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Tidally excited oscillations in hot white dwarfs
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Abstract
We study the flux variation in helium white dwarfs (WDs) induced by dynamical tides for a variety of WD models with effective temperatures ranging from $T$=10 kK to $T$=26 kK. At linear order, we find the dynamical tide can significantly perturb the observed flux in hot WDs. If the temperature $T\gtrsim14$ kK, then the dynamical tide may induce a fractional change in the flux by >1% when the orbital period is $P_{\rm orb}\simeq 20-60\,{\rm min}$. The ratio between the flux modulation due to the dynamical tide and that due to the equilibrium tide (i.e., ellipsoidal variability) increases as the WD's radius decreases, and it could exceed O(10) if the WD has a radius $R\lesssim0.03 R_\odot$. Unlike the ellipsoidal variability which is in phase with the orbital motion, the pulsation caused by the dynamical tide may have a substantial phase shift. A cold WD with $T\lesssim 10$ kK, on the other hand, is unlikely to show observable pulsations due to the dynamical tide. At shorter orbital periods, the dynamical tide may become highly nonlinear. We approximate this regime by treating the waves as one-way traveling waves and find the flux variation is typically reduced to 0.1%-1% and the excess phase is likely to be 90 degrees (though with large uncertainty). Even in the traveling-wave limit, the flux perturbation due to dynamical tide could still exceed the ellipsoidal variability for compact WDs with $R\lesssim0.02 R_\odot$. We further estimate the nonlinear flux perturbations oscillating at four times the orbital frequency dominated by a self-coupled parent g-mode driving low-order daughter p-modes. The nonlinear flux variation could be nearly 50% of the linear variation for very hot WD models with $T\gtrsim26$ kK and 1% linear flux variation. We thus predict both the linear and nonlinear flux variations due to dynamical tides are likely to have significant observational signatures.
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We update the capabilities of the open-knowledge software instrument Modules for Experiments in Stellar Astrophysics (MESA). RSP is a new functionality in MESAstar that models the nonlinear radial stellar pulsations that characterize RR Lyrae, Cepheids, and other classes of variable stars. We significantly enhance numerical energy conservation capabilities, including during mass changes. For example, this enables calculations through the He flash that conserve energy to better than 0.001%. To improve the modeling of rotating stars in MESA, we introduce a new approach to modifying the pressure and temperature equations of stellar structure, as well as a formulation of the projection effects of gravity darkening. A new scheme for tracking convective boundaries yields reliable values of the convective core mass and allows the natural emergence of adiabatic semiconvection regions during both core hydrogen- and helium-burning phases. We quantify the parallel performance of MESA on current-generation multicore architectures and demonstrate improvements in the computational efficiency of radiative levitation. We report updates to the equation of state and nuclear reaction physics modules. We briefly discuss the current treatment of fallback in core-collapse supernova models and the thermodynamic evolution of supernova explosions. We close by discussing the new MESA Testhub software infrastructure to enhance source code development.
The Zwicky Transient Facility (ZTF), a public–private enterprise, is a new time-domain survey employing a dedicated camera on the Palomar 48-inch Schmidt telescope with a 47 deg ² field of view and an 8 second readout time. It is well positioned in the development of time-domain astronomy, offering operations at 10% of the scale and style of the Large Synoptic Survey Telescope (LSST) with a single 1-m class survey telescope. The public surveys will cover the observable northern sky every three nights in g and r filters and the visible Galactic plane every night in g and r . Alerts generated by these surveys are sent in real time to brokers. A consortium of universities that provided funding (“partnership”) are undertaking several boutique surveys. The combination of these surveys producing one million alerts per night allows for exploration of transient and variable astrophysical phenomena brighter than r ∼ 20.5 on timescales of minutes to years. We describe the primary science objectives driving ZTF, including the physics of supernovae and relativistic explosions, multi-messenger astrophysics, supernova cosmology, active galactic nuclei, and tidal disruption events, stellar variability, and solar system objects.
We describe here the most ambitious survey currently planned in the optical, the Large Synoptic Survey Telescope (LSST). The LSST design is driven by four main science themes: probing dark energy and dark matter, taking an inventory of the solar system, exploring the transient optical sky, and mapping the Milky Way. LSST will be a large, wide-field ground-based system designed to obtain repeated images covering the sky visible from Cerro Pachón in northern Chile. The telescope will have an 8.4 m (6.5 m effective) primary mirror, a 9.6 deg ² field of view, a 3.2-gigapixel camera, and six filters (ugrizy) covering the wavelength range 320-1050 nm. The project is in the construction phase and will begin regular survey operations by 2022. About 90% of the observing time will be devoted to a deep-wide-fast survey mode that will uniformly observe a 18,000 deg ² region about 800 times (summed over all six bands) during the anticipated 10 yr of operations and will yield a co-added map to r ∼27.5. These data will result in databases including about 32 trillion observations of 20 billion galaxies and a similar number of stars, and they will serve the majority of the primary science programs. The remaining 10% of the observing time will be allocated to special projects such as Very Deep and Very Fast time domain surveys, whose details are currently under discussion. We illustrate how the LSST science drivers led to these choices of system parameters, and we describe the expected data products and their characteristics. © 2019. The American Astronomical Society. All rights reserved..
The Zwicky Transient Facility (ZTF) is a new optical time-domain survey that uses the Palomar 48 inch Schmidt telescope. A custom-built wide-field camera provides a 47 deg^2 field of view and 8 s readout time, yielding more than an order of magnitude improvement in survey speed relative to its predecessor survey, the Palomar Transient Factory. We describe the design and implementation of the camera and observing system. The ZTF data system at the Infrared Processing and Analysis Center provides near-real-time reduction to identify moving and varying objects. We outline the analysis pipelines, data products, and associated archive. Finally, we present on-sky performance analysis and first scientific results from commissioning and the early survey. ZTF's public alert stream will serve as a useful precursor for that of the Large Synoptic Survey Telescope.
The Zwicky Transient Facility (ZTF) is a new robotic time-domain survey currently in progress using the Palomar 48-inch Schmidt Telescope. ZTF uses a 47 square degree field with a 600 megapixel camera to scan the entire northern visible sky at rates of ~3760 square degrees/hour to median depths of g ~ 20.8 and r ~ 20.6 mag (AB, 5sigma in 30 sec). We describe the Science Data System that is housed at IPAC, Caltech. This comprises the data-processing pipelines, alert production system, data archive, and user interfaces for accessing and analyzing the products. The realtime pipeline employs a novel image-differencing algorithm, optimized for the detection of point source transient events. These events are vetted for reliability using a machine-learned classifier and combined with contextual information to generate data-rich alert packets. The packets become available for distribution typically within 13 minutes (95th percentile) of observation. Detected events are also linked to generate candidate moving-object tracks using a novel algorithm. Objects that move fast enough to streak in the individual exposures are also extracted and vetted. The reconstructed astrometric accuracy per science image with respect to Gaia is typically 45 to 85 milliarcsec. This is the RMS per axis on the sky for sources extracted with photometric S/N >= 10. The derived photometric precision (repeatability) at bright unsaturated fluxes varies between 8 and 25 millimag. Photometric calibration accuracy with respect to Pan-STARRS1 is generally better than 2%. The products support a broad range of scientific applications: fast and young supernovae, rare flux transients, variable stars, eclipsing binaries, variability from active galactic nuclei, counterparts to gravitational wave sources, a more complete census of Type Ia supernovae, and Solar System objects.
We update the capabilities of the software instrument Modules for Experiments in Stellar Astrophysics (MESA) and enhance its ease of use and availability. Our new approach to locating convective boundaries is consistent with the physics of convection, and yields reliable values of the convective core mass during both hydrogen and helium burning phases. Stars with $M<8\,{\rm M_\odot}$ become white dwarfs and cool to the point where the electrons are degenerate and the ions are strongly coupled, a realm now available to study with MESA due to improved treatments of element diffusion, latent heat release, and blending of equations of state. Studies of the final fates of massive stars are extended in MESA by our addition of an approximate Riemann solver that captures shocks and conserves energy to high accuracy during dynamic epochs. We also introduce a 1D capability for modeling the effects of Rayleigh-Taylor instabilities that, in combination with the coupling to a public version of the STELLA radiation transfer instrument, creates new avenues for exploring Type II supernovae properties. These capabilities are exhibited with exploratory models of pair-instability supernova, pulsational pair-instability supernova, and the formation of stellar mass black holes. The applicability of MESA is now widened by the capability of importing multi-dimensional hydrodynamic models into MESA. We close by introducing software modules for handling floating point exceptions and stellar model optimization, and four new software tools -- MESAWeb, MESA-Docker, pyMESA, and mesastar.org -- to enhance MESA's education and research impact.
TianQin is a proposal for a space-borne detector of gravitational waves in
the millihertz frequencies. The experiment relies on a constellation of three
drag-free spacecraft orbiting the Earth. Inter-spacecraft laser interferometry
is used to monitor the distances between the test masses. The experiment is
designed to be capable of detecting a signal with high confidence from a single
source of gravitational waves within a few months of observing time. We
describe the preliminary mission concept for TianQin, including the candidate
source and experimental designs. We present estimates for the major
constituents of the experiment's error budget and discuss the project's overall
feasibility. Given the current level of technology readiness, we expect TianQin
to be flown in the second half of the next decade.
We substantially update the capabilities of the open-source software
instrument Modules for Experiments in Stellar Astrophysics (MESA). MESA can now
simultaneously evolve an interacting pair of differentially rotating stars
undergoing transfer and loss of mass and angular momentum, greatly enhancing
the prior ability to model binary evolution. New MESA capabilities in fully
coupled calculation of nuclear networks with hundreds of isotopes now allow
MESA to accurately simulate advanced burning stages needed to construct
supernova progenitor models. Implicit hydrodynamics with shocks can now be
treated with MESA, enabling modeling of the entire massive star lifecycle, from
pre-main sequence evolution to the onset of core collapse and nucleosynthesis
from the resulting explosion. Coupling of the GYRE non-adiabatic pulsation
instrument with MESA allows for new explorations of the instability strips for
massive stars while also accelerating the astrophysical use of asteroseismology
data. We improve treatment of mass accretion, giving more accurate and robust
near-surface profiles. A new MESA capability to calculate weak reaction rates
"on-the-fly" from input nuclear data allows better simulation of accretion
induced collapse of massive white dwarfs and the fate of some massive stars. We
discuss the ongoing challenge of chemical diffusion in the strongly coupled
plasma regime, and exhibit improvements in MESA that now allow for the
simulation of radiative levitation of heavy elements in hot stars. We close by
noting that the MESA software infrastructure provides bit-for-bit consistency
for all results across all the supported platforms, a profound enabling
capability for accelerating MESA's development.
In this paper we review the current status of research on the observational
and theoretical characteristics of isolated and binary magnetic white dwarfs
(MWDs).
Magnetic fields of isolated MWDs are observed to lie in the range 10^3-10^9G.
While the upper limit cutoff appears to be real, the lower limit is more
difficult to investigate. The incidence of magnetism below a few 10^3G still
needs to be established by sensitive spectropolarimetric surveys conducted on
8m class telescopes.
Highly magnetic WDs tend to exhibit a complex and non-dipolar field structure
with some objects showing the presence of higher order multipoles. There is no
evidence that fields of highly magnetic WDs decay over time, which is
consistent with the estimated Ohmic decay times scales of ~10^11 yrs. MWDs, as
a class, also appear to be more massive than their weakly or non-magnetic
counterparts.
MWDs are also found in binary systems where they accrete matter from a
low-mass donor star. These binaries, called magnetic Cataclysmic Variables
(MCVs) and comprise about 20-25\% of all known CVs. Zeeman and cyclotron
spectroscopy of MCVs have revealed the presence of fields in the range $\sim
7-230$\,MG. Complex field geometries have been inferred in the high field MCVs
(the polars) whilst magnetic field strength and structure in the lower field
group (intermediate polars, IPs) are much harder to establish.
The origin of fields in MWDs is still being debated. While the fossil field
hypothesis remains an attractive possibility, field generation within the
common envelope of a binary system has been gaining momentum, since it would
explain the absence of MWDs paired with non-degenerate companions and also the
lack of relatively wide pre-MCVs.
Tidal interactions play an important role in the evolution and ultimate fate
of compact white dwarf (WD) binaries. Not only do tides affect the pre-merger
state (such as temperature and rotation rate) of the WDs, but they may also
determine which systems merge and which undergo stable mass transfer. In this
paper, we attempt to quantify the effects of rotation on tidal angular momentum
transport in binary stars, with specific calculations applied to WD stellar
models. We incorporate the effect of rotation using the traditional
approximation, in which the dynamically excited gravity waves within the WDs
are transformed into gravito-inertial Hough waves. The Coriolis force has only
a minor effect on prograde gravity waves, and previous results predicting the
tidal spin-up and heating of inspiraling WDs are not significantly modified.
However, rotation strongly alters retrograde gravity waves and inertial waves,
with important consequences for the tidal spin-down of accreting WDs. We
identify new dynamical tidal forcing terms that arise from a proper separation
of the equilibrium and dynamical tide components; these new forcing terms are
very important for systems near synchronous rotation. Additionally, we discuss
the impact of Stokes drift currents on the wave angular momentum flux. Finally,
we speculate on how tidal interactions will affect super-synchronously rotating
WDs in accreting systems.
We present a new oscillation code, GYRE, which solves the stellar pulsation
equations (both adiabatic and non-adiabatic) using a novel Magnus Multiple
Shooting numerical scheme devised to overcome certain weaknesses of the usual
relaxation and shooting schemes appearing in the literature. The code is
accurate (up to 6th order in the number of grid points), robust, efficiently
makes use of multiple processor cores and/or nodes, and is freely available in
source form for use and distribution. We verify the code against analytic
solutions and results from other oscillation codes, in all cases finding good
agreement. Then, we use the code to explore how the asteroseismic observables
of a 1.5 M_sun star change as it evolves through the red-giant bump.
We develop the formalism required to study the nonlinear interaction of modes in rotating Newtonian stars in the weakly nonlinear regime. The formalism simplifies and extends previous treatments. At linear order, we elucidate and extend slightly a formalism due to Schutz, show how to decompose a general motion of a rotating star into a sum over modes, and obtain uncoupled equations of motion for the mode amplitudes under the influence of an external force. Nonlinear effects are added perturbatively via three-mode couplings. We describe a new, efficient way to compute the coupling coefficients, to zeroth order in the stellar rotation rate, using spin-weighted spherical harmonics. We apply this formalism to derive some properties of the coupling coefficients relevant to the nonlinear interactions of unstable r-modes in neutron stars, postponing numerical integrations of the coupled equations of motion to a later paper. From an astrophysical viewpoint, the most interesting result of this paper is that many couplings of r-modes to other rotational modes (modes with zero frequencies in the non-rotating limit) are small: either they vanish altogether because of various selection rules, or they vanish to lowest order in the angular velocity. In zero-buoyancy stars, the coupling of three r-modes is forbidden entirely and the coupling of two r-modes to one hybrid rotational mode vanishes to zeroth order in rotation frequency. In incompressible stars, the coupling of any three rotational modes vanishes to zeroth order in rotation frequency.
Tidal dissipation in compact white dwarf (WD) binary systems significantly
influences the physical conditions (such as surface temperature and rotation
rate) of the WDs prior to mass transfer or merger. In these systems, the
dominant tidal effects involve the excitation of gravity waves and their
dissipation in the outer envelope of the star. We calculate the amplitude of
tidally excited gravity waves in low-mass (0.3M_\odot) helium-core (He) WDs as
a function of the tidal forcing frequency \omega. Like carbon-oxygen (CO) WDs
studied in our previous paper, we find that the dimensionless tidal torque
F(\omega) (inversely proportional to the effective tidal quality factor) has an
erratic dependence on \omega. On average, F(\omega) scales approximately as
\omega^6, and is several orders of magnitude smaller for He WDs than for CO
WDs. We find that tidal torques can begin to synchronize the WD rotation when
the orbital period is less than about a hour, although a nearly constant
asynchronization is maintained even at small periods. We examine where the
tidally excited gravity waves experience non-linear breaking or resonant
absorption at a critical layer, allowing us to estimate the location and
magnitude of tidal heating in the WD envelope. We then incorporate tidal
heating in the MESA stellar evolution code, calculating the physical conditions
of the WD as a function of orbital period for different WD models. We find that
tidal heating makes a significant contribution to the WD luminosity for
short-period (~10 min) systems such as SDSS J0651+2844. We also find that for
WDs containing a hydrogen envelope, tidal heating can trigger runaway hydrogen
shell burning, leading to a nova-like event before the onset of mass transfer.
Stellar physics and evolution calculations enable a broad range of research in astrophysics. Modules for Experiments in Stellar Astrophysics (MESA) is a suite of open source, robust, efficient, thread-safe libraries for a wide range of applications in computational stellar astrophysics. A one-dimensional stellar evolution module, MESAstar, combines many of the numerical and physics modules for simulations of a wide range of stellar evolution scenarios ranging from very low mass to massive stars, including advanced evolutionary phases. MESAstar solves the fully coupled structure and composition equations simultaneously. It uses adaptive mesh refinement and sophisticated timestep controls, and supports shared memory parallelism based on OpenMP. State-of-the-art modules provide equation of state, opacity, nuclear reaction rates, element diffusion data, and atmosphere boundary conditions. Each module is constructed as a separate Fortran 95 library with its own explicitly defined public interface to facilitate independent development. Several detailed examples indicate the extensive verification and testing that is continuously performed and demonstrate the wide range of capabilities that MESA possesses. These examples include evolutionary tracks of very low mass stars, brown dwarfs, and gas giant planets to very old ages; the complete evolutionary track of a 1 M ☉ star from the pre-main sequence (PMS) to a cooling white dwarf; the solar sound speed profile; the evolution of intermediate-mass stars through the He-core burning phase and thermal pulses on the He-shell burning asymptotic giant branch phase; the interior structure of slowly pulsating B Stars and Beta Cepheids; the complete evolutionary tracks of massive stars from the PMS to the onset of core collapse; mass transfer from stars undergoing Roche lobe overflow; and the evolution of helium accretion onto a neutron star. MESA can be downloaded from the project Web site (http://mesa.sourceforge.net/).
The study of Type Ia supernovae (SNIa) has lead to greatly improved insights
into many fields in astrophysics, however a theoretical explanation of the
origin of these events is still lacking. We investigate the potential
contribution to the SNIa rate from the population of merging double
carbon-oxygen white dwarfs. We aim to develope a model that fits the observed
SNIa progenitors as well as the observed close double white dwarf population.
We differentiate between two scenarios for the common envelope (CE) evolution;
the alpha-formalism based on the energy equation and the gamma-formalism that
is based on the angular momentum equation. In one model we apply the
alpha-formalism always. In the second model the gamma-formalism is applied,
unless the binary contains a compact object or the CE is triggered by a tidal
instability for which the alpha-formalism is used. The binary population
synthesis code SeBa was used to evolve binary systems from the zero-age main
sequence to the formation of double white dwarfs and subsequent mergers. SeBa
has been thoroughly updated since the last publication of the content of the
code. The limited sample of observed double white dwarfs is better represented
by the simulated population using the gamma-formalism than the alpha-formalism.
For both CE formalisms, we find that although the morphology of the simulated
delay time distribution matches that of the observations within the errors, the
normalisation and time-integrated rate per stellar mass are a factor 7-12 lower
than observed. Furthermore, the characteristics of the simulated populations of
merging double carbon-oxygen white dwarfs are discussed and put in the context
of alternative SNIa models for merging double white dwarfs.
Compact binary white dwarfs (WDs) undergoing orbital decay due to
gravitational radiation can experience significant tidal heating prior to
merger. In these WDs, the dominant tidal effect involves the excitation of
outgoing gravity waves in the inner stellar envelope and the dissipation of
these waves in the outer envelope. As the binary orbit decays, the WDs are
synchronized from outside in (with the envelope synchronized first, followed by
the core). We examine the deposition of tidal heat in the envelope of a
Carbon-Oxygen WD and study how such tidal heating affects the structure and
evolution of the WD. We show that significant tidal heating can occur in the
star's degenerate hydrogen layer. This layer heats up faster than it cools,
triggering runaway nuclear fusion. Such "tidal novae" may occur in all WD
binaries containing a CO WD, at orbital periods between 5 min and 20 min, and
precede the final merger by 10^5-10^6 years.
We perform a stability analysis of a tidally excited nonlinear internal
gravity wave near the centre of a solar-type star in two-dimensions. The
motivation is to understand the tidal interaction between short-period planets
and their solar-type host stars, which involves the launching of gravity waves
at the top of the radiation zone that propagate towards the stellar centre.
Studying the instabilities of these waves near the centre, where nonlinearities
are most important, is essential, since it may have implications for the
survival of these planets. When the waves have sufficient amplitude to overturn
the stratification, they break and form a critical layer, which efficiently
absorbs subsequent ingoing wave angular momentum, and can result in the planet
spiralling into the star. However, previous simulations do not find the waves
to undergo instability for smaller amplitudes. This work has two aims: to
determine any instabilities that set in for small-amplitude waves, and to
further understand the breaking of large-amplitude waves. Our main result is
that the waves undergo parametric instabilities for any amplitude. However,
because the nonlinearity is spatially localised in the innermost wavelengths,
their growth rates are sufficiently small that they do not result in
astrophysically important tidal dissipation. The resulting modified tidal
quality factors are estimated to be Q'_star>10^7, and possibly much greater, so
the dissipation is much weaker than that which results from critical-layer
absorption. These results support our explanation for the survival of all
currently observed short-period planets around solar-type main-sequence stars:
that planets unable to cause wave breaking at the centre of their host stars
are likely to survive against tidal decay. This hypothesis will be tested by
ongoing and future observations of transiting planets, such as WASP and Kepler.
We study two models for AM CVn stars: white dwarfs accreting (i) from a helium white dwarf companion and (ii) from a helium-star donor. We show that in the first model possibly no accretion disk forms at the onset of the mass transfer. The stability and the rate of mass transfer then depend on the tidal coupling between the accretor and the orbital motion. In the second model the formation of AM CVn stars may be prevented by detonation of the CO white dwarf accretor and the disruption of the system. With the most favourable conditions for the formation of AM CVn stars we find a current Galactic birth rate of $6.8 10^{-3} {\rm yr^{-1}}$. Unfavourable conditions give $1.1 10^{-3} {\rm yr^{-1}}$. The expected total number of the systems in the Galaxy is $9.4 10^{7}$ and $1.6 10^{7}$, respectively. We model very simple selection effects to get some idea about the currently expected observable population and discuss the (quite good) agreement with the observed systems.
We present an improved version of the method of photometric mode identification of Heynderickx et al. (1994). Our new version is based on the inclusion of precise non-adiabatic eigenfunctions determined in the outer stellar atmosphere according to the formalism recently proposed by Dupret et al.(2002). Our improved photometric mode identification technique is therefore no longer dependent on ad hoc parameters for the non-adiabatic effects. It contains the complete physical conditions of the outer atmosphere of the star, provided that rotation does not play a key role. We apply our improved method to the two slowly pulsating B stars HD 74560 and HD 138764 and to the beta Cephei star EN (16) Lac. Besides identifying the degree l of the pulsating stars, our method is also a tool for improving the knowledge of stellar interiors and atmospheres, by imposing constraints on parameters such as the metallicity and the mixing-length parameter alpha (a procedure we label non-adiabatic asteroseismology). Comment: 10 pages, 9 figures Accepted for publication in Astronomy and Astrophysics
In binaries composed of either early-type stars or white dwarfs, the dominant tidal process involves the excitation of internal gravity waves (IGWs), which propagate towards the stellar surface, and their dissipation via non-linear wave breaking. We perform 2D hydrodynamical simulations of this wave breaking process in a stratified, isothermal atmosphere. We find that, after an initial transient phase, the dissipation of the IGWs naturally generates a sharp critical layer, separating the lower stationary region (with no mean flow) and the upper ‘synchronized’ region (with the mean flow velocity equal to the horizontal wave phase speed). While the critical layer is steepened by absorption of these waves, it is simultaneously broadened by Kelvin–Helmholtz instabilities such that, in steady state, the critical layer width is determined by the Richardson criterion. We study the absorption and reflection of incident waves off the critical layer and provide analytical formulae describing its long-term evolution. The result of this study is important for characterizing the evolution of tidally heated white dwarfs and other binary stars.
Compact white dwarf (WD) binaries are important sources for space-based gravitational-wave (GW) observatories, and an increasing number of them are being identified by surveys like Extremely Low Mass (ELM) and Zwicky Transient Facility (ZTF). We study the effects of non-linear dynamical tides in such binaries. We focus on the global three-mode parametric instability and show that it has a much lower threshold energy than the local wave-breaking condition studied previously. By integrating networks of coupled modes, we calculate the tidal dissipation rate as a function of orbital period. We construct phenomenological models that match these numerical results and use them to evaluate the spin and luminosity evolution of a WD binary. While in linear theory the WD’s spin frequency can lock to the orbital frequency, we find that such a lock cannot be maintained when non-linear effects are taken into account. Instead, as the orbit decays, the spin and orbit go in and out of synchronization. Each time they go out of synchronization, there is a brief but significant dip in the tidal heating rate. While most WDs in compact binaries should have luminosities that are similar to previous traveling-wave estimates, a few per cent should be about 10 times dimmer because they reside in heating rate dips. This offers a potential explanation for the low luminosity of the CO WD in J0651. Lastly, we consider the impact of tides on the GW signal and show that the Laser Interferometer Space Antenna (LISA) and TianGO can constrain the WD’s moment of inertia to better than $1{{\ \rm per\ cent}}$ for centi-Hz systems.
We report the discovery of a 1201 s orbital period binary, the third shortest-period detached binary known. Sloan Digital Sky Survey J232230.20 + 050942.06 contains two He-core white dwarfs orbiting with a 27° inclination. Located 0.76 kpc from the Sun, the binary has an estimated Laser Interferometer Space Antenna (LISA) 4 yr signal-to-noise ratio of 40. J2322 + 0509 is the first He + He white dwarf LISA verification binary, a source class that is predicted to account for one-third of resolved LISA ultra-compact binary detections.
We present the final sample of 98 detached double white dwarf (WD) binaries found in the Extremely Low Mass (ELM) Survey, a spectroscopic survey targeting <0.3 M ⊙ He-core WDs completed in the Sloan Digital Sky Survey footprint. Over the course of the survey we observed ancillary low-mass WD candidates like GD 278, which we show is a P = 0.19 day double WD binary, as well as candidates that turn out to be field blue straggler/subdwarf A-type stars with luminosities too high to be WDs given their Gaia parallaxes. Here, we define a clean sample of ELM WDs that is complete within our target selection and magnitude range 15 < g 0 < 20 mag. The measurements are consistent with 100% of ELM WDs being 0.0089 < P < 1.5 day double WD binaries, 35% of which belong to the Galactic halo. We infer that these are mostly He+CO WD binaries given the measurement constraints. The merger rate of the observed He+CO WD binaries exceeds the formation rate of stable mass-transfer AM CVn binaries by a factor of 25, and so the majority of He+CO WD binaries must experience unstable mass transfer and merge. The systems with the shortest periods, such as J0651+2844, are signature LISA verification binaries that can be studied with gravitational waves and light.
The Zwicky Transient Facility (ZTF) Observing System (OS) is the data collector for the ZTF project to study astrophysical phenomena in the time domain. ZTF OS is based upon the 48-inch aperture Schmidt-type design Samuel Oschin Telescope at the Palomar Observatory in Southern California. It incorporates new telescope aspheric corrector optics, dome and telescope drives, a large-format exposure shutter, a flat-field illumination system, a robotic bandpass filter exchanger, and the key element: a new 47-square-degree, 600 megapixel cryogenic CCD mosaic science camera, along with supporting equipment. The OS collects and delivers digitized survey data to the ZTF Data System (DS). Here, we describe the ZTF OS design, optical implementation, delivered image quality, detector performance, and robotic survey efficiency.
We report the discovery of a detached double white dwarf binary with an orbital period of ≈20.6 minutes, PTF J053332.05+020911.6. The visible object in this binary, PTF J0533+0209B, is a ≈0.17 M⊙ mass white dwarf with a helium-dominated atmosphere containing traces of hydrogen. This object exhibits ellipsoidal variations due to tidal deformation, and is the visible component in a single-lined spectroscopic binary with a velocity semi-amplitude of K_B = 618.7 ± 6.9 km s⁻¹. We have detected significant orbital decay due to the emission of gravitational radiation, and we expect that the Laser Interferometer Space Antenna (LISA) will detect this system with a signal to noise of 8.4^(+4.2)_(-3.0) after four years of operation. Because this system already has a well-determined orbital period, radial velocity semi-amplitude, temperature, atmospheric composition, surface gravity, and orbital decay rate, a LISA signal will help fully constrain the properties of this system by providing a direct measurement of its inclination. Thus, this binary demonstrates the synergy between electromagnetic and gravitational radiation for constraining the physical properties of an astrophysical object.
Tidal interactions can play an important role as compact white dwarf (WD) binaries are driven together by gravitational waves (GWs). This will modify the strain evolution measured by future space-based GW detectors and impact the potential outcome of the mergers. Surveys now and in the near future will generate an unprecedented population of detached WD binaries to constrain tidal interactions. Motivated by this, I summarize the deviations between a binary evolving under the influence of only GW emission and a binary that is also experiencing some degree of tidal locking. I present analytic relations for the first and second derivative of the orbital period and braking index. Measurements of these quantities will allow the inference of tidal interactions, even when the masses of the component WDs are not well constrained. Finally, I discuss tidal heating and how it can provide complimentary information.
We present a numerical parameter survey of sub-Chandrasekhar mass white dwarf (WD) explosions. Carbon-oxygen WDs accreting a helium shell have the potential to explode in the sub-Chandrasekhar mass regime. Previous studies have shown how the ignition of a helium shell can either directly ignite the WD at the core-shell interface or propagate a shock wave into the the core causing a central ignition. We examine the explosions of WDs from 0.6 to 1.2 M o with helium shells of 0.01, 0.05, and 0.08 M o . Distinct observational signatures of sub-Chandrasekhar mass WD explosions are predicted for two categories of shell size. Thicker-shell models show an early time flux excess, which is caused by the presence of radioactive material in the ashes of the helium shell, and red colors due to these ashes creating significant line blanketing in the UV through the blue portion of the spectrum. Thin shell models reproduce several typical Type Ia supernova signatures. We identify a relationship between Si ii velocity and luminosity that, for the first time, identifies a subclass of observed supernovae that are consistent with these models. This subclass is further delineated by the absence of carbon in their atmospheres. We suggest that the proposed difference in the ratio of selective to total extinction between the high velocity and normal velocity Type Ia supernovae is not due to differences in the properties of the dust around these events, but is rather an artifact of applying a single extinction correction to two intrinsically different populations of supernovae. © 2019. The American Astronomical Society. All rights reserved.
Motivated by recent interest in the phenomenon of waves transport in massive stars, we examine whether the heat-driven gravity (g) modes excited in slowly-pulsating B (SPB) stars can significantly modify the stars' internal rotation. We develop a formalism for the differential torque exerted by g modes, and implement this formalism using the GYRE oscillation code and the MESASTAR stellar evolution code. Focusing first on a $4.21$ $M_\odot$ model, we simulate 1,000 years of stellar evolution under the combined effects of the torque due to a single unstable prograde g mode (with an amplitude chosen on the basis of observational constraints), and diffusive angular momentum transport due to convection, overshooting, and rotational instabilities. We find that the g mode rapidly extracts angular momentum from the surface layers, depositing it deeper in the stellar interior. The angular momentum transport is so efficient that by the end of the simulation the initially non-rotating surface layers are spun in the retrograde direction to $\approx30\%$ of the critical rate. However, the additional inclusion of magnetic stresses in our simulations, almost completely inhibits this spin-up. Expanding our simulations to cover the whole instability strip, we show that the same general behavior is seen in all SPB stars. After providing some caveats to contextualize our results, we hypothesize that the observed slower surface rotation of SPB stars (as compared to other B-type stars) may be the direct consequence of the angular momentum transport that our simulations demonstrate.
Heartbeat stars are eccentric binary stars in short period orbits whose light curves are shaped by tidal distortion, reflection, and Doppler beaming. Some heartbeat stars exhibit tidally excited oscillations and present new opportunities for understanding the physics of tidal dissipation within stars. We present detailed methods to compute the forced amplitudes, frequencies, and phases of tidally excited oscillations in eccentric binary systems. Our methods i) factor out the equilibrium tide for easier comparison with observations, ii) account for rotation using the traditional approximation, iii) incorporate non-adiabatic effects to reliably compute surface luminosity perturbations, iv) allow for spin-orbit misalignment, and v) correctly sum over contributions from many oscillation modes. We also derive some basic probability theory that can be used to compare models with data in a statistical manner. Application of this theory to heartbeat systems can be used to determine whether observed tidally excited oscillations can be explained by chance resonances with stellar oscillation modes, or whether a resonance locking process is operating.
The detonation of a sub-Chandrasekhar-mass white dwarf (WD) has emerged as one of the most promising Type Ia supernova (SN Ia) progenitor scenarios. Recent studies have suggested that the rapid transfer of a very small amount of helium from one WD to another is sufficient to ignite a helium shell detonation that subsequently triggers a carbon core detonation, yielding a "dynamically-driven double degenerate double detonation" SN Ia. Because the helium shell that surrounds the core explosion is so minimal, this scenario approaches the limiting case of a bare C/O WD detonation. Motivated by discrepancies in previous literature and by a recent need for detailed nucleosynthetic data, we revisit simulations of naked C/O WD detonations in this paper. We disagree to some extent with the nucleosynthetic results of the most cited previous work on sub-Chandrasekhar-mass bare C/O WD detonations; e.g., we find that a median-brightness SN Ia is produced by the detonation of a 1.0 Msol WD instead of a more massive and rarer 1.1 Msol WD. The neutron-rich nucleosynthesis in our simulations agrees broadly with some observational constraints, although tensions remain with others. There are also some discrepancies related to the velocities of the outer ejecta, but overall our synthetic light curves and spectra are roughly consistent with observations. We are hopeful that future multi-dimensional simulations will resolve these issues and further bolster the dynamically-driven double degenerate double detonation scenario's potential to explain most SNe Ia.
The characteristic peaked shape of the light curves of the large-amplitude ZZ Ceti stars is reproduced by non-adiabatic calculations
where the horizontal motions and the pressure changes are assumed to be sinusoidal but where the temperature changes in the
ionization zone are treated non-linearly. The non-sinusoidal shape is associated with the change between convective and radiative
energy transport in the deeper layers of the hydrogen ionization zone. Quantitative agreement with the observations is obtained
if the modes which cause the large-amplitude brightness changes are assumed to be of spherical degree $\ell = 1$.
We examine the dynamics of resonance locking in detached, tidally interacting
binary systems. In a resonance lock, a given stellar or planetary mode is
trapped in a highly resonant state for an extended period of time, during which
the spin and orbital frequencies vary in concert to maintain the resonance.
This phenomenon is qualitatively similar to resonance capture in planetary
dynamics. We show that resonance locks can accelerate the course of tidal
evolution in eccentric systems and also efficiently couple spin and orbital
evolution in circular binaries. Previous analyses of resonance locking have not
treated the mode amplitude as a fully dynamical variable, but rather assumed
the adiabatic (i.e. Lorentzian) approximation valid only in the limit of
relatively strong mode damping. We relax this approximation, analytically
derive conditions under which the fixed point associated with resonance locking
is stable, and further check these analytic results using numerical
integrations of the coupled mode, spin, and orbital evolution equations. These
show that resonance locking can sometimes take the form of complex limit cycles
or even chaotic trajectories. We provide simple analytic formulae that define
the binary and mode parameter regimes in which resonance locks of some kind
occur (stable, limit cycle, or chaotic). We briefly discuss the astrophysical
implications of our results for white dwarf and neutron star binaries as well
as eccentric stellar binaries.
We theoretically discuss adiabatic dipolar oscillations of stars, fully taking into account the variation in the gravitational
field. By suitably choosing the dependent variables, and using the first integral specific to dipolar oscillations, we derive
the second-order system of ordinary differential equations, which is the same in form as that obtained by neglecting the Eulerian
perturbation to the gravitational potential. The derived system suggests that the conventional expressions of the critical
frequencies should be corrected. In addition, we present a rigorous scheme to classify the dipolar eigenmodes of linear adiabatic
oscillations of spherically symmetric stars.
A weakly nonlinear fluid wave propagating within a star can be unstable to three-wave interactions. The resonant parametric instability is a well-known form of three-wave interaction in which a primary wave of frequency ωa
excites a pair of secondary waves of frequency ωb
+ ωc
ωa
. Here we consider a nonresonant form of three-wave interaction in which a low-frequency primary wave excites a high-frequency p-mode and a low-frequency g-mode such that ωb
+ ωc
ωa
. We show that a p-mode can couple so strongly to a g-mode of similar radial wavelength that this type of nonresonant interaction is unstable even if the primary wave amplitude is small. As an application, we analyze the stability of the tide in coalescing neutron star binaries to p-g mode coupling. We find that the equilibrium tide and dynamical tide are both p-g unstable at gravitational wave frequencies f
gw 20 Hz and drive short wavelength p-g mode pairs to significant energies on very short timescales (much less than the orbital decay time due to gravitational radiation). Resonant parametric coupling to the tide is, by contrast, either stable or drives modes at a much smaller rate. We do not solve for the saturation of the p-g instability and therefore we cannot say precisely how it influences the evolution of neutron star binaries. However, we show that if even a single daughter mode saturates near its wave breaking amplitude, the p-g instability of the equilibrium tide will (1) induce significant orbital phase errors (Δ 1 radian) that accumulate primarily at low frequencies (f
gw 50 Hz) and (2) heat the neutron star core to a temperature of T ~ 1010 K. Since there are at least ~100 unstable p-g daughter pairs, Δ and T are potentially much larger than these values. Tides might therefore significantly influence the gravitational wave signal and electromagnetic emission from coalescing neutron star binaries at much larger orbital separations than previously thought.
Tidal mass transfer in double degenerate systems is explored. The
sequence of double white dwarfs divides naturally into three segments:
(1) low-mass helium/helium pairs are unstable to dynamical time-scale
mass transfer and probably coalesce to form helium-burning sdO stars;
(2) in helium/carbon-oxygen pairs, mass transfer occurs on the time
scale for gravitational radiation losses; the accreted helium is quickly
ignited, and the accretor expands to dimensions characteristic of R CrB
stars, engulfing its companion star; and (3) carbon-oxygen/carbon-oxygen
pairs are again unstable to dynamical time-scale mass transfer and,
since their total masses exceed the Chandrasekhar limit, are destined to
become supernovae. Inactive lifetimes in these latter systems between
creation and interaction can exceed 10 billion years. Birthrates of R
CrB stars and Type I supernovae by evolution of double white dwarfs are
in reasonable agreement with observational estimates.
Formation frequencies of binary systems which may become Type I
supernovae are estimated. Presupernova systems consist of a CO or He
degenerate dwarf and a (potential) mass donor (main-sequence star = MS;
low-mass red giant = RG; asymptotic giant branch star = AGB; CO or He
degenerate dwarf = CODD or HeDD). Mass transfer is driven by nuclear
evolution (E), capture from wind (W), a magnetic stellar wind (MSW), or
gravitational wave radiation (GWR). For several scenarios, the
composition of accretor, nature of donor, driving mechanism, and
formation frequency (in 10-3 yr-1 per
1010 L_sun; in the B band), respectively, are the following:
(1) CO, RG, E, 10-2- 10-3; (2) CO, AGB, W, 4; (3)
CO, MS, MSW, 2; (4) He, MS, MSW, 2; (5) CO or He, near-MS, E+MSW, 3; (6)
CO, CODD, GWR, 8; (7) CO, HeDD, GWR, 1; (8) He, HeDD, GWR, 5. The
galactic Type I supernova frequency is 10.
We produce the first results of an investigation aimed at understanding
the characteristics of both the light curves and the instantaneous
spectra obtained through time-resolved observations of ZZ Ceti stars.
Our ultimate aim is to constrain mode identification in these pulsating
stars. We first provide a theoretical framework for the computation of
the emergent flux from these objects. In order to make the detailed
numerical results amenable to physical interpretation, we next develop
first-and second-order analytic expressions for the expected amplitudes
of pulsation in terms of temperature perturbations. Our calculations
reproduce the harmonics and cross-frequency terms observed in many light
curves of ZZ Ceti stars. These nonlinear effects are readily explainable
in terms of the nonlinear response of the emergent flux to changes of
the local temperature at the stellar surface. We provide analytic
results which should be useful in the analysis of fast photometric
observations obtained either in white light, in the UBV system, or in
the uvby system.
We substantially update the capabilities of the open source software package Modules for Experiments in Stellar Astrophysics (MESA), and its one-dimensional stellar evolution module, MESA
star. Improvements in MESA
star's ability to model the evolution of giant planets now extends its applicability down to masses as low as one-tenth that of Jupiter. The dramatic improvement in asteroseismology enabled by the space-based Kepler and CoRoT missions motivates our full coupling of the ADIPLS adiabatic pulsation code with MESA
star. This also motivates a numerical recasting of the Ledoux criterion that is more easily implemented when many nuclei are present at non-negligible abundances. This impacts the way in which MESA
star calculates semi-convective and thermohaline mixing. We exhibit the evolution of 3-8 M
☉ stars through the end of core He burning, the onset of He thermal pulses, and arrival on the white dwarf cooling sequence. We implement diffusion of angular momentum and chemical abundances that enable calculations of rotating-star models, which we compare thoroughly with earlier work. We introduce a new treatment of radiation-dominated envelopes that allows the uninterrupted evolution of massive stars to core collapse. This enables the generation of new sets of supernovae, long gamma-ray burst, and pair-instability progenitor models. We substantially modify the way in which MESA
star solves the fully coupled stellar structure and composition equations, and we show how this has improved the scaling of MESA's calculational speed on multi-core processors. Updates to the modules for equation of state, opacity, nuclear reaction rates, and atmospheric boundary conditions are also provided. We describe the MESA Software Development Kit that packages all the required components needed to form a unified, maintained, and well-validated build environment for MESA. We also highlight a few tools developed by the community for rapid visualization of MESA
star results.
We calculate the tidal response of helium and carbon/oxygen (C/O) white dwarf
(WD) binaries inspiraling due to gravitational wave emission. We show that
resonance locks, previously considered in binaries with an early-type star,
occur universally in WD binaries. In a resonance lock, the orbital and spin
frequencies evolve in lockstep, so that the tidal forcing frequency is
approximately constant and a particular normal mode remains resonant, producing
efficient tidal dissipation and nearly synchronous rotation. We show that
analogous locks between the spin and orbital frequencies can occur not only
with global standing modes, but even when damping is so efficient that the
resonant tidal response becomes a traveling wave. We derive simple analytic
formulas for the tidal quality factor Q and tidal heating rate during a g-mode
resonance lock, and verify our results numerically. We find that Q ~ 10^7 for
orbital periods ~ 1 - 2 hr in C/O WDs, and Q ~ 10^9 for P_orb ~ 3 - 10 hr in
helium WDs. Typically tidal heating occurs sufficiently close to the surface
that the energy should be observable as surface emission. Moreover, near an
orbital period of ~ 10 min, the tidal heating rate reaches ~ 10^{-2} L_\sun,
rivaling the luminosities of our fiducial WD models. Recent observations of the
13-minute double-WD binary J0651 are roughly consistent with our theoretical
predictions. Tides naturally tend to generate differential rotation; however,
we show that the fossil magnetic field strength of a typical WD can maintain
solid-body rotation down to at least P_orb ~ 10 min even in the presence of a
tidal torque concentrated near the WD surface.
We study the tidal excitation of gravity modes (g-modes) in compact white dwarf binary systems with periods ranging from minutes to hours. As the orbit of the system decays via gravitational radiation, the orbital frequency increases and sweeps through a series of resonances with the g-modes of the white dwarf. At each resonance, the tidal force excites the g-mode to a relatively large amplitude, transferring the orbital energy to the stellar oscillation. We calculate the eigenfrequencies of g-modes and their coupling coefficients with the tidal field for realistic non-rotating white dwarf models. Using these mode properties, we numerically compute the excited mode amplitude in the linear approximation as the orbit passes though the resonance, including the back reaction of the mode on the orbit. We also derive analytical estimates for the mode amplitude and the duration of the resonance, which accurately reproduce our numerical results for most binary parameters. We find that the g-modes can be excited to a dimensionless (mass-weighted) amplitude up to 0.1, with the mode energy approaching 10−3 of the gravitational binding energy of the star. Therefore the low-frequency (≲10−2 Hz) gravitational waveforms produced by the binaries, detectable by LISA, are strongly affected by the tidal resonances. Our results also suggest that thousands of years prior to the binary merger, the white dwarf may be heated up significantly by tidal interactions. However, more study is needed since the physical amplitudes of the excited oscillation modes become highly non-linear in the outer layer of the star, which can reduce the mode amplitude attained by tidal excitation.
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.
We develop a general framework for interpreting and analyzing high-precision
lightcurves from eccentric stellar binaries. Although our methods are general,
we focus on the recently discovered Kepler system KOI-54, a face-on binary of
two A stars with $e=0.83$ and an orbital period of 42 days. KOI-54 exhibits
strong ellipsoidal variability during its periastron passage; its lightcurve
also contains ~20 pulsations at perfect harmonics of the orbital frequency, and
another ~10 nonharmonic pulsations. Analysis of such data is a new form of
asteroseismology in which oscillation amplitudes and phases rather than
frequencies contain information that can be mined to constrain stellar
properties. We qualitatively explain the physics of mode excitation and the
range of harmonics expected to be observed. To quantitatively model observed
pulsation spectra, we develop and apply a linear, tidally forced, nonadiabatic
stellar oscillation formalism including the Coriolis force. We produce temporal
power spectra for KOI-54 that are semi-quantitatively consistent with the
observations. Both stars in the KOI-54 system are expected to be rotating
pseudosynchronously, with resonant nonaxisymmetric modes providing a key
contribution to the total torque; such resonances provide a possible
explanation for the two largest-amplitude harmonic pulsations observed in
KOI-54, although we find quantitative problems with this interpretation. We
show in detail that the nonharmonic pulsations observed in KOI-54 can be
produced by nonlinear three-mode coupling. The methods developed in this paper
can be generalized in the future to determine the best-fit stellar parameters
given pulsation data. We also derive an analytic model of KOI-54's ellipsoidal
variability, including both tidal distortion and stellar irradiation, which can
be used to model other similar systems.
We study the excitation and damping of tides in close binary systems, accounting for the leading-order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct physical effects: three-mode nonlinear interactions, i.e., the redistribution of energy among stellar modes of oscillation, and nonlinear excitation of stellar normal modes by the time-varying gravitational potential of the companion. This paper, the first in a series, presents the formalism for studying nonlinear tides and studies the nonlinear stability of the linear tidal flow. Although the formalism we present is applicable to binaries containing stars, planets, and/or compact objects, we focus on non-rotating solar-type stars with stellar or planetary companions. Our primary results include the following: (1) The linear tidal solution almost universally used in studies of binary evolution is unstable over much of the parameter space in which it is employed. More specifically, resonantly excited internal gravity waves in solar-type stars are nonlinearly unstable to parametric resonance for companion masses M' 10-100 M
⊕ at orbital periods P ≈ 1-10 days. The nearly static "equilibrium" tidal distortion is, however, stable to parametric resonance except for solar binaries with P 2-5 days. (2) For companion masses larger than a few Jupiter masses, the dynamical tide causes short length scale waves to grow so rapidly that they must be treated as traveling waves, rather than standing waves. (3) We show that the global three-wave treatment of parametric instability typically used in the astrophysics literature does not yield the fastest-growing daughter modes or instability threshold in many cases. We find a form of parametric instability in which a single parent wave excites a very large number of daughter waves (N ≈ 103[P/10 days] for a solar-type star) and drives them as a single coherent unit with growth rates that are a factor of ≈N faster than the standard three-wave parametric instability. These are local instabilities viewed through the lens of global analysis; the coherent global growth rate follows local rates in the regions where the shear is strongest. In solar-type stars, the dynamical tide is unstable to this collective version of the parametric instability for even sub-Jupiter companion masses with P a month. (4) Independent of the parametric instability, the dynamical and equilibrium tides excite a wide range of stellar p-modes and g-modes by nonlinear inhomogeneous forcing; this coupling appears particularly efficient at draining energy out of the dynamical tide and may be more important than either wave breaking or parametric resonance at determining the nonlinear dissipation of the dynamical tide.
Hundreds of substellar companions to solar-type stars will be discovered with
the Kepler satellite. Kepler's extreme photometric precision gives access to
low-amplitude stellar variability contributed by a variety of physical
processes. We discuss in detail the periodic flux modulations arising from the
tidal force on the star due to a substellar companion. An analytic expression
for the variability is derived in the equilibrium-tide approximation. We
demonstrate analytically and through numerical solutions of the linear,
nonadiabatic stellar oscillation equations that the equilibrium-tide formula
works extremely well for stars of mass <1.4 Msun with thick surface convection
zones. More massive stars with largely radiative envelopes do not conform to
the equilibrium-tide approximation and can exhibit flux variations $\ga$10
times larger than naive estimates. Over the full range of stellar masses
considered, we treat the oscillatory response of the convection zone by
adapting a prescription that A. J. Brickhill developed for pulsating white
dwarfs. Compared to other sources of periodic variability, the ellipsoidal
lightcurve has a distinct dependence on time and system parameters. We suggest
that ellipsoidal oscillations induced by giant planets may be detectable from
as many as ~100 of the 10^5 Kepler target stars. (Abridged)
We calculate the excitation and dissipation of low-frequency tidal
oscillations in uniformly rotating solar-type stars. For tidal frequencies
smaller than twice the spin frequency, inertial waves are excited in the
convective envelope and are dissipated by turbulent viscosity. Enhanced
dissipation occurs over the entire frequency range rather than in a series of
very narrow resonant peaks, and is relatively insensitive to the effective
viscosity. Hough waves are excited at the base of the convective zone and
propagate into the radiative interior. We calculate the associated dissipation
rate under the assumption that they do not reflect coherently from the center
of the star. Tidal dissipation in a model based on the present Sun is
significantly enhanced through the inclusion of the Coriolis force but may
still fall short of that required to explain the circularization of close
binary stars. However, the dependence of the results on the spin frequency,
tidal frequency, and stellar model indicate that a more detailed evolutionary
study including inertial and Hough waves is required. We also discuss the case
of higher tidal frequencies appropriate to stars with very close planetary
companions. The survival of even the closest hot Jupiters can be plausibly
explained provided that the Hough waves they generate are not damped at the
center of the star. We argue that this is the case because the tide excited by
a hot Jupiter in the present Sun would marginally fail to achieve nonlinearity.
As conditions at the center of the star evolve, nonlinearity may set in at a
critical age, resulting in a relatively rapid inspiral of the hot Jupiter.
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Amaro-Seoane P., et al., 2017, arXiv e-prints, p. arXiv:1702.00786
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Burdge K. B., et al., 2020, arXiv e-prints, p. arXiv:2009.02567
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Kuns K. A., Yu H., Chen Y., Adhikari R. X., 2019, arXiv e-prints, p.
arXiv:1908.06004