Milliarcsecond resolution observations of cool stars are becoming increasingly common and sophisticated as recent advances in telescope technology mature. To varying degrees, these observations rely up on stellar models for interpretation of their data, while at the same time present particular challenges to those models. Indications of departures from spherical symmetry are beginning to be observed as increasingly rich image information is obtained by a new generation of interferometers. Examination the subtle variations of wavelength-specific sizes exhibits rich structure, connected to the atmospheric chemistry. For the pulsating stars, such as Mira variables, that structure varies with time, with the phase lags between the various sizes being connected to the atmospheric dynamics. Complex morphologies associated with atmospheric winds have been revealed with these high resolution experiments. A review of these recent results will be presented, concentrated on their implications upon stellar modelling, and the prospects for future observational data.

I want to start by addressing the question, ‘What is inversion?’ My answer would be that inversion is the process of going from data to making inferences about the object under study. In the case of helioseismology, the data at the present time are principally the mode frequencies, and the object under study is the solar interior.

This paper is an interim report of our inferences about the hydrostatic structure of the Sun, following the first report of the GONG team in Science (Gough et al., 1996). That work confirms that the spherically averaged structure of the Sun is more or less in agreement with current standard solar models. However, there remain some significant deviations which we regard as important clues to the existence of dynamical phenomena which are not taken into account in standard solar modelling.

The Medium-l Program of the Michelson Doppler Imager (MDI) instrument on board SOHO provides continuous observations of oscillation modes of angular degree, l, from 0 to ∼ 300. The initial results show that the noise in the Medium-l oscillation power spectrum is substantially lower than in ground-based measurements. This enables us to detect lower amplitude modes and, thus, to extend the range of measured mode frequencies. The MDI observations also reveal the asymmetry of oscillation spectral lines. The line asymmetries agree with the theory of mode excitation by acoustic sources localized in the upper convective boundary layer. The sound-speed profile inferred from the mean frequencies gives evidence for a sharp variation at the edge of the energy-generating core. In a thin layer just beneath the convection zone, helium appears to be less abundant than predicted by theory. Inverting the multiplet frequency splittings from MDI, we detect significant rotational shear in this thin layer.

During rapid solidification, deviations from local interfacial equilibrium are manifested by solute trapping and interfacial undercooling. Both the solute trapping function and the interface velocity-temperature function have been measured in the Si:As alloy system following pulsed laser melting, permitting us to test models for nonequilibrium interface kinetics. The results are consistent with the Continuous Growth Model “without solute drag” of Aziz and Kaplan and are inconsistent with models that incorporate solute drag effects during solidification.

It is important for understanding stellar evolution to constrain observationally how overshoot occurs for stellar conditions. Simplified models of the dynamics (eg. Zahn 1991) indicate that overshoot results in a slightly subadiabatic region beyond the convectively unstable layers, followed by an almost discontinuous transition to radiative stratification. Abrupt changes such as this contribute with a characteristic periodic signal to the frequencies ωn,l, of modes of low degree l (Gough 1990). This signature may therefore be detectable for distant stars. Here we show that the signal is sensitive to the “severity” of the overshoot and, of practical importance for the solar case, how it may be extracted from modes of higher degree. Finally we apply our method to solar data.

To analyze the applicability of the method, we consider four stellar models, Z 1 — Z 4, with solar mass, radius (R) and luminosity; of these, Z 2 and Z 4 have overshoot. The bases of the nearly adiabatically stratified region in the models are at radii r d/R = .729, .713, .713 and .700 respectively.

We present results of investigations of different inversion methods for inferring from helioseismic observations the rotation rate in the solar interior as a function of radius and latitude, using a mode set similar to that which is expected from the GONG network.

The rotation of a star perturbs the frequency wnlm of a normal mode by

where n, l and m are the mode ‘quantum’ numbers, θ the colatitude, Ω the rotation rate and Knlm a known function. Until now the observations have not been in terms of individual Δwnlm ’s; rather, coefficients ai(n,l) of a parametrization of the m-dependence of Δwnlm have been given. By representing the latitudinal dependence of the rotation rate in terms of an expansion in cos θ, an inversion of the ai , can be carried out as a series of 1-dimensional inversions. Such inversions have been dubbed “1.5-dimensional”. Our present implementation of a 1.5D procedure follows Schou et al. (1992), and uses a 1, a 3 and a 5.

The effect of the interfacial thermal resistance and the laser energy density on film morphology and the extent of evaporation was studied in the excimer laser processing of copper-sapphire couples. Copper films of 80 nm thickness were sputter-deposited on sapphire substrates and laser-irradiated with energy densities in the range of 0.2 to 3.5 J/cm2. The changes in film morphology and thickness as a function of laser energy density were analyzed by energy dispersive x-ray spectroscopy. Four regimes can be established as a function of the laser energy density. First, for low energy densities up to a critical value, the film is partially removed by thermal stresses. Second, as the energy density is increased above that critical value, larger portions of the film remain attached to the substrate. In this regime adhesion enhancement takes place. Third, a further increase in the energy density results in film evaporation. Finally, the decrease in the specific mass removal rate of copper is related to the formation of a laser generated plasma that shields the sample from the incoming radiation. In this last regime, an intermediate compound may form at the substrate surface. The data were correlated with results from a computer model of the heat flow during laser processing of metal-ceramic couples.

A novel laser-assisted technique for e-beam epitaxial growth of Gex Si1−x alloys on <100> Si has been investigated. During deposition, a XeCl excimer laser is used to either heat, or to melt and crystallize, the Gex Si1−x continuously as the material is evaporated. This process of heating or melting and crystallizing can be continued until the desired film thickness is achieved. At incident laser energy densities which produce melt, the underlying crystalline seed ensures epitaxial growth during the subsequent solidification. Depositions of films up to 3 at.% Ge under this liquid regime, with substrates held nominally at room temperature, exhibited complete epitaxial growth. At energy densities below the melt threshold, enhanced surface mobility for epitaxial alignment is required. Depositions in this regime exhibit only partial epitaxial growth with conversion to fine grained polycrystalline growth after short distances.

We have performed nanosecond-resolution measurements of the lateral electrical resistivity of thin metal films on insulating substrates. Comparison of transient resistivity measurements with optical reflectivity measurements and heat-flow calculations permits the determination of the position and velocity of a planar crystal/melt interface, and an estimate of undercooling during pulsed laser melting of metals. We report detailed results for rapid solidification of Ni, including the observation of hypercooling of .liquid Ni.

Magnetic fields contribute to the splitting of the degeneracy of modes of like order and degree. The splitting is estimated for some simple hypothetical toroidal magnetic field configurations in the sun, and the results are compared with previous asymptotic estimates. Splitting by a field confined to a thin layer at the base of the convection zone is found not to agree with recent measurements.

The component of the frequency splitting of solar five-minute oscillations observed by Duvall, Harvey and Pomerantz that is even in azimuthal degree measures latitudinal and depth variations in the structure of the sun. We indicate how the data hint that there is a shallow perturbation, possibly associated with a magnetic field, that is concentrated at low latitudes.