disk observations. This makes us confident that our technique can represent an alternative approach which can complement classical solar reconstruction efforts. Moreover, this technique, based on broad-band observations, can be utilized to estimate the activity on Sun-like stars, that cannot be resolved spatially, hosting extra-solar planetary systems.

     

The Solar Ionization Rate of the Interplanetary Hydrogen as a Function of a Heliomagnetic Latitude: A New Model for the Interplanetary Lyman Alpha Studies

In this work we have modelled the solar wind proton flux which varies as a function of distance to the heliomagnetic equator and its effects on the interplanetary Lyman α radiation. The results imply that a groove observed in Lyman α intensity patterns toward the upwind direction Bertaux et al. disappears when the tilt angle of the heliomagnetic equator is larger than 20^°.The observations by Bertaux et al. were measured during the solar wind minimum when the tilt angle of the streamer belt is low. During the solar wind maximum when the tilt angle of the streamer belt is large the Lyman α groove should disappear according to our results. This revised version was published online in July 2006 with corrections to the Cover Date.     

Application of a Magnetic-field-induced Transition in Fe X to Solar and Stellar Coronal Magnetic Field Measurements

Magnetic fields play a key role in driving a broad range of dynamic phenomena in the atmospheres of the Sun and other stars.Routine and accurate measurements of the magnetic fields at all the atmospheric layers are of critical importance to understand these magnetic activities,but in the solar and stellar coronae such a measurement is still a challenge due to the weak field strength and the high temperature.Recently,a magnetic-field-induced transition(MIT) of Fe X at 257.26 ? has been proposed f...     

Evolution of Relative Magnetic Helicity: Method of Computation and Its Application to a Simulated Solar Corona above an Active Region

For a better understanding of solar magnetic field evolution it is appropriate to evaluate the magnetic helicity based on observations and to compare it with numerical simulation results. We have developed a method for calculating the vector potential of a magnetic field given in a finite volume; the method requires the magnetic flux to be balanced on all the side boundaries of the considered volume. Our method uses a fast Laplace/Poisson solver to obtain the vector potentials for a given magnetic field and for the corresponding potential (current-free) field. This allows an efficient calculation of the relative magnetic helicity in a finite 3D volume. We tested our approach on a theoretical model (Low and Lou, Astrophys. J. 352, 343, 1990) and also applied our method to the magnetic field above active region NOAA 8210 obtained by a photospheric-data-driven MHD model. We found that the amount of accumulated relative magnetic helicity coincides well with the relative helicity inflow through the boundaries in the ideal and non-ideal cases. The temporal evolution of relative magnetic helicity is consistent with that of magnetic energy. The maximum value of normalized helicity, H _m/Φ²=0.0298, is reached just before a drastic energy release by magnetic reconnection. This value is close to the corresponding value inferred from the formula that connects the magnetic flux and the accumulated magnetic helicity based on the observations of solar active regions.     

Determination of Electron Flux Spectra in a Solar Flare with an Augmented Regularization Method: Application to Rhessi Data

Kontar et al. (2004) have shown how to recover mean source electron spectra in solar flares through a physical constraint regularization analysis of the bremsstrahlung photon spectra I() that they produce. They emphasize the use of non-square inversion techniques, and preconditioning combined with physical properties of the spectra to achieve the most meaningful solution to the problem. Higher-order regularization techniques may be used to generate forms with certain desirable properties (e.g., higher-order derivatives). They further note that such analysis may be used to infer properties of the electron energy spectra at energies well above the maximum photon energy observed. In this paper we apply these techniques to data from a solar flare observed by RHESSI on 26 February, 2002. Results using different orders of regularization are presented and compared for various time intervals. Clear evidence is presented for a change in the value of the high-energy cutoff in the mean source electron spectrum with time. We also show how the construction of the injected electron spectrum F₀(E₀) (assuming that Coulomb collisions in a cold target dominate the electron transport) is facilitated by the use of higher-order regularization methods.     

Ultraviolet photolysis of amino acids in a 100 K water ice matrix: Application to the outer Solar System bodies

We report the rates of decomposition by ultraviolet (UV) photolysis of four amino acids in millimeter-thick crystalline water ice matrices at 100 K to constrain the survivability of these important organic molecules within ice lying near the surfaces of outer Solar System bodies. We UV-irradiated crystalline ice samples containing known concentrations of the amino acids glycine, aspartic acid, glutamic acid, and phenylalanine, then we measured the surviving concentrations using high performance liquid chromatography (HPLC) with fluorescence detection. From these experiments, we determine photolytic decomposition rates and half-lives. The half-life varies linearly with the ice thickness for all acids studied here. For example, glycine is the most resistant to photolytic destruction with a half-life of 50, 12, and 3.7 h in 1.6, 0.28, and 0.14 mm thick ices, respectively. We explain this linear variation of half-life with thickness as a consequence of extinction, mostly due to scattering, within these macroscopically thick ice samples. Applied to low latitude surface ice on Jupiter's satellite Europa, this analysis indicates that the concentration of any of these amino acids within the top meter of similar ice will be halved within a ∼10 year timescale.     

Gamma-Rays and Neutrons as a Probe of Flare Proton Spectra: the Solar Flare of 11 June 1991

The large flare of 11 June 1991 (GOES class X12) was detected by the Total Absorption Shower Counter (TASC) segment of the EGRET gamma-ray telescope on board the Compton Gamma Ray Observatory. Significant gamma-ray emission was observed over the entire energy range to which the TASC was sensitive –1 to 140 MeV. Several phases were identified which showed major changes in the intensity and spectral shape of the flare gamma-rays. Furthermore, a 'delayed' phase during which a response consistent with the detection of energetic neutrons and pion-decay gamma-rays was seen, implying a qualitative change in the spectral shape of the accelerated ion spectrum. The similarity of the characteristics of this delayed phase (pion and energetic neutron production) to those in other large flares hint at a common particle acceleration mechanism.     

Numerical implementation of a perturbation theory up to the third order for rotating polytropic stars: Application to a solar model

Numerical treatment of a pertubation theory up to the third order yields quantitative estimates for an interesting polytropic solar model possessing differential rotation of Clement's type. A suitably defined reduction factor, otherwise referred to as strength, moderates the effects of the differential rotation and the so resulting limiting state represents efficiently uniform rotation of the model. The numerical results obtained are compared to respective ones derived from an original numerical implementation of a second-order perturbation theory.     

The Whole Heliosphere Interval in the Context of a Long and Structured Solar Minimum: An Overview from Sun to Earth

Throughout months of extremely low solar activity during the recent extended solar-cycle minimum, structural evolution continued to be observed from the Sun through the solar wind and to the Earth. In 2008, the presence of long-lived and large low-latitude coronal holes meant that geospace was periodically impacted by high-speed streams, even though solar irradiance, activity, and interplanetary magnetic fields had reached levels as low as, or lower than, observed in past minima. This time period, which includes the first Whole Heliosphere Interval (WHI 1: Carrington Rotation (CR) 2068), illustrates the effects of fast solar-wind streams on the Earth in an otherwise quiet heliosphere. By the end of 2008, sunspots and solar irradiance had reached their lowest levels for this minimum (e.g., WHI 2: CR 2078), and continued solar magnetic-flux evolution had led to a flattening of the heliospheric current sheet and the decay of the low-latitude coronal holes and associated Earth-intersecting high-speed solar-wind streams. As the new solar cycle slowly began, solar-wind and geospace observables stayed low or continued to decline, reaching very low levels by June??C?July 2009. At this point (e.g., WHI 3: CR 2085) the Sun?CEarth system, taken as a whole, was at its quietest. In this article we present an overview of observations that span the period 2008??C?2009, with highlighted discussion of CRs 2068, 2078, and 2085. We show side-by-side observables from the Sun??s interior through its surface and atmosphere, through the solar wind and heliosphere and to the Earth??s space environment and upper atmosphere, and reference detailed studies of these various regimes within this topical issue and elsewhere.     

Transfer of Polarized Radiation: Nonlinear Integral Equations for I-Matrices in the General Case and for Resonance Scattering in a Weak Magnetic Field

General equations of the Wiener-Hopf type for a matrix source function with nonsymmetrical kernel matrices are considered in the form of continuous superpositions of exponentials. Certain problems in the transfer of polarized radiation reduce to equations of this kind. In general there are two different H-matrices in the theory (which are a generalization of the Ambartsumian-Chandrasekhar scalar H-function), generated by an initial equation of the Wiener-Hopf type and its analog, but with the kernel matrix and the unknown matrix of the source function being transposed. In addition there are two corresponding I-matrices, actually consisting of Laplace transforms of the matrix source functions, through which the Stokes vector of the escaping radiation is directly determined. In the problem of diffuse reflection from a half-space, the I-matrices are expressed in terms of a product of these two H-matrices, and for the latter there is a system of nonlinear equations which is a generalization of the corresponding Ambartsumian-Chandrasekhar scalar equation. In the problem of the emission of partially polarized radiation from a half-space containing uniformly distributed internal sources we have obtained a system of two nonlinear equations for the I-matrices directly. In the special case of a symmetrical kernel matrix, this system of two equations reduces to one equation. It is shown that in the case of resonance scattering in a weak magnetic field (the Hanle effect) in the approximation of complete frequency redistribution, the system of two nonlinear equations for the I-matrices (of dimension 6×6) also reduces to one nonlinear equation, although the kernel matrix for the main integral equation for the matrix source function () is not symmetrical. For this case we have found a matrix generalization of the so-called law, consisting of an equation of the type (0)Â ^T (0) = (where T denotes transposition) at the boundary of a half-space containing uniformly distributed primary sources of partially polarized radiation.     

Development of a Code to Analyze the Solar White-Light Images from the Kodaikanal Observatory: Detection of Sunspots,Computation of Heliographic Coordinates and Area

Sunspots are the most conspicuous aspects of the Sun. They have a lower temperature, as compared to the surrounding photosphere; hence, sunspots appear as dark regions on a brighter background. Sunspots cyclically appear and disappear with a 11-year periodicity and are associated with a strong magnetic field ( ～10³ G) structure. Sunspots consist of a dark umbra, surrounded by a lighter penumbra. Study of umbra–penumbra area ratio can be used to give a rough idea as to how the convective energy of the Sun is transported from the interior, as the sunspot’s thermal structure is related to this convective medium.An algorithm to extract sunspots from the white-light solar images obtained from the Kodaikanal Observatory is proposed. This algorithm computes the radius and center of the solar disk uniquely and removes the limb darkening from the image. It also separates the umbra and computes the position as well as the area of the sunspots. The estimated results are compared with the Debrecen photoheliographic results. It is shown that both area and position measurements are in quite good agreement.     

The Solar Spectral Irradiance as a Function of the Mg <Emphasis Type="SmallCaps">ii</Emphasis> Index for Atmosphere and Climate Modelling

We present a new method to reconstruct the solar spectrum irradiance in the Ly α – 400 nm region, and its variability, based on the Mg ii index and neutron-monitor measurements. Measurements of the solar spectral irradiance available in the literature have been made with different instruments at different times and different spectral ranges. However, climate studies require harmonised data sets. This new approach has the advantage of being independent of the absolute calibration and aging of the instruments. First, the Mg ii index is derived using solar spectra from Ly α (121 nm) to 410 nm measured from 1978 to 2010 by several space missions. The variability of the spectra with respect to a chosen reference spectrum as a function of time and wavelength is scaled to the derived Mg ii index. The set of coefficients expressing the spectral variability can be applied to the chosen reference spectrum to reconstruct the solar spectra within a given time frame or Mg ii index values. The accuracy of this method is estimated using two approaches: direct comparison with particular cases where solar spectra are available from independent measurements, and calculating the standard deviation between the measured spectra and their reconstruction. From direct comparisons with measurements we obtain an accuracy of about 1 to 2%, which degrades towards Ly α. In a further step, we extend our solar spectral-irradiance reconstruction back to the Maunder Minimum introducing the relationship between the Mg ii index and the neutron-monitor data. Consistent measurements of the Mg ii index are not available prior to 1978. However, we remark that over the last three solar cycles, the Mg ii index shows strong correlation with the modulation potential determined from the neutron-monitor data. Assuming that this correlation can be applied to the past, we reconstruct the Mg ii index from the modulation potential back to the Maunder Minimum, and obtain the corresponding solar spectral-irradiance reconstruction back to that period. As there is no direct measurement of the spectral irradiance for this period we discuss this methodology in light of the other proposed approaches available in the literature. The use of the cosmogenic-isotope data provides a major advantage: it provides information about solar activity over several thousands years. Using technology of today, we can calibrate the solar irradiance against activity and thus reconstruct it for the times when cosmogenic-isotope data are available. This calibration can be re-assessed at any time, if necessary.     

Linear stability of collinear equilibrium points around an asteroid as a two-connected-mass: Application to fast rotating Asteroid 2000EB14

This note discusses the stability of collinear equilibrium points around a rotating system composed of two masses rigidly connected by a massless rod in the case, where the centripetal force outweighs the gravitational force. It is found that a stable region appears at L₁ when the ratio of gravitational to centripetal acceleration is less than 0.125, and that there is always no stable area at L₂ and L₃; the result is applied to the fast rotating Asteroid 2000EB₁₄.     

Tail Emission from a Ring-like Jet: Its Application to Shallow Decays of Early Afterglows and GRB 050709

Similar to the case of pulsars the magnetic axis and the spin axis of gamma-ray burst sources may not lie on the same line. This may cause the formation of a ring-like jet due to collimation of the processing magnetic axis. We analyze the tail emission from such a jet, and find that it has a shallow decay phase with a temporal index of -1/2 if the Lorentz factor of the ejecta is not very high, which is consistent with the shallow decay phase of some early X-ray afterglow detected by Swift. The ring-like jet has a tail cusp with sharp rising and very sharp decay. This effect can provide an explanation for the re-brightening and sharp decay of the X-ray afterglow of GRB 050709.     

Vesta as the howardite,eucrite and diogenite parent body: Implications for the size of a core and for large-scale differentiation

Abstract— If Vesta is the parent body of the howardite, eucrite, and diogenite (HED) meteorites, then geo-chemical and petrologic constraints for the meteorites may be used in conjunction with astronomical constraints for the size and mass of Vesta to (1) determine the size of a possible metal core in Vesta and (2) model the igneous differentiation and internal structure of Vesta. The density of Vesta and petrologic models for HED meteorites together suggest that the amount of metal in the parent body is <25 mass%, with a best estimate of ～5%, assuming no porosity. For a porosity of up to 5% in the silicate fraction of the asteroid, the permissible metal content is <30%. These results suggest that any metal core in the HED parent body and Vesta is not unusually large. A variety of geochemical and other data for HED meteorites are consistent with the idea that they originated in a magma ocean. It appears that diogenites formed by crystal accumulation in a magma ocean cumulate pile and that most noncumulate eucrites (excepting such eucrites as Bouvante and Statinem) formed by subsequent crystallization of the residual melts. Modelling results suggest that the HED parent body is enriched in rare earth elements by a factor of ～2.5–3.5 relative to CI-chondrites and that it has approximately chondritic Mg/Si and Al/Sc ratios. Stokes settling calculations for a Vesta-wide, nonturbulent magma ocean suggest that early-crystallizing magnesian olivine, orthopyroxene, and pigeonite would have settled relatively quickly, permitting fractional crystallization to occur, but that later-crystallizing phases would have settled (or floated) an order of magnitude more slowly, allowing, instead, a closer approach to equilibrium crystallization for the more evolved (eucritic) melts. This would have inhibited the formation of a plagioclase-flotation crust on Vesta. Plausible models for the interior of Vesta, which are consistent with the data for HED meteorites and Vesta, include a metal core (<130 km radius), an olivine-rich mantle (～65–220 km thick), a lower crustal unit (～12–43 km thick) composed of pyroxenite, from which diogenites were derived, and an upper crustal unit (～23–42 km thick), from which eucrites originated. The present shape of Vesta (with ～60 km difference in the maximum and minimum radius) suggests that all of the crustal materials, and possibly some of the underlying olivine from the mantle, could have been locally excavated or exposed by impact cratering.     

The adapted solar wind system as cause for a momentum transfer to the sun and its consequences for the orbital motions of keplerian objects

In the following paper we argue that each wind-driving star in relative motion with respect to the ambient interstellar medium experiences a force exerted on its central wind-generating body. The exact magnitude of this force depends on the actual geometry of the counterflow configuration of stellar and interstellar winds for a particular kinematic situation which is especially sensitive to whether the interstellar flow is subsonic or supersonic. It will, however, be demonstrated here that this force is of an accelerating nature, i.e., it operates like a rocket-motor, as long as the peculiar motion of the wind-driving star with respect to the ambient interstellar medium remains subsonic.Here we use a specific analytical model to describe theoretically the specific counterflow configuration for the case of the solar system in a subsonic peculiar motion with respect to the local interstellar medium assuming irrotational and incompressible flows. We can work out a quantitative number for the accelerating force governing the Sun's motion at present. The net reaction force exerted on the solar body is then mediated by the asymmetric boundary conditions to which the distant solar wind field has to adapt.Next we study the indirect action of such a force on orbiting Keplerian objects like planets, planetesimals and comets. Since this force only influences the central solar body, but not the planets themselves, the problem is different from the treatment of a constant perturbation force perturbing the Keplerian orbits. We present a perturbation analysis treating the action of a corresponding position-dependent perturbation force resulting in secular changes of the orbital elements of Keplerian objects. It is found that changes are accumulating more rapidly in time the closer to the sun the orbiting bodies are. Main axis and perihelion distances are systematically increasing. Especially pronounced are changes in the perihelion position angle of the objects. For solar wind mass losses larger than the Sun's present value by a factor of 1000 (T-Tauri phase of the Sun,) the migration periods calculated for the planet Mercury are of the same order of magnitude as that for corresponding general relativistic migration.