Dr. Philip Arras (University of Virginia) and collaborators will investigate the energy lost by binary stars via tides. Dissipation of gravitational tides in close binary systems acts to synchronize the rotation and circularize the orbit. Despite decades of intense observational and theoretical study, the physical mechanism for tidal dissipation in fluid objects remains a mystery. Physically motivated, accurate theories of tides are crucial to understand the origin of close binaries, their subsequent orbital evolution, and thermal evolution due to tidal heating. Theories of tidal dissipation find application in a broad range of systems, from the survival of exoplanets, to the circularization of binaries containing a Sun-like star, to the fate of compact binaries which are strong gravitational wave sources.
Previous investigations of tidal dissipation assumed the flow is laminar and much of the focus was on linear damping mechanisms, such as radiative diffusion or turbulent viscosity arising in convection zones. Such studies fail by orders of magnitude to produce the level of dissipation needed to explain the observed systems. In recent studies of tides by this research team, it was discovered that the linear tidal flow is unstable, leading to the growth of small scale waves and tidally-induced turbulence. In essence, the laminar flow often assumed does not exist for the types of situations in which it is employed. Nonlinear damping from this tidally-induced turbulence provides a promising alternative to conventional linear damping mechanisms.
The authors will develop the theory of nonlinear tides by studying, for each type of stellar or planetary structure of interest, the stability of linear tidal flow, tidally induced turbulence, synchronization and circularization rates, and depth-dependent internal heating. The primary applications of their calculations on tidal dissipation are to close-in gas giant extrasolar planets, solar-type binaries, and inspiraling binaries containing white dwarfs or neutron stars.
The planned research will have impact on a wide variety of problems in astrophysics, due to the ubiquitous importance of tides in close binaries. It will shed light on longstanding puzzles in the evolution of extrasolar planetary systems and stellar binaries, and will elucidate the impact of tidal heating on the internal structure of Hot Jupiters. The work on close white dwarf and neutron star binaries will determine if tides can alter the orbital evolution of these systems, which has important implications for both electromagnetic and gravitational wave measurements. This project involves training of a postdoc and a graduate student. The team will disseminate the results from their research to the astronomical community and to general public.
Tidal friction plays a fundamental role in the evolution of close binary systems containing stars (and/or planets). The exchange of energy and angular momentum between the orbit and the star can cause the orbit to expand or shrink, increase or decrease the rotation rate of the star, and also heat the interior of the star. Closest to home, friction in the tide raised in the Earth by the Moon is causing the Moon to move away at a few centimeters per year. Tidal friction in distant exotic binaries containing two compact stars may have more dramatic effects, leading to significant heating in these stars, and possibly powerful sources of light associated with the mergers of the stars. The key quantity required to understand the importance of tides is the rate at which energy in the tidal flow can be dissipated into heat. Our work attempted to investigate if nonlinear fluid dynamical effects could account for the large amounts of tidal friction inferred from observations of binary star systems, and if these effects could be important in other systems where the role of tides is as yet unknown. In the absence of the tidal force, the star evolves slowly through nuclear burning processes and cooling through radiation. This is the background on top of which waves ring around in the star. The tidal force from the companion pushes on the star and excites the waves. Specifically, tides can excite the surface wave (f-mode, like a surface water wave), the acoustic waves (p-modes, familiar from sounds we hear), and the gravity waves (which sometimes make patterns in clouds on Earth). These are the waves studied in the field of "astroseismology". In the linear approximation for tides, these waves ring around in the star and deposit their energy through some frictional process, like diffusion of heat, or viscosity. The contribution of our work is to study how the waves in stars interact nonlinearly. For an example here on Earth, when two water waves collide, their nonlinear interaction can create additional waves that are free to travel away from the interaction site. The same effect happens in stars, between each different type of wave. In addition, a new nonlinear effect we have pointed out is that the tidal gravitational field of the companion can directly excite (at least two) waves in the star, an affect we call the nonlinear tide. Why should these nonlinear interactions matter? Because they tend to create waves of shorter lengthscale, and these shorter lengthscale waves are much more susceptible to frictional effects, nonlinear wave interactions can turn waves with large wavelengths into waves with short lengthscales which can damp faster. This is our proposed mechanism for increasing the tidal friction, and hence rate at which orbits and spins evolve due to tides. We have developed the mathematical theory for the interaction of waves in stars, and have carried out detailed calculations for the excitation, nonlinear interaction and damping of waves in stars, and the associated orbit and spin evolution. These calculations have been applied to a number of astrophysical objects, from stars like our Sun, to slightly larger or smaller stars, to evolved stars like white dwarfs and main sequence stars. The NSF funding was primarily used to supper young researchers early in their career.
