Engineering topics

Christensen-Dalsgaard, J.

Publications and source records attributed to Christensen-Dalsgaard, J..

15 records

NASA NTRS2003

A Comparison of Solar p-Mode Parameters from MDI and Gong: Mode Frequencies and Structure Inversions

Helioseismic analysis of solar global oscillations allows investigation of the internal structure of the Sun. One important test of the reliability of the inferences from helioseismology is that the results from independent sets of contemporaneous data are consistent with one another. Here we compare mode frequencies from the Global Oscillation Network Group and Michelson Doppler Imager on board SOHO and resulting inversion results on the Sun's internal structure. The average relative differences between the data sets are typically less than 1 x 10(exp -5) substantially smaller than the formal errors in the differences; however, in some cases the frequency differences show a systematic behavior that might nonetheless influence the inversion results. We find that the differences in frequencies are not a result of instrumental effects but are almost entirely related to the data pipeline software. Inversion of the frequencies shows that their differences do not result in any significant effects on the resulting inferences on solar structure. We have also experimented with fitting asymmetric profiles to the oscillation power spectra and find that, compared with the symmetric fits, this causes no significant change in the inversion results.

Basu, S.↗

NASA NTRS1994

On comparing helioseismic two-dimensional inversion methods

We consider inversion techniques for investigating the structure and dynamics of the solar interior as functions of radius and latitude. In particular, we look at the problem of inferring the radial and latitudinal dependence of the Sun's internal rotation, using a fully two-dimensional least-squares inversion algorithm. Concepts such as averaging kernels, measures of resolution, and trade-off curves, which have previously been used in the one-dimensional case, are generalized to facilitate a comparison of two-dimensional methods. We investigate the weighting given to different modes and discuss the implications of this for observational strategies. As an illustration we use a mode set whose properties are similar to those expected for data from the GONG network.

Schou, J.↗

NASA NTRS1992

Sources of uncertainty in direct seismological measurements of the solar helium abundance

The methods by which Dappen et al. (1988, 1990, 1991) and Dziembowski et al. (1990, 1991, 1992) recently obtained discrepant estimates of the helium abundance in the solar convection zone are compared. The aim of the investigation reported in this paper is to identify the main source of the discrepancy. Using as proxy data eigenfrequencies of a set of modes of a theoretical solar model, computed with the same physics as were the frequencies of a reference model with which these data are compared, the two methods yield similar results. Thus we ascertain that the principal source of the discrepancy is not in the inversions themselves, which yield essentially a measure of the variation of the adiabatic exponent gamma of the material in the He II ionization zone. Instead it is in the approximations adopted in the treatment of heavy elements in the equation of state used to relate the variation of gamma to chemical composition. We obtain acceptably consistent results when inverting solar data by two methods using the same equation of state. We attempt to identify the likely residual sources of uncertainty.

Kosovichev, A. G.↗

NASA NTRS1992

On the rate of destruction of lithium in late-type main-sequence stars

It it shown that the rate of destruction of lithium by nuclear reactions in the outer mixed layers of late-type main-sequence stars depends on both the depth of the region where mixing occurs and the stratification within it. The mixed region includes and probably extends beneath the base of the convection zone. As the star evolves on the main sequence, the properties of the convection zone vary in a simple manner. If the mixed layer behaves similarly, then the mean destruction rate can easily be related to the present local value evaluated at the base of the mixed layer. In the case of the sun, it is found that if mixing is rapid compared with the nuclear destruction rate, then the mean destruction rate is approximately equal to one-half the present local value.

Christensen-Dalsgaard, J.↗

NASA NTRS1992

The influence of a vertical magnetic field on oscillations in an isothermal stratified atmosphere

The effect of a uniform vertical magnetic field on the modes of an isothermal stratified atmosphere is examined. The general solutions of the wave equation for an isothermal magnetized medium are given. Asymptotic expansions of these solutions are presented in the strong- and weak-field limits. For a weak field, it is found that, to lowest order of the present perturbation expansion, the oscillation spectrum can be analyzed in terms of p- and g-like modes, magnetic Lamb modes, and magnetic or slow modes. The frequency corrections for each of the modes due to coupling with the remaining modes are calculated. It is demonstrated that when the frequencies of different modes are almost identical, strong mode coupling occurs and the waves acquire a mixed character. An analysis of the solutions in the vicinity of the degenerate frequencies is carried out. The solutions reveal the presence of avoided crossings, which occur at the otherwise degenerate frequencies. Examples of different types of avoided crossings are given.

Hasan, S. S.↗

NASA NTRS1992

Solar models with enhanced energy transport in the core

The discrepancy between the observed and computed flux of solar neutrinos can be eliminated if the temperature gradient in the core of the model, and hence its central temperature, is reduced. This could in principle be accomplished by reducing the core opacity; alternatively, it has been proposed that a fraction of the energy transport in the solar core results from the motion of hypothetical particles (the so-called WIMPs). The resulting changes in solar structure have measurable effects on the frequencies of the solar 5-minute oscillations. Here, models are considered where the opacity in the solar core has been decreased in a manner which roughly simulates the effects of the WIMPs. The analysis of the models and their frequencies provides insight into the consequences of modifications to the physics of solar models. In particular, it is found that models with the observed neutrino flux are inconsistent with observations of low-degree solar oscillations.

Christensen-Dalsgaard, J.↗

NASA NTRS1991

The depth of the solar convection zone

The transition of the temperature gradient between being subadiabatic and adiabatic at the base of the solar convection zone gives rise to a clear signature in the sound speed. Helioseismic measurements of the sound speed therefore permit a determination of the location of the base of the convection zone. Two techniques were tested by applying them to artifical data, obtained by adding simulated noise to frequencies computed from two different solar models. The determinations appear to be relatively insensitive to uncertainties of the physics of the solar interior. From an analysis of observed frequencies of solar oscillation it is concluded that the depth of the solar convection zone is (0.287 + or - 0.003) solar radii.

Christensen-Dalsgaard, J.↗

NASA NTRS1991

The response of the adiabatic exponent Gamma(1) to modifications of solar models

Guenther et al. (1989) investigated the effet of varying the abundance of elemental Ne on solar models and found that the changes in some aspects of these models in the ionization zones of helium and hydrogen were nonmonotonic functions of the assumed Ne abundance. In this paper, the results of Guenther et al. are examined, and it is found that the apparent nonmonotonic behavior of the models was caused by slight errors in the radii of their models, combined with the fact that the adiabatic exponent Gamma(1) was compared at fixed distance r from the center of the model. When the models are compared at fixed fractional radius r/R, the differences in the values of Gamma(1) were found to behave in a much more regular way.

Christensen-Dalsgaard, J.↗

NASA NTRS1985

Seismology of the sun

The use of the sun's oscillations, caused by the constructive interference between internally reflected waves, to study the interior of the sun is examined. Pressure and buoyancy have the strongest influence on oscillations; pressure fluctuations at high frequency produce acoustic waves and at low frequency buoyancy produces internal gravity waves. The theory of acoustic wave frequency, which is used to determine measurements of sound speed and rate of rotation of the solar interior as well as the thickness of the convection zone, is presented. The classification of solar oscillations is described. The models for acoustic modes of low degree and intermediate degree are discussed. The effect of internal speed, gravity modes, and solar rotation on solar models is determined. The oscillation frequencies yield an He abundance that is consistent with cosmology, but they reinforce the severity of the neutrino problem.

Christensen-Dalsgaard, J.↗

NASA NTRS1985

Speed of sound in the solar interior

The sound speed of the solar interior is directly determinable on the basis of the frequencies of solar 5-min oscillations, irrespective of solar model, and relying only on a simple asymptotic description of the oscillations in terms of trapped acoustic waves. It is plausible that, by using this asymptotic determination as an initial trial in a more accurate inversion, and imposing constraints of smoothness on the solution resulting from the iteration, a good model representing the large scale structure of the sun which satisfies the observed frequencies may be determined.

Christensen-Dalsgaard, J.↗

NASA NTRS1984

Rotational Inversion from Global Solar Oscillations

The degree to which various sets of solar oscillations can resolve the solar internal rotation was investigated. Genuine observations were simulated by the following procedure; first an artificial angular velocity was invented, and from it the rotational splitting of a set of normal modes was calculated; to that was added some random noise. The result was treated as artificial data and an attempt to recover the rotation law by using the Backus-Gilbert optimal averaging procedure was made. Neither the original rotation law nor the amount of noise that had been added was known. The conclusion was compared with the actual artificial angular velocity.

Christensen-Dalsgaard, J.↗

NASA NTRS1984

Implications of Observed Frequencies of Solar P Modes

A preliminary comparison is made of the observed frequencies of 5 min P modes with theoretical frequencies for a traditional solar model. The differences between observations and theory can be understood qualitatively in terms of two separate sources of error in the frequency calculation, one near the solar surface and the other at the base of the convection zone. There is no indication of errors in the deep interior of the model.

Christensen-Dalsgaard, J.↗

NASA NTRS1984

Optimized Response Functions for 2-dimensional Observations of Solar Oscillations

Response functions are calculated for solar oscillation observations made in Doppler velocity which is averaged over a grid of 30" x 30" pixels. In a simulation of an analysis scheme proposed for the HAO/SPO Fourier Tachometer the responses for the individual pixels are combined using Chebychev weighting functions. It is shown how a technique developed for geophysical inversion may be used to find linear combinations concentrated within a fairly narrow range of l and m values of these transformed responses. The extension to bidirectional observations is discussed.

Christensen-Dalsgaard, J.↗

NASA NTRS1984

Analysis and Interpretation of Synthetic Time Strings of Oscillation Data

Artificial strings of solar oscillation data with gaps and noise, corresponding to the output of different spatial filter functions, were analyzed. Peaks in the power spectrum are identified for values of the degree l from 0 to 18, and rotational splitting is estimated. The filters prove effective in facilitating identification of essentially all the real peaks in the power spectrum. Estimates of peak frequencies and amplitudes and rotational splitting frequencies are in reasonably good agreement with the input values. Spurious peaks in autocorrelation spectra correspond to the frequency spacing between power peaks with the same order n, differing by one or two in the degree l.

Mihalas, B. W.↗

NASA NTRS1982

Observation of additional low-degree 5-min modes of solar oscillation

High-order solar oscillations with degrees l=3, 4, and 5 could be detected. The observations were made by measuring the difference between the shifts in the Fe 5,124 spectrum line from light integrated from a central circular portion of the solar disk and from an annular portion exterior to it. The frequencies of the octupole modes agree well with the values obtained from whole-disk measurements at the South Pole. A least-squares fit of the observed frequencies to values interpolated between and extrapolated from the predictions of a sequence of solar models with different chemical compositions selects two models. One, a helium-rich solution, agrees with that of similar analyses of whole-disk data. The extrapolated solution has a relatively deep convection zone, and is thus consistent with analyses of 5-min oscillations of high degree.

Scherrer, P. H.↗