An analytic approach to the connection between stellar structure parameters and the neutrino emission rate in a simple stellar model

In order to obtain the internal structure of a main-sequence star such as the Sun usually one has to solve the detailed structure equations numerically. This paper is an attempt to construct analytic models for the stellar nuclear energy generation. We give closed-form analytic results for the stellar luminosity and stellar neutrino emission rate when the radial matter density of the spherical star under consideration is linear. For the numerical estimation of the neutrino flux of a specified stellar nuclear reaction we take into account parameters of the standard solar model. The present paper gives for the first time the connection between stellar structure parameters and neutrino fluxes in an analytic stellar model.     

日冕物质抛射的理想MHD模型研究

概括了日冕物质抛射的一些观测结果和它们与其它太阳活动现象的相关性。简要回顾了较早期日冕物质抛射的理论研究,着重介绍了最近研究得较多的理论机制,即能量储存机制,以及其中的磁通量绳突变模型与其它理论模型的MHD数值和解析研究以及相应的重要应用．     

Rotational dynamics of a solar system body under solar radiation torques

The rotational dynamics of a small solar system body subject to solar radiation torques is investigated. A set of averaged evolutionary equations are derived as an analytic function of a set of spherical harmonic coefficients that describe the torque acting on the body due to solar radiation. The analysis also includes the effect of thermal inertia. The resulting equations are studied and a set of possible dynamical outcomes for the rotation rate and obliquity of a small body are found and characterized.     

Force-free magnetic arcades relevant to two-ribbon solar flares

Simple analytic models for the passive evolution of arcade-like magnetic fields through a series of force-free equilibria are presented. At the photospheric boundary, the normal magnetic field component is prescribed together with either the longitudinal field component or the photospheric shear. Analytic progress is made by considering either cylindrically symmetric solutions or using the separation of variables technique. Two distinct cylindrically symmetric force-free fields are obtained that possess the same normal field component and photospheric shear. The scond field contains a magnetic bubble. As the shear increases beyond a critical value, so the magnetic energy of the first configuration exceeds that of the second. The possibility is therefore suggested of an eruption of the first field outwards towards the second. Such an eruptive instability is proposed as the origin of a two-ribbon solar flare.A new analytic solution to the force-free field equations, of separable form, is discovered and it is pointed out that the existence of shear in a magnetic field does not preclude it from being potential.Now at AWRE, Aldermaston, Reading, Berkshire.     

A comprehensive view of solar-terrestrial relationships in terms of a chain of four dynamo-powered plasma acceleration processes

This paper emphasizes an effort to link processes which relate solar activity and magnetospheric disturbances in terms of energy transfer through a chain of four elements. In this view, each element is explicitly thought to be powered by a dynamo, namely the solar wind generation dynamo, the solar flare dynamo, the solar wind-magnetosphere dynamo and the auroral dynamo, respectively. Each dynamo powers a plasma acceleration process by the Lorentz force and the plasma flows thus generated are the solar wind, the flare-generated solar wind disturbance, the magnetospheric plasma convection and the ionospheric convection, respectively. Each plasma flow conveys the energy from one element to the next in the chain. Some of the kinetic energy of the photospheric plasma is eventually deposited in the polar ionosphere as heat energy.     

Mechanical wave-energy fluxin magnetoatmospheres: Discrete and continuous spectra

This paper deals with a rather general class of magnetoatmospheres — media for which the restoring forces of buoyancy, compressibility and magnetic tension/pressure are important in sustaining wave motion. The magnetic field has the general form (B ₀(z), 0,0) and there is also an aligned shear flow (U ₀(z), 0, 0) present. After discussion of the equilibrium and stability of such systems, and certain mathematical properties of a particular system (an isothermal atmosphere with uniform magnetic field, of interest in solar physics), theory is developed which enables expressions to be written down for the mechanical wave energy flux associated with wave motion due to a transient source. These analytic expressions are very general and contain contributions from the continuous and discrete frequency spectra, corresponding respectively to freely propagating and trapped (or surface) waves. These fluxes are evaluated for various ranges of magnetic field, horizontal wavenumber, characteristic source times and frequency, for a simple constant-parameter atmosphere. The source is taken to be a transient fluctuation of the lower boundary, (modelling convective overshoot) which is taken to be located at the level ₅₀₀₀=0.08 in the solar atmosphere. The relative distribution of wave energy flux in the various modes is discussed in the context of solar physics parameters. The possible significance of leaky modes arising from supergranular or other flow, for the local flux balance in the solar chromosphere is outlined.     

On the Magnetic Correspondence between the Photosphere and the Heliosphere

The solar magnetic field maps every point in the corona to a corresponding place on the solar surface. Identifying the magnetic connection map is difficult at low latitudes near the heliospheric current sheet, but remarkably simple in coronal hole interiors. We present a simple analytic magnetic model (‘pseudocurrent extrapolation’) that reproduces the global structure of the corona, with significant physical advantages over other nearly analytic models such as source-surface potential field extrapolation. We use the model to demonstrate that local horizontal structure is preserved across altitude in the central portions of solar coronal holes, up to at least 30 R_s, in agreement with observations. We argue that the preserved horizontal structure may be used to track the magnetic footpoint associated with the location of a hypothetical spacecraft traveling through the solar corona, to relate in situ measurements of the young solar wind at ∼10–30 R_s to particular source regions at the solar surface. Further, we discuss the relationship between readily observable geometrical distortions and physical parameters of interest such as the field-aligned current density.     

Energetics of two-ribbon solar flares

A theory of two-ribbon solar flares is presented which identifies the primary energy release site with the tops of the flare loops. The flare loops are formed by magnetic reconnection of a locally opened field configuration produced by the eruption of a pre-flare filament. Such eruptions are commonly observed about 15 min prior to the flare itself. It is proposed that the flare loops represent the primary energy release site even during the earliest phase of the flare, i.e., the flare loops are in fact the flare itself.Based upon the supposition that the energy release at the loop tops is in the form of Joulean dissipation of magnetic energy at the rising reconnection site, a quantitative model of the energy release process is developed based upon an analytic reconnecting magnetic field geometry believed to represent the basic process. Predicted curves of energy density vs time are compared with X-ray observations taken aboard Skylab for the events of 29 July, 13 August, and 21 August in 1973. Considering the crudity of the model, the comparisons appear reasonable. The predicted field strengths necessary to produce the observed energy density curves are also reasonable, being in the range 100–1000 G.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The survival and disruption of cold dark matter microhaloes: implications for direct and indirect detection experiments

If the dark matter particle is a neutralino, then the first structures to form are cuspy cold dark matter (CDM) haloes collapsing after redshifts   z ≈ 100  in the mass range  10⁻⁶–10⁻³ M_⊙  . We carry out a detailed study of the survival of these microhaloes in the Galaxy as they experience tidal encounters with stars, molecular clouds, and other dark matter substructures. We test the validity of analytic impulsive heating calculations using high-resolution N -body simulations. A major limitation of analytic estimates is that mean energy inputs are compared to mean binding energies, instead of the actual mass lost from the system. This energy criterion leads to an overestimate of the stripped mass and an underestimate of the disruption time-scale, since CDM haloes are strongly bound in their inner parts. We show that a significant fraction of material from CDM microhaloes can be unbound by encounters with Galactic substructure and stars; however, the cuspy central regions remain relatively intact. Furthermore, the microhaloes near the solar radius are those which collapse significantly earlier than average and will suffer very little mass-loss. Thus, we expect a fraction of surviving bound microhaloes, a smooth component with narrow features in phase space, which may be uncovered by direct detection experiments, as well as numerous surviving cuspy cores with proper motions of arcminutes per year, which can be detected indirectly via their annihilation into gamma-rays.     

Direct and Indirect Thermospheric Heating Sources for Solar Cycles 21–23

Solar variability is often cast in terms of radiative emission and the associated long-term climate response; however, growing societal reliance on technology is creating more interest in day-to-day solar variability. This variability is associated with both solar radiative and solar wind emissions. In this paper we explore the combined effects of radiative and solar wind fluctuations at Earth. The fluctuations in radiative and geomagnetic power create an extended interval of solar maximum for the upper atmosphere. We use a trio of empirical models to estimate, over the last three solar cycles, the relative contributions of solar extreme ultraviolet (UV) power, Joule power, and particle kinetic power to the Earth’s upper atmosphere energy budget. Daily power values are derived from three source models. The SOLAR2000 solar irradiance specification model provides estimates of the daily extreme and far UV solar power input. Geomagnetic power is derived from a combination of satellite-estimated particle precipitation power and an empirical model of Joule power from hemispherically integrated estimates of high-latitude energy deposition. During the interval 1975 to 2003, the average daily contributions were: particles – 36 GW, Joule – 95 GW and solar – 464 GW for a total of 595 GW. Solar wind-driven geomagnetic power provided 22% of the total global upper atmospheric energy. In the top 15 power events, geomagnetic power contributed two-thirds of the total power budget. In each of these events, Joule power alone exceeded solar power. With rising activity, Joule power becomes the most variable element of solar upper atmosphere interactions.     

Acceleration of the solar wind by whistler waves from coronal holes

We investigate the possibility of an additional acceleration of the high speed solar wind by whistler waves propagating outward from a coronal hole. We consider a stationary, spherically symmetric model and assume a radial wind flow as well as a radial magnetic field. The energy equation consists of (a) energy transfer of the electron beam which excites the whistler waves, and (b) energy transfer of the whistler waves described by conservation of wave action density. The momentum conservation equation includes the momentum transfer of two gases (a thermal gas and an electron beam). The variation of the temperature is described by a polytropic law. The variation of solar wind velocity with the radial distance is calculated for different values of energy density of the whistler waves. It is shown that the acceleration of high speed solar wind in the coronal hole due to the whistler waves is very important. We have calculated that the solar wind velocity at the earth's orbit is about equal to 670 km/sec (for wave energy density about 10^?4 erg cm^?3 at 1.1R⊙). It is in approximate agreement with the observed values.     

Solar flare alpha to proton ratio changes following interplanetary disturbances

A discussion is presented on the half hour averaged low energy solar alpha to solar proton flux ratios observed following the three large solar flares of May 23, 1967. One of the large changes observed in the particle ratios (following a sudden commencement (SC) storm observed on the earth) is interpreted as due to a source effect. The second large change, again observed following an SC, is observed in the equal velocity and equal rigidity ratios and not in the equal energy/charge ratios. This observation suggests that electric fields in an interplanetary disturbance may be the cause of the modulations.     

Nonradial stellar oscillations excited by turbulent convection

The resonant excitation of the large-scale nonradial oscillations of a star by turbulent convection is considered. In the case of an incompressible inhomogeneous liquid sphere and a spherical shell we have demonstrated the excitation of oscillations and have obtained the explicit analytic expressions for the oscillation amplitudes. The effect of uniform axial rotation of a star upon the oscillations has also been considered. The estimates of the r.m.s. velocities of the excited quadrupole oscillations based on solar parameters do not contradict the observations of the 160 min. solar oscillations. Results are briefly discussed and applications are also made to the case of nonradial oscillations of outer convection zones of white dwarfs, Jupiter and Saturn.     

A variational approach to the question of temporal stability of equilibrium models of solar prominences

Using a Lagrangian approach to the equations describing small amplitude departures from equilibrium of solar prominences, we derive seven quantities which, by analogy to the concepts of energy, momentum and angular momentum, are conserved under circumstances corresponding to ignorable coordinates of classical mechanics. In a pragmatic sense it is expected that these conservation laws will be useful as criteria of accuracy in obtaining eigen-frequencies for the perturbation equations when numerical techniques are employed.We also demonstrate that: (i) the perturbation equations (which are not self-adjoint) follow from an external variation of a Lagrangian; (ii) the equations adjoint to the perturbation equations also follow from an extremal variation of the same Lagrangian; (iii) the Lagrangian approach automatically gives the conserved quantities, together with a variational principle for computing the eigen-frequencies of the perturbation equations.In view of the paucity of analytic solutions (and their eigen-frequencies) to the perturbation equations (due essentially to the complicated spatial dependence of thermodynamic quantities describing the equilibria) we believe that the technique developed here - which is capable of handling complicated spatial dependences and which has internal criteria for assessing accuracy of any given numerical convergence scheme - is a valuable addition to the arsenal of methods used for discussing the equilibria, and their stability, of models thought to represent the basic physical processes underlying the quiescent solar prominence phenomenon.     

Are solar flares a result of a sudden conversion of magnetic energy stored prior to their onset?

It has long been believed that solar flares result from a sudden conversion of magnetic energy stored prior to their onset. However, it is difficult to prove such an idea without knowing both the rate of energy input and the rate of energy output in the flare region. In spite of the fact that a similar mechanism has long been contemplated, magnetospheric substorms are found to be directly driven by an enhanced dynamo process. The results suggest also that the presence of magnetic energy in the magnetotail does not mean that it can be consumed for substorms. Implications of this finding for solar flares are discussed.     

A model of flare-produced magneto-radiative shock with increasing energy

An exact solution for a spherically-symmetric model of a magneto-radiative shock wave in the solar wind caused by the explosive energy release of a solar flare has been, obtained in the case when energy released is an increasing function of the time. It has been shown that due to increasing energy, density, pressure, radiation flux, magnetic field and shock velocity change considerably.     

CME-Flare Association Deduced from Catastrophic Model of CMEs

Based on our previous works regarding solar eruptions, we focus on the relationships among different eruptive phenomena, such as solar flares, eruptive prominences and coronal mass ejections (CMEs). The three processes show clear correlations under certain circumstances. The correlation between a CME and solar flare depends the energy that stored in the relevant magnetic structure, which is available to drive the eruption: the more energy that is stored, the better the correlation is; otherwise, the correlation is poor. The correlation between a CME and eruptive prominence, on the other hand, depends on the plasma mass concentration in the configuration prior to the eruption: if the mass concentration is significant, a CME starts with an eruptive prominence, otherwise, a CME develops an without an apparent associated eruptive prominence. These results confirm that solar flares, eruptive prominences and CMEs are different significances of a single physical process that is related to the energy release in a disrupted coronal magnetic field. The impact of gravity on CME propagation and the above correlations is also investigated. Our calculations indicate that the effect of gravity is not significant unless the strength of the background field in the disrupted magnetic configuration becomes weak, say weaker than 30 G.     

Bicentennial decrease of the solar constant leads to the Earth’s unbalanced heat budget and deep climate cooling

Long-wave energy emitted by the Earth-atmosphere into space is characterized by changes in power over time that always lag behind the changes in power of the absorbed solar radiation due to slow variation in enthalpy of the Earth-atmosphere system. Long-term variation of the solar energy radiation absorbed by the Earth remains uncompensated by the energy radiated into space over the interval of time that is determined by the thermal inertia. The basic state of the climate system is when the debit and credit sides in the Earth’s global annual mean energy budget (including the air and water envelopes) are almost always unbalanced. The annual mean balance of the heat budget of the Earth-atmosphere over a long time period will reliably define the behavior and magnitude of the energy excess accumulated by the Earth or energy deficit to allow us to determine adequately and to predict beforehand the trend and amplitude of the forthcoming climate change using the prognosis of variations in the total solar irradiance (solar constant). The decrease in solar constant has been observed since the early 1990s. The Earth as a planet will have a negative balance in the energy budget in the future as well, because the Sun is entering the decline phase of the bicentennial luminosity changes. This will lead to a drop in temperature in approximately 2014. The increase in albedo and decrease in greenhouse gas concentration in the atmosphere will result in the additional decrease in absorbed portion of the solar energy and reduced greenhouse effect. The additional drop in temperature exceeding the effect of decreased solar constant can occur as a result of successive feedback effects. A deep bicentennial minimum in solar constant is to be anticipated in 2042 ± 11 and the 19th Little Ice Age (for the last 7500 years) may occur in 2055 ± 11.     

Magnetic Energy of Force-Free Fields with Detached Field Lines

Using an axisymmetrical ideal MHD model in spherical coordinates, we present a numerical study of magnetic configurations characterized by a levitating flux rope embedded in a bipolar background field whose normal field at the solar surface is the same or very close to that of a central dipole. The characteristic plasma β (the ratio between gas pressure and magnetic pressure) is taken to be sosmall (β= 10^-4) that the magnetic field is close to being force-free. The system as a whole is then let evolve quasi-statically with a slow increase of either the annular magnetic flux or the axial magnetic flux of the rope, and the total magneticenergy of the system grows accordingly. It is found that there exists an energy threshold: the flux rope sticks to the solar surface in equilibrium if the magneticenergy of the system is below the threshold, whereas it loses equilibrium if the threshold is exceeded. The energy threshold is found to be larger than that of thecorresponding fully-open magnetic field by a factor of nearly 1.08 irrespective as towhether the background field is completely closed or partly open, or whether the magnetic energy is enhanced by an increase of annular or axial flux of the rope.This gives an example showing that a force-free magnetic field may have an energy larger than the corresponding open field energy if part of the field lines is allowed tobe detached from the solar surface. The implication of such a conclusion in coronal mass ejections is briefly discussed and some comments are made on the maximum energy of force-free magnetic fields.     

Interstellar matter and the location of the shock front

The initially supersonic flow of the solar wind passes through a magnetic shock front where its velocity is supposed to be reduced to subsonic values. The location of this shock front is primarily determined by the energy density of the external interstellar magnetic field and the momentum density of the solar wind plasma. Interstellar hydrogen penetrating into the heliosphere undergoes charge exchange processes with the solar wind protons and ionization processes by the solar EUV radiation. This results in an extraction of momentum from the solar wind plasma. Changes of the geometry and the location of the shock front due to this interaction are studied in detail and it is shown that the distance of the magnetic shock front from the Sun decreases from 200 to 80 AU for an increase of the interstellar hydrogen density from 0.1 to 1.0 cm⁻³. The geometry of the shock front is essentially spherical with a pronounced embayment in the direction opposite to the approach of interstellar matter which depends very much on the temperature of the interstellar gas. Due to the energy loss by the interaction with neutral matter the solar wind plasma reduces its velocity with increasing distance from the Sun. This modifies Parker's solution of a constant solar wind velocity.