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Register a new userDynamical tides excited in rotating stars of different masses and ages and the formation of close in orbits
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We study the tidal response of rotating solar mass stars, as well as more massive rotating stars, of different ages in the context of tidal captures leading to either giant exoplanets on close in orbits, or the formation of binary systems in star clusters. To do this, we adopt approaches based on normal mode and associated overlap integral evaluation, developed in a companion paper by Ivanov et al., and direct numerical simulation, to evaluate energy and angular momentum exchanges between the orbit and normal modes. The two approaches are found to be in essential agreement apart from when encounters occur near to pseudosynchronization, where the stellar angular velocity and the orbital angular velocity at periastron are approximately matched. We find that the strength of tidal interaction being expressed in dimensionless natural units is significantly weaker for the more massive stars, as compared to the solar mass stars, because of the lack of significant convective regions in the former case. On the other hand the interaction is found to be stronger for retrograde as opposed to prograde orbits in all cases. In addition, for a given pericentre distance, tidal interactions also strengthen for more evolved stars on account of their radial expansion. In agreement with previous work based on simplified polytropic models, we find that energy transferred to their central stars could play a significant role in the early stages of the circularisation of potential Hot Jupiters.
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Zahns theory of dynamical tides is analyzed critically. We compare the results of this theory with our numerical calculations for stars with a convective core and a radiative envelope and with masses of one and a half and two solar masses. We show that for a binary system consisting of stars of one and a half or two solar masses and a point object with a mass equal to the solar mass and with an orbital period of one day under the assumption of a dense spectrum and moderately rapid dissipation, the evolution time scales of the semimajor axis will be shorter than those in Zahns theory by several orders of magnitude
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 effects: three-mode nonlinear interactions and nonlinear excitation of modes by the time-varying gravitational potential of the companion. This paper presents the formalism for studying nonlinear tides and studies the nonlinear stability of the linear tidal flow. Although the formalism is applicable to binaries containing stars, planets, or compact objects, we focus on solar type stars with stellar or planetary companions. Our primary results include: (1) The linear tidal solution often used in studies of binary evolution is unstable over much of the parameter space in which it is employed. More specifically, resonantly excited gravity waves are unstable to parametric resonance for companion masses M > 10-100 M_Earth at orbital periods P = 1-10 days. The nearly static equilibrium tide is, however, parametrically stable except for solar binaries with P < 2-5 days. (2) For companion masses larger than a few Jupiter masses, the dynamical tide causes waves to grow so rapidly that they must be treated as traveling waves rather than standing waves. (3) We find a novel form of parametric instability in which a single parent wave excites a very large number of daughter waves (N = 10^3[P / 10 days]) and drives them as a single coherent unit with growth rates that are ~N times faster than the standard three wave parametric instability. (4) Independent of the parametric instability, 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.
(abbreviated) We extend the theory of close encounters of a planet on a parabolic orbit with a star to include the effects of tides induced on the central rotating star. Orbits with arbitrary inclination to the stellar rotation axis are considered. We obtain results both from an analytic treatment and numerical one that are in satisfactory agreement. These results are applied to the initial phase of the tidal circularisation problem. We find that both tides induced in the star and planet can lead to a significant decrease of the orbital semi-major axis for orbits having periastron distances smaller than 5-6 stellar radii (corresponding to periods $sim 4-5$ days after the circularisation has been completed) with tides in the star being much stronger for retrograde orbits compared to prograde orbits. We use the simple Skumanich law for the stellar rotation with its rotational period equal to one month at the age of 5Gyr. The strength of tidal interactions is characterised by circularisation time scale, $t_{ev}$ defined as a time scale of evolution of the planets semi-major axis due to tides considered as a function of orbital period $P_{obs}$ after the process of tidal circularisation has been completed. We find that the ratio of the initial circularisation time scales corresponding to prograde and retrograde orbits is of order 1.5-2 for a planet of one Jupiter mass and $P_{obs}sim $ four days. It grows with the mass of the planet, being of order five for a five Jupiter mass planet with the same $P_{orb}$. Thus, the effect of stellar rotation may provide a bias in the formation of planetary systems having planets on close orbits around their host stars, as a consequence of planet-planet scattering, favouring systems with retrograde orbits. The results may also be applied to the problem of tidal capture of stars in young stellar clusters.
The accuracy of masses of pre-main sequence (PMS) stars derived from their locations on the Hertzsprung-Russell Diagram (HRD) can be tested by comparison with accurate and precise masses determined independently. We present 29 single stars in the Taurus star-forming region (SFR) and 3 in the Ophiuchus SFR with masses measured dynamically to a precision of at least $10 %$. Our results include 9 updated mass determinations and 3 that have not had their dynamical masses published before. This list of stars with fundamental, dynamical masses, M$_{dyn}$, is drawn from a larger list of 39 targets in the Taurus SFR and 6 in the Ophiuchus SFR. Placing the stars with accurate and precise dynamical masses on HRDs that do not include internal magnetic fields underestimates the mass compared to M$_{dyn}$ by about $30 %$. Placing them on an HRD that does include magnetic fields yields mass estimates in much better agreement with M$_{dyn}$, with an average difference between M$_{dyn}$ and the estimated track mass of $0.01pm0.02$~msun. The ages of the stars, 3--10 MY on tracks that include magnetic fields, is older than the 1--3 MY indicated by the non-magnetic models. The older ages of T Tauri stars predicted by the magnetic models increase the time available for evolution of their disks and formation of the giant gas exoplanets. The agreement between our M$_{dyn}$ values and the masses on the magnetic field tracks provides indirect support for these older ages.
We report new dynamical masses for 5 pre-main sequence (PMS) stars in the L1495 region of the Taurus star-forming region (SFR) and 6 in the L1688 region of the Ophiuchus SFR. Since these regions have VLBA parallaxes these are absolute measurements of the stars masses and are independent of their effective temperatures and luminosities. Seven of the stars have masses $<0.6$ solar masses, thus providing data in a mass range with little data, and of these, 6 are measured to precision $< 5 %$. We find 8 stars with masses in the range 0.09 to 1.1 solar mass that agree well with the current generation of PMS evolutionary models. The ages of the stars we measured in the Taurus SFR are in the range 1-3 MY, and $<1$ MY for those in L1688. We also measured the dynamical masses of 14 stars in the ALMA archival data for Akeson~&~Jensens Cycle 0 project on binaries in the Taurus SFR. We find that the masses of 7 of the targets are so large that they cannot be reconciled with reported values of their luminosity and effective temperature. We suggest that these targets are themselves binaries or triples.
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