On the degeneracy of the tidal Love number k_2 in multi-layer planetary models: application to Saturn and GJ 436b
Abstract
Context. In order to accurately model giant planets, a whole set of observational constraints is needed. As the conventional constraints for extrasolar planets like mass, radius, and temperature allow for a large number of acceptable models, a new planetary parameter is desirable in order to further constrain planetary models. Such a parameter may be the tidal Love number k_2. Aims. In this paper we aim to study the capability of k_2 to reveal further information about the interior structure of a planet. Methods. With theoretical planetary models we investigate how the tidal Love number k_2 responds to the internal density distribution of a planet. In particular, we demonstrate the effect of the degeneracy of k_2 due to a density discontinuity in the envelope of a three-layer planetary model. Results. The effect of a possible outer density discontinuity masks the effect of the core mass on the Love number k_2. Hence, there is no unique relationship between the Love number k_2 and the core mass of a planet. We show that the degeneracy of k2 with respect to a layer boundary in the envelope also occurs in existing planets, e.g. Saturn and the Hot Neptune GJ 436b. As a result of the degeneracy, the planetary parameter k_2 cannot be used to further constrain the core mass of state-of-the-art Saturn models and for GJ 436b only a maximum possible core mass can be derived from a given k_2. To significantly narrow the uncertainty about the core mass of GJ 436b the combined knowledge of k_2 and atmospheric metallicity and temperature profile is necessary.
Additional Information
© 2011 ESO. Received 22 September 2010, Accepted 23 December 2010. Published online 18 February 2011. We acknowledge helpful discussions with Ralph Neuhäuser. U.K. and R.R. acknowledge support from the DFG SPP 1385 "Young Planets".Attached Files
Published - Kramm2011p13401Astron_Astrophys.pdf
Accepted Version - 1101.0997.pdf
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Additional details
- Eprint ID
- 23341
- Resolver ID
- CaltechAUTHORS:20110414-145217228
- Deutsche Forschungsgemeinschaft (DFG)
- SPP 1385
- Created
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2011-04-14Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field
- Caltech groups
- Division of Geological and Planetary Sciences (GPS)