Sculpting the Valley in the Radius Distribution of Small Exoplanets as a by-product of Planet Formation: The Core-Powered Mass-Loss Mechanism

Abstract: Recent observations revealed a bimodal radius distribution of small, short-period exoplanets with a paucity in their occurrence, a radius `valley', around $1.5-2.0$ $R_\oplus$. In this work, we investigate the effect of a planet's own cooling luminosity on its thermal evolution and atmospheric mass-loss (core-powered mass-loss) and determine its observational consequences for the radius distribution of small, close-in exoplanets. Using simple analytical descriptions and numerical simulations, we demonstrate that planetary evolution based on the core-powered mass-loss mechanism alone (i.e., without any photoevaporation) can produce the observed valley in the radius distribution. Our results match the valley's location, shape and slope in planet radius-orbital period parameter space, and the relative magnitudes of the planet occurrence rate above and below the valley. We find that the slope of the valley is, to first order, dictated by the atmospheric mass-loss timescale at the Bondi radius and given by $\text{d log} R_p/ \text{d log} P \simeq 1/(3(1-\beta))$ which evaluates to $ -0.11$ for $ \beta \simeq 4$, where $M_c/M_\oplus = (R_c/R_{\oplus})^{\beta} (\rho_{c*}/\rho_{\oplus})^{\beta/3}$ is the mass-radius relation of the core. This choice for $\beta$ yields good agreement with observations and attests to the significance of internal compression for massive planetary cores. We further find that the location of the valley scales as $\rho_{c*}^{-4/9}$ and that the observed planet population must have predominantly rocky cores with typical water-ice fractions of less than $\sim 20\%$. Furthermore, we show that the relative magnitude of the planet occurrence rate above and below the valley is sensitive to the details of the planet-mass distribution but that the location of the valley is not.

• The paper reveals that core-powered mass-loss effectively sculpts the observed valley in the radius distribution of small exoplanets.
• It uses advanced thermal evolution models to illustrate how energy-driven mass loss shapes planetary sizes over time.
• The findings emphasize the role of planetary core composition and formation history in explaining exoplanet radius variations.

Overview of the \LaTeX\ Guide for MNRAS Authors

The paper under discussion is a comprehensive guide authored by Keith T. Smith for preparing manuscripts for submission to the "Monthly Notices of the Royal Astronomical Society" (MNRAS) using the mnras \LaTeX\ class package. This document addresses the technical specifications required for authors to use \LaTeX\ effectively, specifically tailored for compliance with MNRAS publication standards.

Structured Content Overview

The guide meticulously outlines the necessary steps for acquiring, installing, and utilizing the MNRAS \LaTeX\ package. It elaborates on:

• Basic Structure: The document starts with fundamental elements such as the title, authorship, and affiliations, adhering to prescribed MNRAS formats. It highlights dual versions of titles and author lists for standard display and running headers.
• Document Preparation: Guidance is provided on preparing and submitting manuscripts, emphasizing adherence to the template files provided (e.g., mnras_template.tex), which ensures alignment with MNRAS formatting protocols.
• Formatting Options and Requirements: Detailed explanations of class options are presented, such as document layout choices (e.g., onecolumn, doublespacing), citation management through usenatbib, and graphics handling via usegraphicx.
• Mathematical and Symbolic Notation: The guide specifies the treatment of mathematical equations and symbols, including specialized astronomy-related symbols and the \ion command for correctly formatting ionization states.
• Figures and Tables: Recommendations for inserting and formatting figures and tables are provided, emphasizing automated numbering and avoidance of placement concern by the authors as this is addressed during the publication’s production process.

Implementation of References and Citations

MNRAS adheres to the Harvard citation style, which requires the natbib package for handling citations. The guidance includes employing Bib\ for managing references, offering much-needed automation in formatting and integrating references with minimized manual intervention.

Practical and Theoretical Implications

Practically, this guide serves as an essential resource for astronomers and astrophysicists aiming to publish in MNRAS. It ensures submissions meet the journal’s stringent formatting requirements, thereby reducing potential delays in the publication process. From a theoretical standpoint, the guide reinforces the importance of consistency and precision in the dissemination of research findings, aligning with the broader ethos of scientific communication.

Speculation on Future Developments

As \LaTeX\ and publication protocols evolve, one might envision further enhancements or modifications to this guide. Automation tools, potentially aided by AI, could further streamline the manuscript preparation process. Such developments may include enhanced template functionalities that integrate with other document preparation systems or improved error-checking features to assist authors in meeting publication standards effortlessly.

In conclusion, Keith T. Smith’s guide remains an invaluable resource for authors preparing submissions for MNRAS, detailing the meticulous requirements for consistency in the presentation of scientific research. The comprehensive instructions ensure that researchers can focus more on the content of their work and less on formatting intricacies, fostering a more efficient path to publication.