[Paper Review] Kepler-9 revisited 60% the mass with six times more data

Stefan Dreizler, A. Ofir|arXiv (Cornell University)|Mar 6, 2014

Stellar, planetary, and galactic studies3 citations

TL;DR

This study re-analyzes the Kepler-9 system using six times more Kepler data, revealing that Kepler-9b and -9c have significantly lower masses and densities than previously thought—45.1 and 31.0 Earth masses, respectively, with bulk densities of 0.18 and 0.14 g cm⁻³—making them among the least dense exoplanets known. The refined transit timing variations (TTVs) from photometry alone now constrain masses with 7% precision, suggesting possible evidence for a non-transiting outer planet in radial velocity data.

ABSTRACT

Kepler-9 was the first case where transit timing variations have been used to confirm the planets in this system. Following predictions of dramatic TTVs - larger than a week - we re-analyse the system based on the full Kepler data set. We re-processed all available data for Kepler-9 removing short and long term trends, measured the times of mid-transit and used those for dynamical analysis of the system. The newly determined masses and radii of Kepler-9b and -9c change the nature of these planets relative to the one described in Holman et al. 2010 (hereafter H10) with very low, but relatively well charcterised (to better than 7%), bulk densities of 0.18 and 0.14 g cm$^3$ (about 1/3 of the H10 value). We constrain the masses (45.1 and 31.0 M$_\oplus$, for Kepler-9b and -9c respectively) from photometry alone, allowing us to see possible indications for an outer non-transiting planet in the radial velocity data. At $2R_\oplus$ Kepler-9d is determined to be larger than suggested before - suggesting that it is a low-mass low-density planet. The comparison between the H10 analysis and our new analysis suggests that small formal error in the TTV inversion may be misleading if the data does not cover a significant fraction of the interaction time scale.

Motivation & Objective

• To re-analyze the Kepler-9 system using the full Kepler dataset, which spans over 1426 days—six times longer than the original study.
• To reassess the masses and radii of Kepler-9b, -9c, and -9d using improved transit timing variation (TTV) analysis and photometric modeling.
• To evaluate whether the original TTV predictions from Holman et al. (2010) were accurate and to assess the impact of data coverage on TTV inversion reliability.
• To investigate the dynamical implications of the updated parameters, including the potential presence of a non-transiting outer planet.

Proposed method

• Re-processed all Kepler long-cadence photometry from quarters 1 to 16 (1426 days) using the SARS algorithm to correct for short-term systematic trends.
• Fitted individual mid-transit times for Kepler-9b and -9c using iterative modeling that corrected for long-term trends and transit signals, achieving high-precision timing.
• Applied linear ephemerides for Kepler-9d, which showed no significant TTVs, to determine its orbital parameters.
• Used the refined mid-transit times to perform a dynamical analysis of the system, enabling mass determination from photometry alone.
• Compared the new results with the original Holman et al. (2010) analysis to assess the impact of data coverage on TTV inversion accuracy.
• Evaluated radial velocity data for consistency with the new planetary masses and searched for signs of additional non-transiting planets.

Experimental results

Research questions

• RQ1 How do the updated masses and radii of Kepler-9b and -9c compare to the original estimates from Holman et al. (2010), and what are the implications for their bulk composition?
• RQ2 To what extent do the observed TTVs in Kepler-9 differ from the predictions made in the original study, and what does this imply about the system's dynamical evolution?
• RQ3 Can planetary masses be reliably derived from photometry alone using TTVs, and how does data coverage affect the precision of such mass determinations?
• RQ4 Is there evidence in the radial velocity data for a non-transiting planet in the Kepler-9 system, consistent with the new dynamical constraints?
• RQ5 How do the revised parameters of Kepler-9d—particularly its larger radius—alter its classification and potential composition compared to the original interpretation?

Key findings

• The mass of Kepler-9b is now determined to be 45.1 M⊕ with a 7% uncertainty, significantly lower than the original estimate, resulting in a bulk density of 0.18 g cm⁻³.
• Kepler-9c has a mass of 31.0 M⊕ and a bulk density of 0.14 g cm⁻³, making it one of the least dense exoplanets known.
• The radii of Kepler-9b and -9c are slightly larger than in the original study, with formal errors reduced by a factor of 5 to 8 due to increased data coverage.
• The TTV amplitudes observed are much smaller than predicted in Holman et al. (2010), with a span of only ±0.6 to −0.9 days, and a timescale about half as long as originally expected.
• The new analysis suggests that small formal errors in TTV inversion can be misleading if the data does not cover a significant fraction of the interaction timescale.
• Kepler-9d is now found to have a radius of 2.00 ± 0.05 R⊕, larger than previously thought, indicating it may be a low-mass, low-density planet with a significant volatile fraction rather than a rocky world.