Ming-Tsung Sun

On the numerical computation of nonlinear force-free magnetic fields

An algorithm has been developed to extrapolate nonlinear force-free magnetic fields from the photosphere, given the proper boundary conditions. This paper presents the results of this work, describing the mathematical formalism that was developed, the numerical techniques employed, and comments on the stability criteria and accuracy developed for these numerical schemes. An analytical solution is used for a benchmark test; the results show that the computational accuracy for the case of a nonlinear force-free magnetic field was on the order of a few percent (less than 5 percent). This newly developed scheme was applied to analyze a solar vector magnetogram, and the results were compared with the results deduced from the classical potential field method. The comparison shows that additional physical features of the vector magnetogram were revealed in the nonlinear force-free case. 41 refs.

Taiwan Oscillation Network

The Taiwan Oscillation Network (TON) is a ground-based network to measure solar intensity oscillations to study the internal structure of the Sun. K-line full-disk images of 1000 pixels diameter are taken at a rate of one image per minute. Such data would provide information onp-modes withl as high as 1000. The TON will consist of six identical telescope systems at proper longitudes around the world. Three telescope systems have been installed at Teide Observatory (Tenerife), Huairou Solar Observing Station (near Beijing), and Big Bear Solar Observatory (California). The telescopes at these three sites have been taking data simultaneously since October of 1994. Anl – v diagram derived from 512 images is included to show the quality of the data.

Probing the subsurface structure of active regions with the phase information in acoustic imaging

We present the phase information of solar p-mode waves constructed with an acoustic imaging technique in the solar interior. There exists a phase shift between the time series constructed with ingoing waves and outgoing waves. We find that this phase shift is different in an active region and the quiet Sun. The p-mode travel time is shorter in the magnetic regions than in the quiet Sun. We construct a three-dimensional phase shift map of the solar interior. As with the acoustic absorption images, the phase shift features of the active region in maps at the surface correlate with magnetic fields. The vertical extension of phase shift features in the active region is smaller in the phase maps constructed with shorter wavelengths. This indicates the vertical spatial resolution of these three-dimensional phase maps is sensitive to the range of modes used in constructing the signal. The actual depths of the phase shift features in the active region may be smaller than those shown in the three-dimensional phase maps.

Acoustic Imaging in Helioseismology

The time-variant acoustic signal at a point in the solar interior can be constructed from observations at the surface, based on the knowledge of how acoustic waves travel in the Sun: the time-distance relation of the p-modes. The basic principle and properties of this imaging technique are discussed in detail. The helioseismic data used in this study were taken with the Taiwan Oscillation Network (TON). The time series of observed acoustic signals on the solar surface is treated as a phased array. The time-distance relation provides the phase information among the phased array elements. The signal at any location at any time can be reconstructed by summing the observed signal at array elements in phase and with a proper normalization. The time series of the constructed acoustic signal contains information on frequency, phase, and intensity. We use the constructed intensity to obtain three-dimensional acoustic absorption images. The features in the absorption images correlate with the magnetic field in the active region. The vertical extension of absorption features in the active region is smaller in images constructed with shorter wavelengths. This indicates that the vertical resolution of the three-dimensional images depends on the range of modes used in constructing the signal. The actual depths of the absorption features in the active region may be smaller than those shown in the three-dimensional images.

A Study of Sunspots with Phase Time and Travel Time of p-Mode Waves in Acoustic Imaging

Solar acoustic signals constructed with the technique of acoustic imaging contain both intensity and phase information. The phase of constructed signals can be studied by computing the cross-correlation function between time series constructed with ingoing and outgoing waves. The envelope peak of the cross-correlation function provides information about wave travel time, associated with the group velocity along the wave path. The phase time of the cross-correlation function provides information about phase changes along the wave path, including the phase change at boundaries of the mode cavity and boundaries of flux tubes. We study the active region NOAA 7978 using the data taken with the Michelson Doppler Imager (MDI) instrument. We construct two-dimensional phase-shift maps and envelope-shift maps of the active region at the surface by determining the phase time and envelope time of the cross-correlation function at each point. Both phase time and envelope time in magnetic regions are smaller than those in the quiet Sun. The phase shift and envelope shift at each point are computed by subtracting the average values in the quiet Sun. The envelope shift is greater than the phase shift by about 2.5 minutes inside sunspots. Both the envelope shift and the phase shift in sunspots increase approximately linearly with frequency. The difference between the envelope shift and phase shift is the same at different frequencies. There is evidence for an additional phase shift in sunspots relative to plages. We discuss inferences about the structure of sunspots from these phenomena.

Comparison of Two Fitting Methods for Ring Diagram Analysis of Very High l Solar Oscillations

A new method of fitting tridimensional power spectra of solar oscillations is described and compared with a previous one whose use has been more common. The new method fits the parameters of the Lorentzian profiles in a bidimensional k - ω diagram constructed from an azimuthal average of the tridimensional one. The horizontal velocities are then determined keeping these parameters fixed, greatly reducing the computation time. Both methods are compared for two radial orders (n = 3, 4) of a tridimensional power spectrum obtained for a region of about 15° square around solar disk center. The images used in this work correspond to a 3 day set of 1080 × 1080 pixel intensity images obtained at the Observatorio del Teide on 1994 November 8-10 with the Taiwanese Oscillation Network (TON) instrument. The results of the fitted velocities agree within the estimated errors for the two methods. The reduction of the computing time obtained with the new method makes it convenient for the ring diagram analysis.

SPATIAL DISTRIBUTIONS OF ABSORPTION, LOCAL SUPPRESSION, AND EMISSIVITY REDUCTION OF SOLAR ACOUSTIC WAVES IN MAGNETIC REGIONS

Observed acoustic power in magnetic regions is lower than the quiet Sun because of absorption, emissivity reduction, and local suppression of solar acoustic waves in magnetic regions. In the previous studies, we have developed a method to measure the coefficients of absorption, emissivity reduction, and local suppression of sunspots. In this study, we go one step further to measure the spatial distributions of three coefficients in two active regions, NOAA 9055 and 9057. The maps of absorption, emissivity reduction, and local suppression coefficients correlate with the magnetic map, including plage regions, except the emissivity reduction coefficient of NOAA 9055 where the emissivity reduction coefficient is too weak and lost among the noise.

MEASUREMENTS OF ABSORPTION, EMISSIVITY REDUCTION, AND LOCAL SUPPRESSION OF SOLAR ACOUSTIC WAVES IN SUNSPOTS

The power of solar acoustic waves in magnetic regions is lower relative to the quiet Sun. Absorption, emissivity reduction, and local suppression of acoustic waves contribute to the observed power reduction in magnetic regions. We propose a model for the energy budget of acoustic waves propagating through a sunspot in terms of the coefficients of absorption, emissivity reduction, and local suppression of the sunspot. Using the property that the waves emitted along the wave path between two points have no correlation with the signal at the starting point, we can separate the effects of these three mechanisms. Applying this method to helioseismic data filtered with direction and phase-velocity filters, we measure the fraction of the contribution of each mechanism to the power deficit in the umbra of the leading sunspot of NOAA 9057. The contribution from absorption is 23.3 ± 1.3%, emissivity reduction 8.2 ± 1.4%, and local suppression 68.5 ± 1.5%, for a wave packet corresponding to a phase velocity of 6.98 × 10–5 rad s–1.

Measurements of Absorption of Acoustic Waves in Sunspots with Direction Filters and Cross Correlation

Observations show that the power of solar acoustic waves is reduced inside magnetic regions. Several mechanisms, including absorption, emissivity reduction, and local suppression, may contribute to the observed power reduction in magnetic regions. So far there is no way to distinguish absorption from emissivity reduction in a magnetic region. In this study, we use the property that the waves emitted along the wave path between two points have no correlation with the signal at the starting point to separate absorption from emissivity reduction in a sunspot, and measure the absorption coefficient in the sunspot. This method uses the direction filter, phase-velocity filter, and cross correlation. We apply this method to an active region, NOAA 9062. The absorption coefficient of the leading sunspot of NOAA 9062 is 0.23 ± 0.01 determined from the wave packet traveling northward with a phase velocity of 6.98 × 10 −5 rad s −1 , corresponding to l = 300 at 3.33 mHz. The absorption coefficient is 0.17 ± 0.03 determined from the wave packet traveling southward. The corresponding contribution of absorption to the power deficit in the sunspot is 0.15 ± 0.01, in units of power in the quiet Sun, for the northward waves, and 0.11 ± 0.02 for the southward waves.

Numerical investigation of macro- and micro-mechanics of a ceramic veneer bonded with various cement thicknesses using the typical and submodeling finite element approaches

OBJECTIVES This study investigates the influence of cement thickness on the macro- and micro-mechanical responses in a ceramic veneer adjacent to an incisal overlapped incisor. METHODS Seven finite element (FE) ceramic veneer macro-models with different cement thicknesses (10-180mum) were generated. A 10N load was applied with an angulation of 60 degrees to the longitudinal tooth axis. Seven FE micro-models corresponding to the macro-models were constructed at an enamel-adhesive interface where the stress concentration was found. Based on an interfacial scanning electron microscope (SEM) micrograph, morphology of resin tags in the micro-models was generated. The micro-model boundary conditions were determined from the macro-model results. The principal stress on each node in the macro- and micro-models was calculated to investigate interfacial mechanics. A tensile test was performed to obtain an ultimate cement tensile strength to determine the material failure parameters. RESULTS The highest stress concentration within the cement was found at the resin tag base of the enamel-adhesive interface in lingual side. Maximum stress values from 10.6 to 14.7MPa for the micro-models were higher (44-48%) than that from 7.2 to 10.0MPa for the macro-models when the cement layers increased. Based on the ultimate tensile strength (11.8MPa), bonding failure could found when the micro-models with the cement layers presented more than about 50mum. This seems to correspond with data from previous studies. CONCLUSIONS Higher stresses develop in the adhesive as the cement thickness increases. Cement thicknesses less than 50mum might reduce the adhesive bonding failure.