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The Mass of KOI-94d and a Relation for Planet Radius, Mass, and Incident Flux

Weiss, Lauren M. and Marcy, Geoffrey W. and Rowe, Jason F. and Howard, Andrew W. and Isaacson, Howard and Fortney, Jonathan J. and Miller, Neil and Demory, Brice-Olivier and Fischer, Debra A. and Adams, Elisabeth R. and Dupree, Andrea K. and Howell, Steve B. and Kolbl, Rea and Johnson, John Asher and Horch, Elliott P. and Everett, Mark E. and Fabrycky, Daniel C. and Seager, Sara (2013) The Mass of KOI-94d and a Relation for Planet Radius, Mass, and Incident Flux. Astrophysical Journal, 768 (1). Art. No. 14. ISSN 0004-637X.

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We measure the mass of a modestly irradiated giant planet, KOI-94d. We wish to determine whether this planet, which is in a 22 day orbit and receives 2700 times as much incident flux as Jupiter, is as dense as Jupiter or rarefied like inflated hot Jupiters. KOI-94 also hosts at least three smaller transiting planets, all of which were detected by the Kepler mission. With 26 radial velocities of KOI-94 from the W. M. Keck Observatory and a simultaneous fit to the Kepler light curve, we measure the mass of the giant planet and determine that it is not inflated. Support for the planetary interpretation of the other three candidates comes from gravitational interactions through transit timing variations, the statistical robustness of multi-planet systems against false positives, and several lines of evidence that no other star resides within the photometric aperture. We report the properties of KOI-94b (M_P = 10.5 ± 4.6 M_⊕, R_P = 1.71 ± 0.16 R_⊕, P = 3.74 days), KOI-94c (M_P = 15.6^(+5.7)_(-15.6) M_⊕, R_P = 4.32 ± 0.41 R_⊕, P = 10.4 days), KOI-94d (M_P = 106 ± 11 M_⊕, R_P = 11.27 ± 1.06 R_⊕, P = 22.3 days), and KOI-94e (M_P = 35^(+18)_(-28) M_⊕, R_P = 6.56 ± 0.62 R_⊕, P = 54.3 days). The radial velocity analyses of KOI-94b and KOI-94e offer marginal (>2σ) mass detections, whereas the observations of KOI-94c offer only an upper limit to its mass. Using the KOI-94 system and other planets with published values for both mass and radius (138 exoplanets total, including 35 with M_P < 150 M_⊕), we establish two fundamental planes for exoplanets that relate their mass, incident flux, and radius from a few Earth masses up to 13 Jupiter masses: (R_P/R_⊕) = 1.78(M_P/M_⊕)0.53(F/erg s^(–1) cm^(–2))^(–0.03) for M_P < 150 M_⊕, and R_P/R_⊕ = 2.45(M_P/M_⊕)^(–0.039)(F/erg s^(–1) cm^(–2))0.094 for M_P > 150 M_⊕. These equations can be used to predict the radius or mass of a planet.

Item Type:Article
Related URLs:
URLURL TypeDescription
Weiss, Lauren M.0000-0002-3725-3058
Marcy, Geoffrey W.0000-0002-2909-0113
Rowe, Jason F.0000-0002-5904-1865
Howard, Andrew W.0000-0001-8638-0320
Isaacson, Howard0000-0002-0531-1073
Fortney, Jonathan J.0000-0002-9843-4354
Demory, Brice-Olivier0000-0002-9355-5165
Fischer, Debra A.0000-0003-2221-0861
Howell, Steve B.0000-0002-2532-2853
Johnson, John Asher0000-0001-9808-7172
Horch, Elliott P.0000-0003-2159-1463
Everett, Mark E.0000-0002-0885-7215
Fabrycky, Daniel C.0000-0003-3750-0183
Seager, Sara0000-0002-6892-6948
Additional Information:© 2013 American Astronomical Society. Received 2012 October 31; accepted 2013 March 12; published 2013 April 9. Based in part on observations obtained at the W. M. Keck Observatory, which is operated by the University of California and the California Institute of Technology. This project was possible thanks to NASA’s Kepler mission, which provided the photometry of KOI-94 and identified it as a target worthy of follow-up. The authors thank the Kepler Team as a whole, and also a few individuals for their specific roles: Bill Borucki and David Koch for designing the mission, and Natalie Batalha for leadership in the scientific analysis of the Kepler planetary candidates. L.M.W. thanks Yoram Lithwick for helpful conversations and assistance in interpreting the TTV data. L.M.W. is financially supported by the National Science Foundation Graduate Research Fellowship Program, Grant DGE 1106400. Spectra of KOI-94 were obtained at the W. M. Keck Observatory. The authors wish to extend special thanks to those of Hawai‘ian ancestry on whose sacred mountain of Mauna Kea we are privileged to be guests. Without their generous hospitality, the Keck observations presented herein would not have been possible.
Funding AgencyGrant Number
NSF Graduate Research FellowshipDGE-1106400
Subject Keywords:planets and satellites: composition; stars: individual (KOI-94, KIC 6462863, 2MASS J19491993+4153280); techniques: photometric; techniques: spectroscopic
Issue or Number:1
Record Number:CaltechAUTHORS:20130603-103612469
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Official Citation:The Mass of KOI-94d and a Relation for Planet Radius, Mass, and Incident Flux Lauren M. Weiss, Geoffrey W. Marcy, Jason F. Rowe, Andrew W. Howard, Howard Isaacson, Jonathan J. Fortney, Neil Miller, Brice-Olivier Demory, Debra A. Fischer, Elisabeth R. Adams, Andrea K. Dupree, Steve B. Howell, Rea Kolbl, John Asher Johnson, Elliott P. Horch, Mark E. Everett, Daniel C. Fabrycky, and Sara Seager doi:10.1088/0004-637X/768/1/14
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38754
Deposited By: Ruth Sustaita
Deposited On:03 Jun 2013 18:04
Last Modified:09 Mar 2020 13:19

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