Revised Masses and Densities of the Planets around Kepler-10

Abstract: Determining which small exoplanets have stony-iron compositions is necessary for quantifying the occurrence of such planets and for understanding the physics of planet formation. Kepler-10 hosts the stony-iron world Kepler-10b (K10b), and also contains what has been reported to be the largest solid silicate-ice planet, Kepler-10c (K10c). Using 220 radial velocities (RVs), including 72 precise RVs from Keck-HIRES of which 20 are new from 2014-2015, and 17 quarters of Kepler photometry, we obtain the most complete picture of the Kepler-10 system to date. We find that K10b (Rp=1.47 Re) has mass 3.72$\pm$0.42 Me and density 6.46$\pm$0.73 g/cc. Modeling the interior of K10b as an iron core overlaid with a silicate mantle, we find that the iron core constitutes 0.17$\pm$0.11 of the planet mass. For K10c (Rp=2.35 Re) we measure Mp=13.98$\pm$1.79 Me and $\rho$=5.94$\pm$0.76 g/cc, significantly lower than the mass computed in Dumusque et al. (2014, 17.2$\pm$1.9 Me). Internal compositional modeling reveals that at least $10\%$ of the radius of Kepler-10c is a volatile envelope composed of hydrogen-helium ($0.2\%$ of the mass, $16\%$ of the radius) or super-ionic water ($28\%$ of the mass, $29\%$ of the radius). Analysis of only HIRES data yields a higher mass for K10b and a lower mass for K10c than does analysis of the HARPS-N data alone, with the mass estimates for K10c formally inconsistent by 3$\sigma$. Splitting the RVs from each instrument leads to inconsistent measurements for the mass of planet c in each data set. This suggests that time-correlated noise is present and that the uncertainties in the planet masses (especially K10c) exceed our formal estimates. Transit timing variations (TTVs) of K10c indicate the likely presence of a third planet in the system, KOI-72.X. The TTVs and RVs are consistent with KOI-72.X having an orbital period of 24, 71, or 101 days, and a mass from 1-7 Me.

• The paper refines planetary mass and density estimates, confirming Kepler-10b as a rocky planet and indicating Kepler-10c’s significant volatile envelope.
• The study combines Keck-HIRES, HARPS-N RV data and 17 quarters of Kepler photometry to address discrepancies caused by time-correlated noise in the measurements.
• The research identifies transit timing variations that suggest the presence of an additional planetary body, KOI-72.X, with orbital periods of 24, 71, or 101 days.

Insights into the Revised Masses and Densities of the Planets around Kepler-10

The study presents a detailed examination of the stellar system Kepler-10 using an extensive dataset drawn from Keck-HIRES and HARPS-N radial velocity (RV) observations and 17 quarters of Kepler photometry. The core objective was to reevaluate the masses and densities of the two known planets, Kepler-10b and Kepler-10c, and to investigate the transit timing variations (TTVs) potentially signaling additional planetary bodies within the system.

Key Findings

1. Planetary Masses and Densities:
   • Kepler-10b, with a radius of approximately $1.47 R_\oplus$, is affirmed to have a mass of $3.72 M_\oplus$ and a density of $6.46\ \text{g/cm}^3$. Modeling suggests a predominately stony-iron composition with its iron core constituting approximately $17\%$ of its total mass, reinforcing the classification of Kepler-10b as a rocky planet.
   • Kepler-10c presents a more complex scenario. Previously reported as the "largest rocky planet," the study recalibrates its mass to $13.98 M_\oplus$ with a reduced density of $5.94\ \text{g/cm}^3$. This revised density rules out a purely rocky composition, suggesting instead a significant volatile envelope, possibly composed of hydrogen-helium or super-ionic water comprising major portions of its radius and mass.
2. Discrepancies in Data:
   • The research highlights an inconsistency in mass measurements when RV data from HIRES and HARPS-N are analyzed independently, particularly for Kepler-10c. The discrepancy suggests significant time-correlated noise, raising concerns about potential overestimations or underestimations of planetary masses due to instrument-specific biases or stellar activity.
3. Additional Planetary Body:
   • A tentative identification of a third body, labeled KOI-72.X, is inferred from TTVs of Kepler-10c. Potential orbital periods for KOI-72.X are derived using analytic models and span 24, 71, or 101 days, with a mass estimate ranging between $1$ and $7 M_\oplus$.

Implications and Future Work

• Impact on Exoplanet Composition Modeling: The findings challenge and refine the typical classifications of exoplanets between 1-4 Earth radii, particularly around the transition zone from stony-iron worlds to planets with significant volatile envelopes. Kepler-10c serves as a crucial data point in understanding larger super-Earths that inhabit this transition zone.
• Instrumental and Observational Challenges: The study emphasizes the need for comprehensive, cross-instrument analyses in order to mitigate time-correlated noise and ensure robust mass estimates. This is particularly pertinent in characterizing planetary systems with small planets where low signal-to-noise ratios can lead to significant deviations in derived planetary properties.
• Broader Applicability: The methodological applications of reconciling RV data with photometric TTVs serve as a methodological blueprint for uncovering hidden planets in other multi-planetary systems. This approach could be vital in identifying non-transiting exoplanets, which may otherwise slip through the cracks of classical detection methods.

In conclusion, the research underscores the complex dynamics and compositional diversity present in exoplanetary systems. The Kepler-10 system, through meticulous observation and analysis, offers compelling insights into the structure and formation of small exoplanets. As astrophysical techniques evolve, further studies should focus on integrating diverse observational methods to reduce uncertainties and enhance our understanding of these distant worlds.