THE MASS–RADIUS RELATION FOR 65 EXOPLANETS SMALLER THAN 4 EARTH RADII

By L. Weiss, G. Marcy. 2013

455 citations recorded by the source corpus.

We study the masses and radii of 65 exoplanets smaller than 4 R⊕ with orbital periods shorter than 100 days. We calculate the weighted mean densities of planets in bins of 0.5 R⊕ and identify a density maximum of 7.6  g cm−3 at 1.4 R⊕. On average, planets with radii up to RP = 1.5 R⊕ increase in density with increasing radius. Above 1.5 R⊕, the average planet density rapidly decreases with increasing radius, indicating that these planets have a large fraction of volatiles by volume overlying a rocky core. Including the solar system terrestrial planets with the exoplanets below 1.5 R⊕, we find ρP = 2.43 + 3.39(RP/R⊕) g cm−3 for RP < 1.5 R⊕, which is consistent with rocky compositions. For 1.5 ⩽ RP/R⊕ < 4, we find MP/M⊕ = 2.69(RP/R⊕)0.93. The rms of planet masses to the fit between 1.5 and 4 R⊕ is 4.3 M⊕ with reduced χ2 = 6.2. The large scatter indicates a diversity in planet composition at a given radius. The compositional diversity can be due to planets of a given volume (as determined by their large H/He envelopes) containing rocky cores of different masses or compositions.

Subfields: Astronomy and Astrophysics, Instrumentation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b5e76ea848ab0be765c066a15f2f8c948bfc9137

How researchers see this paper

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In Astronomy and Astrophysics

1. D. Charbonneau
2. Jon Fortney
3. Timothy Morton
4. J. Owen
5. J. Johnson
6. J. Winn
7. Andrew W. Howard
8. E. Petigura

In Instrumentation

1. D. Charbonneau
2. J. Owen
3. Timothy Morton
4. Jon Fortney
5. E. Gaidos
6. J. Johnson
7. J. Winn
8. Andrew W. Howard

In Statistical and Nonlinear Physics

1. Timothy Morton
2. J. Owen
3. C. Mordasini
4. Y. Lithwick
5. Yanqin Wu
6. Leslie A. Rogers
7. Sheng Jin
8. Jon Fortney

Citations in the corpus

• Spacing of Kepler Planets: Sculpting by Dynamical Instability (2015, background): “This is corroborated by the presence of hydrogen envelopes on these low-mass planets, for both Neptunes (e.g. Borucki et al. 2010) and superEarths (Wu & Lithwick 2013; Weiss & Marcy 2014).”
• The California-Kepler Survey. I. High-resolution Spectroscopy of 1305 Stars Hosting Kepler Transiting Planets (2017, background): “Marcy et al. (2014) measured the masses of 49 planets and found evidence for a transition from rock- to gas-dominated compositions with increasing planet size (Weiss & Marcy 2014; Rogers 2015; Wolfgang & Lopez 2015).”
• Multiple Disk Gaps and Rings Generated by a Single Super-Earth (2017, background): “These planets generally weigh less than 20M⊕, as determined from transit-timing analyses (e.g., Jontof-Hutter et al. 2014; Wu & Lithwick 2013) and radial velocity measurements (e.g., Weiss & Marcy 2014; Marcy et al. 2014; Dumusque et al. 2014; Dressing et al. 2015).”
• ECCENTRICITY FROM TRANSIT PHOTOMETRY: SMALL PLANETS IN KEPLER MULTI-PLANET SYSTEMS HAVE LOW ECCENTRICITIES (2015, methodology): “The masses for the planets in our sample were estimated based on the radius, using Weiss et al. (2013) for planets with R ≥ 4 R⊕ and following Weiss & Marcy (2014) for planets where R ≤ 4 R⊕.”
• DISCOVERY AND VALIDATION OF Kepler-452b: A 1.6 R⨁ SUPER EARTH EXOPLANET IN THE HABITABLE ZONE OF A G2 STAR (2015, methodology): “Specifically, we took the deterministic mass–density relation from Equations (1)–(3) in Weiss & Marcy (2014): MP = min { 2.43 + 3.39RP 5.513 RP 3, 2.69R0.”
• The Evaporation Valley in the Kepler Planets (2017, background): “…Lithwick 2013; Hadden & Lithwick 2014; Jontof-Hutter et al. 2016; Hadden & Lithwick 2016) or radial-velocity (RV) follow-up (e.g. Marcy et al. 2014; Weiss & Marcy 2014) quickly told us that many of these planets had compositions unlike the small terrestrial planets in our own solar system (e.g.…”
• The California-Kepler Survey. IV. Metal-rich Stars Host a Greater Diversity of Planets (2017, background): “RV mass measurements of transiting planets have revealed that planets smaller than 1.7 R⊕ have bulk densities consistent with rocky compositions (e.g. Weiss & Marcy 2014; Rogers 2015), at least for the shortperiod planets (P .”
• The California-Kepler Survey. III. A Gap in the Radius Distribution of Small Planets (2017, background): “Planets with larger radii and measured masses are mostly low-density and require an extended atmosphere to simultaneously explain their masses and radii (Marcy et al. 2014; Weiss & Marcy 2014; Rogers 2015; Wolfgang & Lopez 2015).”
• MAKE SUPER-EARTHS, NOT JUPITERS: ACCRETING NEBULAR GAS ONTO SOLID CORES AT 0.1 AU AND BEYOND (2014, background): “Most of their measured masses range from 5–10M⊕ (Wu & Lithwick 2013; Weiss & Marcy 2014) Because our model gas envelopes are not heated, they are especially susceptible to runaway; i.e., our calculated runaway times trun are strict lower bounds.”
• PROBABILISTIC FORECASTING OF THE MASSES AND RADII OF OTHER WORLDS (2016, background): “In previous works, such transitional points are often held as fixed, assumed locations (e.g., Weiss & Marcy 2014 assume a physically motivated, but not freely inferred, break at 1.5 R⊕).”
• Observing the Atmospheres of Known Temperate Earth-sized Planets with JWST (2017, methodology): “We use an empirical mass–radius relationship from Weiss & Marcy (2014), which is consistent with a rocky terrestrial composition (Zeng et al. 2016).”
• DENSITIES AND ECCENTRICITIES OF 139 KEPLER PLANETS FROM TRANSIT TIME VARIATIONS (2013, background): “Weiss & Marcy (2014) report m ≈ 7 M⊕ × (R/3R⊕)0.93, for planets in the size range 1.5R⊕ < R < 4R⊕, based primarily on RV measurements.”
• Can we constrain the interior structure of rocky exoplanets from mass and radius measurements (2015, unknown): “…4.8 +2.5 −3.6 Gilliland et al. (2013) 30.58 Kepler-78b 1.173+0.159−0.089 1.86 +0.38 −0.25 Pepe et al. (2013) 6.35 Kepler-93b 1.50 ±0.03 2.59± 2.00 Weiss & Marcy (2014) 4.23 Kepler-97b 1.48 ±0.13 3.51± 1.90 Weiss & Marcy (2014) 5.97 Kepler-99b 1.48 ±0.08 6.15± 1.30 Weiss & Marcy…”
• AN ANCIENT EXTRASOLAR SYSTEM WITH FIVE SUB-EARTH-SIZE PLANETS (2015, background): “Since these planets are all sub-Earth-sized and likely of similar composition (Weiss & Marcy 2014), the monotonic increase in planetary size as a function of orbital distance would imply that the masses of the planets increase outward.”
• The planet nine hypothesis (2019, unknown): “5R⊕, respectively (Weiss and Marcy, 2014).”
• Kepler Planet Masses and Eccentricities from TTV Analysis (2016, methodology): “Although this trend has been noted before (e.g., Weiss & Marcy 2014; Dai et al. 2015), it is sometimes suggested that this discrepancy is due to mass errors in either the TTV or RV measurements.”
• HUBBLE SPACE TELESCOPE NEAR-IR TRANSMISSION SPECTROSCOPY OF THE SUPER-EARTH HD 97658B (2014, methodology): “…obtained using either the radial velocity or transit timing techniques, it is possible to constrain the average densities and corresponding bulk compositions of the super-Earths in the Kepler sample (e.g., Lithwick et al. 2012; Hadden & Lithwick 2013; Weiss & Marcy 2014; Marcy et al. 2014).”
• Water loss from terrestrial planets orbiting ultracool dwarfs: implications for the planets of TRAPPIST-1 (2016, background): “The three planets of the TRAPPIST-1 system (Gillon et al. 2016) are Earth-sized planets, and thus probably rocky (Weiss & Marcy 2014; Rogers 2015).”