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

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

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

TIC 184743498: The First Tri-Axial Stellar Pulsator

We have discovered a $\delta$ Scuti pulsator in a tight binary (P = 1.053 d) with nine pulsation modes whose frequencies are between 38 and 56 d$^{-1}$. Each of these modes exhibits amplitude modulations and $\pi$-rad phase shifts twice per orbital cycle. Five of these modes exhibit amplitude and phase shifts that are readily explained by dipole pulsations along an axis that is aligned with the binary's tidal axis. The novelty of the system lies in the remaining four pulsation modes, which we show are dipole pulsations along an axis that is perpendicular to both the tidal axis and the binary's orbital angular momentum axis. There are additionally two pulsation modes whose amplitudes and phases do not change significantly with orbital phase; they are explained as dipole modes along an axis aligned with the orbital/rotation axis. Hence, we propose that TIC 184743498 is a tri-axial pulsator, the first of its kind.Comment: Submitted to MNRAS, 12 figures, 4 table

Pulsation in the white dwarf HE 1017−1352

We report the detection of periodic variations on the Teff 32 000 K DA white dwarf star HE 1017−1352. We obtained time series photometry using the 4.1-m Southern Astrophysical Research telescope on three separate nights for a total of 16.8 h. From the frequency analysis, we found four periods of 605, 556, 508, and 869 s with significant amplitudes above the 1/1000 false alarm probability detection limit. The detected modes are compatible with low harmonic degree g-mode non-radial pulsations with radial order higher than ∼9. This detection confirms the pulsation nature of HE 1017−1352 and thus the existence of the new pulsating class of hot DA white dwarf stars. In addition, we detect a long period of 1.52 h, compatible with a rotation period of DA white dwarf stars

Asteroseismic measurement of slow, nearly uniform surface-to-core rotation in the main-sequence F star KIC 9244992

We have found a rotationally split series of core g-mode triplets and surface p-mode multiplets in a main-sequence F star, KIC 9244992. Comparison with models shows that the star has a mass of about 1.45 M�, and is at an advanced stage of main-sequence evolution in which the central hydrogen abundance mass fraction is reduced to about 0.1. This is the second case, following KIC 11145123, of an asteroseismic determination of the rotation of the deep core and surface of an A-F main-sequence star. We have found, essentially model independently, that the rotation near the surface, obtained from p-mode splittings, is 66 d, slightly slower than the rotation of 64 d in the core, measured by g-mode splittings. KIC 9244992 is similar to KIC 11145123 in that both are near the end of main-sequence stage with very slow and nearly uniform rotation. This indicates the angular momentum transport in the interior of an A-F star during the main-sequence stage is much stronger than that expected from standard theoretical formulations

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

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

Asteroseismic measurement of surface-to-core rotation in a main-sequence A star, KIC 11145123

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 toproduce 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