Pulsational frequency and amplitude modulation in the δ Sct star KIC 7106205

Analysis of the Kepler δ Sct star KIC 7106205 showed amplitude modulation in a single pressure mode, whilst all other pressure and gravity modes remained stable in amplitude and phase over the 1470 d length of the data set. The Kepler data set was divided into a series with time bins of equal length for which consecutive Fourier transforms were calculated. An optimum fixed frequency, calculated from a least-squares fit of all data, allowed amplitude and phase of each pulsation mode for each time bin to be tracked. The single pressure mode at ν = 13.3942 d-1 changed significantly in amplitude, from 5.16 ± 0.03 to 0.53 ± 0.06 mmag, but also varied quasi-sinusoidally in phase, with a characteristic period similar to the length of the data set. All other p and g modes were stable in both amplitude and phase, which is clear evidence that the visible pulsation mode energy is not conserved within this star. Possible causes of the observed amplitude and phase modulation and the missing mode energy are discussed

FM stars: A Fourier view of pulsating binary stars, a new technique for measuring radial velocities photometrically

Some pulsating stars are good clocks. When they are found in binary stars, the frequencies of their luminosity variations are modulated by the Doppler effect caused by orbital motion. For each pulsation frequency this manifests itself as a multiplet separated by the orbital frequency in the Fourier transform of the light curve of the star. We derive the theoretical relations to exploit data from the Fourier transform to derive all the parameters of a binary system traditionally extracted from spectroscopic radial velocities, including the mass function which is easily derived from the amplitude ratio of the first orbital sidelobes to the central frequency for each pulsation frequency. This is a new technique that yields radial velocities from the Doppler shift of a pulsation frequency, thus eliminates the need to obtain spectra. For binary stars with pulsating components, an orbital solution can be obtained from the light curve alone. We give a complete derivation of this and demonstrate it both with artificial data, and with a case of a hierarchical eclipsing binary with {\it Kepler} mission data, KIC 4150611 (HD 181469). We show that it is possible to detect Jupiter-mass planets orbiting $\delta$ Sct and other pulsating stars with our technique. We also show how to distinguish orbital frequency multiplets from potentially similar nonradial $m$-mode multiplets and from oblique pulsation multiplets.Comment: 15 pages, 14 figures, accepted for publication in MNRA

FM stars II: a Fourier view of pulsating binary stars - determining binary orbital parameters photometrically for highly eccentric cases

Continuous and precise space-based photometry has made it possible to measure the orbital frequency modulation of pulsating stars in binary systems with extremely high precision over long time spans. Frequency modulation caused by binary orbital motion manifests itself as a multiplet with equal spacing of the orbital frequency in the Fourier transform. The amplitudes and phases of the peaks in these multiplets reflect the orbital properties, hence the orbital parameters can be extracted by analysing such precise photometric data alone. We derive analytically the theoretical relations between the multiplet properties and the orbital parameters, and present a method for determining these parameters, including the eccentricity and the argument of periapsis, from a quintuplet or a higher order multiplet. This is achievable with the photometry alone, without spectroscopic radial velocity measurements. We apply this method to Kepler mission data of KIC 8264492, KIC 9651065, and KIC 10990452, each of which is shown to have an eccentricity exceeding 0.5. Radial velocity curves are also derived from the Kepler photometric data. We demonstrate that the results are in good agreement with those obtained by another technique based on the analysis of the pulsation phases

A unifying explanation of complex frequency spectra of gamma Dor, SPB and Be stars: combination frequencies and highly non-sinusoidal light curves

There are many Slowly Pulsating B (SPB) stars and γ Dor stars in the Kepler mission data set. The light curves of these pulsating stars have been classified phenomenologically into stars with symmetric light curves and with asymmetric light curves. In the same effective temperature ranges as the γ Dor and SPB stars, there are variable stars with downward light curves that have been conjectured to be caused by spots. Among these phenomenological classes of stars, some show ‘frequency groups’ in their amplitude spectra that have not previously been understood. While it has been recognized that non-linear pulsation gives rise to combination frequencies in a Fourier description of the light curves of these stars, such combination frequencies have been considered to be a only a minor constituent of the amplitude spectra. In this paper, we unify the Fourier description of the light curves of these groups of stars, showing that many of them can be understood in terms of only a few base frequencies, which we attribute to g-mode pulsations, and combination frequencies, where sometimes a very large number of combination frequencies dominate the amplitude spectra. The frequency groups seen in these stars are thus tremendously simplified. We show observationally that the combination frequencies can have amplitudes greater than the base frequency amplitudes, and we show theoretically how this arises. Thus for some γ Dor and SPB stars, combination frequencies can have the highest observed amplitudes. Among the B stars are pulsating Be stars that show emission lines in their spectra from occasional ejection of material into a circumstellar disc. Our analysis gives strong support to the understanding of these pulsating Be stars as rapidly rotating SPB stars, explained entirely by g-mode pulsations

Asteroseismic measurement of surface-to-core rotation in a main-sequence star

We have discovered rotationally split core g-mode triplets and surface p-mode triplets and quintuplets in a terminal age main-sequence A star, KIC 11145123, that shows both δ Sct p-mode pulsations and γ Dor g-mode pulsations. This gives the first robust determination of the rotation of the deep core and surface of a main-sequence star, essentially model-independently. We find its rotation to be nearly uniform with a period near 100 d, but we show with high confidence that the surface rotates slightly faster than the core. A strong angular momentum transfer mechanism must be operating to produce the nearly rigid rotation, and a mechanism other than viscosity must be operating to produce a more rapidly rotating surface than core. Our asteroseismic result, along with previous asteroseismic constraints on internal rotation in some B stars, and measurements of internal rotation in some subgiant, giant and white dwarf stars, has made angular momentum transport in stars throughout their lifetimes an observational science

E´ chelle diagrams and period spacings of g modes in: Doradus stars from four years of Kepler observations

We use photometry from the Kepler Mission to study oscillations in Doradus stars. Some stars show remarkably clear sequences of g modes and we use period ´echelle diagrams to measure period spacings and identifyrotationally split multiplets with ` = 1 and ` = 2.We find small deviations from regular period spacings that arise from the gradient in the chemical composition just outside the convective core. We also find stars for which the period spacing shows a strong linear trend as a function of period, consistent with relatively rapid rotation. Overall, th

Long period Ap stars discovered with TESS data

Context. The TESS space mission has a primary goal to search for exoplanets around bright, nearby stars. Because of the high precision photometry required for the main mission, it also is producing superb data for asteroseismology, eclipsing binary stars, gyrochronology – any field of stellar astronomy where the data are variable light curves. Aims. In this work we show that the TESS data are excellent for astrophysical inference from peculiar stars that show no variability. The Ap stars have the strongest magnetic fields of any main-sequence stars. Some Ap stars have also been shown to have rotation periods of months, years, decades and even centuries. The astrophysical cause of their slow rotation – the braking mechanism – is not known with certainty. These stars are rare: there are currently about 3 dozen with known periods. Methods. The magnetic Ap stars have long-lived spots that allow precise determination of their rotation periods. We argue, and show, that most Ap stars with TESS data that show no low-frequency variability must have rotation periods longer than, at least, a TESS sector of 27 d. Results. From this we find 60 Ap stars in the southern ecliptic hemisphere TESS data with no rotational variability, of which at most a few can be pole-on, and six likely have nearly aligned magnetic and rotation axes. Of the other 54, 31 were previously known to have long rotation periods or very low projected equatorial velocities, which proves our technique; 23 are new discoveries. These are now prime targets for long-term magnetic studies. We also find that 12 of the 54 (22 per cent) long-period Ap stars are roAp stars, versus only 3 per cent (29 out of 960) of the other Ap stars studied with TESS in sectors 1−13, showing that the roAp phenomenon is correlated with rotation, although this correlation is not necessarily causal. In addition to probing rotation in Ap stars, these constant stars are also excellent targets to characterise the instrumental behaviour of the TESS cameras, as well as for the CHEOPS and PLATO missions. Conclusions. This work demonstrates astrophysical inference from nonvariable stars – we can get “something for nothing”

Asteroseismology Across the Hertzsprung–Russell Diagram

Asteroseismology has grown from its beginnings three decades ago to a mature field teeming with discoveries and applications. This phenomenal growth has been enabled by space photometry with precision 10–100 times better than ground-based observations, with nearly continuous light curves for durations of weeks to years, and by large-scale ground-based surveys spanning years designed to detect all time-variable phenomena. The new high-precision data are full of surprises, deepening our understanding of the physics of stars. ▪ This review explores asteroseismic developments from the past decade primarily as a result of light curves from the Kepler and Transiting Exoplanet Survey Satellite space missions for massive upper main sequence OBAF stars, pre-main-sequence stars, peculiar stars, classical pulsators, white dwarfs and subdwarfs, and tidally interacting close binaries. ▪ The space missions have increased the numbers of pulsators in many classes by an order of magnitude. ▪ Asteroseismology measures fundamental stellar parameters and stellar interior physics—mass, radius, age, metallicity, luminosity, distance, magnetic fields, interior rotation, angular momentum transfer, convective overshoot, core-burning stage—supporting disparate fields such as galactic archeology, exoplanet host stars, supernovae progenitors, gamma-ray and gravitational wave precursors, close binary star origins and evolution, and standard candles. ▪ Stars are the luminous tracers of the Universe. Asteroseismology significantly improves models of stellar structure and evolution on which all inference from stars depends

Spectroscopic and asteroseismic analysis of the remarkable main-sequence A star KIC 11145123

A spectroscopic analysis was carried out to clarify the properties of KIC 11145123 -- the first main-sequence star with a determination of core-to-surface rotation -- based on spectra observed with the High Dispersion Spectrograph (HDS) of the Subaru telescope. The atmospheric parameters ($T_{\rm eff} = 7600$ K, $\log g = 4.2$, $\xi = 3.1$ km s$^{-1}$ and ${\rm [Fe/H]} = -0.71$ dex), the radial and rotation velocities, and elemental abundances were obtained by analysing line strengths and fitting line profiles, which were calculated with a 1D LTE model atmosphere. The main properties of KIC 11145123 are: (1) A low ${\rm [Fe/H]} = -0.71\pm0.11$ dex and a high radial velocity of $-135.4 \pm 0.2$ km s$^{-1}$. These are remarkable among late-A stars. Our best asteroseismic models with this low [Fe/H] have slightly high helium abundance and low masses of 1.4 M$_\odot$. All of these results strongly suggest that KIC 11145123 is a Population II blue straggler; (2) The projected rotation velocity confirms the asteroseismically predicted slow rotation of the star; (3) Comparisons of abundance patterns between KIC 11145123 and Am, Ap, and blue stragglers show that KIC 11145123 is neither an Am star nor an Ap star, but has abundances consistent with a blue straggler. We conclude that the remarkably long 100-d rotation period of this star is a consequence of it being a blue straggler, but both pathways for the formation of blue stragglers -- merger and mass loss in a binary system -- pose difficulties for our understanding of the exceedingly slow rotation. In particular, we show that there is no evidence of any secondary companion star, and we put stringent limits on the possible mass of any such purported companion through the phase modulation (PM) technique.Comment: 19 pages, of which the final 7 are appendixed data tables. Ten figures, some of which do require colour. Accepted for publication in MNRA

Tidally Trapped Pulsations in Binary Stars

Abstract A new class of pulsating binary stars was recently discovered, whose pulsation amplitudes are strongly modulated with orbital phase. Stars in close binaries are tidally distorted, so we examine how a star’s tidally induced asphericity affects its oscillation mode frequencies and eigenfunctions. We explain the pulsation amplitude modulation via tidal mode coupling such that the pulsations are effectively confined to certain regions of the star, e.g., the tidal pole or the tidal equator. In addition to a rigorous mathematical formalism to compute this coupling, we provide a more intuitive semi-analytic description of the process. We discuss three resulting effects: 1. Tidal alignment, i.e., the alignment of oscillation modes about the tidal axis rather than the rotation axis; 2. Tidal trapping, e.g., the confinement of oscillations near the tidal poles or the tidal equator; 3. Tidal amplification, i.e., increased flux perturbations near the tidal poles where acoustic modes can propagate closer to the surface of the star. Together, these phenomena can account for the pulsation amplitude and phase modulation of the recently discovered class of “tidally tilted pulsators.” We compare our theory to the three tidally tilted pulsators HD 74423, CO Cam, and TIC 63328020, finding that tidally trapped modes that are axisymmetric about the tidal axis can largely explain the first two, while a non-axisymmetric tidally aligned mode is present in the latter. Finally, we discuss implications and limitations of the theory, and we make predictions for the many new tidally tilted pulsators likely to be discovered in the near future