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

EPIC 201585823, a rare triple-mode RR Lyrae star discovered in K2 mission data

We have discovered a new, rare triple-mode RR Lyr star, EPIC 201585823, in the Kepler K2 mission Campaign 1 data. This star pulsates primarily in the fundamental and first-overtone radial modes, and, in addition, a third non-radial mode. The ratio of the period of the non-radial mode to that of the first-overtone radial mode, 0.616 285, is remarkably similar to that seen in 11 other triple-mode RR Lyr stars, and in 260 RRc stars observed in the Galactic bulge. This systematic character promises new constraints on RR Lyr star models. We detected subharmonics of the non-radial mode frequency, which are a signature of period doubling of this oscillation; we note that this phenomenon is ubiquitous in RRc and RRd stars observed from space, and from ground with sufficient precision. The non-radial mode and subharmonic frequencies are not constant in frequency or in amplitude. The amplitude spectrum of EPIC 201585823 is dominated by many combination frequencies among the three interacting pulsation mode frequencies. Inspection of the phase relationships of the combination frequencies in a phasor plot explains the ‘upward’ shape of the light curve. We also found that raw data with custom masks encompassing all pixels with significant signal for the star, but without correction for pointing changes, is best for frequency analysis of this star, and, by implication, other RR Lyr stars observed by the K2 mission. We compare several pipeline reductions of the K2 mission data for this star

Metal-Rich SX Phe Stars in theKeplerField

High-resolution spectroscopic observations have been made for 32 of the 34 candidate SX Phe stars identified in the Kepler field by Balona & Nemec (2012). All available long- and short-cadence Q0-Q17 Kepler photometry has been analyzed for the 34 candidates. Radial velocities (RVs), space motions (U, V, W), projected rotation veloc- ities (v sin i), spectral types, and atmospheric characteristics (Teff , log g, [M/H], vmic, etc.) were derived from ∼160 spectra taken with the ESPaDOnS spectrograph on the Canada- France-Hawaii 3.6-m telescope and with the ARCES spectrograph on the Apache Point Observatory 3.5-m telescope. Two thirds of the stars are fast rotators with v sin i > 50 km/s, including four stars with v sin i > 200 km/s. Three of the stars have (negative) RVs > 250 km/s and retrograde space motions, and seven stars have total space motions > 400 km/s. All the spectroscopically measured SX Phe candidates have positions in a Toomre diagram that are consistent with being bona fide halo and thick-disk stars. Although several stars show a marked metal weakness, the mean [Fe/H] of the sample is near 0.0 dex (σ ∼ 0.25 dex), which is considerably more metal-rich than is normally expected for a sample of Pop. II stars. Observed pulsation frequency modulations and optical time delays suggest that at least eight of the SX Phe stars are in binary systems, some of which show signif- icant RV variations. Six of the time-delay binaries have secondary masses ranging from 0.05 to 0.70 Mo and orbital periods in the range 9 to 1570 days. Another star appears to be an ellipsoidal variable with a 2.3-day orbital period; and two other systems have orbital periods longer than the ∼4-year sampling interval of the Kepler data

Finding binaries from phase modulation of pulsating stars with Kepler: V. Orbital parameters, with eccentricity and mass-ratio distributions of 341 new binaries

The orbital parameters of binaries at intermediate periods (102–103 d) are difficult to measure with conventional methods and are very incomplete. We have undertaken a new survey, applying our pulsation timing method to Kepler light curves of 2224 main-sequence A/F stars and found 341 non-eclipsing binaries. We calculate the orbital parameters for 317 PB1 systems (single-pulsator binaries) and 24 PB2s (double-pulsators), tripling the number of intermediate-mass binaries with full orbital solutions. The method reaches down to small mass ratios q ≈ 0.02 and yields a highly homogeneous sample. We parametrize the mass- ratio distribution using both inversion and Markov-Chain Monte Carlo forward-modelling techniques, and find it to be skewed towards low-mass companions, peaking at q ≈ 0.2. While solar-type primaries exhibit a brown dwarf desert across short and intermediate periods, we find a small but statistically significant (2.6σ ) population of extreme-mass-ratio companions (q 0.1, we measure the binary fraction of current A/F primaries to be 15.4 per cent ± 1.4 per cent, though we find that a large fraction of the companions (21 per cent ± 6 per cent) are white dwarfs in post-mass-transfer systems with primaries that are now blue stragglers, some of which are the progenitors of Type Ia supernovae, barium stars, symbiotics, and related phenomena. Excluding these white dwarfs, we determine the binary fraction of original A/F primaries to be 13.9 per cent ± 2.1 per cent over the same parameter space. Combining our measurements with those in the literature, we find the binary fraction across these periods is a constant 5 per cent for primaries M1 < 0.8 M , but then increases linearly with log M1, demonstrating that natal discs around more massive protostars M1 2: 1M become increasingly more prone to fragmentation. Finally, we find the eccentricity distribution of the main-sequence pairs to be much less eccentric than the thermal distribution

KIC 4768731: a bright long-period roAp star in theKeplerfield

We report the identification of 61.45 d−1 (711.2 μHz) oscillations, with amplitudes of 62.6 μmag, in KIC 4768731 (HD 225914) using Kepler photometry. This relatively bright (V = 9.17) chemically peculiar star with spectral type A5 Vp SrCr(Eu) has previously been found to exhibit rotational modulation with a period of 5.21 d. Fourier analysis reveals a simple dipole pulsator with an amplitude that has remained stable over a 4-yr time span, but with a frequency that is variable. Analysis of high-resolution spectra yields stellar parameters of Teff = 8100 ± 200 K, log g = 4.0 ± 0.2, [Fe/H] = +0.31 ± 0.24 and v sin i = 14.8 ± 1.6 km s−1. Line profile variations caused by rotation are also evident. Lines of Sr, Cr, Eu, Mg and Si are strongest when the star is brightest, while Y and Ba vary in antiphase with the other elements. The abundances of rare earth elements are only modestly enhanced compared to other roAp stars of similar Teff and log g. Radial velocities in the literature suggest a significant change over the past 30 yr, but the radial velocities presented here show no significant change over a period of 4 yr

Validation of the frequency modulation technique applied to the pulsating δ Sct–γ Dor eclipsing binary star KIC 8569819

KIC 8569819 is an eclipsing binary star with an early F primary and G secondary in a 20.85-d eccentric orbit. The primary is a δ Sct–γ Dor star pulsating in both p modes and g modes. Using four years of Kepler Mission photometric data, we independently model the light curve using the traditional technique with the modelling code PHOEBE, and we study the orbital characteristics using the new frequency modulation technique. We show that both methods provide the equivalent orbital period, eccentricity and argument of periastron, thus illustrating and validating the FM technique. In the amplitude spectrum of the p-mode pulsations, we also discovered an FM signal compatible with a third body in the system, a low-mass M dwarf in an 861-d orbit around the primary pair. However, the eclipses show no timing variations, indicating that the FM signal is a consequence of the intrinsic change in pulsation frequency, thus providing a cautionary tale. Our analysis shows the potential of the FM technique using Kepler data, and we discuss the prospects to detect planets and brown dwarfs in Kepler data for A and F stars even in the absence of transits and with no spectroscopic radial velocity curves. This opens the possibility of finding planets orbiting hotter stars that cannot be found by traditional techniques

A unifying explanation of complex frequency spectra of γ 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

The single-sided pulsator CO Camelopardalis

Abstract CO Cam (TIC 160268882) is the second “single-sided pulsator” to be discovered. These are stars where one hemisphere pulsates with a significantly higher amplitude than the other side of the star. CO Cam is a binary star comprised of an Am δ Sct primary star with Teff = 7070 ± 150 K, and a spectroscopically undetected G main-sequence secondary star. The dominant pulsating side of the primary star is centred on the L1 point. We have modelled the spectral energy distribution combined with radial velocities, and independently the TESS light curve combined with radial velocities. Both of these give excellent agreement and robust system parameters for both stars. The δ Sct star is an oblique pulsator with at least four low radial overtone (probably) f modes with the pulsation axis coinciding with the tidal axis of the star, the line of apsides. Preliminary theoretical modelling indicates that the modes must produce much larger flux perturbations near the L1 point, although this is difficult to understand because the pulsating star does not come near to filling its Roche lobe. More detailed models of distorted pulsating stars should be developed. These newly discovered single-sided pulsators offer new opportunities for astrophysical inference from stars that are oblique pulsators in close binary stars

Finding binaries from phase modulation of pulsating stars with Kepler: V. Orbital parameters, with eccentricity and mass-ratio distributions of 341 new binaries

The orbital parameters of binaries at intermediate periods (102-103 d) are difficult to measure with conventional methods and are very incomplete. We have undertaken a new survey, applying our pulsation timing method to Kepler light curves of 2224 main-sequence A/F stars and found 341 non-eclipsing binaries. We calculate the orbital parameters for 317 PB1 systems (single-pulsator binaries) and 24 PB2s (double-pulsators), tripling the number of intermediate-mass binaries with full orbital solutions. The method reaches down to small mass ratios q ≈ 0.02 and yields a highly homogeneous sample. We parametrize the massratio distribution using both inversion and Markov-Chain Monte Carlo forward-modelling techniques, and find it to be skewed towards low-mass companions, peaking at q ≈ 0.2. While solar-type primaries exhibit a brown dwarf desert across short and intermediate periods, we find a small but statistically significant (2.6σ) population of extreme-mass-ratio companions (q [removed] 0.1, we measure the binary fraction of current A/F primaries to be 15.4 percent ± 1.4 per cent, though we find that a large fraction of the companions (21 percent ± 6 per cent) are white dwarfs in post-mass-transfer systems with primaries that are now blue stragglers, some of which are the progenitors of Type Ia supernovae, barium stars, symbiotics, and related phenomena. Excluding these white dwarfs, we determine the binary fraction of original A/F primaries to be 13.9 percent ± 2.1 per cent over the same parameter space. Combining our measurements with those in the literature, we find the binary fraction across these periods is a constant 5 per cent for primaries M1 < 0.8M⊙, but then increases linearly with log M1, demonstrating that natal discs around more massive protostars M1 ≳ 1M⊙ become increasingly more prone to fragmentation. Finally, we find the eccentricity distribution of the main-sequence pairs to be much less eccentric than the thermal distribution

Discovery of multiple p-mode pulsation frequencies in the roAp star, HD 86181

We report the frequency analysis of a known roAp star, HD 86181 (TIC 469246567), with new inferences from TESS data. We derive the rotation frequency to be νrot = 0.48753 ± 0.00001d−1. The pulsation frequency spectrum is rich, consisting of two doublets and one quintuplet, which we interpret to be oblique pulsation multiplets from consecutive, high-overtone dipole, quadrupole and dipole modes. The central frequency of the quintuplet is 232.7701d−1 (2.694 mHz). The phases of the sidelobes, the pulsation phase modulation, and a spherical harmonic decomposition all show that the quadrupole mode is distorted. Following the oblique pulsator model, we calculate the rotation inclination, i, and magnetic obliquity, β, of this star, which provide detailed information about the pulsation geometry. The i and β derived from the best fit of the pulsation amplitude and phase modulation to a theoretical model, including the magnetic field effect, slightly differ from those calculated for a pure quadrupole, indicating the contributions from l = 4, 6, 8, ... are small. Non-adiabatic models with different envelope convection conditions and physics configurations were considered for this star. It is shown that models with envelope convection almost fully suppressed can explain the excitation at the observed pulsation frequencies