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J/AJ/154/5    Transit timing variations of 145 Kepler planets    (Hadden+, 2017)

Kepler planet masses and eccentricities from TTV analysis. Hadden S., Lithwick Y. <Astron. J., 154, 5-5 (2017)> =2017AJ....154....5H (SIMBAD/NED BibCode)
ADC_Keywords: Stars, double and multiple ; Planets ; Stars, masses Keywords: planets and satellites: detection Abstract: We conduct a uniform analysis of the transit timing variations (TTVs) of 145 planets from 55 Kepler multiplanet systems to infer planet masses and eccentricities. Eighty of these planets do not have previously reported mass and eccentricity measurements. We employ two complementary methods to fit TTVs: Markov chain Monte Carlo simulations based on N-body integration, and an analytic fitting approach. Mass measurements of 49 planets, including 12 without previously reported masses, meet our criterion for classification as robust. Using mass and radius measurements, we infer the masses of planets' gaseous envelopes for both our TTV sample and transiting planets with radial velocity observations. Insight from analytic TTV formulae allows us to partially circumvent degeneracies inherent to inferring eccentricities from TTV observations. We find that planet eccentricities are generally small, typically a few percent, but in many instances are nonzero. Description: We compute Markov chain Monte Carlo (MCMC) fits to the Transit Timing Variations (TTVs) of 55 Kepler multiplanet systems exhibiting significant TTVs, 33 of which do not have N-body TTV fits reported previously in the literature. In addition, our work provides a uniform treatment of TTV systems that have previously been analyzed elsewhere. File Summary:
FileName Lrecl Records Explanations
ReadMe 80 . This file table1.dat 152 145 Masses from Transit Timing Variations (TTVs) table2.dat 119 90 Combined eccentricities of adjacent Transit Timing Variation (TTV) planet pairs table3.dat 54 41 Transiting radial velocity planets refs.dat 161 51 References
See also: V/133 : Kepler Input Catalog (Kepler Mission Team, 2009) J/ApJS/225/9 : Kepler TTVs. IX. (Holczer+, 2016) J/ApJS/217/16 : Kepler planetary candidates. V. 3yr Q1-Q12 (Rowe+, 2015) J/ApJ/800/135 : HARPS-N radial velocities of KOI-69 (Dressing+, 2015) J/ApJ/790/146 : Planets in Kepler's multi-transiting systems (Fabrycky+, 2014) J/ApJ/789/154 : Kepler-10 RV measurements by HARPS-N (Dumusque+, 2014) J/ApJ/787/80 : 139 Kepler planets transit time variations (Hadden+, 2014) J/ApJ/784/45 : Kepler's multiple planet candidates. III. (Rowe+, 2014) J/ApJS/210/20 : Small Kepler planets radial velocities (Marcy+, 2014) J/A+A/549/A10 : Transits of GJ 1214 (Harpsoe+, 2013) J/ApJ/750/114 : Kepler TTVs. IV. 4 multiple-planet systems (Fabrycky+, 2012) J/ApJ/749/15 : The Kepler-20 planetary system (Gautier+, 2012) J/ApJ/736/19 : Kepler planetary candidates. II. (Borucki+, 2011) J/ApJ/728/138 : Follow-up photometry of HAT-P-26 (Hartman+, 2011) J/PASP/123/412 : Exoplanet Orbit Database (Wright+, 2011) J/ApJS/197/8 : Kepler's multiple transiting planets (Lissauer+, 2011) J/ApJ/710/1724 : Follow-up photometry for HAT-P-11 (Bakos+, 2010) J/A+A/520/A66 : CoRoT-8b light and RV curves (Borde+, 2010) Byte-by-byte Description of file: table1.dat
Bytes Format Units Label Explanations
1- 13 A13 --- Name Planet name (1) 15 I1 --- R [0/1] Robust flag (1=planet mass inference is robust, 0=otherwise); see Section 3 17- 23 F7.3 d Per [3.072/199.67] Orbital period 25- 28 F4.1 Rgeo Rad [0.4/13.1] Planet radius (2) 30- 33 F4.2 Rgeo E_Rad [0.03/2.3] 1σ upper error bound on Rad 35- 38 F4.2 Rgeo e_Rad [0.03/2.1] 1σ lower error bound on Rad 40 A1 --- r_Rad [a-g] Source of planet-star radius ratio (3) 42- 44 F3.1 Msun Mstar [0.5/1.4] Mass of host star 46- 49 F4.2 Msun E_Mstar [0.03/0.2] 1σ upper error bound on Mstar 51- 54 F4.2 Msun e_Mstar [0.02/0.3] 1σ lower error bound on Mstar 56 A1 --- l_Md [01] Md upper limit flag (1=upper, 0=otherwise) (3) 58- 63 F6.2 Mgeo Md [0.01/527.7] Planet mass from default prior (2) 65- 69 F5.2 Mgeo E_Md [0.01/44.1]? 1σ upper error bound on Md 71- 74 F4.2 Mgeo e_Md [0.01/9.7]? 1σ lower error bound on Md 76- 81 F6.2 g/cm3 rhod [0.01/172.9] Planet density from default prior (2) 83- 87 F5.2 g/cm3 E_rhod [0.01/20.6]? 1σ upper error bound on rhod 89- 92 F4.2 g/cm3 e_rhod [0.01/5.7]? 1σ lower error bound on rhod 94 A1 --- l_Mh [0/1] Mh upper limit flag (1=upper, 0=otherwise) (3) 96-100 F5.1 Mgeo Mh [0.1/529.9] Planet mass from high mass prior (2) 102-107 F6.2 Mgeo E_Mh [0.05/101.4]? 1σ upper error bound on Mh 109-112 F4.2 Mgeo e_Mh [0/9.3]? 1σ lower error bound on Mh 114-119 F6.2 g/cm3 rhoh [0.02/306.8] Planet density from high mass prior 121-126 F6.2 g/cm3 E_rhoh [0.01/110.5]? 1σ upper error bound on rhoh 128-131 F4.2 g/cm3 e_rhoh [0.02/9.4]? 1σ lower error bound on rhoh 133-152 A20 --- Ref Reference for planets with masses previously inferred from N-body Transit Timing Variation (TTV) fits or radial velocity observations; in refs.dat file
Note (1): Values and uncertainties reflect the peak posterior probabilities and 68.3% credible regions. The peak posterior probabilities are computed by finding the maximum likelihood of a kernel density estimate computed from the posterior sample. Credible regions are so-called "highest posterior density intervals": the smallest parameter range containing 68.3% of the posterior sample. Note (2): Planet radii, masses, and densities incorporate the following: planet-star mass ratios sampled from our Markov chain Monte Carlo (MCMC) posteriors, planet-star radius ratios from the light-curve fit posteriors of Rowe et al. 2015 (Cat. J/ApJS/217/16), and randomly generated samples of host star properties. For the latter, samples of host star radii, masses, and densities are generated based on values reported in the Kepler stellar Q1-17 data release DR25, hosted on the exoplanet archive. For each Kepler system, random samples of stellar mass, radius, and density are drawn from skew-normal distributions (Azzalini 1985 J. Stat. 12 171), with scale and shape parameters chosen to match the reported ±1σ error bars. For some planets, the Rowe et al. 2015 (Cat. J/ApJS/217/16) light-curve fit posteriors are missing or contain a large number of points with impact parameters b>1 and are clearly pathological. The radii of these planets are computed using planet-star radius ratios from other sources as indicated. Note (3): Upper limit flag is defined as follows: 1 = If Md, rhod, Mh, rhoh are consistent with 0 and 1σ (68.3%) upper bounds are given; 0 = Otherwise.
Byte-by-byte Description of file: table2.dat
Bytes Format Units Label Explanations
1- 13 A13 --- Planet1 Planet 1 of the pair 15- 26 A12 --- Planet2 Planet 2 of the pair 28- 30 A3 --- MMR Planet pair's nearest first- or second-order Mean-Motion-Resonance (MMR) 32- 37 F6.4 --- Delta [0.0002/0.172] Normalized distance to resonance Δ (1) 39- 43 F5.3 --- Zd [0.001/0.26] Combined eccentricity, default prior (|Z|) (2) 45- 50 F6.4 --- E_Zd [0.0002/0.173] 1σ upper error bound on Zd (2) 52- 57 F6.4 --- e_Zd [0.0002/0.16] 1σ lower error bound on Zd (2) 59- 64 F6.4 --- Zp-d [0/0.244] Projected Z, default prior (Zproj) (3) 66- 71 F6.4 --- E_Zp-d [0.0002/0.11] 1σ upper error bound on Zp-d 73- 78 F6.4 --- e_Zp-d [0.0002/0.22] 1σ lower error bound on Zp-d 80- 84 F5.3 --- Zh [0.001/0.088] Combined eccentricity, high mass prior (|Z|) (2) 86- 91 F6.4 --- E_Zh [0.0001/0.029] 1σ upper error bound on Zh (2) 93- 98 F6.4 --- e_Zh [0.0001/0.045] 1σ lower error bound on Zh (2) 100-105 F6.4 --- Zp-h [0/0.09] Projected Z, high mass prior (Zproj) (3) 107-112 F6.4 --- E_Zp-h [0.0001/0.03] 1σ upper error bound on Zp-h 114-119 F6.4 --- e_Zp-h [0.0001/0.05] 1σ lower error bound on Zp-h
Note (1): Normalized distance to resonance: Δ=(j-k)P'/(jP)-1, where P = Period of the inner planet; P' = Period of the outer planet; k = 1 or 2 as appropriate for a first- or second-order resonance. Note (2): Values and uncertainties reflect the peak posterior probabilities and 68.3% credible regions, computed as described in the caption of Table1. Our Z is defined in terms of free eccentricities (Equation (3)), whereas the Markov chain Monte Carlo (MCMC) outputs total (free+forced) eccentricity; we convert to free eccentricity for this table by subtracting off the analytically calculated forced components. Note (3): In addition to |Z|, it is of interest to know which planets are consistent with Z=0; such planets might have experienced significant damping by tides or other effects. Credible regions in |Z| cannot be used to address this question because |Z| must be non-negative. Therefore, following Zakamska et al. (2011MNRAS.410.1895Z), we define the signed quantity, Zproj, which is the projection of the Zs from the Markov chain Monte Carlo (MCMC) posterior onto the median of their distribution. More precisely, we define the median Zmed, by computing the median real and imaginary components of Z. Then, given Z, the value of Zproj is defined as: Zproj=ZZ*med/|Zmed|, Eq. (8), where the "*" indicates complex conjugate.
Byte-by-byte Description of file: table3.dat
Bytes Format Units Label Explanations
1- 12 A12 --- Name Transiting radial velocity planet name (1) 14- 18 F5.2 d Per [0.36/66.26] Period (2) 20- 23 F4.1 Mgeo Mass [1.6/69.9] Mass (2) 25- 28 F4.1 Mgeo E_Mass [0.4/22] 1σ upper error bound on Mass 30- 33 F4.1 Mgeo e_Mass [0.2/21] 1σ lower error bound on Mass 35- 37 F3.1 Rgeo Rad [0.8/6.4] Radius (2) 39- 42 F4.2 Rgeo E_Rad [0.02/0.8] 1σ upper error bound on Rad 44- 47 F4.2 Rgeo e_Rad [0.02/0.5] 1σ lower error bound on Rad 49- 54 A6 --- Ref Reference; in refs.dat file
Note (1): All planets selected from the NASA Exoplanet Archive ( Only planets with 1σ mass uncertainties inconsistent with 0 are included. We exclude radial velocity measurements of planets from the Kepler-18, 25, 48, and 89 systems since they are also in our Transit Timing Variation (TTV) sample. Note (2): Periods, masses, and radii of transiting radial velocity planets smaller than 8R.
Byte-by-byte Description of file: refs.dat
Bytes Format Units Label Explanations
1- 6 A6 --- Ref Reference code 8- 26 A19 --- BibCode Bibliographic code 28- 48 A21 --- Aut Author's name 50-161 A112 --- Com Comments
History: From electronic version of the journal References: Hadden & Lithwick, Paper I 2016ApJ...828...44H
(End) Prepared by [AAS]; Sylvain Guehenneux [CDS] 17-Aug-2017
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