Detection probability of a low-mass planet for triple lens events: implication of properties of binary-lens superposition

Y.-H. Ryu H.-Y. Chang M.-G. Park 0 Department of Astronomy and Atmospheric Sciences, Kyungpook National University , Daegu 702-701, Korea 1 Department of Physics, Chungbuk National University , Cheongju 361-763, Korea A B S T R A C T In view of the assumption that any planetary system is likely to be composed of more than one planet, and that a multiple planet system with a large-mass planet has a greater chance of detailed follow-up observations, the multiple planet system may be an efficient way to search for sub-Jovian planets. We study the central region of the magnification pattern for the triple lens system composed of a star, a Jovian mass planet and a low-mass planet to answer the question of if the low-mass planet can be detected in high-magnification events. We compare the magnification pattern of the triple lens system with that of a best-fitted binary system composed of a star and a Jovian mass planet, and check the probability of detecting the low-mass secondary planet whose signature will be superposed on that of the primary Jovian mass planet. Detection probabilities of the low-mass planet in the triple lens system are quite similar to the probability of detecting such a low-mass planet in a binary system with a star and only a low-mass planet, which shows that the signature of a low-mass planet can be effectively detected even when it is concurrent with the signature of the more massive planet, implying that the binary superposition approximation works over a relatively broad range of planet mass ratio and separations, and the inaccuracies thereof do not significantly affect the detection probability of the lower-mass secondary planet. Since the signature of the Jovian mass planet will be larger and lasting longer, thereby warranting more intensive follow-up observations, the actual detection rate of the low-mass planet in a triple system with a Jovian mass can be significantly higher than that in a binary system with a low-mass planet only. We conclude that it may be worthwhile to develop an efficient algorithm to search for 'super-Earth' planets in the paradigm of the triple lens model for high-magnification microlensing events. - To detect and characterize extrasolar planets various techniques have been employed so far, which include the radial velocity technique (Mayor & Queloz 1995), the transit method (Charbonneau et al. 2007), direct imaging (Chauvin et al. 2004), pulsar timing analysis (Wolszczan & Frail 1992) and microlensing (Bond et al. 2004; Udalski et al. 2005; Beaulieu et al. 2006; Gould et al. 2006; Bennett et al. 2008; Gaudi et al. 2008; Dong et al. 2009; Janczak et al. 2010; Sumi et al. 2010). Compared to other techniques, the microlensing method has the important advantage of being applicable to planets to which other methods are generally insensitive; E-mail: (Y-HR); (H-YC); (M-GP) Corresponding author. the microlensing technique is sensitive to detecting low-mass planets and cool planets, or even free-floating planets (Bennett & Rhie 2002; Han et al. 2004, 2005). This sensitivity is very important for testing the core accretion theory of planet formation, which predicts that the dominant planets in any planetary system should form in the vicinity of the snow line, which is located at a few au from the host star (Laughlin, Bodenheimer & Adams 2004; Ida & Lin 2005; Kennedy, Kenyon & Bromley 2006). When a microlensing event occurs in a planetary system, the planetary signal appears as a short-duration perturbation to the standard light curve induced by the lens star (Mao & Paczynski 1991; Gould & Loeb 1992; Bennett & Rhie 1996). The planetary lensing signal induced by a planet with the mass of Jupiter lasts for a duration of 1 d and that by a planet with the mass of the Earth lasts 1.5 h. Therefore, the discovery of a terrestrial planet would only be possible by high-cadence anomaly monitoring. In fact, the detection of a significant number of terrestrial extrasolar planets requires well-coordinated efforts involving a network (e.g. MOA-II: Sumi et al. 2010; OGLE-IV: Udalski et al. 2005). MOA-II has reported two low-mass planets with their survey, MOA-2007-BLG-192Lb (Bennett et al. 2008) and OGLE-2007-BLG-368Lb (Sumi et al. 2010), and is preparing one, MOA-2009-BLG-266Lb (in preparation). The planetary perturbation occurs when the source star crosses the caustic or passes close to it. Caustic-crossing events cause conspicuous double-peaks over the smooth light curve induced by a lensing star. However, the perturbations due to caustic-crossing occur without any prior warning so that the current microlensing follow-up observations are focused on high-magnification events for the sake of practicality. For high-magnification events, the source trajectories always pass close to the perturbation region around the central caustic induced by the planet and thus the timing can be predicted fairly accurately (Griest & Safizadeh 1998; Han & Kim 2001; Bond et al. 2002; Rattenbury et al. 2002; Yoo et al. 2004). Griest & Safizadeh (1998) have shown that planets with masses as low as 10 M could be detected with significant probability in events with magnification of 50 by monitoring the peaks of the events with a photometric precision of 1 per cent. Rhie et al. (2000) have first showed that high-magnification events are sensitive to low-mass (Earth-mass) planets (for the lower limit of the planet mass most recently reported, see Yee et al. 2009). Since the discovery of the first extrasolar planet, orbiting a solartype star (Mayor & Queloz 1995), the Extrasolar Planet Encyclopedia1 lists 429 entries, including 45 multiple planetary systems, as of 2010 February 9. The detectable mass of exoplanets is becoming smaller and below the 10-M regime, with the discoveries of Gliese 876d with a mass of 7.5 M (Rivera et al. 2005); three planets around HD 40307 with masses of 4.2, 6.9 and 9.2 M (Mayor et al. 2009a); and Gliese 581e with a mass of 1.9 M (Mayor et al. 2009b) obtained using the radial-velocity technique, as well as OGLE 2005-BLG-390Lb detected by microlensing at a mass of 5.5 M (Beaulieu et al. 2006; Bennett et al. 2008). Many of the discovered super-Earth planets have been revealed through the close re-examination of planetary signals that have already proved the existence of their big brother. Considering that a planetary system is likely to be composed of more than one planet, this kind of strategy to find low-mass planets in the multiple planet systems may become an efficient way to search for terrestrial planets in the sense that it is easier to detect subtle signals when one knows what to look for. The magnification pattern due to the triple-lens systems is known to be well approximated by the superposition of the magnifications due to the planetary caustics (Han et al. 2001), or central caustics (Han 2005), of individual planets. Therefore, we may expect that the detection probability of low-mass planets in a triple system with a Jov (...truncated)