Nonradial Stellar Pulsations Research Articles

WASP-167b/KELT-13b: joint discovery of a hot Jupiter transiting a rapidly rotating F1V star

We report the joint WASP/KELT discovery of WASP-167b/KELT-13b, a transiting hot Jupiter with a 2.02-d orbit around a $V$ = 10.5, F1V star with [Fe/H] = 0.1 $\pm$ 0.1. The 1.5 R$_{\rm Jup}$ planet was confirmed by Doppler tomography of the stellar line profiles during transit. We place a limit of $<$ 8 M$_{\rm Jup}$ on its mass. The planet is in a retrograde orbit with a sky-projected spin-orbit angle of $\lambda = -165^{\circ} \pm 5^{\circ}$. This is in agreement with the known tendency for orbits around hotter stars to be more likely to be misaligned. WASP-167/KELT-13 is one of the few systems where the stellar rotation period is less than the planetary orbital period. We find evidence of non-radial stellar pulsations in the host star, making it a $\delta$-Scuti or $\gamma$-Dor variable. The similarity to WASP-33, a previously known hot-Jupiter host with pulsations, adds to the suggestion that close-in planets might be able to excite stellar pulsations.

The numerical simulation of non-linear non-radial stellar pulsations: a conservative formulation of gravity

The numerical simulation of non-linear non-radial stellar pulsations: a conservative formulation of gravity

Precise radial velocities of giant stars

Context. We have been monitoring 373 very bright (V ≤ 6 mag) G and K giants with high precision optical Doppler spectroscopy for more than a decade at Lick Observatory. Our goal was to discover planetary companions around those stars and to better understand planet formation and evolution around intermediate-mass stars. However, in principle, long-term, g-mode nonradial stellar pulsations or rotating stellar features, such as spots, could effectively mimic a planetary signal in the radial velocity data.

A PULSATIONAL MECHANISM FOR PRODUCING KEPLERIAN DISKS AROUND Be STARS

Classical Be stars are an enigmatic subclass of rapidly rotating hot stars characterized by dense equatorial disks of gas that have been inferred to orbit with Keplerian velocities. Although these disks seem to be ejected from the star and not accreted, there is substantial observational evidence to show that the stars rotate more slowly than required for centrifugally driven mass loss. This paper develops an idea (proposed originally by Hiroyasu Ando and colleagues) that nonradial stellar pulsations inject enough angular momentum into the upper atmosphere to spin up a Keplerian disk. The pulsations themselves are evanescent in the stellar photosphere, but they may be unstable to the generation of resonant oscillations at the acoustic cutoff frequency. A detailed theory of the conversion from pulsations to resonant waves does not yet exist for realistic hot-star atmospheres, so the current models depend on a parameterized approximation for the efficiency of wave excitation. Once resonant waves have been formed, however, they grow in amplitude with increasing height, steepen into shocks, and exert radial and azimuthal Reynolds stresses on the mean fluid. Using reasonable assumptions for the stellar parameters, these processes were found to naturally create the inner boundary conditions required for dense Keplerian disks, even when the underlying B-star photosphere is rotating as slowly as 60% of its critical rotation speed. Because there is evidence for long-term changes in Be-star pulsational properties, this model may also account for the long-term variability of Be stars, including transitions between normal, Be, and shell phases.

High Precision with the Whole Earth Telescope: Lessons and Some Results from XCov20 for the roAp Star HR 1217

AbstractHR1217 is a prototypical rapidly oscillating Ap star that has presented a test to the theory of nonradial stellar pulsation. Prior observations showed a clear pattern of five modes with alternating frequency spacings of 33.3 μHz and 34.6 μHz, with a sixth mode at a problematic spacing of 50.0 μHz (which equals 1.5 × 33.3 μHz) to the highfrequency side. Asymptotic pulsation theory allowed for a frequency spacing of 34 μHz, but hipparcos observations rule out such a spacing. Theoretical calculations of magnetoacoustic modes in Ap stars by Cunha (2001) predicted that there should be a previously undetected mode 34 μHz higher than the main group, with a smaller spacing between it and the highest one. The 20th extended coverage campaign of the Whole Earth Telescope (XCov20) has discovered this frequency as predicted by Cunha (2001). Amplitude modulation of several of the pulsation modes between the 1986 and 2000 data sets has also been discovered, while important parameters for modelling the geometry of the pulsation modes have been shown to be unchanged. With stringent selection of the best data from the WET network the amplitude spectrum shows highest peaks at only 50 μmag and formal errors on the determined amplitudes are 14 μmag. Some lessons for future use of WET for the highest precision photometry on bright stars are discussed.

Interferometric-Doppler Imaging of Nonradial Stellar Pulsations

AbstractWe present the imaging potential of a tomographic technique which combines time-resolved spectroscopy and long baseline interferometry, providing information that cannot be obtained otherwise with each of these techniques separately.

Discovery of the ‘missing’ mode in HR 1217 by the Whole Earth Telescope

ABSTRACT HR1217 is a prototypical rapidly oscillating Ap star that has presented a test tothe theory of nonradial stellar pulsation. Prior observations showed a clear patternof five modes with alternating frequency spacings of 33.3µHz and 34.6µHz, with asixth mode at a problematic spacing of 50.0µHz (which equals 1.5×33.3µHz) to thehigh-frequency side. Asymptotic pulsation theory allowed for a frequency spacing of34µHz, but hipparcos observations rule out such a spacing. Theoretical calculationsof magnetoacoustic modes in Ap stars by Cunha (2001) predicted that there shouldbe a previously undetected mode 34µHz higher than the main group, with a smallerspacing between it and the highest one. In this Letter, we present preliminary resultsfrom a multi-site photometric campaign on the rapidly oscillating Ap star HR1217using the “Whole Earth Telescope”. While a complete analysis of the data will appearin a later paper, one outstanding result from this run is the discovery of a newlydetected frequency in the pulsation spectrum of this star, at the frequency predictedby Cunha (2001).Keywords: Stars: oscillations – stars: variables – stars: individual (HR1217) – stars:magnetic.

Interferometric-Doppler imaging of stellar surface structure

In this paper we discuss the combination of two basic approaches which should potentially generate images of spatially unresolved stars: differential interferometry and classical spectroscopy. Doppler Imaging provides indirect observational information on stellar surface structures by modeling the rotational modulation of the observed flux distribution across spectral lines. Similarly, differential interferometry makes it possible to measure the disturbances of photocentroid location of an unresolved star as a function of wavelength and to deduce the corresponding stellar map. We present the general formalism to reconstruct images from spectroscopy and differential interferometry data for sources with spatially unresolved structures, and we discuss how their combination improves the image reconstructions. This technique, that we call Interferometric-Doppler Imaging (IDI), leads to significant progress in solving some long-standing problems of Doppler Imaging, such as latitude smearing and bias as well as the non-uniqueness of the solution in the special case of an equator-on star. We treat explicitly the most delicate case of non-radial stellar pulsations, for which the cancellation of opposite sign temperature or velocity fields introduces additional difficulties. The performance of the method is demonstrated, using the indirect imaging code built on the basis of the developed approach to reconstruct an input image from a series of generated noisy spectra. The problem of image reconstruction from two-aperture interferometry data has been particularly addressed since it represents the case of most presently operating interferometers.

Doppler Imaging of Non-radially Pulsating Stars

AbstractIn addition to the common applications (temperature, magnetic field, abundance distributions) the Doppler Imaging technique can also be applied to non-radial stellar pulsations (NRP). Due to their rapid rotation, the Be stars are ideal candidates for Doppler Imaging. However, for the stars for which the periodic temporal line profile variability is produced by multiple mode NRP, the classical Doppler image in not an appropriate representation. When the corotating frequencies of existing pulsation modes are non-zero, the reference frame in which the resulting NRP is quasi-stationary cannot be defined. The technique can be applied “mode-by-mode”, which is illustrated in time-wavelength and Fourier frequency domain, using the time-resolved sequence of high resolution, high signal-to-noise ratio spectra of the Be star ζ Oph.

Non-radial stellar oscillations: a perspective from potential scattering (I)

This article is the first in a series designed to gain insight into the stellar oscillation problem from a somewhat novel point of view: that of potential scattering, well-known in the quantum mechanical literature. In this paper the known theoretical foundations are developed and applied in the context of the astrophysical problem, wherein the star itself (rather than any portion of it) is the potential which “scatters” waves and “traps” them. The basis for the identification of a precisely defined scattering problem is the existence of a linear Schrodinger equation associated both globally (Section 2) and locally (Section 8) with the nonlinear eigenvalue equation for nonradial stellar pulsations. The paper is also designed to be a fairly complete account of the relevant mathematical topics that are germane to a study of this kind.

Nonradial, nonadiabatic stellar pulsations

This paper describes how nonradial stellar pulsations can be modeled using a Lagrangian formulation. The adiabatic eigenvalues of this operator are compared to previously published results, using simple stellar models to show the equivalence of this method and other techniques. Nonadiabatic effects are included by appending the thermal equation to the adiabatic operator. At this point, it becomes necessary to include variations in the convective energy transport. Several ways of doing this by freezing the convection are examined. 35 refs.

Contributing factors to flux changes in nonradial stellar pulsations

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 β Cephei, 53 Persei, δ Scuti, rapidly oscillating Ap, Cepheid, and ZZ Ceti variables are compared with model predictions on an amplitude ratio versus phase difference plane\(\left( {A_{co1} /A_{\lambda _1 } ,\phi _{co1} - \phi _{\lambda _1 } } \right)\). 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.

Colour changes in mid-B star variables

AbstractModel predictions of light changes due to non-radial stellar pulsation have been compared with the observations of light and colour changes in mid-B star variables made by Waelkens and Rufener (1985). It is concluded that these observations are consistent with the presence of low l (dipole and quadrupole) non-radial pulsations in the stars. This strengthens Waelkens and Rufener’s hypothesis that these variables may be identified with the 53 Persei stars. The differences between the model predictions for these large Q variables, which have periods in the 1 to 3 day range, and the predictions of small Q models, which apply to β Cephei variables, are explained.

A reviews of: “Theory of stellar pulsation”, “Nonradial oscillations of stars”, and “Nonradial and nonlinear stellar pulsation, proceedings of a workshop in Tucson, Arizona, March 12–16, 1979”

Abstract By John P. Cox. Princeton University Press, 1980. xiv+380 pp. (Hard cover £40; paperback £13.50). (ISBN Hard cover 0691 08252 9, Paperback 0 691 08253 7.) By Wasaburo Unno, Yoji Osaki, Hiroyasu Ando and Hiromoto Shibihashi. University of Tokyo Press, 1979. ix + 323 pp. (¥5800) (ISBN 0 86008 258 X.) Edited by H. A. Hill and W. Dziembowski. Springer-Verlag, Berlin. Heidelberg, New York, 1980. viii+497 pp. (Soft cover DM57; approx $33.70 (ISBN 3 54009994 8 and 0 387 09994 8.)

Baade-Wesselink and related techniques for mode discrimination in nonradial stellar pulsations

Linearized nonradial expressions for light, colour and radial velocity changes are employed to examine the Baade-Wesselink method as applied to the problem of nonradial mode identification in variable stars. It is demonstrated that the usual assumption of a single-valued relation between surface brightness changes and colour variations fails for spherical harmonics withl>1. A Baade-Wesselink expression taking this into account is then given. Using test models for different variable star regimes it is shown that discrimination betweenl=0, 1, and 2 is currently feasible provided adequate attention is paid to pressure effects and to the procedure used to obtain radial velocity data. For higherl, mode discrimination, while possible in principle, is constrained by the stringent requirements on radial velocity measurements and by cases of confusion with lowerl. A review of related but less observationally demanding possible mode discriminators is given. This demonstrates that techniques based on amplitude and phase information in light and colour data may provide reliable discrimination betweenl=0, 1, and 2 when pressure effects are allowed for. For these techniques discrimination of higherl is limited by inadequate model atmosphere limbdarkening information and by confusion with lowerl.

Nonradial and nonlinear stellar pulsation

Nonradial and nonlinear stellar pulsation

On the treatment of convection as a nonradial stellar pulsation

view Abstract Citations (9) References (14) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On the treatment of convection as a nonradial stellar pulsation. Deupree, R. G. Abstract The problem of nonlinear, nonadiabatic, nonradial stellar pulsation has been examined by a computational approach. The difficulties of such an approach are discussed in detail, and the limitations of the present method of solution are listed. A test calculation with a particular RR Lyrae model pulsating in the fundamental mode reveals that convection is present in the second helium ionization zone only when the luminosity amplitude becomes large and even then is present during only part of the pulsation cycle. The convective motion, measured by the nonradial velocity component, grows during rising luminosity, reaches a maximum after maximum luminosity, and decays during the other parts of the cycle. The possible consequences of this phenomenon are briefly discussed. Publication: The Astrophysical Journal Pub Date: June 1975 DOI: 10.1086/153616 Bibcode: 1975ApJ...198..419D Keywords: A Stars; Cepheid Variables; Convective Heat Transfer; Stellar Structure; Amplitude Distribution Analysis; Astronomical Models; Giant Stars; Stellar Luminosity; Astrophysics full text sources ADS |

Nonlinear, Adiabatic, Nonradial Stellar Pulsation: Calculations and Applications

view Abstract Citations (14) References (21) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Nonlinear, Adiabatic, Nonradial Stellar Pulsation: Calculations and Applications Deupree, Robert G. Abstract The computational problem of nonlinear, nonradial, adiabatic stellar pulsation is examined. The successes and failures of several types of difference approximations to the stellar pulsation equations are outlined and illustrated with test models. The best method of solution is applied to the beat phenomenon in the Cephei stars where it is found that in the presence of rotation two modes may be present. It is further indicated that these two modes interact when the frequencies of oscillation are sufficiently close. However, it cannot be definitely concluded that a second mode may be excited when only one mode is initially present, as both modes must be present to some extent in any initial velocity distribution. Subject headings: Cephei stars - pulsation - rotation, stellar Publication: The Astrophysical Journal Pub Date: December 1974 DOI: 10.1086/153256 Bibcode: 1974ApJ...194..393D full text sources ADS |