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On the degeneracy of the tidal Love number k_2 in multi-layer planetary models: application to Saturn and GJ 436b

Kramm, U. and Nettelmann, N. and Redmer, R. and Stevenson, D. J. (2011) On the degeneracy of the tidal Love number k_2 in multi-layer planetary models: application to Saturn and GJ 436b. Astronomy and Astrophysics, 528 . Art. No. A18. ISSN 0004-6361. https://resolver.caltech.edu/CaltechAUTHORS:20110414-145217228

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1051/0004-6361/201015803DOIArticle
http://www.aanda.org/index.php?option=com_article&access=doi&doi=10.1051/0004-6361/201015803&Itemid=129PublisherArticle
https://arxiv.org/abs/1101.0997arXivDiscussion Paper
ORCID:
AuthorORCID
Stevenson, D. J.0000-0001-9432-7159
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”.
Funders:
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)SPP 1385
Subject Keywords:planets and satellites: interiors – planets and satellites: individual: Saturn – planets and satellites: individual: GJ 436b – methods: numerical
Record Number:CaltechAUTHORS:20110414-145217228
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20110414-145217228
Official Citation:On the degeneracy of the tidal Love number k2 in multi-layer planetary models: application to Saturn and GJ 436b U. Kramm, N. Nettelmann, R. Redmer and D. J. Stevenson A&A 528 A18 (2011) DOI: 10.1051/0004-6361/201015803
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:23341
Collection:CaltechAUTHORS
Deposited By: Benjamin Perez
Deposited On:14 Apr 2011 23:07
Last Modified:03 Oct 2019 02:45

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