Jim Fuller

KIC 4544587: an eccentric, short-period binary system with δ Sct pulsations and tidally excited modes

We present Kepler photometry and ground-based spectroscopy of KIC 4544587, a short-period eccentric eclipsing binary system with self-excited pressure and gravity modes, tidally excited modes, tidally influenced p modes and rapid apsidal motion of 182 yr per cycle. The primary and secondary components of KIC 4544587 reside within the d Scuti and γ Dor instability region of the Hertzsprung-Russell diagram, respectively. By applying the binary modelling software PHOEBE to prewhitenedKepler photometric data and radial velocity data obtained using the William Herschel Telescope and 4-m Mayall telescope at Kitt Peak Northern Observatory (KPNO), the fundamental parameters of this important system have been determined, including the stellarmasses, 1.98±0.07 and 1.60±0.06 M⊙, and radii, 1.76±0.03 and 1.42±0.02R⊙, for the primary and secondary components, respectively. Frequency analysis of the residual data revealed 31 modes, 14 in the gravity mode region and 17 in the pressure mode region. Of the 14 gravity modes, 8 are orbital harmonics: a signature of tidal resonance. While the measured amplitude of these modes may be partially attributed to residual signal from binary model subtraction, we demonstrate through consideration of the folded light curve that these frequencies do in fact correspond to tidally excited pulsations. Furthermore, we present an echelle diagram of the pressure mode frequency region (modulo the orbital frequency) and demonstrate that the tides are also influencing the p modes. A first look at asteroseismology hints that the secondary component is responsible for the p modes, which is contrary to our expectation that the hotter star should pulsate in higher radial overtone, higher frequency p modes. ©2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.

Dynamical tides in eccentric binaries and tidally excited stellar pulsations in Kepler KOI-54

Recent observation of the tidally excited stellar oscillations in the main-sequence binary KOI-54 by the Kepler satellite provides a unique opportunity for studying dynamical tides in eccentric binary systems. We develop a general theory of tidal excitation of oscillation modes of rotating binary stars and apply our theory to tidally excited gravity modes (g-modes) in KOI-54. The strongest observed oscillations, which occur at 90 and 91 times the orbital frequency, are likely due to prograde m= 2 modes (relative to the stellar spin axis) locked in resonance with the orbit. The remaining flux oscillations with frequencies that are integer multiples of the orbital frequency are likely due to nearly resonant m= 0 g-modes; such axisymmetric modes generate larger flux variations compared to the m= 2 modes, assuming that the spin inclination angle of the star is comparable to the orbital inclination angle. We examine the process of resonance mode locking under the combined effects of dynamical tides on the stellar spin and orbit and the intrinsic stellar spindown. We show that KOI-54 can naturally evolve into a state in which at least one m= 2 mode is locked in resonance with the orbital frequency. Our analysis provides an explanation for the fact that only oscillations with frequencies less than 90–100 times the orbital frequency are observed. We have also found evidence from the published Kepler result that three-mode non-linear coupling occurs in the KOI-54 system. We suggest that such non-linear mode coupling may explain the observed oscillations that are not harmonics of the orbital frequency.

ANGULAR MOMENTUM TRANSPORT VIA INTERNAL GRAVITY WAVES IN EVOLVING STARS

Recent asteroseismic advances have allowed for direct measurements of the internal rotation rates of many sub-giant and red giant stars. Unlike the nearly rigidly rotating Sun, these evolved stars contain radiative cores that spin faster than their overlying convective envelopes, but slower than they would in the absence of internal angular momentum transport. We investigate the role of internal gravity waves in angular momentum transport in evolving low mass stars. In agreement with previous results, we find that convectively excited gravity waves can prevent the development of strong differential rotation in the radiative cores of Sun-like stars. As stars evolve into sub-giants, however, low frequency gravity waves become strongly attenuated and cannot propagate below the hydrogen burning shell, allowing the spin of the core to decouple from the convective envelope. This decoupling occurs at the base of the sub-giant branch when stars have surface temperatures of roughly 5500 K. However, gravity waves can still spin down the upper radiative region, implying that the observed differential rotation is likely confined to the deep core near the hydrogen burning shell. The torque on the upper radiative region may also prevent the core from accreting high-angular momentum material and slow the rate of core spin-up. The observed spin-down of cores on the red giant branch cannot be totally attributed to gravity waves, but the waves may enhance shear within the radiative region and thus increase the efficacy of viscous/magnetic torques.

A prevalence of dynamo-generated magnetic fields in the cores of intermediate-mass stars.

Magnetic fields play a part in almost all stages of stellar evolution. Most low-mass stars, including the Sun, show surface fields that are generated by dynamo processes in their convective envelopes. Intermediate-mass stars do not have deep convective envelopes, although 10 per cent exhibit strong surface fields that are presumed to be residuals from the star formation process. These stars do have convective cores that might produce internal magnetic fields, and these fields might survive into later stages of stellar evolution, but information has been limited by our inability to measure the fields below the stellar surface. Here we report the strength of dipolar oscillation modes for a sample of 3,600 red giant stars. About 20 per cent of our sample show mode suppression, by strong magnetic fields in the cores, but this fraction is a strong function of mass. Strong core fields occur only in red giants heavier than 1.1 solar masses, and the occurrence rate is at least 50 per cent for intermediate-mass stars (1.6–2.0 solar masses), indicating that powerful dynamos were very common in the previously convective cores of these stars.

Asteroseismology can reveal strong internal magnetic fields in red giant stars

Stellar oscillations as magnetic probes Unlike magnetic fields on the surfaces of stars, those within a star have so far remained difficult to observe. Fuller et al. have developed a method of delving into the magnetic depths by exploiting the oscillations of red giant stars. A high magnetic field can cause sound waves to become trapped within the central regions of the star, damping certain vibration modes. Using seismological techniques, this suppression can help infer the core magnetic field for several red giants. Science, this issue p. 423 Stellar oscillations can be used to measure magnetic fields in the core of red giant stars. Internal stellar magnetic fields are inaccessible to direct observations, and little is known about their amplitude, geometry, and evolution. We demonstrate that strong magnetic fields in the cores of red giant stars can be identified with asteroseismology. The fields can manifest themselves via depressed dipole stellar oscillation modes, arising from a magnetic greenhouse effect that scatters and traps oscillation-mode energy within the core of the star. The Kepler satellite has observed a few dozen red giants with depressed dipole modes, which we interpret as stars with strongly magnetized cores. We find that field strengths larger than ~105 gauss may produce the observed depression, and in one case we infer a minimum core field strength of ≈107 gauss.

CHARACTERIZING THE COOL KOIs. V. KOI-256: A MUTUALLY ECLIPSING POST-COMMON ENVELOPE BINARY

We report that Kepler Object of Interest 256 (KOI-256) is a mutually eclipsing post-common envelope binary (ePCEB), consisting of a cool white dwarf (M_★ = 0.592 ± 0.089 M_☉, R_★ = 0.01345 ± 0.00091 R_☉, T_(eff) = 7100 ± 700 K) and an active M3 dwarf (M_★ = 0.51 ± 0.16 M_☉, R_★ = 0.540 ± 0.014 R_☉, T_(eff) = 3450 ± 50 K) with an orbital period of 1.37865 ± 0.00001 days. KOI-256 is listed as hosting a transiting planet-candidate by Borucki et al. and Batalha et al.; here we report that the planet-candidate transit signal is in fact the occultation of a white dwarf as it passes behind the M dwarf. We combine publicly-available long- and short-cadence Kepler light curves with ground-based measurements to robustly determine the system parameters. The occultation events are readily apparent in the Kepler light curve, as is spin-orbit synchronization of the M dwarf, and we detect the transit of the white dwarf in front of the M dwarf halfway between the occultation events. The size of the white dwarf with respect to the Einstein ring during transit (R_(Ein) = 0.00473 ± 0.00055 R ☉) causes the transit depth to be shallower than expected from pure geometry due to gravitational lensing. KOI-256 is an old, long-period ePCEB and serves as a benchmark object for studying the evolution of binary star systems as well as white dwarfs themselves, thanks largely to the availability of near-continuous, ultra-precise Kepler photometry.

Dynamical tides in compact white dwarf binaries: tidal synchronization and dissipation

In compact white dwarf (WD) binary systems (with periods ranging from minutes to hours), dynamical tides involving the excitation and dissipation of gravity waves play a dominant role in determining the physical conditions (such as rotation rate and temperature) of the WDs prior to mass transfer or binary merger. We calculate the amplitude of the tidally excited gravity waves as a function of the tidal forcing frequency ω= 2(Ω−Ωs) (where Ω is the orbital frequency and Ωs is the spin frequency) for several realistic carbon–oxygen WD models, under the assumption that the outgoing propagating waves are efficiently dissipated in the outer layer of the star by non-linear effects or radiative damping. Unlike main-sequence stars with distinct radiative and convection zones, the mechanism of wave excitation in WDs is more complex due to the sharp features associated with composition changes inside the WD. In our WD models, the gravity waves are launched just below the helium–carbon boundary and propagate outwards. We find that the tidal torque on the WD and the related tidal energy transfer rate, , depend on ω in an erratic way, with varying by orders of magnitude over small frequency ranges. On average, scales approximately as Ω5ω5 for a large range of tidal frequencies. We also study the effects of dynamical tides on the long-term evolution of WD binaries prior to mass transfer or merger. Above a critical orbital frequency Ωc, corresponding to an orbital period of the order of 1h (depending on WD models), dynamical tides efficiently drive Ωs towards Ω, although a small, almost constant degree of synchronization (Ω−Ωs∼ constant) is maintained even at the smallest binary periods. While the orbital decay is always dominated by gravitational radiation, the tidal energy transfer can induce a significant phase error in the low-frequency gravitational waveforms, detectable by the planned Laser Interferometer Space Antenna project. Tidal dissipation may also lead to significant heating of the WD envelope and brightening of the system long before binary merger.

Resonance locking as the source of rapid tidal migration in the Jupiter and Saturn moon systems

The inner moons of Jupiter and Saturn migrate outwards due to tidal energy dissipation within the planets, the details of which remain poorly understood. We demonstrate that resonance locking between moons and internal oscillation modes of the planet can produce rapid tidal migration. Resonance locking arises due to the internal structural evolution of the planet and typically produces an outward migration rate comparable to the age of the Solar system. Resonance locking predicts a similar migration time-scale but a different effective tidal quality factor Q governing the migration of each moon. The theory also predicts nearly constant migration time-scales a function of semimajor axis, such that effective Q values were larger in the past. Recent measurements of Jupiter and Saturns moon systems find effective Q values that are smaller than expected (and are different between moons), and which correspond to migration time-scales of ∼10 Gyr. If confirmed, the measurements are broadly consistent with resonance locking as the dominant source of tidal dissipation in Jupiter and Saturn. Resonance locking also provides solutions to several problems posed by current measurements: it naturally explains the exceptionally small Q governing Rheas migration, it allows the large heating rate of Enceladus to be achieved in an equilibrium eccentricity configuration, and it resolves evolutionary problems arising from present-day migration/heating rates.

The Spin Rate of Pre-collapse Stellar Cores: Wave-driven Angular Momentum Transport in Massive Stars

The core rotation rates of massive stars have a substantial impact on the nature of core-collapse supernovae and their compact remnants. We demonstrate that internal gravity waves (IGW), excited via envelope convection during a red supergiant phase or during vigorous late time burning phases, can have a significant impact on the rotation rate of the pre-SN core. In typical (

Tidal excitations of oscillation modes in compact white dwarf binaries - I. Linear theory

10 \, M_\odot \lesssim M \lesssim 20 \, M_\odot