arXiv:1112.2700v1 [astro-ph.EP] 12 Dec 2011 Mon. Not. R. Astron. Soc. 000, 1–22 (2011) Printed 14 December 2011 (MN L A T E X style file v2.2) A Novel Method to Photometrically Constrain Orbital Eccentricities: Multibody Asterodensity Profiling (MAP) David M. Kipping 1,2⋆ , William R. Dunn 3,† , Jamie M. Jasinski 3,† & Varun P. Manthri 3,† 1 Harvard-Smithsonian Center for Astrophysics, 60, Garden St., Cambridge, MA 02138, USA 2 Carl Sagan Fellow 3 Department of Physics and Astronomy, University College London, Gower St., London WC1E 6BT † These authors contributed equally to the work presented here Accepted 2011 December 12. Received 2011 December 12; in original form 2011 October 23 ABSTRACT We present a novel method to determine eccentricity constraints of extrasolar planets in systems with multiple transiting planets through photometry alone. Our method is highly model independent, making no assumptions about the stellar pa- rameters and requiring no radial velocity, transit timing or occultation events. Our technique exploits the fact the light curve derived stellar density must be the same for all planets transiting a common star. Assuming a circular orbit, the derived stellar density departs from the true value by a predictable factor, Ψ, which contains in- formation on the eccentricity of the system. By comparing multiple stellar densities, any differences must be due to eccentricity and thus meaningful constraints can be placed in the absence of any other information. The technique, dubbed “Multibody Asterodensity Profiling” (MAP), is a new observable which can be used alone or in combination with other observables, such as radial velocities and transit timing vari- ations. An eccentricity prior can also be included as desired. MAP is most sensitive to the minimum pair-combined eccentricity e.g. (e 1 + e 2 ) min . Individual eccentricity constraints are less stringent but an empirical eccentricity posterior is always derivable and is freely available from transit photometry alone. We present a description of our technique using both analytic and numerical im- plementations, followed by two example analyses on synthetic photometry as a proof of principle. We point out that MAP has the potential to constrain the eccentricity, and thus habitability, of Earth-like planets in the absence of radial velocity data, which is likely for terrestrial-mass objects. Key words: planets and satellites: general — eclipses — methods: numerical — planetary systems — techniques: photometric 1 INTRODUCTION In February of 2011, 1235 Kepler transiting candidate plan- ets were announced by Borucki et al. (2011), amongst which the majority are expected to be genuine (Morton & John- son 2011). At the latest counting, the score has since risen to 1781 (Rowe et al. 2011) and is expected to continue rising. Due to the unprecedented yield of new transiting planet can- didates, follow-up with radial velocity (RV) measurements is generally not feasible due to both the typical faintness of the targets and the intensive nature of the required tele- scope time for so many targets. Historically, radial velocity has emerged as the tool of choice to confirm transiting can- ⋆ E-mail: dkipping@cfa.harvard.edu didates and so the Kepler team have devoted considerable effort to find ways to confirm candidates without the need for RV. This has led to some pioneering techniques such as blend analysis (Torres et al. 2011; Fressin et al. 2011) and confirmation through transit timing variations (TTV) (Hol- man et al. 2011; Lissauer et al. 2011). However, even though transiting candidates have been shown to be confirmable without RV, its absence means that the orbital eccentricity, e, of the planets cannot be deter- mined (unless very strong TTVs are detected). One remain- ing avenue to constrain e is to detect an occultation event. Occultations occur exactly half an orbital period after the transit event for a circular orbit 1 but become offset for eccen- 1 There also exists a small light travel time across the system