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 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:
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FileName Lrecl Records Explanations
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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
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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
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Bytes Format Units Label Explanations
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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
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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.
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Byte-by-byte Description of file: table2.dat
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Bytes Format Units Label Explanations
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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
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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 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.
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Byte-by-byte Description of file: table3.dat
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Bytes Format Units Label Explanations
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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
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Note (1): All planets selected from the NASA Exoplanet Archive
(https://exoplanetarchive.ipac.caltech.edu/). 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⊕.
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Byte-by-byte Description of file: refs.dat
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Bytes Format Units Label Explanations
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1- 6 A6 --- Ref Reference code
8- 26 A19 --- BibCode Bibliographic code
28- 48 A21 --- Aut Author's name
50-161 A112 --- Com Comments
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History:
From electronic version of the journal
References:
Hadden & Lithwick, Paper I 2016ApJ...828...44H 2016ApJ...828...44H
(End) Prepared by [AAS]; Sylvain Guehenneux [CDS] 17-Aug-2017