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

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

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”

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

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

K2 observations of the rapidly oscillating Ap star 33 Lib (HD 137949): new frequencies and unique non-linear interactions

We present the analysis of K2 short cadence data of the rapidly oscillating Ap (roAp) star, 33 Librae (HD 137949). The precision afforded to the K2 data allow us to identify at least 11 pulsation modes in this star, compared to the three previously reported. Reoccurring separations between these modes leads us to suggest a large frequency separation, ∆ν, of 78.9 µHz, twice that reported in the literature. Other frequency separations we detect may represent the small frequency separation, δν, but this is inconclusive at this stage due to magnetic perturbation of the frequencies. Due to the highly non-linear pulsation in 33 Lib, we identify harmonics to four times the principal frequency. Furthermore, we note a unique occurrence of non-linear interactions of the 11 identified modes. The frequency separations of the modes around the principal frequency are replicated around the first harmonic, with some interaction with the second harmonic also. Such a phenomenon has not been seen in roAp stars before. With revised stellar parameters, linear non-adiabatic modelling of 33 Lib shows that the pulsations are not greater than the acoustic cutoff frequency, and that the κ-mechanism can excite the observed modes. Our observations are consistent with 33 Lib having a rotation period much larger than 88 d as presented in the literature

Theory and evidence of global Rossby waves in upper main-sequence stars: r-mode oscillations in many Kepler stars

Asteroseismic inference from pressure modes (p modes) and buoyancy, or gravity, modes (g modes) is ubiquitous for stars across the Hertzsprung–Russell diagram. Until now, however, discussion of r modes (global Rossby waves) has been rare. Here we derive the expected frequency ranges of r modes in the observational frame by considering the visibility of these modes. We find that the frequencies of r modes of azimuthal order m appear as groups at slightly lower frequency than m times the rotation frequency. Comparing the visibility curves for r modes with Fourier amplitude spectra of Kepler light curves of upper main-sequence B, A, and F stars, we find that r modes are present in many γ Dor stars (as first discovered by Van Reeth et al.), spotted stars, and so-called heartbeat stars, which are highly eccentric binary stars. We also find a signature of r modes in a frequently bursting Be star observed by Kepler. In the amplitude spectra of moderately to rapidly rotating γ Dor stars, r-mode frequency groups appear at lower frequency than prograde g-mode frequency groups, while in the amplitude spectra of spotted early A to B stars, groups of symmetric (with respect to the equator) r-mode frequencies appear just below the frequency of a structured peak that we suggest represents an approximate stellar rotation rate. In many heartbeat stars, a group of frequencies can be fitted with symmetric m = 1 r modes, which can be used to obtain rotation frequencies of these stars

HD 42659: The only known roAp star in a spectroscopic binary observed with B photometry, TESS, and SALT

We present a multi-instrument analysis of the rapidly oscillating Ap (roAp) star HD 42659. We have obtained B photometric data for this star and use these data, in conjunction with TESS observations, to analyse the high-frequency pulsation in detail. We find a triplet which is split by the rotation frequency of the star (νrot = 0.3756 d−1; Prot = 2.66 d) and present both distorted dipole and distorted quadrupole mode models. We show that the pulsation frequency, 150.9898 d−1 (Ppuls = 9.54 min) is greater than the acoustic cutoff frequency. We utilise 27 high-resolution (R ≃ 65 000), high signal-to-noise (∼ 120) spectra to provide new orbital parameters for this, the only known roAp star to be in a short period binary (Porb = 93.266 d). We find the system to be more eccentric than previously thought, with e = 0.317, and suggest the companion is a mid-F to early-K star. We find no significant trend in the average pulsation mode amplitude with time, as measured by TESS, implying that the companion does not have an affect on the pulsation in this roAp star. We suggest further photometric observations of this star, and further studies to find more roAp stars in close binaries to characterise how binarity may affect the detection of roAp pulsations

Long-period Ap stars discovered with TESS data: Cycles 3 and 4

One of the most challenging aspects of the Ap stars is the extreme differentiation of their rotation periods, which span more than five orders of magnitude. The physical origin of this differentiation remains poorly understood. The consideration of the most slowly rotating Ap stars represents a promising approach to gain insight into the processes responsible for the rotational braking to which the Ap stars are subject. However, historically, the study of these stars focused primarily on the most strongly magnetic among them. This bias introduced an ambiguity in the conclusions that could be drawn, as it did not allow the distinction between the rotational and magnetic effects, nor the investigation of possible correlations between rotational and magnetic properties. We previously showed that the identification of super-slowly rotating Ap (ssrAp) star candidates (defined as Ap stars that have rotation periods Prot > 50 d) through systematic exploitation of the available TESS photometric observations of Ap stars is an effective approach to build a sample devoid of magnetic bias. This approach rests on the presence of brightness spots on the surface of Ap stars that are not distributed symmetrically about their rotation axes and show long-term stability, hence are responsible for photometric variations with the stellar rotation period. In our previous analyses of TESS Cycle 1 and Cycle 2 data, we interpreted the Ap stars showing no such variability over the 27-d duration of a TESS sector as being ssrAp star candidates. Here, we applied the same approach to TESS Cycle 3 and Cycle 4 observations of Ap stars. We show, however, that two issues that had not been fully appreciated until now may lead to spurious identification of ssrAp star candidates. On the one hand, a considerable fraction of the Ap stars in the existing lists turn out to have erroneous or dubious spectral classifications. On the other hand, the TESS data processing may remove part of the variability signal, especially for stars with moderately long periods (20 d ≲ Prot ≲ 50 d). After critical evaluation of these effects, we report the identification of 25 new ssrAp star candidates and of eight stars with moderately long periods. Combining this list with the lists of ssrAp stars from Cycles 1 and 2 and with the list of ssrAp stars that were previously known but whose lack of variability was not detected in our study, we confirmed at a higher significance level the conclusions drawn in our earlier work. These include the lower rate of occurrence of super-slow rotation among weakly magnetic Ap stars than among strongly magnetic ones, the probable existence of a gap between ∼2 and ∼3 kG in the distribution of the magnetic field strengths of the ssrAp stars, and the much higher rate of occurrence of rapid oscillations in ssrAp stars than in the whole population of Ap stars. The next step to gain further understanding of the ssrAp stars will be to obtain high-resolution spectra of those for which such observations have not been made yet, to constrain their rotation velocities and their magnetic fields