Grain opacity and the bulk composition of extrasolar planets

I. Results from scaling the ISM opacity^⋆

¹ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
e-mail: mordasini@mpia.de
² Center for space and habitability, Physikalisches Institut, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland
³ Institut UTINAM, CNRS-UMR 6213, Observatoire de Besançon, BP 1615, 25010 Besançon Cedex, France
⁴ Department of Astronomy and Astrophysics, University of California, Santa Cruz, USA

Received: 12 March 2013
Accepted: 10 March 2014

Abstract

Context. The opacity due to grains in the envelope of a protoplanet κ_gr regulates the accretion rate of gas during formation, meaning that the final bulk composition of planets with a primordial H/He envelope is a function of that opacity. Observationally, for extrasolar planets with known mass and radius it is possible to estimate the bulk composition via internal structure models.

Aims. We want to study the global effects of κ_gr as a poorly known, but important quantity on synthetic planetary populations.

Methods. We first determine the reduction factor of the interstellar medium (ISM) grain opacity f_opa that leads to a gas accretion timescale consistent with grain evolution models for specific cases. In the second part we compare the mass–radius relationship of low-mass planets and the heavy element content of giant planets for different values of the reduction factor with observational constraints.

Results. For f_opa = 1 (full ISM opacity) the synthetic super-Earth and Neptunian planets have radii that are too small (i.e., envelope masses that are too low) compared to observations because at such high opacity, they cannot efficiently accrete H/He during the formation phase. At f_opa = 0.003, the value calibrated with the grain evolution models, the synthetic and actual planets occupy a similar mass–radius domain. Another observable consequence is the metal enrichment of giant planets relative to the host star, Z_pl/Z_star. We find that the mean enrichment of giant planets as a function of mass M can be approximated as Z_pl/Z_star = β(M/M_♃)^α both for synthetic and actual planets. The decrease in Z_pl/Z_star with mass follows α ≈ −0.7 independent of f_opa in synthetic populations, in agreement with the value derived from observations (−0.71 ± 0.10). The absolute enrichment level β decreases from 8.5 at f_opa = 1 to 3.5 at f_opa = 0. At f_opa = 0.003, one finds β = 7.2 which is similar to the result derived from observations (6.3 ± 1.0).

Conclusions. We find observational hints that the opacity in protoplanetary atmospheres is much smaller than in the ISM even if the specific value of κ_gr cannot be constrained in this first study as κ_gr is found by scaling the ISM opacity. Our results for the enrichment of giant planets are also important to distinguish core accretion and gravitational instability. In the simplest picture of core accretion, where first a critical core forms, and afterwards only gas is added, α ≈ −1. If a core accretes all planetesimals inside the feeding zone during runaway gas accretion α ≈ −2/3. The observational result (−0.71 ± 0.10) lies between these two values, pointing to core accretion as the likely formation mechanism.