Retrieval of the fluid Love number $k_2$ in exoplanetary transit curves

TL;DR

This paper introduces an analytical 3D shape model to measure the fluid Love number $k_2$ from exoplanet transit curves, providing insights into planetary internal structure beyond mass and radius measurements.

Contribution

It develops a new shape model accounting for tidal and rotational deformations, enabling more accurate $k_2$ retrieval from transit data.

Findings

A precision of ≤65 ppm/√2 min is needed to reliably measure $k_2$.

The method improves upon previous ellipsoidal models.

Application to synthetic data demonstrates feasibility.

Abstract

We are witness to a great and increasing interest in internal structure, composition and evolution of exoplanets. However, direct measurements of exoplanetary mass and radius cannot be uniquely interpreted in terms of interior structure, justifying the need for an additional observable. The second degree fluid Love number, $k_2$, is proportional to the concentration of mass towards the body's center, hence providing valuable additional information about the internal structure. When hydrostatic equilibrium is assumed for the planetary interior, $k_2$ is a direct function of the planetary shape. Previous attempts were made to link the observed tidally and rotationally induced planetary oblateness in photometric light curves to $k_2$ using ellipsoidal shape models. Here, we construct an analytical 3D shape model function of the true planetary mean radius, that properly accounts for tidal and rotational deformations. Measuring the true planetary mean radius is critical when one wishes to compare the measured $k_2$ to interior theoretical expectations. We illustrate the feasibility of our method and show, by applying a Differential Evolution Markov Chain to synthetic data of WASP-121b, that a precision $\leq$ 65 ppm/$\sqrt{2\,min}$ is required to reliably retrieve $k_2$ with present understanding of stellar limb darkening, therefore improving recent results based on ellipsoidal shape models. Any improvement on stellar limb darkening would increase such performance.

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An example of a Research Note of the American Astronomical Society (RNAAS)

Ethan Vishniac

Editor-in-Chief

Johns Hopkins University

Chris Lintott

RNAAS Editor

Oxford University

Greg J. Schwarz

American Astronomical Society

2000 Florida Ave., NW, Suite 300

Washington, DC 20009-1231, USA

August Muench

American Astronomical Society

2000 Florida Ave., NW, Suite 300

Washington, DC 20009-1231, USA

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Research Notes of the American Astronomical Society (RNAAS) is a publication in the AAS portfolio (alongside ApJ, AJ, ApJ Supplements, and ApJ Letters) through which authors can promptly and briefly share materials of interest with the astronomical community in a form that will be searchable via ADS and permanently archived.

The astronomical community has long faced a challenge in disseminating information that may not meet the criteria for a traditional journal article. There have generally been few options available for sharing works in progress, comments and clarifications, null results, and timely reports of observations (such as the spectrum of a supernova), as well as results that wouldn’t traditionally merit a full paper (such as the discovery of a single exoplanet or contributions to the monitoring of variable sources).

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