Radial P-modes Research Articles

A Rapidly Evolving High-amplitude δ Scuti Star Crossing the Hertzsprung Gap

In this work, we report the discovery of the rapidly evolving high-amplitude δ Scuti star KIC 6382916 (J19480292+4146558), which is crossing the Hertzsprung gap. According to the analysis of the archival data, we find three independent pulsation modes, whose amplitudes and frequencies vary distinctly in 4 yr. The linear period variation rates of the first two modes are about 3–4 times larger than the best seismic model constructed by the standard evolution theory, while that of the third one is about 8 times larger than the first two modes. What is more interesting is that almost all the combinations of the third mode have frequency peaks 0.0815 c day−1 away from them in the frequency domain. A framework is proposed to interpret the markedly large frequency and amplitude variation rates of the third mode, in which we employ a new pulsation mode (resonating integration mode) generated by the resonance between a radial p-mode and a nonradial mixed mode. Moreover, global analysis of the interactions between the three independent pulsation modes and their harmonics/combinations is performed based on the interaction diagrams of their amplitudes and phases, which would be a useful tool for future asteroseismology research.

Empirical relations for the sensitivities of solar-like oscillations to magnetic perturbations

ABSTRACT Oscillation mode frequencies of stars are typically treated as static for a given stellar model. However, in reality they can be perturbed by time-varying sources such as magnetic fields and flows. We calculate the sensitivities of radial p-mode oscillations of a set of models for masses between 0.7 and 3.0 M⊙ from the main sequence to the early asymptotic giant branch. We fit these mode sensitivities with polynomials in fundamental stellar parameters for six stages of stellar evolution. We find that the best-fitting relations differ from those proposed in the literature and change between stages of stellar evolution. Together with a measure of the strength of the perturbation, e.g. of the level of magnetic activity, the presented relations can be used for assessing whether a star’s observed oscillation frequencies are likely to be close to the unperturbed ground state or whether they should be adjusted.

Modelling the asymmetries of the Sun’s radial p-mode line profiles

Context. The advent of space-borne missions has substantially increased the number and quality of the measured power spectrum of solar-like oscillators. It now allows for the p-mode line profiles to be resolved and facilitates an estimation of their asymmetry. The fact that this asymmetry can be measured for a variety of stars other than the Sun calls for a revisiting of acoustic mode asymmetry modelling. This asymmetry has been shown to be related to a highly localised source of stochastic driving in layers just beneath the surface. However, existing models assume a very simplified, point-like source of excitation. Furthermore, mode asymmetry could also be impacted by a correlation between the acoustic noise and the oscillating mode. Prior studies have modelled this impact, but only in a parametrised fashion, which deprives them of their predictive power. Aims. In this paper, we aim to develop a predictive model for solar radial p-mode line profiles in the velocity spectrum. Unlike the approach favoured by prior studies, this model is not described by free parameters and we do not use fitting procedures to match the observations. Instead, we use an analytical turbulence model coupled with constraints extracted from a 3D hydrodynamic simulation of the solar atmosphere. We then compare the resulting asymmetries with their observationally derived counterpart. Methods. We model the velocity power spectral density by convolving a realistic stochastic source term with the Green’s function associated with the radial homogeneous wave equation. We compute the Green’s function by numerically integrating the wave equation and we use theoretical considerations to model the source term. We reconstruct the velocity power spectral density and extract the line profile of radial p-modes as well as their asymmetry. Results. We find that stochastic excitation localised beneath the mode upper turning point generates negative asymmetry for ν < νmax and positive asymmetry for ν > νmax. On the other hand, stochastic excitation localised above this limit generates negative asymmetry throughout the p-mode spectrum. As a result of the spatial extent of the source of excitation, both cases play a role in the total observed asymmetries. By taking this spatial extent into account and using a realistic description of the spectrum of turbulent kinetic energy, both a qualitative and quantitative agreement can be found with solar observations performed by the GONG network. We also find that the impact of the correlation between acoustic noise and oscillation is negligible for mode asymmetry in the velocity spectrum.

Study of pulsational instabilities in models of δ Scuti pulsators discovered under the Nainital-Cape Survey

Under the Nainital-Cape Survey, eight Scuti type pulsators have been discovered with the pulsation periods in the range of several minutes to few hours. In order to understand these observed pulsational variabilities, we have performed non-adiabatic linear stability analyses of these stars having mass in the range of 1 to 3 Mʘ. Several low order pressure modes (p-modes) are found to be unstable where the pulsation pe-riods associated with these unstable modes are in good agreement with the observed periods. Particularly for HD 118660, HD 113878, HD 102480, HD 98851, and HD 25515, we demonstrate that the observed variabilities can be explained with the low order radial p-mode pulsations.

Atomic diffusion and observations of pulsating A stars

Atomic diffusion – important in many contexts in stellar astrophysics and an important thread running through this meeting – is most spectacularly observable in the atmospheres of some A stars. The magnetic Ap stars and the non-magnetic Am stars show directly abundance anomalies caused by gravitational settling and radiative levitation. Over the last decade spectroscopic studies have begun to provide maps of abundance distributions in the magnetic Ap stars in three dimensions. Interestingly, high radial overtone p-mode pulsations in roAp stars have also given three-dimensional views of the stellar atmospheres with studies of rotational and line profile variations of pulsation amplitudes and phases. These detailed looks at the effects of microscopic atmospheric changes in the strongly non-LTE and magnetic upper atmospheric layers of Ap stars provide perhaps the most exciting challenge to atomic diffusion theory in terms of detailed explanation and prediction. Am stars were at one time thought not to pulsate because of gravitational settling of He from the He ii ionization zone that provides the κ-mechanism driving for δ Sct pulsations in A stars. In the last few years we have found with SuperWASP and Kepler observations that many Am stars do pulsate. More than half of all A stars pulsate at Kepler micromagnitude precision, yet there is a subset of A stars that truly do not pulsate at that level. Are these Am stars with the strongest signature of atomic diffusion? Is atomic diffusion the reason for the pulsational stability of these stars? The answers are not yet known.

MOST ★ observations of the Herbig Ae δ-Scuti star HD 34282

MOST observations and model analysis of the Herbig Ae star HD 34282 (V1366 Ori) reveal {\delta}-Scuti pulsations. 22 frequencies are observed, 10 of which confirm those previously identified by Amado et al. (2006), and 12 of which are newly discovered in this work. We show that the weighted-average frequency in each group fits the radial p-mode frequencies of viable models. We argue that the observed pulsation spectrum extends just to the edge to the acoustic cut-off frequency and show that this also is consistent with our best-fitting models.

MOST found evidence for solar-type oscillations in the K2 giant star HD20884

Abstract We found evidence for radial p-modes and nonradial mixed modes in the oscilla-tion spectrum of the K giant HD20884 based on 20.6 days of nearly continuoushigh-precisionphotometryobtainedbytheCanadianmicrosatelliteMOST 1 .Os-cillation frequencies range from 5-31µHz (periods of about 2.3d - 9hr) withluminosity amplitudes between about 300 and 950 ppm and mode lifetimes ex-ceeding 10 days are indicated. The mode identifications are based on searchesof a large grid of models for a best fit to the frequencies and temperature ofHD20884. The latter is better constrained now by spectroscopy obtained atthe David Dunlap Observatory as part of this work. Individual Objects: HD20884, HD20790, κ 1 Ceti, ǫOph, ξHya, HD146490 Introduction Our understanding of the Sun’s structure has been revolutionised over the last threedecades by helioseismology. This technique allows investigations of the solar interiorby observing p-modes at the stellar surface. Observing sun-like oscillations in otherstars was hampered for a long time by the extremely small pulsation amplitudes. Forstars cooler and more luminous than the Sun, the expected amplitudes are greater andshould be more easily observable. However, the larger radii of red giants extend theirpulsation periods from ∼5 minutes in the Sun to a range of several hours to severaldays. This again complicates groundbased detections and frequency identifications,especially due to daily aliasing.As ultra-precise rapid photometry from space and high-precision radial velocitymeasurements from the ground became available, detections of stochastically drivenoscillations were reported for several giants (see Bouchy & Carrier 2003 for a review).Examples include the G9.5 giant ǫOph, based on radial velocities from the CORALIEand ELODIE spectrographs (De Ridder et al. 2006) and Fabry Imaging photometryfromtheMOSTsatellite(Barbanetal. 2007), andtheG7giantξHya, basedonradialvelocity measurements with the CORALIE spectrograph (Frandsen et al. 2002), orthe K2.5 giant star GSC09137-03505 where Kallinger et al. (2005) found oscillations,based on Fine Guidance Sensor photometry by the Hubble Space Telescope.If pulsating red giants do indeed have radial and observable nonradial modes withrelatively long lifetimes, then these modes will enable to constrain the deep interiorof red giant stars, as well as set limits to the excitation mechanisms. But recentinvestigations (e.g., Barban et al. 2007 or Stello et al. 2006 ) suggest that only radialmodes with very short lifetimes (< 3 days) should be observable in red giants. Onthe other hand, Kallinger et al. (2008b) report strong evidence for the existence ofradial and nonradial modes in ǫOph (with lifetimes longer than 10 days) based on

Nonradial p-modes in the G9.5 giant ϵ Ophiuchi? Pulsation model fits to MOST photometry

The G9.5 giant ϵ Oph shows evidence of radial p-mode pulsations in both radial velocity and luminosity. We re-examine the observed frequencies in the photometry and radial velocities and find a best model fit to 18 of the 21 most significant photometric frequencies. The observed frequencies are matched to both radial and nonradial modes in the best model fit. The small scatter of the frequencies about the model predicted frequencies indicate that the average lifetimes of the modes could be as long as 10–20 d. The best fit model itself, constrained only by the observed frequencies, lies within ± of ϵ Oph's position in the HR-diagram and the interferometrically determined radius.

Nonradial Oscillations on a Pre–Main‐Sequence Star

We show that the modes observed on the pulsating pre-main-sequence (PMS) star NGC 6383 170 can be interpreted as a combination of radial and nonradial p-modes. Using a dense grid of PMS models and oscillation spectra, we have identified models that match the observed oscillation spectrum within 1 σ of the frequency uncertainties and are consistent with the star's position in the H-R diagram.

Searching for p-modes in n Boötis &amp; Procyon using MOST satellite data

Die Serie Communications in Asteroseismology (CoAst) stellt eine international gefragte Plattform für wissenschaftliche Publikationen der neuesten Forschungsergebnisse auf dem Gebiet der Asteroseismologie dar. Forschungsgegenstand der Asteroseismologie sind veränderliche und pulsierende Sterne. Neben den halbjährlich erscheinenden regulären Ausgaben mit Beiträgen aus der laufenden Forschung werden auch Sonderausgaben für Konferenzberichte bzw. Programmhandbücher herausgegeben. Die Arbeiten in Vol.151 berichten über ein breites Spektrum der asteroseismologischen Forschung: Neben Beiträgen über die erdgebundene photometrische sowie spektroskopische Beobachtung von pulsierenden Sternen werden auch die neuesten Ergebnisse aus den Beobachtungen mit dem MOST-Satelliten besprochen. Theoretische Arbeiten über Konvektion und Opazitäten ergänzen diese Ausgabe. Contents: D. B. Guenther, T. Kallinger, P. Reegen, W. W. Weiss, J. M. Matthews, R. Kuschnig, A. F. J. Moffat, S. M. Rucinski, D. Sasselov and G. A. H. Walker: Searching for ρ-modes in η Boötis & Procyon using MOST satellite data; L. Fox Machado; J. H. Peña, G. Muñoz and B. Vargas: On the nature of the δ Scuti star star HD 115520; D. Sinachopoulos and P. Gavras: Photometric observations and frequency analysis of the δ Scuti NT Hya; J. C. Suárez, E. Michel, G. Houdek, F. Pérez Hernández and Y. Lebreton: Asteroseismology of δ Scuti Stars in open clusters: Praesepe; J. C. Suárez, R. Garrido and A. Moya: Analysis of II1/0 (Ω) period ratios in the presence of near degeneracy; A. Miglio, J. Montalbán and M.-A. Dupret: Revised instability domains of SPB and β Cephei stars; P. J. Amado: Near infrared spectroscopy of the HADS stars V703 Sco and 1 Mon: First steps towards the use of near-IR spectroscopy for the study of δ Scuti stars; C. Schoenaers and A. E. Lynas-Gray: A new slowly pulsating subdwarf-B star: HD 4539; M. Breger and P. Beck: Call for papers for the next issue of CoAst

Whole Earth Telescope Observations of the Pulsating Subdwarf B Star PG 0014+067

PG 0014+067 is one of the most promising pulsating subdwarf B stars for seismic analysis, as it has a rich pulsation spectrum. The richness of its pulsations, however, poses a fundamental challenge to understanding the pulsations of these stars, as the mode density is too complex to be explained only with radial and nonradial low degree (l < 3) p-modes without rotational splittings. One proposed solution, for the case of PG 0014+067 in particular, assigns some modes with high degree (l=3). On the other hand, theoretical models of sdB stars suggest that they may retain rapidly rotating cores, and so the high mode density may result from the presence of a few rotationally-split triplet (l=1), quintuplet (l=2) modes, along with radial (l=0) p-modes. To examine alternative theoretical models for these stars, we need better frequency resolution and denser longitude coverage. Therefore, we observed this star with the Whole Earth Telescope for two weeks in October 2004. In this paper we report the results of Whole Earth Telescope observations of the pulsating subdwarf B star PG 0014+067. We find that the frequencies seen in PG 0014+067 do not appear to fit any theoretical model currently available; however, we find a simple empirical relation that is able to match all of the well-determined frequencies in this star.

Stellar Model Analysis of the Oscillation Spectrum of η Bootis Obtained fromMOST

Eight consecutive low-frequency radial p-modes are identified in the G0 IV star η Bootis based on 27 days of ultraprecise rapid photometry obtained by the MOST (Microvariability and Oscillations of Stars) satellite. The MOST data extend smoothly, to lower overtones, the sequence of radial p-modes reported in earlier ground-based spectroscopy by other groups. The sampling is nearly continuous; hence, the ambiguities in p-mode identifications due to aliases, such as the cycle day-1 alias found in ground observations, are not an issue. The lower overtone modes from the MOST data constrain the interior structure of the model of η Boo, giving a best fit on a grid of ~300,000 stellar models for a composition of (X,Z) = (0.71,0.04), a mass of M = 1.71 ± 0.05 M☉, and an age of t = 2.40 ± 0.03 Gyr. The surface temperature and luminosity of this model, which were constrained only by using the oscillation modes, are close (1 σ) to current best estimates of η Boo's surface temperature and luminosity. With the interior fit anchored by the lower overtone modes seen by MOST, standard models are not able to fit the higher overtone modes with the same level of accuracy. The discrepancy, model minus observed frequency, increases from 0.5 μHz at 250 μHz to 5 μHz at 1000 μHz and is similar to the discrepancy that exists between the Sun's observed p-mode frequencies and the p-mode frequencies of the standard solar model. This discrepancy promises to be a powerful constraint on models of three-dimensional convection.

A WHITE DWARF-NEUTRON STAR RELATIVISTIC BINARY MODEL FOR SOFT GAMMA-RAY REPEATERS

A scenario for soft gamma-ray repeaters (SGRs) is introduced in which gravitational radiation reaction (GRR) effects drive the dynamics of an ultrashort orbital period X-ray binary embracing a high-mass donor white dwarf (WD) to a rapidly rotating low magnetized massive neutron star (NS) surrounded by a thick, dense and massive accretion torus. Driven by GRR, over timescales of ΔTrep~ 10 years, the binary separation reduces, the WD overflows its Roche lobe and the mass transfer drives unstable the accretion disk around the NS. As the binary circular orbital period is a multiple integer number (m) of the period of the WD fundamental mode,37the WD is since long pulsating at its fundamental mode; and most of its harmonics, due to the tidal interaction with its NS orbital companion. Hence, when the powerful irradiation glows onto the WD; from the fireball ejected as part of the disk matter slumps onto the NS, it is partially absorbed. This huge energy excites other WD radial (p-mode) pulsations.34,35After each mass-transfer episode the binary separation (and orbital period) is augmented significantly1,5due to the binary's angular momentum redistribution. Thus a new adiabatic inspiral phase driven by GRR reaction starts which brings the binary close again, and the process repeats after a time span ΔTrep. This model allows to explain most of SGRs observational features: their recurrent activity, energetics of giant superoutbursts and quiescent stages, and particularly the intriguing subpulses discovered by BeppoSAX,10which are suggested here to be overtones of the WD radial fundamental mode (see the accompanying paper).31

Excitation of Radial P-Modes in the Sun and Stars

P-mode oscillations in the Sun and stars are excited stochastically by Reynolds stress and entropy fluctuations produced by convection in their outer envelopes. The excitation rate of radial oscillations of stars near the main sequence from K to F and a subgiant K IV star have been calculated from numerical simulations of their surface convection zones. P-mode excitation increases with increasing effective temperature (until envelope convection ceases in the F stars) and also increases with decreasing gravity. The frequency of the maximum excitation decreases with decreasing surface gravity.

Adiabatic Survey of Subdwarf B Star Oscillations. II. Effects of Model Parameters on Pulsation Modes

We present additional results obtained from a systematic adiabatic survey of the pulsation properties of extreme horizontal branch models identified with the subdwarf B stars. This survey is aimed at providing the most basic theoretical tools with which to analyze the asteroseismological characteristics of the recently discovered class of pulsating sdB stars (the EC 14026 stars). In this paper, the second of a series of three, we use an adiabatic pulsation code to compute the low-order, radial and nonradial (from l = 1 through l = 3) p, f, and g oscillation modes of a large grid of static envelope models of subdwarf B stars in order to explore thoroughly parameter space. We first demonstrate that such static models are sufficiently reliable for computations of the pulsation mode properties in these stars. This step is necessary if we are to understand the effects of various model parameters on the pulsation periods of sdB stars, effects that remain hopelessly tangled in evolutionary models. We show, in particular, that low-order radial and nonradial p-modes obtained from static structures do not experience significant period variations compared to modes computed with evolutionary models. This is not surprising because the acoustic modes probe mainly the envelope and are not sensitive to the details of the deep core, which are, of course, ignored in static models. In contrast, we find that the g-mode periods computed with static models are systematically overestimated, and we provide a detailed explanation of this phenomenon. We note, however, that the qualitative behaviors of the g-mode properties are still very well reproduced with static models. Moreover, because the pulsation periods observed in the vast majority of the known EC 14026 stars can be unambiguously identified with low-order acoustic modes, we conclude that static envelope models are valuable additions to the tools that we have at our disposal for carrying out asteroseismological analyses of these stars. On this basis, and in the light of the results presented in the first paper of this series, we next discuss and interpret the pulsation mode behaviors as functions of the main model parameters: the effective temperature Teff, the logarithmic surface gravity log g, the mass of the H-rich envelope Menv, and the total mass of the star Mtot. To achieve this goal, a large grid of 11,200 static envelope models is built and some 1,256,600 adiabatic modes (including p-, f-, and g-modes) are computed. The grid covers the whole volume of parameter space where real subdwarf B stars are expected: 22,000 ≤ Teff ≤ 41,000K, 4.9 ≤ log g ≤ 6.4, 8 × 10-6 ≤ Menv/M⊙ ≤ 8 × 10-3, and 0.46 ≤ Mtot/M⊙ ≤ 0.50. We find that both p- and g-mode periods are very sensitive to the log g parameter, while only g-modes respond significantly to variations of the effective temperature. We stress, however, that mode bumping and avoided crossing phenomena blur somewhat the differences between nonradial acoustic and gravity modes (in effect, these become mixed modes) in the high-Teff, low-gravity part of the explored log g-Teff plane. We show that changing the mass of the H-rich envelope has a significant impact, through the trapping and microtrapping effects, on both the g-mode and, more importantly from a practical point of view, the p-mode period spectra. This raises the exciting possibility of using the signature of the Menv parameter on the acoustic mode periods to constrain the H-rich envelope mass of the EC 14026 stars from their observed period spectra. We also find that the Mtot parameter has a slight, although noticeable, impact on the p- and g-mode periods within the narrow mass range considered in this survey.

Turbulent convection and pulsational stability of variable stars: non-adiabatic oscillations of the solar p-modes

By using a non-local time-dependent theory of convection, the non-adiabatic oscillations of the radial p-modes of the Sun were calculated. The coupling between convection and oscillation and the influence of departure from radiative equilibrium on oscillations of p-modes were investigated in detail. The results of numerical calculations show that when the coupling between convection and oscillations is ignored, all the low-order radial p-modes with are pulsationally unstable and all the intermediate- and high-order radial p-modes are pulsationally stable. When the coupling between convection and oscillations is taken into consideration, only the intermediate-order p-modes with are pulsationally unstable and all the low-order and high-order p-modes are pulsationally stable. The behaviour of stability of the solar p-mode oscillations described above is the result of the joint action of radiation and convection on oscillations. In the interior of the convection zone, the thermodynamic coupling between convection and oscillations gives rise to damping of solar oscillations, but at the top of the convection zone, it causes excitation. The thermodynamic coupling between convection and oscillations plays a key role in the stabilization of low-frequency solar p-modes and also in the excitation of the intermediate-order solar p-mode oscillations with periods of about 5 min. The turbulent pressure generally causes excitation. The radiative damping in the outer atmosphere and the turbulent viscosity are the main damping mechanisms of the high-order solar p-modes. For the low-order p-mode oscillations with the departure from radiative equilibrium (DRE) does not have a significant effect. With the increase of frequency, the influence of the outer atmosphere and the DRE grows rapidly. The generalized Eddington approximations (GEA) developed by Unno & Spiegel and Mihalas are much better than the usual radiative diffusion approximation. Our conclusion is as follows: the coupling between convection and oscillations is an important excitation and damping mechanism for solar 5-min oscillations. However, it cannot be used to interpret all the observational characteristics of solar p-modes. There must be excitation and damping mechanisms other than the radiation and the ‘regular’ coupling between convection and oscillations.

Evolutionary Model and Oscillation Frequencies for alpha Ursae Majoris: A Comparison with Observations.

Inspired by the observations of low-amplitude oscillations of alpha Ursae Majoris A by Buzasi et al. using the WIRE satellite, a grid of stellar evolutionary tracks has been constructed to derive physically consistent interior models for the nearby red giant. The pulsation properties of these models were then calculated and compared with the observations. It is found that, by adopting the correct metallicity and for a normal helium abundance, only models in the mass range of 4.0-4.5 M middle dot in circle fall within the observational error box for alpha UMa A. This mass range is compatible, within the uncertainties, with the mass derived from the astrometric mass function. Analysis of the pulsation spectra of the models indicates that the observed alpha UMa oscillations can be most simply interpreted as radial (i.e., l=0) p-mode oscillations of low radial order n. The lowest frequencies observed by Buzasi et al. are compatible, within the observational errors, with model frequencies of radial orders n=0, 1, and 2 for models in the mass range of 4.0-4.5 M middle dot in circle. The higher frequencies observed can also be tentatively interpreted as higher n-valued radial p-modes, if we allow that some n-values are not presently observed. The theoretical l=1, 2, and 3 modes in the observed frequency range are g-modes with a mixed mode character, that is, with p-mode-like characteristics near the surface and g-mode-like characteristics in the interior. The calculated radial p-mode frequencies are nearly equally spaced, separated by 2-3 µHz. The nonradial modes are very densely packed throughout the observed frequency range and, even if excited to significant amplitudes at the surface, are unlikely to be resolved by the present observations.

Effect of nonlinear interactions on p-mode frequencies and line widths

We calculate the effect of nonlinear interactions among solar acoustic modes upon the modal frequencies and energy loss rates (or line widths). The frequency shift for a radial p-mode of frequency 3 mHz is found to be about -0.5 µHz. The magnitude of nonlinear frequency shift increases more rapidly with frequency than the inverse mode mass (mode mass is defined as the ratio of energy in the mode to its surface velocity amplitude squared). This frequency shift is primarily due to nonresonant three-mode interactions and is dominated by high l surface gravity waves (ƒ-modes) and p-modes. The line width of a radial p-mode of frequency 3 mHz, due to resonant nonlinear interactions, is about 0.3 µHz. This result is consistent with that of Kumar & Goldreich (1989). We also find, in agreement with these authors, that the most important nonlinear interactions of trapped p-modes involve ƒ-modes and high-frequency p-modes (frequency greater than about 5 mHz) which propagate in the solar photosphere. Thus, using the arguments advanced by Kumar & Goldreich (1989), we conclude that nonlinear couplings cannot saturate the overstable solar p-modes at their small observed amplitudes. Both the nonlinear frequency shifts and line widths, at a fixed frequency, are proportional to the inverse of mode mass which for modes of degree greater than about 100 is ~ l^(0.8). Therefore, the frequency of an ƒ-mode of l = 1000, due to nonlinear interactions, is decreased by approximately 0.4%.

Theoretical Eigenfrequencies of Solar Oscillations of Low Harmonic Degree l in Five-Minute Range

AbstractWe have calculated eigenfrequencies of radial and nonradial p-mode oscillations with low harmonic index l (l = 0, 1, 2, 3, and 4) for a standard solar model with normal composition and appoximately the correct age. It is found that theoretical eigenfrequencies calculated for our standard model agree approximately with observed peaks in the power spectra for the full-disk five minute oscillation of the Sun (Claverie et al., 1980; Grec et al., 1983; Scherrer et al., 1983) in agreement with other recent works (Christensen-Dalsgaard and Gough, 1980; Scuflaire et al., 1981). However, there still remains a slight discrepancy between theory and observations in such a sense that the theoretical eigenfrequencies are slightly lower than observations (see Figure 1).

Theoretical eigenfrequencies of solar oscillations of low harmonic degree l in five-minute range

We have calculated eigenfrequencies of radial and nonradial p-mode oscillations with low harmonic index l (l = 0, 1, 2, 3, and 4) for a standard solar model with normal composition and appoximately the correct age. It is found that theoretical eigenfrequencies calculated for our standard model agree approximately with observed peaks in the power spectra for the full-disk five minute oscillation of the Sun (Claverie et al., 1980; Grec et al., 1983; Scherrer et al., 1983) in agreement with other recent works (Christensen-Dalsgaard and Gough, 1980; Scuflaire et al., 1981). However, there still remains a slight discrepancy between theory and observations in such a sense that the theoretical eigenfrequencies are slightly lower than observations (see Figure 1). Eigenfrequencies of nonradial p-modes with high degree l for the same model are also calculated for comparison with observations of the conventional five-minute oscillation with shorter horizontal wavelength. It is found that theoretical eigenfrequencies lie slightly above the observed ridges in the diagnostic (k, ω)-diagram, which is in accord with Ulrich and Rhodes (1977) and Berthomieu et al. (1980) because our standard model has a slightly shallow convective zone. It remains to be seen whether improvement in the equilibrium model can remove this small discrepancy, concurrently with a better agreement between theory and observation for the whole-disk oscillations of low degree. A full account of this work will be found in Shibahashi and Osaki (1981).