Astrophys.J. 614 (2004) 955-959 The currently feasible method of detection of Earth-mass planets is transit
photometry, with detection probability decreasing with a planet's distance from
the star. ...The existence or otherwise of short-period terrestrial planets will
tell us much about the planet formation process, and such planets are likely to
be detected first if they exist. Tidal forces are intense for short-period
planets, and result in decay of the orbit on a timescale which depends on
properties of the star as long as the orbit is circular. However, if an
eccentric companion planet exists, orbital eccentricity ($e_i$) is induced and
the decay timescale depends on properties of the short-period planet, reducing
by a factor of order $10^5 e_i^2$ if it is terrestrial. Here we examine the
influence companion planets have on the tidal and dynamical evolution of
short-period planets with terrestrial structure, and show that the relativistic
potential of the star is fundamental to their survival.
We review the tidal capture mechanism for binary formation, an important
process in globular cluster cores and perhaps open cluster cores. Tidal capture
binaries may be the precursors for some of the ...low-mass X-ray binaries observed
in abundance in globular clusters. They may also play an important role in
globular cluster dynamics. We summarize the chaos model for tidal interaction
(Mardling 1995, ApJ, 450, 722, 732), and discuss how this affects our
understanding of the circularization process which follows capture.
Globular clusters cores harbour many low-mass X-ray binaries, cataclysmic
variables, and millisecond pulsar binaries which are likely to have been formed
via the process of tidal capture. Tidal ...capture binaries were originally
thought to be responsible for halting core collapse and for subsequent
re-expansion via the process of ``binary heating''. The standard model, now
suggests that these binaries are no longer viable as a direct energy source. We
present the results of a study which suggests that tidal capture binaries may
indeed be a significant direct source of energy for the cores of globular
clusters. We show that following capture, these binaries go through a short,
violent chaotic phase, with the orbital eccentricity (and hence the tidal
energy) suffering large changes on a very short timescale. This is followed by
a long quiescent phase in which the tidal energy remains small while the orbit
circularizes only via normal dissipative effects. This quiescent phase allows
captured main sequence stars to evolve in the absence of large tides, a fact
important for the production of low-mass X-ray binaries and cataclysmic
variables.
A self-consistent, adiabatic model for the {\it long-time} behaviour of tidal
capture binaries is presented. It is shown that most capture orbits behave
chaotically, with the eccentricity following a ...quasi-random walk between the
values of $\appless 1$ and some lower limit associated with the periastron
separation at capture.
If dissipation is taken into account, the binary goes through a short and
violent chaotic phase, followed by a long quiescent phase in which it slowly
circularizes from a high eccentricity on a much longer timescale than
previously thought. A consequence is that merger is less likely than previously
thought, and hence such binaries will be available as a heat source to the
cores of globular clusters, particularly while they are in the less tightly
bound, highly eccentric phase.
If the model is correct, any highly eccentric binaries observed in globular
clusters which contain a main-sequence star will most likely be found to have a
period derivative much smaller than that predicted by the standard model.
We also predict that the companion of PSR B1718-19 in NGC 6342 which is a
globular cluster binary likely to have been formed by tidal capture (Wijers \&
Paczy\'{n}ski 1993) will be found to have a mass of around $0.2M_\odot$.
The model may be used to describe the evolution of low-mass X-ray binaries,
pulsar binaries, and cataclysmic binaries which abound in globular clusters.
A self-consistent model for binary evolution devised by Gingold \& Monaghan
(1980) is used to show that two distinctly different types of behaviour are
possible for close eccentric binaries. The ...model is based on a linear adiabatic
normal mode analysis of the problem, which allows detailed examination of the
transfer of energy from the orbit to the tides. We show that for most binaries,
energy is exchanged quasi-periodically, with the system regulating itself so
that the maximum tidal energy always remains small, and no circularization
takes place. In contrast, for a range of eccentricities and periastron
separations, {\it chaotic} behaviour prevails, with the eccentricity following
a random walk and with the energy transferred to the tides during a single
periastron passage being up to an order of magnitude larger than that
transferred during the initial periastron passage.
These results have important consequences for the study of tidal capture
binaries. The standard model (see, for example, McMillan, McDermott \& Taam
1987) assumes that the energy transferred to the tides during a periastron
encounter is independent of the oscillatory state of the stars, and that the
amount of tidal energy present at any time can be calculated using a formula
which (accurately) gives the amount deposited after the first encounter (Press
\& Teukolsky 1977). The calculations presented here show that a self-consistent
treatment is necessary in order to study the dynamical evolution of tidal
capture binaries. We conclude that the tidal capture process would not be
possible were it not for the existence of chaotic behaviour.
Astrophys.J. 610 (2004) 464-476 The negligible eccentricity of all extra solar planets with periods less than
six days can be accounted for by dissipation of tidal disturbances within their
envelopes ...which are induced by their host stars. In the period range of 7-21
days, planets with circular orbits coexist with planets with eccentric orbits.
These will be referred to as the borderline planets. We propose that this
discrepancy can be attributed to the variation in spin-down rates of young
stars. In particular, prior to spin-down, dissipation of a planet's tidal
disturbance within the envelope of a sufficiently rapidly spinning star can
excite eccentricity growth, and for a more slowly spinning star, at least
reduce the eccentricity damping rate. In contrast, tidal dissipation within the
envelope of a slowly spinning low-mass mature star can enhance the eccentricity
damping process. Based on these results, we suggest that short-period planets
around relatively young stars may have a much larger dispersion in eccentricity
than those around mature stars. We also suggest that because the rate of
angular momentum loss from G and K dwarfs via stellar winds is much faster than
the tidal transfer of angular momentum between themselves and their very-short
(3-4 days) period planets, they cannot establish a dynamical configuration in
which the stellar and planetary spins are approximately parallel and
synchronous with the orbital frequency. In principle, however, such
configurations may be established for planets (around G and K dwarfs) with
orbital periods of up to several weeks. In contrast to G and K dwarfs, the
angular momentum loss due to stellar winds is much weaker in F dwarfs. It is
therefore possible for synchronized short-period planets to exist around such
stars. The planet around Tau Boo is one such example.
Multiple systems play an important role in the evolution of star clusters.
First we discuss several formation mechanisms which depend on the presence of
binaries, either primordial or of dynamical ...origin. Hierarchical configurations
are often stable over long times and yet may experience evolution of the
internal orbital parameters. We describe an attempt to model the eccentricity
change induced by the outer component using an averaging method, together with
the effects due to tidal dissipation and apsidal motion acting on the inner
binary. This treatment is adopted for systems with high induced eccentricity
which gives rise to some interesting outcomes of significant period shrinkage.
We review the tidal capture mechanism for binary formation, an important process in globular cluster cores and perhaps open cluster cores. Tidal capture binaries may be the precursors for some of the ...low-mass X-ray binaries observed in abundance in globular clusters. They may also play an important role in globular cluster dynamics. We summarize the chaos model for tidal interaction (Mardling 1995, ApJ, 450, 722, 732), and discuss how this affects our understanding of the circularization process which follows capture.
The currently feasible method of detection of Earth-mass planets is transit photometry, with detection probability decreasing with a planet's distance from the star. The existence or otherwise of ...short-period terrestrial planets will tell us much about the planet formation process, and such planets are likely to be detected first if they exist. Tidal forces are intense for short-period planets, and result in decay of the orbit on a timescale which depends on properties of the star as long as the orbit is circular. However, if an eccentric companion planet exists, orbital eccentricity (\(e_i\)) is induced and the decay timescale depends on properties of the short-period planet, reducing by a factor of order \(10^5 e_i^2\) if it is terrestrial. Here we examine the influence companion planets have on the tidal and dynamical evolution of short-period planets with terrestrial structure, and show that the relativistic potential of the star is fundamental to their survival.
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