Search

In this paper we study the dynamics of the stellar interior of the early red-giant star KIC 4448777 by asteroseismic inversion of 14 splittings of the dipole mixed modes obtained from {\it Kepler} observations. In order to overcome the complexity of the oscillation pattern typical of red-giant stars, we present a procedure which involves a combination of different methods to extract the rotational splittings from the power spectrum. We find not only that the core rotates faster than the surface, confirming previous inversion results generated for other red giants (Deheuvels et al. 2012,2014), but we also estimate the variation of the angular velocity within the helium core with a spatial resolution of $\Delta r=0.001R$ and verify the hypothesis of a sharp discontinuity in the inner stellar rotation (Deheuvels et al. 2014). The results show that the entire core rotates rigidly with an angular velocity of about $\langle\Omega_c/2\pi\rangle=748\pm18$~nHz and provide evidence for an angular velocity decrease through a region between the helium core and part of the hydrogen burning shell; however we do not succeed to characterize the rotational slope, due to the intrinsic limits of the applied techniques. The angular velocity, from the edge of the core and through the hydrogen burning shell, appears to decrease with increasing distance from the center, reaching an average value in the convective envelope of $\langle\Omega_s/2\pi\rangle=68\pm22$~nHz. Hence, the core in KIC~4448777 is rotating from a minimum of 8 to a maximum of 17 times faster than the envelope. We conclude that a set of data which includes only dipolar modes is sufficient to infer quite accurately the rotation of a red giant not only in the dense core but also, with a lower level of confidence, in part of the radiative region and in the convective envelope., Comment: accepted for publication on ApJ

Regular intrinsic brightness variations observed in many stars are caused by pulsations. These pulsations provide information on the global and structural parameters of the star. The pulsation periods range from seconds to years, depending on the compactness of the star and properties of the matter that forms its outer layers. Here, we report the discovery of more than a dozen of previously unknown short-period variable stars: blue large-amplitude pulsators. These objects show very regular brightness variations with periods in the range of 20-40 min and amplitudes of 0.2-0.4 mag in the optical passbands. The phased light curves have a characteristic sawtooth shape, similar to the shape of classical Cepheids and RR Lyrae-type stars pulsating in the fundamental mode. The objects are significantly bluer than main sequence stars observed in the same fields, which indicates that all of them are hot stars. Follow-up spectroscopy confirms a high surface temperature of about 30,000 K. Temperature and colour changes over the cycle prove the pulsational nature of the variables. However, large-amplitude pulsations at such short periods are not observed in any known type of stars, including hot objects. Long-term photometric observations show that the variable stars are very stable over time. Derived rates of period change are of the order of 10^-7 per year and, in most cases, they are positive. According to pulsation theory, such large-amplitude oscillations may occur in evolved low-mass stars that have inflated helium-enriched envelopes. The evolutionary path that could lead to such stellar configurations remains unknown., Published in Nature Astronomy

Over the recent years, the Petersen diagram for classical pulsators, Cepheids and RR Lyr stars, populated with a few hundreds of new multiperiodic variables. We review our analyses of the OGLE data, which resulted in the significant extension of the known, and in the discovery of a few new and distinct forms of multiperiodic pulsation. The showcase includes not only radial mode pulsators, but also radial-non-radial pulsators and stars with significant modulation observed on top of the beat pulsation. First theoretical models explaining the new forms of stellar variability are briefly discussed., Comment: 5 pages; to be published in the proceedings of the 22nd Los Alamos Stellar Pulsation Conference "Wide-field variability surveys: a 21st-century perspective", San Pedro de Atacama, Chile, Nov. 28 - Dec. 2, 2016

We discuss the potential of asteroseismic inversion to study the internal dynamics of solar-type stars and to reconstruct the evolution of the internal rotation from the main sequence to the red-giant phase. In particular, we consider the use of gravity and mixed modes and the application of different inversion methods.

Attempts to interpret the observed oscillation spectrum of the SPB star HD 50230 are reported. We argue that a nearly equidistant period spacing found in the oscillation spectrum of the star is most likely accidental. The observed period distribution requires excitation of modes with the degree $\ell>4$. Much more may be learned from the rich oscillation spectrum of the star but most of the work is still ahead of us., Proceedings IAU Symposium No. 301

We report the discovery of a new subclass of double-mode RR Lyrae stars in the Large and Small Magellanic Clouds. The sample of 22 pulsating stars have been extracted from the latest edition of the OGLE collection of RR Lyrae variables in the Magellanic System. The stars pulsating simultaneously in the fundamental (F) and first-overtone (1O) modes have distinctly different properties than regular double-mode RR Lyrae variables (RRd stars). The $P_{1O}/P_F$ period ratios of our anomalous RRd stars are within a range 0.725-0.738, while "classical" double-mode RR Lyrae variables have period ratios in the range 0.742-0.748. In contrast to the typical RRd stars, in the majority of the anomalous pulsators the F-mode amplitudes are higher than the 1O-mode amplitudes. The light curves associated with the F-mode in the anomalous RRd stars show different morphology than the light curves of, both, regular RRd stars and single-mode RRab stars. Most of the anomalous double-mode stars show long-term modulations of the amplitudes (Blazhko-like effect). Translating the period ratios into the abundance parameter, Z, we find for our stars Z in the range (0.002,0.005) - an order of magnitude higher values than typical for RR Lyrae stars. The mass range of the RRd stars inferred from the $W_I$ vs. $P_F$ diagram is (0.55-0.75) of the solar mass. These parameters cannot be accounted for with single star evolution assuming a Reimers-like mass loss. Much greater mass loss caused by interaction with other stars is postulated. We blame the peculiar pulsation properties of our stars to the parametric resonance instability of the 1O-mode to excitation of the F- and 2O-modes as with the inferred parameters of the stars $2\omega_{\rm 1O}\approx\omega_{\rm F}+\omega_{\rm 2O}$., Comment: 11 pages, 7 figures, accepted for publication in MNRAS

We analyse observations of 1568 δ Scuti stars in the public archive of the Kepler satellite. We compare the location of these stars in the Hertzsprung–Russell (HR) diagram with that calculated by linear, non-adiabatic pulsation models. There is generally a good agreement and it appears that many of the hotter δ Scuti stars are pulsating in overtones as high as radial order n= 8. Models predict unstable modes of intermediate and high spherical harmonic, l, which are trapped in the envelope. The instability strip for these modes extends well beyond the blue edge for l≤ 4 and should be visible in the Kepler data. However, stars with these predicted properties are not seen. Moreover, we find that the observed frequency range does not agree with the models. Another challenge is to understand why more than half of the stars in the δ Sct instability strip are not pulsating. The distribution of amplitudes argues strongly against the notion that the pulsation amplitudes are below the Kepler detection limit. The mode density of δ Scuti stars is surprisingly low and suggests that modes of a high degree are not common. We do not find any stars with mode densities as high as that found in the CoRoT observations of HD 50844. The periodograms of stars in the same part of the HR diagram vary widely. However, we have identified a group of δ Scuti stars characterized by a single dominant frequency in which a period–luminosity law is present. In many cases the dominant frequency is accompanied by a close frequency of lower amplitude. The problem of low frequencies in hot δ Scuti stars remains unresolved. We confirm that these frequencies have long lifetimes and are not likely to be of stochastic origin. By carefully examining the periodograms of δ Sct stars in the low-frequency regime, we were able to identify a group of δ Sct stars with low-frequency peaks closely resembling those attributed to pure γ Dor stars. These stars lie in the region of the HR diagram where ground-based γ Dor stars are located. None is found hotter than the blue edge of γ Dor pulsation. We suspect that these are genuine γ Dor/δ Sct hybrids.

Low-frequency oscillations are unstable in a wide range of stellar models and have been detected in a number of B-type stars. For such modes, even a moderate rotation significantly affects amplitude distribution over stellar surface and hence their visibility conditions. Adopting the traditional approximation, we study effects of rotation on relative amplitudes in photometric passbands and in radial velocity. We present numerical results for unstable modes in a selected stellar model of a 6 M ๏ main sequence star. The goal is to show how observable amplitudes, which are tools for mode identification, depend on the rotation rate and on the aspect angle.

The current status of our understanding of the diversity of B-star pulsation is presented with an emphasis on unsolved problems. Not all detected modes are found unstable in standard models. The proposed way of extending the instability by invoking an iron accumulation in the driving zone is not free of difficulties. There are still controversies regarding the excitation of slow modes in Be stars. Nonlinear modelling of radial pulsations in β Cephei stars results in much higher amplitudes than observed. There must be hidden modes involved but we may only speculate about their nature.

We report the discovery of a new group of double-periodic RR Lyrae stars from the analysis of the OGLE-IV Galactic bulge photometry. In 11 stars identified in the OGLE catalog as first overtone pulsators (RRc stars) we detect additional longer period variability of low amplitude, in the mmag regime. One additional star of the same type is identified in a published analysis of the Kepler space photometry. The period ratio between the shorter first overtone period and a new, longer period lies in a narrow range around 0.686. Thus, the additional period is longer than the expected period of the undetected radial fundamental mode. The obvious conclusion that addition periodicity corresponds to a gravity or a mixed mode faces difficulties, however., 5 pages, 4 figures, accepted for publication in MNRAS Letters

In addition to revealing spherical harmonic degrees, $\ell$, of excited modes, pulsational amplitudes and phases from multicolour photometry and radial velocity data yield a valuable constraints on stellar atmospheric parameters and on subphotospheric convection. Multiperiodic pulsators are of particular interest because each mode yields independent constraints. We present an analysis of data on twelve modes observed in FG Vir star., Comment: 7 pages, 5 figures, in the proceedings of IAU Symposium 224: "The A-star Puzzle", eds. J. Zverko, W. W. Weiss, J. Ziznowsky, S. J. Adelman

In δ Scuti star models the photometric amplitudes and phases exhibit a strong dependence on convection, which enters through the complex parameter,f, that describes the bolometric flux variation. We present a new method of extracting l and f from multi-colour data and apply it to several δ Scuti stars. The inferred values of f are sufficiently accurate to yield a useful constraint on models of stellar convection.

We derive formulae connecting the frequency variations in the spectrum of solar oscillations to the dynamical quantities that are expected to change over the solar activity cycle. This is done for both centroids and the asymmetric part of the fine structure (so-called even-a coefficients). We consider the near-surface, small-scale magnetic and turbulent velocity fields, as well as horizontal magnetic fields buried near the base of the convective zone. For the centroids we also discuss the effect of temperature variation. We demonstrate that there is a full, one-to-one correspondence between the expansion coefficients of the fine structure and those of both the averaged small-scale velocity and magnetic fields. Measured changes in the centroid frequencies and the even-a's over the rising phase solar cycle may be accounted for by a decrease in the turbulent velocity of order 1%. We show that the mean temperature decrease associated with the net decrease in the efficiency of convective transport may also significantly contribute to the increase of the centroid frequencies. Alternatively, the increase may be accounted for by an increase of the small-scale magnetic field of order 100 G, if the growing field is predominantly radial. We also show that global seismology can be used to detect a field at the level of a few times 10^5 G, if such a field were present and confined to a thin layer near the base of the convective envelope., Comment: ApJ, accepted

In Delta Scuti star models, the calculated amplitude ratios and phase differences for multi-colour photometry exhibit a strong dependence on convection. These observables are tools for determination of the spherical harmonic degree of the excited modes. The dependence on convection enters through the complex parameter f, which describes bolometric flux perturbation. We present a method of simultaneous determination of f and spherical harmonic degree from multi-colour data and apply it to three Delta Scuti stars. The method indeed works. Determination of the degree appears unique and the inferred f's are sufficiently accurate to yield a useful constraint on models of stellar convection. Furthermore, the method helps to refine stellar parameters, especially if the identified mode is radial., Comment: 9 pages, 12 figures, to appear in Astronomy and Astrophysics

Changes in the earth`s climate depend on changes in the net sunlight reaching us. The net depends on the sun`s output and earth`s reflectance, or albedo. Here we develop the limits on the changes in the sun`s output in historical times based on the physics of the origin of solar cycle changes. Many have suggested that the sun`s output could have been less during the Maunder minimum, whereas the variation over the solar cycle is only about . The frequencies of solar oscillations (f- and p-modes) evolve through the solar cycle, and provide the most exact measure of the cycle-dependent changes in the sun. But precisely what are they probing? The changes in the sun`s output, structure and oscillation frequencies are driven by some combination of changes in the magnetic field, thermal structure and velocity field. It has been unclear what is the precise combination of the three. One way or another, this thorny issue rests on an understanding of the response of the solar structure to increased magnetic field, but this is complicated. Thus, we do not understand the origin of the sun`s irradiance increase with increasing magnetic activity. Until recently, it seemed that an unphysically large magnetic field change was required to account for the frequency evolution during the cycle. However, the problem seems to have been solved (Dziembowski, Goode & Schou 2001) using f-mode data on size variations of the sun. From this and the work of Dziembowski & Goode (2003), we suggest that in historical times the sun couldn`t be much dimmer than it is at activity minimum.

The oblique pulsator model accounts for most of the pulsation properties of the rapidly oscillating Ap (roAp) stars. The model predicts that modes are seen as equidistant multiplets separated by the angular frequency of rotation. The relative amplitudes of the components may be calculated and directly compared with observations. The eects of rotation introduce amplitude asymmetry, that is peaks corresponding to azimuthal numbers m and m are unequal. In this paper we propose improvements to the model that consist of including eects of the centrifugal force and in using a non-perturbative treatment of the magnetic field influence. We show that in roAp stars the centrifugal force is the primary source of the rotational frequency shift. Although the amplitude asymmetry arises from the Coriolis force, its size is strongly aected by the centrifugal force. For dipole modes ('= 1) we develop a simple geometrical picture of pulsation in the presence of rotation and a magnetic field. We provide some numerical results for a representative model of roAp stars which is applied to the case of HR 3831. We find that the mode that agrees with the observed amplitude ratios in this star significantly departs from alignment with the magnetic axis. We discuss problems posed by the observational data of HR 3831, emphasizing diculties of the standard oblique pulsator model which assumes that the excited mode is nearly aligned with the magnetic field. The rapidly oscillating Ap (roAp) stars are high order p-mode pulsators. The pulsation periods are in the 5-15 min range which is nearly the same as that of the solar oscillations. However, the mode amplitudes in roAp stars, with typical val- ues of one millimagnitude, are higher by three orders of mag- nitude than those in the Sun. Kurtz (1982) argued that the mag- netic field must play an essential role in roAp oscillations as the maxima of the oscillation amplitudes coincide with the max- ima of the longitudinal field. The properties of the magnetic field in roAp stars are similar to that in the whole group of Ap stars. The observed field is predominantly dipolar and has a kiloGauss strength. Since their discovery two decades ago (Kurtz 1978), the number of roAp stars has grown to 32. Most of the pulsation data in roAp stars may be interpreted in terms of rotating dipole modes that Kurtz assumed to be symmetric around the magnetic axis. The model provides a natural explanation of the observed multiplets in the spectrum of the oscillations in which the components are split by ex- actly the frequency of rotation. Dziembowski & Goode (1985) generalized the oblique pulsator model bytaking into account

We present new results on the effects of a strong dipole magnetic field and rotation on p-mode oscillations. We take into account both Coriolis and centrifugal distortion as manifestations of rotation. We apply these improvements to the case of dipole (l = 1) modes. We show that these modes, during the pulsation cycle, move the stellar surface in a plane, which is inclined from both magnetic and rotation axes. In general, the displacement vector describes an ellipse in that plane. This work is devoted to the study of the roAp star pulsations.

We describe systematic changes in the centroid frequencies and the splitting coefficients as found using data from MDI on board SOHO, covering cycle 23. The data allow us to construct a seismic map of the evolving solar activity -- covering all latitudes. At lower latitudes, the temporal evolution closely tracks that of {\it butterfly diagram}. The additional information from higher latitudes in the map is of a significant activity in the polar region, peaking at activity minimum in 1996. The most plausible source of solar oscillation frequency changes over the solar cycle is the evolution of the radial component of the small-scale magnetic field. The amplitude of the required mean field changes is about 100 G at the photosphere, and increasing going inward., Comment: IAU Colloquium 185 "Radial and Nonradial Pulsations as Probes of Stellar Physics"

We present results of a search for identification of modes responsible for the six most significant frequency peaks detected in the rapidly rotating SPB star $\mu$ Eridani. All published and some unpublished photometric data are used in our new analysis. The mode identification is carried out with the method developed by Daszy\'nska-Daszkiewicz et al. employing the phases and amplitudes from multi-band photometric data and relying on the traditional approximation for the treatment of oscillations in rotating stars. Models consistent with the observed mean parameters are considered. For the five frequency peaks, the candidates for the identifications are searched amongst unstable modes. In the case of the third frequency, which is an exact multiple of the orbital frequency, this condition is relaxed. The systematic search is continued up to a harmonic degree $\ell =6$. Determination of the angular numbers, $(\ell,m)$, is done simultaneously with the rotation rate, $V_{\rm rot}$, and the inclination angle, $i$, constrained by the spectroscopic data on the projected rotational velocity, $V_{\rm rot}\sin i$, which is assumed constant. All the peaks may be accounted for with g-modes of high radial orders and the degrees $\ell\le 6$. There are differences in some identifications between the models. For the two lowest--amplitude peaks the identifications are not unique. Nonetheless, the equatorial velocity is constrained to a narrow range of (135, 140) km/s. Our work presents the first application of the photometric method of mode identification in the framework of the traditional approximation and we believe that it opens a new promising direction in studies of SPB stars., Comment: accepted for publication in MNRAS

There is growing observational evidence that the variability of red giants could be caused by excitation of global modes of oscillation. The most recent evidence of such oscillations was reported for alpha UMa by Buzasi et al.(2000). We address the problem of radial and nonradial mode excitation in red giants from the theoretical point of view. In particular, we present the results of numerical computations of oscillation properties of a model of alpha UMa and of several models of a 2M_sun star in the red-giant phase. In the red giant stars by far most of the nonradial modes are confined to to the deep interior, where they have the g-mode character. Only modes at resonant frequencies of the p-mode cavity have substantial amplitudes in the outer layers. We have shown that such modes can be unstable with the linear growth rates similar to those of corresponding to radial modes. We have been unable to explain the observed oscillation properties of alpha UMa, either in terms of mode instability or in terms of stochastic excitation by turbulent convection. Modes at the lowest frequencies, which exhibit the largest amplitudes and may correspond to the first three radial modes, are found stable if all effects of convection are taken into account. The observed frequency dependence of amplitudes does not agree with what one expects from stochastic excitation. The predicted fundamental mode amplitude is by about two orders of magnitude smaller than those of high frequency modes, which is in stark disagreement with the observations.

During the rise of Cycle 23, we have found a sizable, systematic evolution of the Solar and Heliospheric Observatory/Michelson Doppler Imager solar oscillation frequencies implying significant changes in the spherically symmetric structure of the Sun's outer layers as well as in its asphericity up to a P18 Legendre distortion. We conducted a search for corresponding asymmetries in Ca II K data from Big Bear Solar Observatory. We found tight temporal and angular correlations of the respective asphericities up through P10. This result emphasizes the role of the magnetic field in producing the frequency changes. We carried out inversions of the frequency differences and the splitting coefficients assuming that the source of the evolving changes is a varying stochastic magnetic field. With respect to the most recent activity minimum, we detected a significant perturbation in the spherical part at a depth of 25-100 Mm, which may be interpreted as being a result of a magnetic perturbation, B2, of about (60KG)2 and/or a relative temperature perturbation of about 1.2 × 10-4. Larger, although less statistically significant, perturbations of the interior structure were found in the aspherical distortion.

ABSTRA C T Observational evidence for excitation of non-radial modes in stars is confronted with the results of linear stability surveys for stellar models. We consider various types of pulsators on the upper main sequence as well as stars in the Cepheid strip. Our stability survey covers the whole range of spherical harmonic degrees, ‘, where instability is found. There is fair agreement between the theoretical instability strip and the location of z Oph stars, but the observed and calculated periods do not agree in some stars. We suggest that either pulsation is not responsible for the z Oph phenomenon or else there are serious errors in mode identification in these cases. We do not find instability at long periods for early B-type stars, supporting the idea that pulsation is not responsible for the periodic variations in Be stars. The agreement between the observed and calculated periods of high-degree modes in d Sct stars is not very satisfactory. This is attributed to problems in mode identification. We discuss unstable modes of high degree in Cepheid models as a possible mechanism for the low-amplitude radial velocities seen in some stars within the instability strip. We find, however, that the observed periods are at least a factor of 2 longer than the calculated periods. Finally, we discuss the possibility of observing modes of high degree photometrically. We suggest that a large number of high-degree modes may become detectable by future space-borne photometric missions. The confusion arising from these modes may greatly reduce the value of such observations for asteroseismology. However, they will be very important in studying the mechanism of mode selection.

We have analyzed time changes in centroid frequencies and multiplet frequency splittings of solar oscillations determined with the Michelson Doppler Imager instrument (MDI) on SOHO. The data were divided into five consecutive 72 day sets covering the period from 1996 May 1 through 1997 April 25. We have detected a significant trend in the a4 and a6 frequency splitting coefficients, which reflects a decrease in the P4 distortion (described by the fourth-degree Legendre polynomial of colatitude) and an increase in the P6 distortion. The rise of the latter distortion seems to coincide precisely with the rise in the number of new cycle sunspots. Such sharp and detailed clues to activity onset are new and do not exist in splitting data from the rising phase of the last cycle. The relative differences among the solar radii inferred from the f-mode frequencies from the five sets (at most 6 × 10-6 or 4 km) are formally significant, reaching a minimum during the observed period.

We discuss two problems connected with the application of the method of photometric amplitudes and phases for mode identification. The first one concerns the effect of rotational mode coupling in β Cep models. The second one deals with the strong dependence of the photometric observables on convection in δ Scuti stars.

The splitting of the frequencies of the global resonant acoustic modes of the Sun by large-scale flows and rotation permits study of the variation of angular velocity Ω with both radius and latitude within the turbulent convection zone and the deeper radiative interior. The nearly uninterrupted Doppler imaging observations, provided by the Solar Oscillations Investigation (SOI) using the Michelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory (SOHO) spacecraft positioned at the L1 Lagrangian point in continuous sunlight, yield oscillation power spectra with very high signal-to-noise ratios that allow frequency splittings to be determined with exceptional accuracy. This paper reports on joint helioseismic analyses of solar rotation in the convection zone and in the outer part of the radiative core. Inversions have been obtained for a medium-l mode set (involving modes of angular degree l extending to about 250) obtained from the first 144 day interval of SOI-MDI observations in 1996. Drawing inferences about the solar internal rotation from the splitting data is a subtle process. By applying more than one inversion technique to the data, we get some indication of what are the more robust and less robust features of our inversion solutions. Here we have used seven different inversion methods. To test the reliability and sensitivity of these methods, we have performed a set of controlled experiments utilizing artificial data. This gives us some confidence in the inferences we can draw from the real solar data. The inversions of SOI-MDI data have confirmed that the decrease of Ω with latitude seen at the surface extends with little radial variation through much of the convection zone, at the base of which is an adjustment layer, called the tachocline, leading to nearly uniform rotation deeper in the radiative interior. A prominent rotational shearing layer in which Ω increases just below the surface is discernible at low to mid latitudes. Using the new data, we have also been able to study the solar rotation closer to the poles than has been achieved in previous investigations. The data have revealed that the angular velocity is distinctly lower at high latitudes than the values previously extrapolated from measurements at lower latitudes based on surface Doppler observations and helioseismology. Furthermore, we have found some evidence near latitudes of 75° of a submerged polar jet which is rotating more rapidly than its immediate surroundings. Superposed on the relatively smooth latitudinal variation in Ω are alternating zonal bands of slightly faster and slower rotation, each extending some 10° to 15° in latitude. These relatively weak banded flows have been followed by inversion to a depth of about 5% of the solar radius and appear to coincide with the evolving pattern of torsional oscillations reported from earlier surface Doppler studies.

ABSTRA C T We study the possibility of the excitation of non-radial oscillations in classical pulsating stars. The stability of an RR Lyrae model is examined through non-adiabatic non-radial calculations. We also explore stability in the presence of non-linear coupling between radial and non-radial modes of nearly identical frequency. In our model, a large number of unstable low-degree (, o 1; 2) modes have frequencies in the vicinity of unstable radial mode frequencies. The growth rates of such modes, however, are considerably smaller than those of the radial modes. We also recover an earlier result that at higher degrees (, o 6‐12) there are modes trapped in the envelope with growth rates similar to those of radial modes. Subsequently, monomode radial pulsation of this model is considered. The destabilizing effect of the 1:1 resonance between the radial mode and nearby non-radial modes of low degrees is studied, with the assumption that the excited radial mode saturates the linear instability of all other modes. The instability depends on the radial mode amplitude, the frequency difference, the damping rate of the non-radial mode, and the strength of the nonlinear coupling between the modes considered. At the pulsation amplitudes typical for RR Lyrae stars, the instability of the monomode radial pulsation and the concomitant resonant excitation of some non-radial oscillation modes is found to be very likely.

The SSM, invented in early nineteen sixties, remains a useful construction. There are now much larger number of its predictions that may be compared with observations than when it was first introduced. Seismic sounding based on oscillations frequencies provides the best test of the physical input for modelling stellar evolution. The results of the test must be viewed as a support for the standard theory of stellar evolution. However, significant differences in the sound-speed, photospheric He abundance, and other parameters between the Sun and the current models remain. Shortcomings in the EOS and in treatment of convection have been revealed. The differences in the sound-speed in the radiative interior may be explained by small opacity errors but other explanations are possible. Results of seismic sounding support the idea that the element mixing in the outer part of the radiative interior occurred during a significant fraction of the Sun’s life. Such mixing is considered as a possible explanation of the deficit of lithium. The shortcomings of SSM cannot explain the deficits of measured neutrino fluxes.

Relativistic calculations of the effects of the pion cloud on the electromagnetic properties of the nucleon are presented. Light-cone formalism is used to construct the physical nucleon wave function that contains two components: a bare nucleon and a pion associated by recoil baryon with the nucleon or delta quantum numbers. Both sectors are coupled by a relativistic light-cone interaction Hamiltonian. A perturbative treatment is used to solve for the physical nucleon state. The elastic electromagnetic nucleon form factors G{sub E}{sup p,n}(Q{sup 2}) and G{sub M}{sup p,n}(Q{sup 2}) are computed in terms of matrix elements of current operator and the nucleon wave function. The Q{sup 2}-dependence of contributions to the nucleon form factor from the various sectors of the model space is calculated and compared. The nature of the observed deviations from form-factor scaling and dipole parametrization is discussed. {copyright} 1997 Academic Press, Inc.

Dopplergrams from the Michelson Doppler Imager (MDI) instrument on board the SOHO spacecraft have been used to accurately measure frequencies of the Sun’s fundamental mode in the medium angular degree range, ( f ) l 5 88‐250. The comparison of these frequencies with the corresponding frequencies of the standard solar models suggests that the apparent photospheric solar radius (695.99 Mm) used to calibrate the models should be reduced by approximately 0.3 Mm. The precise value of the seismologically determined solar radius depends on the description of the subsurface layer of superadiabatic convection. The discrepancy between the “seismic” and apparent photospheric radii is not explained by the known systematic errors in the helioseismic and photospheric measurements. If confirmed, this discrepancy represents an interesting new challenge to theories of solar convection and solar modeling.

Multimode pulsations have been discovered in a large variety of main sequence stars and white dwarfs. There are abundant and accurate data on p- and g- mode frequencies in these objects. So far, however, use of these data for sounding interiors has been very limited. The main obstacle is the difficulty in identification of detected modes that is in assignment of spherical harmonic degree, l, azimuthal order, m, and radial order, n, to the modes detected in power spectra of variable stars. This has never been a problem in helioseismology. Even in the case of whole disc measurements a simple structure of power spectra enables an unambiguous mode identification. Such a situation is very rare in asteroseismology. Perhaps oscillating white dwarfs PG 1159-035 and GD 358 are the only examples. Methods of determining the l and m from observational data on the excited modes are available. However, their implementation to – typically low amplitude – multimode pulsators is difficult. In most cases mode identification cannot be separated from determination of stellar parameters.

Unsubtracted dispersion relations are used to link new data obtained in the time-like region with the electromagnetic structure of the nucleons as measured in the space-like region. Simple analytic representations of the magnetic form factor of the proton GpM(Q2) and the electric form factor of the neutron GnE(Q2) are derived which have the following properties built-in: the correct normalization and slope at Q2 = 0 and correct asymptotic behavior at |Q2| → ∞. The pred of perturbative QCD at asymptotic Q2 and meson physics at low Q2 are combined to fit the existing data in the entire range of the four-momentum transfer squared. This leads to the following observations: (i) Measurements of cross sections for the reaction p p → e + e − taken at the Fermilab E-760 match measurements made at the SLAC-136 experiment only if the logarithmic falloff of Q4GpM(Q2), expected from leading twist predictions of perturbative quantum chromodynamics, is included. (ii) Analytic continuation of the neutron time-like form factor into the space-like interval 0.1 GeV2 ≤ Q2 ≤ 1 GeV2 using the limited FENICE data gives a factor of ∼ 2 inconsistency in GnE(Q2) with the recent Saclay and Mainz measurements.

Lots of information on solar-like oscillations in red giants has been obtained thanks to observations with CoRoT and Kepler space telescopes. Data on dipolar modes appear most interesting. We study properties of dipolar oscillations in luminous red giants to explain mechanism of mode trapping in the convective envelope and to assess what may be learned from the new data. Equations for adiabatic oscillations are solved by numerical integration down to the bottom of convective envelope, where the boundary condition is applied. The condition is based on asymptotic decomposition of the fourth order system into components describing a running wave and a uniform shift of radiative core. If the luminosity of a red giant is sufficiently high, for instance at M = 2 Msun greater than about 100 Lsun, the dipolar modes become effectively trapped in the acoustic cavity, which covers the outer part of convective envelope. Energy loss caused by gravity wave emission at the envelope base is a secondary or negligible source of damping. Frequencies are insensitive to structure of the deep interior., Comment: 10 pages, 7 figures, accepted for publication in Astronomy and Astrophysics

The deep-inelastic scattering structure function ratio F 2 n / F 2 p and the nucleon spin asymmetries are found to be strongly x-dependent. In the context of the parton model, the observed inhomogeneities mean that quarks with different flavors and spins carry different fractions of the nucleon momentum. We show that all of these asymmetry effects can be qualitatively understood in terms of the admixtures of excited-state configurations in the nucleon wave function due to color hyperfine interactions.

We show that the OPAL opacities, in addition to explaining the origin of the pulsations of β Cep stars, also predict the existence of a large region in the main-sequence band at lower luminosities, where high-order g-modes of low harmonic degree 1 are unstable. The excitation mechanism remains the same, and is due to the usual κ-effect acting in the metal opacity bump (T≃2×10 5 K), The new instability domain nearly bridges the gap in spectral types between δ Sct and β Cep stars. The periods of the unstable modes are in the range 0.4-3.5 d for l=1 and 2. We propose that this excitation mechanism causes photometric variability in the slowly pulsating B-type stars (SPB stars), and perhaps in other B stars for which variability in the same period range has been reported

An improved version of the OPAL opacities, with the metal abundance parameter Z having values of 0.02 and 0.03, has been used in a stability survey for models of 7- to 16-M ○ . stars in the main-sequence (MS) and early post-MS evolutionary phases. All β Cep stars lie within the domain of the HR diagram where pulsational instability is caused by the opacity mechanism acting in the metal opacity bump at T ≃ 2 × 10 5 K. For most of the objects, a value of Z = 0.02 suffices to account for the pulsation. The positions of β Cep stars in the HR diagram correspond to models in an advanced phase of core hydrogen burning, constructed without allowing for effects of the convective overshooting

Nonlinear effects determining the amplitudes of unstable modes of oscillations in stellar modes, are reviewed. The two basic processes - saturation of the driving mechanism and resonant mode coupling - are discussed within the framework of the amplitude equation formalism. There are difficult problems in the theory of multiple mode interaction that must be solved to make a prediction of amplitude spectra possible. The observed spectra for δ Scu stars and other multiperiodic variables, exhibit no simple pattern that would suggest a solution of the theoretical problems.

Small amplitude oscillations are observed in red giant branch (RGB) stars. Data on such oscillations are a source of information about the objects, notably about properties of convection in their envelopes and about the systems these objects inhabit. The OGLE-III catalog contains data for about 80 thousand small amplitude variable red giants (OSARGs) in the Large Magellanic Cloud. We want to explain variability in OSARGs as the solar-like oscillation and to associate the peaks in power spectra with frequencies of acoustic modes. We use data on reddening-free magnitudes of the objects and interpret them in terms of stellar physical parameters using tabulated isochrones calculated for ages and composition parameters corresponding to the upper RGB of the LMC. Massive data on the peak frequencies and amplitudes are compared with expectations for stochastically excited oscillations. The frequencies are also compared with those calculated for radial modes in envelope models with parameters taken from the isochrones. In stars close to the tip of the RGB, the peaks in power spectra are found in the 0.1-1.0 $\mu$Hz range, which is consistent with extrapolation of the frequency-luminosity relation for the solar-like oscillation. The dominant peaks occur close to the first two radial overtones. The increase in amplitude with luminosity is slower than linear. The exponent s=0.9 is similar to what is found from recent analysis of CoRoT data on less luminous red giants. Frequency separations between dominant peaks are found to be smaller by about 20% than calculated separations between these modes. After examining various possibilities, we left this discrepancy unexplained. The small amplitude variability of stars at the RGB tip is likely to be caused by a stochastic excitation of acoustic oscillations, but interpreting of individual peaks in power spectra presents a problem., Comment: Accepted for publication in Astronomy and Astrophysics, 6 pages, 6 figures

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.

Data on multimode Cepheids from OGLE-III catalog of the LMC Cepheids are confronted with results from model calculations. Models whose radial mode periods are consistent with observation are not always in agreement with published evolutionary models. Nonradial mode interpretation is considered for the cases of unusual period ratios. The greatest challenge for stellar pulsation theory is explanation of double-mode pulsators with period ratios near 0.6., Comment: 3 pages, 4 figures, Stellar Pulsation: Challenges for Theory and Observation, Santa Fe, NM, 31 May - 5 June, 2009

Using measured frequencies of the solar p-modes, the fractional mass content of helium in the Sun's envelope is determined. It is found that its value lies between 0.23 and 0.24. This result appears to be unaffected by the uncertainties in the treatment of the atmosphere and the outer convective zone, but it relies in a sensitive way on calculation of thermodynamical quantities

The authors argue that it is inappropriate to use SU(3) flavour symmetry in analysing the recent EMC measurement of the proton spin structure function and then present a light-cone, quark-proton model analysis without using SU(3). The nucleon is described as a bound state of three relativistic quarks on the light-cone. The constituent quarks have their own internal structure in terms of valence quarks, a quark-antiquark sea and gluons. The EMC result, taken in conjunction with the Bjorken sum rule, gives, separately, the valence quark and an effective sea contribution to the proton spin, demonstrating explicit cancellation of the valence and sea contributions.

Many among δ Scuti variables were shown to be multiperiodic and all of them probably are. Being in various stages of early evolutionary phase these stars seem excellent candidates for seismic testing the basic assumptions and physics of the stellar evolution theory. What hinders any major progress in the field is an unresolved problem of connecting sparse spectra of the observed oscillation frequencies to dense spectra calculated for the models. Determination of the rotation rate in the interior is probably the most important goal of asteroseismology. In the case of δ Scuti stars there is a complication following from the high density of the spectrum that the standard formula for the rotational splitting may not be valid. To understand mode selection mechanism we have to go beyond the linear adiabatic theory of stellar oscillations. There are still uncertainties in determining mode stability, but the real difficulty lies in prediction which of many unstable models may reach detectable amplitudes. Trapping in the envelope is a possible mechanism of mode selection, but it is not clear yet whether it finds support in observational data. Observational information on spherical harmonics associated with the observed periodicities is crucial for mode identification. This was obtained with use of both photometric and spectroscopic data for number of δ Scuti stars. There are, however, uncertainties which must be clarified with new data and improved methods of their analysis. Efforts in obtaining periodograms for unevolved objects having simple theoretical frequency spectra are encouraged.

Measurements of the nucleon form factor and structure function indicate an inhomogeneous distribution of flavor, charge and spin within the nucleon. It is argued that the ordinary constituent quark model can explain the observed inhomogeneity as arising from spin-dependent interaction between quarks in this model. This agreement suggests a specific bound quark picture of the nucleon structure with a moderate diquark correlation.

The efforts to resolve the solar neutrino problem resulted in a considerable progress in reliability and accuracy in modelling the Sun's interior. Implications from helioseismic sounding supports the standard picture of the solar evolution. A comparison of neutrino fluxes measured in various experiments seems to rule out a non-standard solar core as the solution of the neutrino problem.

An attempt is made to interpret the differences in pulsational behavior between horizontal branch and main sequence (or early post-main sequence) variables. Results of linear stability studies for d Scuti stars are reviewed and supplemented with new calculations. The function of the opacity mechanism in generating instability to a variety of radial and nonradial modes is discussed. The highest excitation rates for these variables, though still much lower than in the case of Cepheids, are found in fundamental modes with higher spherical harmonic orders, l and among higher overtones with low values of l It is argued that amplitudes in δ Scuti stars are limited by nonlinear mode coupling, resulting in lower amplitudes and multiperiodicity, rather than by saturation of the opacity mechanism as is the case with horizontal branch variables.