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\title{RESONANT TIDES IN CLOSE ORBITING PLANETS}

\author{S.~H.\ Lubow, C.~A.\ Tout,\thanks{Konkoly Observatory of the
Hungarian Academy of Sciences, H-1525, Budapest, P.O.B.~67,
Hungary}\morethanks{On leave from the University of Cambridge}
and M.~Livio \\
\\
Space Telescope Science Institute\\
\\
3700 San Martin Drive\\
\\
Baltimore, MD 21218}

\pub{The Astrophysical Journal}

\maketitle

\abstract{The outer layers of a gas giant planet in a close orbit
are isothermal due to heating by the star, and therefore these
layers are convectively stable. A resonant tidal torque is exerted
at the outer boundary of the interior convection zone. Tidal dissipation
occurs through nonlinear damping. This process is similar to that
previously considered for high-mass binary stars. Two novel aspects
of the planet case are (1)~the torque is exerted in a region where
$H/r_p \ll 1$, for density scale height $H$ and planet radius $r_p$,
and (2)~at high spin rates, effects of Coriolis forces are critical
in permitting a resonance to occur.

Gravity waves carrying angular momentum are launched outward from the
resonant region. As these waves damp by nonlinear processes, an
over-synchronous planet is spun down towards synchronism with the orbit.
The torques are powerful enough to have spun down planet 51~Peg~B below
Jupiter's spin rate in about $10^2$~yr, and to approximate synchronism
($\omega_{spin} \sim \omega_{orbit}$) in about $10^5$~yr. These estimates
ignore effects of tidal heating, which are likely important at the spin
rate of Jupiter or higher. Fast-rotating Jupiter-mass planets with orbital
periods of up to about 40~days can be spun down to less than one tenth the
spin rate of Jupiter within $ 10^{10}$~yr. A planet's photosphere would
be spun down even more effectively than is estimated above, if its outer
layers can rotate differentially. A crude estimate suggests that eccentricity
is damped on timescales of about $10^{10}$~yr, so a more detailed analysis
is required to determine the significance of this effect.}