# System Geometries and Transit / Eclipse Probabilities

## Abstract

Transiting exoplanets provide access to data to study the mass-radius relation and internal structure of extrasolar planets. Long-period transiting planets allow insight into planetary environments similar to the Solar System where, in contrast to hot Jupiters, planets are not constantly exposed to the intense radiation of their parent stars. Observations of secondary eclipses additionally permit studies of exoplanet temperatures and large-scale exo-atmospheric properties. We show how transit and eclipse probabilities are related to planet-star system geometries, particularly for long-period, eccentric orbits. The resulting target selection and observational strategies represent the principal ingredients of our photometric survey of known radial-velocity planets with the aim of detecting transit signatures (TERMS).

NASA Exoplanet Science Institute, California Institute of Technology, MC 100-22, Pasadena, CA 91125, USA [kaspar@caltech.edu] \affil Pennsylvania State University, 418 Davey Lab, University Park, PA 16802, USA \affil Dept. of Astronomy & Astrophysics, University of California at Santa Cruz, Santa Cruz, CA 95064, USA \affil Astronomy Dept. & Space Sciences Laboratory, University of California at Berkeley, Berkeley, CA 94720, USA

## 1 Transit/Eclipse Probabilities

The geometric probabilities with which an existing planet will transit its parent star () or be eclipsed by its parent star () are given by the following equations (Barnes 2007; Burke 2008; Kane & von Braun 2008, 2009; von Braun & Kane 2010)

(1) |

and

(2) |

where and are planetary and stellar radii, respectively, and , , and are the orbital semi-major axis, eccentricity, and argument of periastron. When averaging over all possible values of , increases with increasing eccentricity (left panel in Fig. 1). For fixed eccentricities, equations 1 and 2 show that is highest for , whereas is highest for (right panel in Fig. 1).

## 2 Terms

The Transit Ephemerides Refinement and Monitoring Survey (TERMS) takes advantage of the combinations of (measured) and of planets detected by the radial velocity (RV) method to search for transiting signatures among these planets (Kane et al. 2009). In the process, we use concurrently obtained RV data to minimize the size of the transit window for our photometric observations.

Barnes, J. W. 2007, \pasp, 119, 986 \referenceBurke, C. J. 2008, \apj, 679, 1566 \referenceButler, R. P., et al. 2006, \apj, 646, 505 \referenceKane, S. R., & von Braun, K. 2008, \apj, 689, 492 \referenceKane, S. R., & von Braun, K. 2009, \pasp, 121, 1096 \referenceKane, S. R., et al. 2009, \pasp, 121, 1386 \referencevon Braun, K. & Kane, S. R. 2010, ASP Conf. Series, 430, 551