A Robust Measure of Tidal Circularization in Coeval Binary Populations: The solar-type spectroscopic Binary Population in The Open Cluster M35

We present a new homogeneous sample of 32 spectroscopic binary orbits in the young (~ 150 Myr) main-sequence open cluster M35. The distribution of orbital eccentricity vs. orbital period (e-log(P)) displays a distinct transition from eccentric to circular orbits at an orbital period of ~ 10 days. The transition is due to tidal circularization of the closest binaries. The population of binary orbits in M35 provide a significantly improved constraint on the rate of tidal circularization at an age of 150 Myr. We propose a new and more robust diagnostic of the degree of tidal circularization in a binary population based on a functional fit to the e-log(P) distribution. We call this new measure the tidal circularization period. The tidal circularization period of a binary population represents the orbital period at which a binary orbit with the most frequent initial orbital eccentricity circularizes (defined as e = 0.01) at the age of the population. We determine the tidal circularizationperiod for M35 as well as for 7 additional binary populations spanning ages from the pre main-sequence (~ 3 Myr) to late main-sequence (~ 10 Gyr), and use Monte Carlo error analysis to determine the uncertainties on the derived circularization periods. We conclude that current theories of tidal circularization cannot account for the distribution of tidal circularization periods with population age.Comment: 37 pages, 9 figures, to be published in The Astrophysical Journal, February 200

Tidal dissipation in rotating giant planets

[Abridged] Tides may play an important role in determining the observed distributions of mass, orbital period, and eccentricity of the extrasolar planets. In addition, tidal interactions between giant planets in the solar system and their moons are thought to be responsible for the orbital migration of the satellites, leading to their capture into resonant configurations. We treat the underlying fluid dynamical problem with the aim of determining the efficiency of tidal dissipation in gaseous giant planets. In cases of interest, the tidal forcing frequencies are comparable to the spin frequency of the planet but small compared to its dynamical frequency. We therefore study the linearized response of a slowly and possibly differentially rotating planet to low-frequency tidal forcing. Convective regions of the planet support inertial waves, while any radiative regions support generalized Hough waves. We present illustrative numerical calculations of the tidal dissipation rate and argue that inertial waves provide a natural avenue for efficient tidal dissipation in most cases of interest. The resulting value of Q depends in a highly erratic way on the forcing frequency, but we provide evidence that the relevant frequency-averaged dissipation rate may be asymptotically independent of the viscosity in the limit of small Ekman number. In short-period extrasolar planets, if the stellar irradiation of the planet leads to the formation of a radiative outer layer that supports generalized Hough modes, the tidal dissipation rate can be enhanced through the excitation and damping of these waves. These dissipative mechanisms offer a promising explanation of the historical evolution and current state of the Galilean satellites as well as the observed circularization of the orbits of short-period extrasolar planets.Comment: 74 pages, 12 figures, submitted to The Astrophysical Journa

X-ray Emission from the Weak-lined T Tauri Binary System KH 15D

The unique eclipsing, weak-lined T Tauri star KH 15D has been detected as an X-ray source in a 95.7 ks exposure from the Chandra X-ray Observatory archives. A maximum X-ray luminosity of 1.5 x 10^{29} erg s$^{-1}$ is derived in the 0.5--8 keV band, corresponding to L_{X}/L_bol = 7.5 x 10^{-5}. Comparison with samples of stars of similar effective temperature in NGC 2264 and in the Orion Nebula Cluster shows that this is about an order of magnitude low for a typical star of its mass and age. We argue that the relatively low luminosity cannot be attributed to absorption along the line of sight but implies a real deficiency in X-ray production. Possible causes for this are considered in the context of a recently proposed eccentric binary model for KH 15D. In particular, we note that the visible component rotates rather slowly for a weak-lined T Tauri star and has possibly been pseudosynchronized by tidal interaction with the primary near periastron

Gravity Survey of the Serpent Mound Area, Southern Ohio

Author Institution: Department of Geology, The Ohio State University, Columbus, Ohio 43210Over most of south-central Ohio, the sedimentary Paleozoic rocks exposed at the surface are relatively flat-lying, but in the Serpent Mound area of Highland and Adams Counties they show a circular feature, four miles in diameter, in which the rocks are complexly faulted. This structure has not yet been satisfactorily explained; two of the hypotheses proposed to explain its origin are 1) that it was caused by a "cryptovolcanic" event and 2) that it is an "astrobleme," produced by the impact of a meteoritic body. These two possible mechanisms might be distinguished by the attendant differences in the density variations produced: the cryptovolcanic structure could be associated with large lateral variations in density at the level of the basement rocks, while the meteoritic impact could produce shatter zones and brecciated layers, and small reductions in density in the rock lying closer to the surface. A closely-spaced network of gravity stations extending beyond the limits of the surface expression of the ring structure shows no gravity anomaly pattern that can be related to the surface features. Supporters of the astrobleme hypothesis are more likely to find this evidence useful than are the cryptovolcanists

Implications of a Sub-Threshold Resonance for Stellar Beryllium Depletion

Abundance measurements of the light elements lithium, beryllium, and boron are playing an increasingly important role in the study of stellar physics. Because these elements are easily destroyed in stars at temperatures 2--4 million K, the abundances in the surface convective zone are diagnostics of the star's internal workings. Standard stellar models cannot explain depletion patterns observed in low mass stars, and so are not accounting for all the relevant physical processes. These processes have important implications for stellar evolution and primordial lithium production in big bang nucleosynthesis. Because beryllium is destroyed at slightly higher temperatures than lithium, observations of both light elements can differentiate between the various proposed depletion mechanisms. Unfortunately, the reaction rate for the main destruction channel, 9Be(p,alpha)6Li, is uncertain. A level in the compound nucleus 10B is only 25.7 keV below the reaction's energetic threshold. The angular momentum and parity of this level are not well known; current estimates indicate that the resonance entrance channel is either s- or d-wave. We show that an s-wave resonance can easily increase the reaction rate by an order of magnitude at temperatures of approximately 4 million K. Observations of sub-solar mass stars can constrain the strength of the resonance, as can experimental measurements at lab energies lower than 30 keV.Comment: 9 pages, 1 ps figure, uses AASTeX macros and epsfig.sty. Reference added, typos corrected. To appear in ApJ, 10 March 199

Origin of Tidal Dissipation in Jupiter: II. the Value of Q

The process of tidal dissipation inside Jupiter is not yet understood. Its tidal quality factor ($Q$) is inferred to lie between $10^5$ and $10^6$. We examine effects of inertial-modes on tidal dissipation in a neutrally bouyant, core-less, uniformly rotating planet. The rate of dissipation caused by resonantly excited inertial-modes depends on the following three parameters: how well they are coupled to the tidal potential, how strongly they are dissipated (by the turbulent viscosity), and how densely distributed they are in frequency. We find that as a function of tidal frequency, the $Q$ value exhibits large fluctuations, with its maximum value set by the group of inertial-modes that have a typical offset from an exact resonance of order their turbulent damping rates. In our model, inertial-modes shed their tidally acquired energy very close to the surface within a narrow latitudinal zone (the 'singularity belt'), and the tidal luminosity escapes freely out of the planet. Strength of coupling between the tidal potential and inertial-modes is sensitive to the presence of density discontinuities inside Jupiter. In the case of a discreet density jump (as may be caused by the transition between metallic and molecular hydrogen), we find a time-averaged $Q \sim 10^7$. Even though it remains unclear whether tidal dissipation due to resonant inertial-modes is the correct answer to the problem, it is impressive that our simple treatment here already leads to three to five orders of magnitude stronger damping than that from the equilibrium tide. Moreover, our conclusions are not affected by the presence of a small solid core, a different prescription for the turbulent viscosity, or nonlinear mode coupling, but they depend critically on the static stability in the upper atmosphere of Jupiter.Comment: 27 pages, incl. 11 figures, ApJ in print, expanded discussions (nonlinearity, radiative envelope

Equipotential Surfaces and Lagrangian points in Non-synchronous, Eccentric Binary and Planetary Systems

We investigate the existence and properties of equipotential surfaces and Lagrangian points in non-synchronous, eccentric binary star and planetary systems under the assumption of quasi-static equilibrium. We adopt a binary potential that accounts for non-synchronous rotation and eccentric orbits, and calculate the positions of the Lagrangian points as functions of the mass ratio, the degree of asynchronism, the orbital eccentricity, and the position of the stars or planets in their relative orbit. We find that the geometry of the equipotential surfaces may facilitate non-conservative mass transfer in non-synchronous, eccentric binary star and planetary systems, especially if the component stars or planets are rotating super-synchronously at the periastron of their relative orbit. We also calculate the volume-equivalent radius of the Roche lobe as a function of the four parameters mentioned above. Contrary to common practice, we find that replacing the radius of a circular orbit in the fitting formula of Eggleton (1983) with the instantaneous distance between the components of eccentric binary or planetary systems does not always lead to a good approximation to the volume-equivalent radius of the Roche-lobe. We therefore provide generalized analytic fitting formulae for the volume-equivalent Roche lobe radius appropriate for non-synchronous, eccentric binary star and planetary systems. These formulae are accurate to better than 1% throughout the relevant 2-dimensional parameter space that covers a dynamic range of 16 and 6 orders of magnitude in the two dimensions.Comment: 12 pages, 10 figures, 2 Tables, Accepted by the Astrophysical Journa

The Binarity of Eta Carinae and its Similarity to Related Astrophysical Objects

I examine some aspects of the interaction between the massive star Eta Carinae and its companion, in particular during the eclipse-like event, known as the spectroscopic event or the shell event. The spectroscopic event is thought to occur when near periastron passages the stellar companion induces much higher mass loss rate from the primary star, and/or enters into a much denser environment around the primary star. I find that enhanced mass loss rate during periastron passages, if it occurs, might explain the high eccentricity of the system. However, there is not yet a good model to explain the presumed enhanced mass loss rate during periastron passages. In the region where the winds from the two stars collide, a dense slow flow is formed, such that large dust grains may be formed. Unlike the case during the 19th century Great Eruption, the companion does not accrete mass during most of its orbital motion. However, near periastron passages short accretion episodes may occur, which may lead to pulsed ejection of two jets by the companion. The companion may ionize a non-negligible region in its surrounding, resembling the situation in symbiotic systems. I discuss the relation of some of these processes to other astrophysical objects, by that incorporating Eta Car to a large class of astrophysical bipolar nebulae.Comment: Updated version. ApJ, in pres

On the tidal interaction of a solar-type star with an orbiting companion: Excitation of g mode oscillation and orbital evolution

We calculate the dynamical tides raised on a non-rotating solar-type star by a close stellar or planetary companion. Dissipation arising from a turbulent viscosity operating in the convection zone and radiative damping in the radiative core are considered. We compute the torque exerted on the star by a companion in circular orbit, and determine the potentially observable magnitude of the tidally induced velocity at the stellar photosphere. These calculations are compared with the results obtained by assuming that a very small frequency limit can be taken in order to calculate the tidal response (equilibrium tide). For a standard solar model, the latter is found to give a relatively poor approximation at the periods of interest of several days, even when the system is far from resonance with a normal mode. It is shown that although the companion may go through a succession of resonances as it spirals in under the action of the tides, for a fixed spectrum of normal modes its migration is controlled essentially by the non-resonant interaction. We find that the turbulent viscosity that is required to provide the observed circularization rates of main sequence solar-type binaries is about fifty times larger than that simply estimated from mixing length theory for non-rotating stars. We discuss the means by which this enhanced viscosity might be realized. These calculations are applied to 51 Pegasi. We show that the perturbed velocity induced by the tides at the stellar surface is too small to be observed.Comment: 36 pages including 6 PostScript figures, LaTex -- To be published in ApJ -- Also available at http://www.ucolick.org/~ct/home.htm