Properties of the planetary caustic perturbation

Chung-Uk Lee 0 0 Korea Astronomy and Space Science Institute , Hwaam-Dong, Yuseong-Gu, Daejeon 305-348, Korea A B S T R A C T Just two of 10 extrasolar planets found by microlensing have been detected by the planetary caustic, despite the higher probability of planet detection relative to the central caustic, which has been responsible for four extrasolar planet detections. This is because the perturbations induced by the planetary caustic are unpredictable, thus making it difficult to carry out strategic observations. However, if future high-cadence monitoring surveys are conducted, the majority of planetary caustic events including the events by free-floating planets and wide-separation planets would be detected. Hence, understanding the planetary caustic perturbations becomes important. In this paper, we investigate in detail the pattern of the planetary caustic perturbations. From this study, we find three properties of the planetary caustic perturbations. First, planetary systems with the same star-planet separation (s) basically produce perturbations of constant strength, regardless of the planet-to-star mass ratio (q), but the duration of each perturbation scales with q. Secondly, close planetary systems with the same separation produce essentially the same negative perturbations between two triangular-shaped caustics, regardless of q, but the duration of the perturbations scales with q. Thirdly, the positive perturbations for planetary systems with the same mass ratio become stronger as the caustic shrinks with the increasing |log s|, while the negative perturbations become weaker. We estimate the degeneracy in the determination of q that occurs in planetary caustic events. From this, we find that the mass ratio can be more precisely determined as q increases and |log s| decreases. We also find that the degeneracy range of events for which the source star passes close to the planetary caustic is usually very narrow, and thus it would not significantly affect the determination of q. - The microlensing signal of a planet is a short-duration perturbation on the smooth standard light curve of the primary-induced lensing event occurring on a background source star. The planetary perturbation is induced by the central and planetary caustics, which are typically separated from each other. The central caustic is always formed close to a host star and thus the perturbation induced by the central caustic occurs near the peak of the lensing light curve. In events induced by the central caustic, there exists a s 1/s degeneracy, where s represents the projected starplanet separation normalized to the Einstein radius of the lens system (Griest & Safizadeh 1998; Dominik 1999). The degeneracy arises due to the similarity in the size and shape of the central caustics for s and 1/s. Since the difference in the size and shape of the two central caustics increases as the planet-to-star mass ratio increases, the degeneracy can be broken for events involving giant planets (Chung et al. 2005). High-magnification events for which the source star passes close to the host star are very sensitive for the detection of a planet due to the central caustic (Griest & Safizadeh 1998). Thus, present microlensing follow-up observations (FUN: Dong et al. 2006; PLANET: Albrow et al. 2001; RoboNet: Burgdorf et al. 2007), which intensively monitor events alerted by microlensing survey observations (OGLE: Udalski 2003; MOA: Bond et al. 2002), are biased towards high-magnification events. Due to the reason, four of 10 extrasolar planets found by microlensing (Udalski et al. 2005; Bennett et al. 2008; Gaudi et al. 2008; Dong et al. 2009) were detected by the central caustic. On the other hand, the planetary caustic is formed away from the host star and thus the perturbation induced by the planetary caustic can occur at any part of the lensing light curve. The planetary caustic is much bigger than the central caustic, and thus the probability of detecting a planet by the planetary caustic is much higher than by the central caustic. In spite of the advantage of high detection efficiency, only two of 10 microlensing extrasolar planets (Beaulieu et al. 2006; Sumi et al. 2010) were detected by the planetary caustic. This is because it is hard to carry out strategic observations due to the unpredictable nature of the planetary caustic perturbation. However, if future ground- and space-based surveys with high-cadence monitoring, such as Korean Microlensing Telescope Network (KMTNet; B. Park 2010, private communication) and Microlensing Planet Finder (MPF; Bennett et al. 2004), are conducted, the majority of the planetary caustic events, including the events by free-floating planets and wide-separation planets, would be detected. Hence, understanding the planetary caustic perturbations becomes important. In addition, for the planetary caustic events, there is a degeneracy in the determination of the planet-to-star mass ratio (Gould & Loeb 1992; Gaudi & Gould 1997), which is derived from the duration of the planetary caustic perturbation relative to the total duration of the event. To find out how much the degeneracy affects the determination of the planet-to-star mass ratio, the estimation of the degeneracy is needed. In this paper, we investigate in detail the pattern of the planetary caustic perturbations and estimate the degeneracy in the determination of the planet-to-star mass ratio in planetary caustic events. This paper is organized as follows. In Section 2, we briefly describe the planetary lensing. In Section 3, we investigate perturbation patterns of the planetary caustics for various planetary systems. We also estimate the degeneracy in the planet-to-star mass ratio in the planetary caustic events. We summarize the results in Section 4. 2 P L A N E TA R Y L E N S I N G Planetary lensing is described by the special case of binary lensing with very low mass ratio, and the lensing behaviour is usually well described by that of a single lensing of the host star for most of the event duration. In this case, the lens equation (Witt 1990) is expressed as where = + i and z = x + iy represent the complex notations of the source and image positions, respectively, z denotes the complex conjugate of z, zp is the position of the planet and q is the planet-tostar mass ratio. Here the position of the star is at the centre and all lengths are normalized to the Einstein ring radius of the total mass of the lens system, E. In planetary lensing, the shape and number of the planetary caustics depend on the starplanet separation, unlike the central caustics, which are always single and arrow shaped. For close planets (s < 1), there are two triangular-shaped caustics with three cusps. The two caustics are symmetrically displaced perpendicular to the star planet axis and located at the opposite sides to the planet. The horizontal and vertical widths of the caustic, defined as the separations between the on- (...truncated)