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1.
Carl A. Rouse 《Solar physics》1987,110(2):211-235
Radial and nonradial oscillation equations without and with the gravitation perturbation (with and without the Cowling approximation, CA) are solved numerically using the profile from a more accurate high-Z core (HZC) solar model. This more accurate HZC model was generated with the CRAY X-MP/48 supercomputer at the San Diego Supercomputer Center. Frequencies of oscillation in the five-min band (5MB) and frequencies with period near 160 min are presented in tables and plotted in echelle diagrams. The model was generated by integrating the stellar structure equations from the center to he surface, as done in Rouse (1964), using a maximum space step, ;x
m
= 5 × 10–4, decreasing to 10–6 in the hydrogenionization zone just below the photosphere. Two subsets of space mesh points are used to calculate the oscillation frequencies, viz., one with a maximum space step of 5 × 10–3, decreasing to 10–6 with a total of 621 points (mesh 5I) and the other with a maximum space step of 2 × 10–3, with a total of 867 points (mesh 5J).With the surface boundary condition applied at x = 1.0, the l – 1 degree nonradial frequencies with CA and the l-degree frequencies without CA are in very good agreement with the frequency spacings for observed frequencies of oscillation labeled l = 1 to 5, but with the l – 1 frequencies with CA about 10 Hz or so less than the observations and the l frequencies without CA about 10 Hz or so greater than the observations. And for the Duvall and Harvey (1983) observations labeled l = 10 and l = 20, the l = 9 and l = 19 nonradial solutions with CA agree to about 5 Hz or less with the observations. Considering from the two preceeding papers in this series that increasing the density in the outer envelope and photosphere will increase the 5MB frequencies and applying the outer boundary condition at x > 1.0 will decrease the 5MB frequencies, the net affects of such changes could move one or the other set of frequencies closer to the observations — or require a slightly different model structure to obtain accurate agreements with the values of the observed frequencies throughout the 5MB.In either case, it is concluded that the first-order, radially-symmetric structure of the model outside the HZC is close to the structure of the real Sun. This is of fundamental importance because a real gas adiabatic temperature gradient (Rouse, 1964, 1971) is used in the outer convective region without free parameters.Other aspects of agreements and differences between radial and nonradial solutions, with CA and without CA are discussed. In particular, the l = 4, 6, 8, and 9 g-mode solutions with CA indicate that the observed 160.01 min period may be a common l-mode period of oscillation. More research is proposed. 相似文献
2.
In this study V2109 Cyg (a pulsating δ Scuti star) has been modelled. In treating the oscillation equations perturbation in gravitational potential energy has been taken into account. Both radial and nonradial oscillations are treated with adiabatic approximation. The so called radial fundamental frequency (5.3745 c/d) and the nonradial frequency (5.8332 c/d) were obtained within a satisfactory precision. It was found that the Cowling approximation introduced more error as one went from low overtones to high overtones in radial oscillations. A similar trend was observed in nonradial case with low values of l. By keeping the effective temperatures almost the same as with V2109 Cyg two more models with different masses have also been calculated to see the effect of inclusion of perturbation in gravitational potential energy on oscillation frequencies in different masses. Conclusion arrived is that one must be careful to employ the Cowling approximation especially for high nonradial oscillation frequencies. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
3.
Arthur N. Cox 《Solar physics》1990,128(1):123-131
We consider the rotation independent (m = 0) frequencies of Hill and Gu (1988) and Henning and Scherrer (1988). Comparison with Cox, Guzik, and Kidman (CGK) frequencies shows that CGK are systematically 5.7 ± 0.7% larger. This effect may be due to the larger central density in this model (162 g cm–3) compared to the real Sun. A known systematic error of about one percent in the pressure calculated by the Iben (1965) procedure can account for the higher CGK central helium and density. A check of this increase of g-mode frequency with central density is made by calculating g-mode frequencies for a WIMP model with a central density of 210 g cm–3. This 30% density increase gives a 17% frequency increase, and implies a law with frequency increasing with the 17/30 power of the central density. Thus the 5.7% decrease of frequencies from the model to the real Sun indicates a central density decrease of about 9.7% to about 147 g cm–3. Comparison with the recent van der Raay g-mode frequencies shows that the CGK model frequencies are about 14% larger, as one would expect for these observed frequencies with a large P
0 of 41.2 min.Destabilizing mechanisms of the normal -effect at the top of the convection zone and convection blocking at the bottom of the convection zone for low order and low-l
g-modes produces pulsation driving that does not seem to be damped by radiation and convection effects at the surface. Since the surface motions are very small, photospheric damping does not stabilize these modes at it does for the 5-min p-modes. For higher-order and degree modes, deep damping by radiation flow across nodes overwhelms the destabilization and any small effect. 相似文献
4.
More than 20 real periodicities ranging from 20 days to 2 years modulate the solar irradiance data accumulated since November 1978 by Nimbus 7. Many are quite strong during the first three years (solar maximum) and weak after that. There is a high correspondence between periods in irradiance and 28 periods predicted from the rotation and beating of global solar oscillations (r-modes and g-modes). Angular states = 1, 2, and 3 are detected as well as some unresolved r-mode power at higher . The prominence of beat periods implies a nonlinear system whose effective nonlinear power was measured to be about 2. This analysis constitutes a detection of r-modes in the Sun and determines from them a mean sidereal rotation rate for the convective envelope of 459 ± 4 nHz which converts to a period of 25.2 days (27.ld, synodic). 相似文献
5.
Kosovichev A. G. Schou J. Scherrer P. H. Bogart R. S. Bush R. I. Hoeksema J. T. Aloise J. Bacon L. Burnette A. De Forest C. Giles P. M. Leibrand K. Nigam R. Rubin M. Scott K. Williams S. D. Basu Sarbani Christensen-dalsgaard J. DÄppen W. Duvall T. L. Howe R. Thompson M. J. Gough D. O. Sekii T. Toomre J. Tarbell T. D. Title A. M. Mathur D. Morrison M. Saba J. L. R. Wolfson C. J. Zayer I. Milford P. N. 《Solar physics》1997,170(1):43-61
The medium-l program of the Michelson Doppler Imager instrument on board SOHO provides continuous observations of oscillation modes of angular degree, l, from 0 to 300. The data for the program are partly processed on board because only about 3% of MDI observations can be transmitted continuously to the ground. The on-board data processing, the main component of which is Gaussian-weighted binning, has been optimized to reduce the negative influence of spatial aliasing of the high-degree oscillation modes. The data processing is completed in a data analysis pipeline at the SOI Stanford Support Center to determine the mean multiplet frequencies and splitting coefficients. 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. This is important for inferring the Sun's internal structure and rotation. 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. The results also confirm the previous finding by the GONG (Gough et al., 1996) that, 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. This layer is likely to be the place where the solar dynamo operates. In order to understand how the Sun works, it is extremely important to observe the evolution of this transition layer throughout the 11-year activity cycle. 相似文献
6.
Global oscillations of the Sun (r-modes) with very long periods 1 month are reviewed and studied. Such modes would be trapped in an acoustic cavity formed either by most of the convective envelope or by most of the radiative interior. A turning point frequency giving cavity boundaries is defined and the run of eigenvalues for angular harmonics l 3 are plotted for a conventional solar convection zone. The r-modes show equipartition of oscillatory energy among shells which each contain one antinode in the radial dimension. Toroidal motion is dominant to at least the 14th radial harmonic mode. Viscosity from convective turbulence is strong and would damp any mode in just a few solar rotations if it were the only significant nonadiabatic effect. Radial fine splitting which lifts the degeneracy in n is very small (20 nHz or less) for all n 14 trapped in the envelope. But, if splitting could be detected, we would have a valuable new constraint on solar convection theories. 相似文献
7.
Charles L. Wolff 《Solar physics》1984,93(1):1-13
Solar irradiance measurements from the ACRIM experiment show a clear response to the rotation periods of g-mode oscillations (l = 1, 2, and 3) and their first harmonics. Peaks in the ACRIM spectrum at 16.6, 18.3, 20.7, 36.5, and - 71 days all lie within about 1% of periods arising from g-mode rotation. This means that the g-modes are a fundamental cause of irradiance fluctuations. On time scales of months and less they modulate the irradiance by means of transient flows of global scale which they stimulate in the Sun's convective envelope. Dimensional arguments indicate that the flows carry up heat at an average rate 10-3
L
which is not in conflict with observed changes in the irradiance. Five additional tests for g-modes and large-scale convection are given. An instability is described which undermines diffusion models of sunspot energy storage. 相似文献
8.
Medium resolution CCD-spectrograph observations have been obtained that are suitable for studying long spatial wavelength 5-min oscillations. We find evidence that at wavelengths of order one solar radius the oscillation field is not isotropic. It is also not well described by modes of uniform excitation. The velocity power density per spherical harmonic increases with decreasing l to 1.1 × 103 cm2 s–2 per 3.5 × 10–4 Hz angular frequency bandwidth at l = 4. These results are inconsistent with the data of Fossat and Ricort (1975) as analyzed by Christensen-Dalsgaard and Gough (1982), who found a substantially constant modal amplitude at intermediate l values. It is interesting that other calculations have seen a similar dependence at small l in the growth rate of p-modes due to the -mechanism.Visiting Astronomer, Sacramento Peak Observatory. 相似文献
9.
M. Goossens 《Astrophysics and Space Science》1972,16(3):386-404
A generalization of the perturbation method is applied to the problem of the radial and the non-radial oscillations of a gaseous star which is distorted by a magnetic field. An expression is derived for the perturbation of the oscillation frequencies due to the presence of a weak magnetic field when the equilibrium configuration is a spheroid. The particular application to the homogeneous model with a purely poloidal field inside, due to a current distribution proportional to the distance from the axis of symmetry, and a dipole type field outside is considered in detail. The main result is that the magnetic field has a large and almost stabilizing effect on unstableg-modes, particularly on higher order modes. With the considered magnetic field the surface layers appear to have a large weight. 相似文献
10.
M. K. Das 《Astrophysics and Space Science》1985,116(1):9-19
The radial and nonradial modes of oscillation of partially degenerate stellar masses have been studied. It is found that the radial mode shows a decrease with increased central condensation and the configuration tends, therefore, towards a marginally stable point with increased degeneracy. The nonradial modes forl=2 and 3 also shows a similar trend. However, the decrease is slower than the corresponding radial mode. 相似文献
11.
The CrAO-WSO-network experiment was designed for detection of low-degree oscillations of the Sun representing either its normal g -modes or those driven by, e.g., rapid (hypothetical) rotation of the central solar core. The Doppler-shift measurements were made in 1974–1995 at both sites during about 13600 hr, in all. Taking into account the upper limit (0.08 m s-1) for amplitudes of potential g-modes, attention is paid to the Sun's behaviour at frequencies near the 9th daily harmonic (period P 160.The two main issues follow from analysis of the combined CrAO-WSO data: (a) in 1974–1982 the primary period of solar pulsation was P
0160.0099 ± 0.0016 ± 0.0016 min, but (b) during the last 13 yr it attained a new value, P
1 159.9654 ± 0.0010 min, which happens to be a near-annual sidelobe of P
0. We find therefore that the phase stability of the 160-min mode is no longer present: it appears to be splitted at least into a pair of oscillations,P
0 and P
1, having perhaps different physical origins. But the most striking is the fair coincidence of the strongest peaks in the two data sets: CrAO (1974–1995): P = 159.9662 ±0.0006 min, WSO (1977–1994): P = 159.9663 ± 0.0007 min. The existence of two frequencies,P
-1
0 and P
-1
1, with their separation corresponding to 1-yr period, seems to be difficult to explain in terms of gravity g modes. 相似文献
12.
We present a search for the acoustic oscillation deficit which may exist at the antipodes of sunspots. Dopplergrams from Big Bear Solar Observatory 1988 helioseismology data were selected for five days on which large sunspots were known to be on the unseen hemisphere of the Sun. Acoustic oscillation amplitudes in the antipodal regions of these sunspots were compared with amplitudes in surrounding quiet-Sun regions. We did not detect a statistically significant acoustic amplitude deficit in our data. Our results indicate that the amplitude deficit at the sunspot antipodal points is limited to no more than 3% of the acoustic amplitude in the region, for solar oscillation modes of spherical harmonic degree l 200. We conclude that no strong acoustic deficit exists at the antipodes of sunspots. A more sensitive search, requiring more elaborate observations than we have performed, would be desirable in order to determine if a weak acoustic amplitude deficit exists at some level at the antipodes of sunspots, perhaps at higher spatial frequencies of oscillation. The noise level in any signals detected by such observations would probably limit their usefulness as seismic probes. However, information on the lifetimes of solar oscillation modes can be deduced even if no acoustic amplitude deficit is detected. 相似文献
13.
Helioseismology is a direct and most informative method of studying the structure and dynamics of the Sun. Determining the internal differential rotation of the Sun requires that the frequencies of its eigentones be estimated with a high accuracy, which is possible only on the basis of continuous long-term observations. The longest quasi-continuous series of data have been obtained by the Global Oscillation Network Group (GONG). The parameters of each individual mode of solar acoustic oscillations with low spherical degrees l=0, 1, 2, 3, 4, 5, 6 are determined by using 1260-day-long series of GONG observations. The mean frequency splitting by rotation for the modes of each radial order n is calculated by using all possible combinations between the eigenfrequencies in multiplets. As a result, it has become possible to statistically estimate the splitting and its measurement errors for the modes of each radial order. The mean splitting for each given degree l=1–6 is presented under the assumption of its independence of oscillation frequency, which holds for the achieved accuracy. The frequencies and splittings for the modes with low spherical degrees l, together with the MDI group results for higher degrees l, are used to invert the radial profile of solar angular velocity. Using the SOLA method to solve the inverse problem of restoring the rotation profile has yielded solutions sensitive to the deepest stellar interiors. Our results indicate that the solar core rotates faster than the surface, and there may be a local minimum in angular velocity at its boundary. 相似文献
14.
The increasing central concentration of the Sun with age modifies the acoustic eigenfrequencies. In particular, the frequency separation d
l
=3(2l+3)–1v
n,l
–v
n–1,l+2 for modes with l + 1/2 n decreases as nuclear reactions augment the molecular-weight gradient in the energy-generating core. If, for example, the Sun were older than is generally believed, one might therefore expect d
l
to be smaller than current theoretical predictions. On the other hand, to ensure that the luminosity is consistent with observations, the presumed initial hydrogen abundance would need to be enhanced, thereby reducing the resultant molecular-weight gradient. Thus there is some degree of cancellation of the two major factors that determine d
l
.Various authors have either reported directly on the sensitivity of d
l
, or have provided the information from which it can be calculated. We have added our own computations. There is broad agreement amongst the results: d
l
diminishes with the presumed age of the Sun at the rate of about 1 Hz per Gy for l = 0; the magnitude of the rate appears to decline with increasing l. 相似文献
15.
R. D. Watson 《Astrophysics and Space Science》1988,140(2):255-290
The linearized analytic representation of observed flux changes due to nonradial pulsations is examined under conditions applicable to a variety of pulsating star types. Histograms are presented as a function ofl, documenting the relative importance of local temperature, geometry, pressure, and limb-darkening variations, which are all contributing factors to the predicted flux changes. The most favourable situation for light and colour data to assist in mode discrimination for lowl requires, amongst other things, that the geometry-related factor be significant. This is noted to occur only if theQ value of the pulsation is not grossly different from theQ value of a radial fundamental pulsation. Published light and colour data for Cephei, 53 Persei, Scuti, rapidly oscillating Ap, Cepheid, and ZZ Ceti variables are compared with model predictions on an amplitude ratio versus phase difference plane
. With the notable exception of the rapidly oscillating Ap stars, these comparisons suggest consistency of the nonradial flux change model with other known constraints on the different variable star groups. 相似文献
16.
Global oscillation of the Sun with a period of 160 rain were first discovered in 1974 and since observed in Crimea during the last 6 years; they were confirmed, in 1976–1979, by Doppler measurements at Stanford (Scherrer et al., 1980) and quite recently by observations of Fossat and Grec at the south geographic pole. The average amplitude of the oscillation is about 0.5 m s-1. The phase shows remarkable stability at the period 160.010 min and good agreement between different sites on the Earth; therefore, this oscillation should now be recognized as definitely of solar origin. It is probably accompanied by synchronous fluctuations in the IR brightness and radio-emission of the Sun, and exhibits a dependence of the amplitude on the phase of solar rotation (with a peak of power at 27.2 days).In agreement with results of the Birmingham group and the South Pole observation we also find evidence in favour of a discrete spectrum within the 5 min global oscillations of the Sun, with the average splitting of about 69.5 Hz in frequency.Strict gas-dynamical equations being solved in the adiabatic approximation for a polytropic sphere n = 3 display the pattern of radial oscillations with wave packets separated by 120 m time-intervals filled with high frequency (and split by 117 Hz) oscillations implying a similarity with the observed pattern.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands. 相似文献
17.
Theoretical predictions of the phase separation of heavy elements in internal stellar plasmas, based on the classical Debye-Hückel and mean spherical approximation, have offered a solution to the solar neutrino puzzle. Recent contributions, however, expressed some doubt about the correctness of these calculations. In the present paper, we challenge the latter conclusions by showing that the linearization of the Poisson-Boltzmann equation can be preformed to avoid the negativity of pair correlation functions, and that the importance of classical charge-charge effects is considerably greater than quantum effects in determining the internal energy of solar plasmas. Comparison between gravity and radiation pressure acting on phase-separated high-Z plasma droplets supports the formation of a small iron core in the center of the Sun confirming Rouse's suggestion that the frequencies of the non-radialg-modes and the five-min band of oscillations in the Sun can be explained only by the existence of such a core. The depletion of the Sun's interior of heavy elements results in a decreased opacity and, consequently a higher temperature which finally leads to a chlorine neutrino signal of about 2.5 solar neutrino unit in agreement with Davies's experimental result. Essentially the same high neutrino capture rate as given by the present standard Sun model is predicted for the future gallium experiment. This prediction is in contrast to the neutrino oscillation hypothesis in which a wide range of coupling parameters suppresses both chlorine and gallium signals.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988. 相似文献
18.
This paper presents the latest results obtained from the analysis of the full-disk Doppler shift observations obtained at the geographic South Pole in 1981. About 80 normal modes of oscillation (l = 0–3) have now been identified. Their frequencies range from 1886 Hz (l = 1, n = 12) to 5074.5 Hz (l = 2, n = 35), and their amplitudes are as low as 2.5 cm s-1. Amplitude modulation occurs with periods of 1–2 days, and the individual oscillations appear to be excited randomly and independently. In cases where other groups have observed some of the modes identified by us, the agreement in frequency is good.Proceedings of the 66th IAU Colloquium: Problems in Solar and Stellar Oscillations, held at the Crimean Astrophysical Observatory, U.S.S.R., 1–5 September, 1981. 相似文献
19.
J. A. Guzik 《Astrophysics and Space Science》1993,210(1-2):321-323
Walraven, Walraven and Balona recently discovered several new periodicities in addition to the well-known fundamental and first overtone periods of the high-amplitude Scuti star AI Velorum. Linear nonadiabatic pulsation calculations were performed for an AI Velorum model of mass 1.96M
, 24.05L
, andT
eff 7566 K for the radial and low-degree nonradial modes to help verify the tentative identifications made by Walraven, et al. Comparison of the calculated periods with the observations suggests some alternatives to the identifications proposed by Walraven, et al. 相似文献
20.
M. Goossens 《Astrophysics and Space Science》1977,52(1):3-10
The frequencies of the linear and adiabatic oscillations of a gaseous polytrope with a poloidal magnetic field are determined with the aid of a perturbation method. The influence of the poloidal magnetic field on the different types of spheroidal oscillation modes is discussed. The poloidal magnetic field generally strengthens the stability of the oscillation modes and this effect is the largest in the case of the non-radialp-modes. 相似文献