Classical and relativistic node precessional effects in WASP-33b and perspectives for detecting them |
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| Authors: | Lorenzo Iorio |
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| Institution: | 1.M.I.U.R.,F.R.A.S.,Bari,Italy |
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| Abstract: | WASP-33 is a fast rotating, main sequence star which hosts a hot Jupiter moving along a retrograde and almost polar orbit
with semi-major axis a=0.02 au and eccentricity provisionally set to e=0. The quadrupole mass moment J2*J_{2}^{\star} and the proper angular momentum S
⋆ of the star are 1900 and 400 times, respectively, larger than those of the Sun. Thus, huge classical and general relativistic
non-Keplerian orbital effects should take place in such a system. In particular, the large inclination Ψ⋆ of the orbit of WASP-33b to the star’s equator allows to consider the node precession (W)\dot]\dot{\Omega} and the related time variation dt
d
/dt of the transit duration t
d
. The WASP-33b node rate due to J2*J_{2}^{\star} is 9×109 times larger than the same effect for Mercury induced by the Sun’s oblateness, while the general relativistic gravitomagnetic
node precession is 3×105 times larger than the Lense-Thirring effect for Mercury due to the Sun’s rotation. We also consider the effect of the centrifugal
oblateness of the planet itself and of a putative distant third body X. The magnitudes of the induced time change in the transit
duration are of the order of 3×10−6,2×10−7,8×10−9 for J2*J_{2}^{\star}, the planet’s rotational oblateness and general relativity, respectively. A yet undiscovered planet X with the mass of Jupiter
orbiting at more than 1 au would induce a transit duration variation of less than 4×10−9. A conservative evaluation of the accuracy in measuring dt
d
/dt over 10 yr points towards ≈10−8. The analysis presented here will be applicable also to other exoplanets with similar features if and when they will ne discovered. |
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