Engineering topics
Publications and source records attributed to Kalkofen, W..
The paper lists US solar missions, both those planned and funded by NASA alone as well as those carried out in collaboration with other space agencies. Soe of the missions are now in operation, the others are either planned and approved or under active discussion. The paper also describes the principal scientific objects of the missions and gives some orbital characteristics.
We examine the equilibrium structure of vertical intense magnetic flux tubes on the Sun. Assuming cylindrical geometry, we solve the magnetohydrostatic equations in the thin flux-tube approximation, allowing for energy transport by radiation and convection. The radiative transfer equation is solved in the six-stream approximation, assuming gray opacity and local thermodynamic equilibrium. This constitutes a significant improvement over a previous study, in which the transfer was solved using the multidimensional generalization of the Eddington approximation. Convection in the flux tube is treated using mixing-length theory, with an additional parameter alpha, characterizing the suppression of convective energy transport in the tube by the strong magnetic field. The equations are solved using the method of partial linearization. We present results for tubes with different values of the magnetic field strength and radius at a fixed depth in the atmosphere. In general, we find that, at equal geometric heights, the temperature on the tube axis, compared to the ambient medium, is higher in the photosphere and lower in the convection zone, with the difference becoming larger for thicker tubes. At equal optical depths the tubes are generally hotter than their surroundings. The results are comparatively insensitive to alpha but depend upon whether radiative and convective energy transport operate simultaneously or in separate layers. A comparison of our results with semiempirical models shows that the temperature and intensity contrast are in broad agreement. However, the field strengths of the flux-tube models are somewhat lower than the values inferred from observations.
This work is motivated by the chromospheric 3 minute oscillations observed in the K(sub 2v) bright points. We study acoustic gravity waves in a one-dimensional, gravitationally stratified, isothermal atmosphere. The oscillations are excited either by a velocity pulse imparted to a layer in an atmosphere of infinite vertical extent, or by a piston forming the lower boundary of a semi-infinite medium. We consider both linear and non-linear waves.
We analyze differences in solar oscillations between the chromospheric network and internetwork regions from a 1 hr sequence of spectrograms of a quiet region near disk center. The spectrograms contain Ca II H, Ca I 422.7 nm, and various Fe I blends in the Ca II H wing. They permit vertical tracing of oscillations throughout the photosphere and into the low chromosphere. We find that the rms amplitude of Ca II H line center Doppler fluctuations is about 1.5 km/s for both network and internetwork, but that the character of the oscillations differs markedly in these two regions. Within internetwork areas the chromospheric velocity power spectrum is dominated by oscillations with frequencies at and above the acoustic cutoff frequency. They are well correlated with the oscillations in the underlying photosphere, but they are much reduced in the network. In contrast, the network Ca II H line center velocity and intensity power spectra are dominated by low-frequency oscillations with periods of 5-20 min. Their signature is much clearer in our Ca II H line center measurements than in previously used diagnostics which are contaminated by signals from deeper layers. We find that these long-period oscillations are not correlated with underlying photospheric disturbances, and we discuss their nature.
The thermal structure of the medium inside thin, vertical magnetic flux tubes embedded in a given external atmosphere is investigated, assuming cylindrical symmetry and a depth-independent plasma beta. The variation with tube radius of the temperature on the tube axis is computed and the temperature on the tube wall is estimated. The temperature variation across the flux tube is found to be due to the depth variation of the intensity and to the density stratification of the atmosphere. Since the temperature difference between the axis and the wall is small in thin flux tubes (of the order of 10 percent), the horizontal temperature gradient may often be neglected and the temperature in a tube of given radius may be described by a single function of depth. Thus, a more detailed numerical treatment of the radiative transfer within thin flux tubes can be substantially simplified by neglecting horizontal temperature differences within the flux tube proper.
The stability of current-driven filamentary modes in magnetic flux tubes embedded in a plane-parallel atmosphere in LTE and in hydrostatic equilibrium is discussed. Within the tube, energy transport by radiation only is considered. The dominant contribution to the opacity is due to H- ions and H atoms (in the Paschen continuum). A region in the parameter space of the equilibrium configuration in which the instability is effective is delimited, and the relevance of this process for the formation of structured coronae in late-type stars and accretion disks is discussed.
A model atmosphere within a thin magnetic flux tube that is embedded in an arbitrarily stratified medium is presently constructed by solving the radiative transfer equation in the two-stream approximation for gray opacity, under the assumption that the magnetic field is sufficiently strong to warrant the neglect of both thermal conduction and convective diffusion; energy inside the flux tube therefore being transported solely by radiation. The structure of the internal atmosphere is determined on the basis of the hydrostatic and radiative equilibrium conditions of the tube embedded in an external atmosphere. The gas temperature along the axis of the tube is computed, and the geometry of the flux tube is determined on the basis of magnetic flux conservation and total pressure equilibrium.
The propagation and shock formation of radiatively damped acoustic waves in the solar chromosphere are studied under the assumption that H(-) is the only absorber; the opacity is non-grey. Deviations from local thermodynamic equilibrium (LTE) are permitted. The results of numerical simulations show the depth dependence of the heating by the acoustic waves to be insensitive to the mean state of the atmosphere. After the waves have developed into shocks, their energy flux decays exponentially with a constant damping length of about 1.4 times the pressure scale height, independent of initial flux and wave period. Departures from LTE have a strong influence on the mean temperature structure in dynamical chromosphere models; this is even more pronounced in models with reduced particle density - simulating conditions in magnetic flux tubes - which show significantly increased temperatures in response to mechanical heating. When the energy dissipation of the waves is sufficiently large to dissociate most of the H(-) ions, a strong temperature rise is found that is reminiscent of the temperature structure in the transition zone between chromosphere and corona; the energy flux remaining in the waves then drives mass motions.
Under the assumption that dust is either homogeneously mixed throughout or confined to either 1/2 or 1/4 of the space in question, the effect of absorption and scattering by dust grains on resonance lines that were formed in static gaseous nebulae with plane-parallel stratification is studied and a comparison is made between the total emergent flux in the line from the dust-filled nebula and the emergent flux from a dust-free medium. Many line optical thickness values, and several combinations of the opacity ratio of dust and gas, dust albedo, and collision parameter, are compared. A novel method is used to analytically solve the transfer equation for a spectral line in the presence of scattering and absorbing dust. It is noted that dust distribution can have large effects on the value of the total emergent flux.
The assumptions of Ayres' model of the upper solar atmosphere are examined. It is found that the bistable character of his model is postulated - through the assumptions concerning the opacity sources and the effect of mechanical waves, which are allowed to destroy the CO molecules but not to heat the gas. The neglect of cooling by metal lines is based on their reduced local cooling rate, but it ignores the increased depth over which this cooling occurs. Thus, the bifurcated model of the upper solar atmosphere consists of two models, one cold at the temperature minimum, with a kinetic temperature of 2900 K, and the other hot, with a temperature of 4900 K.
The effect of slow-mode acoustic-type MHD waves propagating outward in the solar atmosphere on the temperature structures predicted by empirical models is investigated analytically. A model is constructed, and numerical results are presented for wing intensities, line profiles, temperature enhancements, waves with higher energy flux, temperature depression, and the Si continuum. The flux in the MgII and CaII UV resonance lines is found to be increased relative to that in the IR continuum, leading to model temperatures which depend systematically on which observations are used in the computation. It is suggested that mechanical heating may take place in smaller regions such as flux tubes rather than uniformly over the surface.
A dynamical model was proposed which is in agreement with the observations that suggest the solar chromosphere is heated preferentially in magnetic regions. The dynamical model requires an energy flux that is large enough to lead to amplitudes for which the apparent temperatures match the empirical line temperatures in the UTV lines. Consistency with the observations of chromospheric emission then requires that the emission take place not uniformly over the solar surface but in smaller spatial regions.
The existence of a physically realizable domain in which approximations that lead to a self consistent solution for flux tube stratification in the solar atmosphere, without ad hoc hypotheses, is proved. The transfer equation is solved assuming that no energy transport other than radiative is present. Convective motions inside the tube are assumed to be suppressed by magnetic forces. Only one parameter, the plasma beta at tau = 0, must be specified, and this can be estimated from observations of spatially resolved flux tubes.
A numerical technique for solving the line transfer equation of a two-level atom in static equilibrium is presented. Complete redistribution of emitted photons is assumed, as is saturation at the line core. Emission intensity is calculated either by a generalized Eddington-Barber relation, a first-order differential equation for the specific intensity, or by a formal transfer integral. Sample calculations are performed of the line transfer equation in a semi-infinite atmosphere with a constant Planck function of the collision parameter and for the Mg II resonance line in a model solar atmosphere experiencing shocks. Attention is focused on the line wings in the latter problem. The first order differential equation approach yields the best intensity values and temperature structure.
A method for defining spherical model atmospheres in radiative/convective and hydrostatic equilibrium is presented. A finite difference form is found for the transfer equation and a matrix operator is developed as the discrete space analog (in curvilinear coordinates) of a formal integral in plane geometry. Pressure is treated as a function of temperature. Flux conservation is maintained within the energy equation, although the correct luminosity transport must be assigned for any given level of the atmosphere. A perturbed integral operator is used in a complete linearization of the transfer and constraint equations. Finally, techniques for generating stable solutions in economical computer time are discussed.
The current empirical models of the solar atmosphere which have kinetic temperatures that are too low at the temperature minimum to balance radiative heating and cooling are examined. It was noted that when there is additional energy input from the dissipation of hydrodynamic waves the apparent imbalance is aggravated. It is suggested that the problem lies in the assumption of a static upper photosphere. It is proposed that the mechanical waves, which further out cause the chromospheric temperature rise, traverse the temperature minimum region with large amplitude and produce the apparent nonconservation of energy as well as other difficulties of the empirical models through nonlinear, time dependent effects.
A static atmosphere with only Lyman continuum radiation in radiative equilibrium is studied for the effects of radiative and collisional ionization on deviations from local thermodynamic equilibrium (LTE). Large increases and decreases of the kinetic temperature (range in T of about factor 2) and, correspondingly, very large over- and underpopulation of the bound state (range in b of about factor 1,000,000) are found, depending on the frequency dependence of the photoionization cross section. Despite these large deviations from LTE, which strongly modify the emergent spectrum, there is almost no effect on the particle densities, the degree of ionization, and the basic structure of the atmosphere.
Deviations for LTE are investigated in an atmosphere of hydrogen atoms with one bound level, satisfying the equations of radiative, hydrostatic, and statistical equilibrium. The departure coefficient and the kinetic temperature as functions of the frequency dependence of the radiative cross section are studied analytically and numerically. Near the outer boundary of the atmosphere, the departure coefficient is smaller than unity when the radiative cross section grows with frequency faster than with the square of frequency; it exceeds unity otherwise. Far from the boundary the departure coefficient tends to exceed unity for any frequency dependence of the radiative cross section. Overpopulation always implies that the kinetic temperature in the statistical-equilibrium atmosphere is higher than the temperature in the corresponding LTE atmosphere. Upper and lower bounds on the kinetic temperature are given for an atmosphere with deviations from LTE only in the optically shallow layers when the emergent intensity can be described by a radiation temperature.