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

Analysis and identification of subsynchronous vibration for a high pressure parallel flow centrifugal compressor

The summary of a complete analytical design evaluation of an existing parallel flow compressor is presented and a field vibration problem that manifested itself as a subsynchronous vibration that tracked at approximately 2/3 of compressor speed is reviewed. The comparison of predicted and observed peak response speeds, frequency spectrum content, and the performance of the bearing-seal systems are presented as the events of the field problem are reviewed. Conclusions and recommendations are made as to the degree of accuracy of the analytical techniques used to evaluate the compressor design

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

Finding non-eclipsing binaries through pulsational phase modulation

We present a method for finding binaries among pulsating stars that were observed by the Kepler Mission. We use entire four-year light curves to accurately mea- sure the frequencies of the strongest pulsation modes, then track the pulsation phases at those frequencies in 10-d segments. This produces a series of time-delay measurements in which binarity is apparent as a periodic modulation whose amplitude gives the projected light travel time across the orbit. Fourier analysis of this time-delay curve provides the pa- rameters of the orbit, including the period, eccentricity, angle of ascending node and time of periastron passage. Differentiating the time-delay curve yields the full radial-velocity curve directly from the Kepler photometry, without the need for spectroscopy. We show examples with delta Scuti stars having large numbers of pulsation modes, including one system in which both components of the binary are pulsating. The method is straightfor- ward to automate, thus radial velocity curves can be derived for hundreds of non-eclipsing binary stars from Kepler photometry alone. This contribution is based largely upon the work by Murphy et al. [1], describing the phase-modulation method in detail

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

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

Solid seeded soybeans in missouri

William J. Murphy and Harry C. Minor (Department of Agronomy), Edward J. Constien (Department of Agricultural Engineering), Donald E. Null (Area Agronomy Extension Specialist, College of Agriculture)New 1/80/15

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

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