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Effects of Mutual Transits by Extrasolar Planet-Companion Systems on Light Curves

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arXiv:0906.2590v1 [astro-ph.EP] 15 Jun 2009Effects of Mutual Transits by ExtrasolarPlanet-Companion Systems on L i ght CurvesMasanao Sato, and Hideki AsadaFaculty of Science and Technology, Hirosaki University, Hirosaki, Aomori 036-8561(Received ; accepted )AbstractWe consider effects of mutual transits by extrasolar planet-companion systems (ina true binary or a planet-satellite system) on light curves. We show that inducedchanges in light curves depend strongly on a r atio between a planet-companion’s or-bital velocity ar ound their host star and a planet-companion’s spin speed around theircommon center of mass. For both of slow and fast spin cases (corresponding to larg eand small separations between them, respectively), a certain asymmetry appears inlight curves. We show that, especially for small separation cases, geometrical blockingof one faint obj ect by the other transiting a parent star causes an apparent increasein light curves and characteristic fluctuations appear as an important evidence of mu-tual transits. We show also that extrasolar mutual transits provide a complement arymethod of measuring the radii of two transiting objects, their separation and mass,and consequently identifying them as a true binary, planet-satellite system or others.Monitoring 105stars for three years with Kepler may lead to a discovery o f a secondEarth-Moon-like system if the fraction of such systems for an averaged star is largerthan 0.05, or it may put upper limits on the fraction as f < 0.05.Key wor ds: techniques: photometric — eclipses — occultations — planets andsatellites: general — stars: planetary systems1. IntroductionIt is of general interest to discover a second Earth-Moon system. Detections of extra-solar planet-satellite or binary planet systems will bring impo r t ant information to planet (andsatellite) formation t heory (e.g., Jewitt and Sheppard 2005, Canup and Ward 2006, Jewitt andHaghighipour 2007).It is not clear whether the IAU definition for planets in the solar system can be a ppliedto extrasolar planets as it is. The IAU definition in 2006 is stated in the following way. Aplanet is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass so that it1assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighborhoodaround its orbit.We call a gravitationally bound system of two extrasolar planet-size objects simply asextrasolar binary planets. They constitute a true binary if the following conditions are satisfiedinstead of (c) in addition to the criteria (a) with r eplacing the Sun by a host star and (b).(c1) Their total mass is dominant in the neighbor hood around their orbits. (c2) Their commoncenter of mass is above their surfaces. If it is below a surface of one object, one may call theman extrasolar planet-satellite.There are theoretical works on the existence of planets with satellites. The solar system’souter gaseous planets have multiple satellites, each of which notably has a similar fraction(∼ 10−4) of their respective planet’s mass. For instance, Canup and Ward (2006 ) found thatthe mass fraction is regulated to ∼ 10−4by a balance between two competing processes of thematerial inflow to the satellites and the satellite loss through orbital decay driven by the gas.They suggested that similar processes could limit the largest satellite of extrasolar giant planets.Such theoretical predictions await future observational tests. There still remains a possibility todetect Jupiter-size binary planets with comparable masses. Furthermore, we should note thattheir model does not hold for solid planets. It may be possible to detect binary solid planets(perhaps Earth-size ones). Therefore, future detection of extrasolar planet-companion systemsor a larger mass fraction (> 10−4) of satellites around gaseous exoplanets will bring importantinformations into the planet and satellite formation theory. In any case, unexpected findingswill open the possibility of new configurations such as binary planets.Recent direct imaging of a planetary mass ∼ 8MJwith an apparent separation of 330AU from the parent star (Lafreni`ere et al. 2008) indicates the likely existence of long-periodexoplanets (> 1000 yr). In this paper, we consider such exoplanets as well as close ones.Since the first detection of a transiting extrasolar planet (Charbonneau et al. 2000),photometric techniques have been successful (e.g., Deming, Seager, Richardson, Harrington2005 for probing atmosphere, Ohta et al. 2005, Winn et al. 2005, Gaudi & Winn 2007, Naritaet al. 2007, 2008 for measuring stellar spins). In addition to C OROT1, Kepler2has been veryrecently launched. It will monitor about 105stars with expected 10 ppm (= 10−5) photometricdifferential sensitivity. This enables to detect a Moon-size object.Sartoretti and Schneider (1999) first suggested a photometric detection of extrasolarsatellites. Cabrera and Schneider (2007) developed a method based on the imaging of a planet-companion as an unresolved system (but resolved fro m its host star) by using planet-companionmutual transits and mutual shadows. As an a lternative method, timing offsets for a singleeclipse have been investigated for eclipsing binary stars as a perturbation of transiting planetsaround the center of mass in the presence of the third body (Deeg et al. 1998, 2000, Doyle1http://www.esa.int/SPECIALS/COROT/2http://kepler.nasa.gov/2et al. 2000). It has been recently extended toward detecting “exomoons” (Szab´o, Szatm´ary,Div´eki, Simon 2006, Simon, Szatm´ary, Szab´o, 2007, Kipping 2009a, 2009b). The purpose ofthe present paper is to investigate effects of mutual transits by extrasolar planet-companionsystems on light curves, especially how the effects depend on their spin velocity relative to theirorbital one around their parent star. Furthermore, we shall discuss extrasolar mutual tra nsits asa complementar y metho d of measuring the system’s parameters such as a planet-companion’sseparation a nd thereby identifying them as a true binary, planet-satellite system or others.Our treatment is applicable both to a true binary and to a planet-satellite system. Ourmethod has analogies in classical ones for eclipsing binaries (e.g., Binnendijk 1960, Aitken 1964).A major difference is that geometrical blocking of one faint object by the other transiting aparent star causes an apparent increase in light curves, whereas eclipsing binaries make adecrease.


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