Hydrodynamic models of solar and stellar flares

This paper discusses the hydrodynamic modeling of flaring plasma confined in magnetic loops and its objectives within the broader scope of flare physics. In particular, the Palermo-Harvard model is discussed along with its applications to the detailed fitting of X-ray light curves of solar flares and to the simulation of high-resolution Ca xix spectra in the impulsive phase. These two approaches provide complementary constraints on the relevant features of solar flares. The extension to the stellar case, with the fitting of the light curve of an X-ray flare which occurred on Proxima Centauri, demonstrates the feasibility of using this kind of model for stars too. Although the stellar observations do not provide the wealth of details available for the Sun, and, therefore, constrain the model more loosely, there are strong motivations to pursue this line of research: the wider range of physical parameters in stellar flares and the possibility of studying further the solar-stellar connection.     

Long-duration solar and stellar flares

According to one of the most popular classifications, solar flares may be assigned either to the category of small short-lived events, or to the category of large, long-duration two-ribbon (2-R) flares. Even if such abroad division oversimplifies the flare phenomenon, our knowledge of the characteristics of stellar flares is so poor, that it is worthwhile to investigate the possibility of adopting this classification scheme for stellar flares as well. In particular we will analyze Einstein observations of a long duration flare on EQ Peg to establish whether it might be considered as a stellar analogy of 2-R solar events. To this end we apply to EQ Peg data a reconnection model, developed originally for solar 2-R flares, and conclude that stellar observations are consistent with model predictions, although additional information is required to identify uniquely the physical parameters of the flare region. Application of the model to integrated observations of a 2-R solar flare, for which high spatial resolution data are also available, shows, however, that future integrated observations may allow us to solve the ambiguities of the model and use it as a diagnostic tool for a better understanding of stellar flares.     

Relativistic isentropic stellar models

Relativistic, isentropic, homogeneous models are constructed by a method that automatically detects instabilities, and evolutionary tracks of central conditions are shown on a (T, ) diagram. Models heavier than 20M become unstable because of pair creation. Iron photodisintegration causes instability in the mass range between 1.5M and 20M . General relativistic effects bring about the onset of instability in models of 1.2–1.5M when the central density is about 10¹⁰ g/cm³. Lighter models become white dwarfs. It is pointed out that general relativistic instability will prevent the formation of neutron stars through hydrostatic evolution and may be relevant in setting off low-mass supernovae.     

An overview of solar and stellar flare research

An overview of the many topics discussed at IAU Colloquium No. 104 is presented as an introduction to the Proceedings. Suggested areas for future research emerging from the conference are summarized.     

The optical continuum of solar and stellar flares

A further development of the Kostyuk-Pikelner's model is presented. The response of the chromosphere heated by non-thermal electrons of the power-law energy spectrum has been studied on the basis of the numerical solution of the one-dimensional time-dependent equations of gravitational gas dynamics. The ionization and energy loss for the emissions in the Lyman and Balmer lines have been determined separately for the optically thin and thick L-line layers. Due to the initial heating, a higher-pressure region is formed. From this region, disturbances propagate upwards (a shock wave with a velocity of more than 1000 km s^-1) and downwards. A temperature jump propagates downwards, and a shock is formed in front of the thermal wave. During a period of several seconds after the beginning of this process, the temperature jump intensifies the downward shock wave and the large radiative loss gives rise to the high density jump ( ₂/ ₁ 100). The numerical solution has been analyzed in detail for the case heating of the ionized and neutral plasma, and a value of this heating is close to the upper limit of the admissible values. In this case, the condensation located between the temperature jump and the shock wave front, may emit in the observed optical continuum.In their essential features, the gas dynamic processes during the flares in red dwarf atmospheres are the same as those in the solar atmosphere. However, the high atmospheric densities, smaller height scale in red dwarf atmospheres, and greater energy of this processes in stellar flares, give rise, in practice, to the regular generation of optical continuum. The photometric parameters of a source with n 0¹⁵ cm^-3, T 9000 K, and _z 10 km are in a good agreement with observations.     

Existence and uniqueness of stellar equilibrium models

The stellar equilibrium equations for given surface pressureP _* and temperatureT _*, and in the absence of convection, are translated into a nonlinear integral equation, in which the radiusR of the star enters as an eigenvalue. We show that under broad mathematical assumptions on the constitutive equations (equation of state, opacity and energy generation) a global existence and uniqueness property can be formulated. If a valueP _M is selected, which restricts the allowed pressure and temperature range |P(r)–P _*|+E|T(r)–T _*P _M (E, arbitrary constant of dimensions of a pressure over temperature), thenat least one solutionP(r),T(r) exists in the pressure-temperature range chosen, for anyR<R _E . This solution isunique forR<R _c .R _E andR _c are expressed in terms of the constitutive equations, and of the pressure-temperature range adopted. A physical argument in favour of the stability of this solution is presented.     

Dynamic screening in solar and stellar nuclear reactions

In the hot, dense plasma of solar and stellar interiors, the Coulomb interaction is screened by the surrounding plasma. Although the standard Salpeter approximation for static screening is widely accepted and used in stellar modeling, the question of dynamic screening has been revisited. In particular, Shaviv and Shaviv apply the techniques of molecular dynamics to the conditions in the solar core in order to numerically determine the dynamic screening effect. By directly calculating the motion of ions and electrons due to Coulomb interactions, they compute the effect of screening without the mean-field assumption inherent in the Salpeter approximation. Here we reproduce their numerical analysis of the screening energy in the plasma of the solar core and conclude that the effects of dynamic screening are relevant and should be included in the treatment of the plasma, especially in the computation of stellar nuclear reaction rates.     

Asteroseismology and interferometry

Asteroseismology provides us with a unique opportunity to improve our understanding of stellar structure and evolution. Recent developments, including the first systematic studies of solar-like pulsators, have boosted the impact of this field of research within astrophysics and have led to a significant increase in the size of the research community. In the present paper we start by reviewing the basic observational and theoretical properties of classical and solar-like pulsators and present results from some of the most recent and outstanding studies of these stars. We centre our review on those classes of pulsators for which interferometric studies are expected to provide a significant input. We discuss current limitations to asteroseismic studies, including difficulties in mode identification and in the accurate determination of global parameters of pulsating stars, and, after a brief review of those aspects of interferometry that are most relevant in this context, anticipate how interferometric observations may contribute to overcome these limitations. Moreover, we present results of recent pilot studies of pulsating stars involving both asteroseismic and interferometric constraints and look into the future, summarizing ongoing efforts concerning the development of future instruments and satellite missions which are expected to have an impact in this field of research.     

The photon-neutrino coupling theory and stellar models

The effect of the photon-neutrino coupling theory, developed by Bandyopadhyay (1968), on stellar structure is studied by constructing a chemically homogeneous model of one solar mass in thermal equilibrium, and taking into account the neutrinos according to the theory. As anticipated, the effect is large and leads to great difficulties in the understanding of stellar constitution.     

Linear and nonlinear oscillations of simple stellar models

A general property for the stability of the one zone model is derived in the case of linear nonadiabatic radial oscillations. The problem of the nonlinear adiabatic radial oscillations of the homogeneous model with a slow rotational velocity is discussed.     

Reference grids of stellar models and oscillation frequencies

We present grids of stellar models and their associated oscillation frequencies that have been used by the CoRoT Seismology Working Group during the scientific preparation of the CoRoT mission. The stellar models have been calculated with the CESAM stellar internal structure and evolution code while the oscillation frequencies have been obtained from the CESAM models by means of the ADIPLS adiabatic oscillation programme. The grids cover a range of masses, chemical compositions and evolutionary stages corresponding to those of the CoRoT primary targets. The stellar models and oscillation frequencies are available on line through the Evolution and Seismic Tools Activity (ESTA) web site.     

Magnetodynamic phenomena in the solar and stellar outer atmospheres

Magnetic effects causing anomalous heating and drastic flarings in the atmospheres of various types of stars are discussed. The best studied examples of these magnetic effects with spatially resolved observations are those in the case of the Sun, but no simple application of the solar knowledge to the stellar cases is allowed, since there are generally very large differences in the physical conditions between the Sun and other types of stars. We examine possible effects of the magnetic field in the respective situations of several types of stars which show X-ray and radio emissions indicating the presence of such activities, and it is concluded that the magnetic field may be playing important roles in producing anomalous heating and drastic flarings also in those stars having very different physical conditions, in ways seemingly very different from, but intrinsically closely related to, those in the case of the Sun.Invited review paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.