An estimate of the k₂ Love number of WASP-18Ab from its radial velocity measurements

Abstract

Context. Increasing our knowledge of the interior structure, composition and density distribution of exoplanets is crucial to make progress in the understanding of exoplanetary formation, migration and habitability. However, the directly measurable mass and radius values offer little constraint on interior structure, because the inverse problem is highly degenerate. Therefore there is a clear need for a third observable of exoplanet interiors. This third observable can be the k 2 fluid Love number which measures the central mass concentration of an exoplanet. Aims. The aims of this paper are (i) to develop a basic model to fit the long-term radial velocity and TTV variations caused by tidal interactions, (ii) to apply the model to the WASP-18Ab system, and (iii) to estimate the Love number of the planet. Methods. Archival radial velocity, transit and occultation timing data are collected and fitted via the model introduced here.Results. The best model fit to the archival radial velocity and timing data of WASP-18Ab was obtained with a Love number of the massive (∼ 10M Jup ) hot Jupiter WASP-18Ab: k 2,Love = 0.62 +0.55 −0.19 . This causes apsidal motion in the system, at a rate of ∼ 0.0087 ± 0.0033 • /days 31.3 ± 11.8 arcseconds/day. When checking possible causes of periastron precession, other than the relativistic term or the non-spherical shape of the components, we found a companion star to the WASP-18 system, named WASP-18B which is a probable M6.5V dwarf with ∼ 0.1 M at 3519 AU distance from the transit host star. We also find that small orbital eccentricities may be real, rather than an apparent effect caused by the non-spherical stellar shape.

The compact multiple system HIP 41431

“…While spectroscopically detected apsidal motions were previously reported for other close binaries (see e. g Ferrero et al 2013). and even for an exoplanet(Csizmadia et al 2019), too, we are not aware of any other systems where such a significant fraction of a complete apsidal revolution period was covered with RV data so densely as in the present case. 11 Note, that the combination of the dynamical and geometrical effects on the light-and ETV curves break the degeneracy between prograde and retrograde solutions, therefore an almost coplanar, but retrograde solution can be ruled out with high confidence.MNRAS 000, 1-19(2019)…”

The Orbit of WASP-12b Is Decaying

“…Based on this equation, along with the precession period from the best-fitting apsidal precession model, we found that the maximum deviation between the RV signal of a precessing orbit with parameters in Table 6 and a circular model would be ∼ 6 m s −1 over a decade. We note that Csizmadia et al (2019) claimed that apsidal precession would result in residuals on the order of K orb ; however that only holds if the anomalistic period could be determined independently. In reality, the anomalistic period would need to be determined using the same data, and the residuals would be on the order of eK orb .…”

“…As for apsidal precession, Csizmadia et al (2019) presented a formula for the associated RV signal: RV = K [e cos ω(t) + cos (ν + ω(t)) +ω n 1 − e 2 3/2 cos (ν + ω(t)) 1 + e cos ν…”

The Transit and Light Curve Modeller

“…periastron precession (cf. Csizmadia, Hellard & Smith 2019), gravitational interaction by a third body (moon, planet(s), brown dwarf, or other star in the system (e.g. Borkovits et al 2011)), magnetic interaction between the star and the planet, mass-loss from the system via stellar wind or by the evaporation of the planet, etc.).…”