O

Fig. 3.16. Top: Data and best-fit model for OGLE-2005-BLG-169. Bottom: Difference between this model and a single-lens model with the same single lens parameters (to, uo, tE, and p). It displays the classical form of a caustic entrance/exit that is often seen in binary microlensing events, where the amplitudes and timescales are several orders of magnitude larger than seen here. MDM data trace the characteristic slope change at the caustic exit (At = 0.092) very well, while the entrance is tracked by a single point at At = —0.1427. The dashed line indicates the time to. Inset: Source path through the caustic geometry. The source size, p, is indicated.

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caustic it's light curve is shown in Fig. 3.16. The bottom panel of Fig. 3.16 indicates that the planetary deviation has a maximum amplitude of about 4% compared to the light curve of the same event without a planet. Such low amplitude deviations are characteristic of the very weak caustics due to low-mass planets near the Einstein ring. However, it is only part of the caustic curve that is so weak. If the source would have passed on the other side of the host star and crossed the backwards "C" shaped part of the caustic in the inset of Fig. 3.16, the planetary signal would have been very much stronger. But, it order to detect the low amplitude signal due to the caustics actually crossed by the source star, it was quite helpful to have continuous observations over the course of three hours from the 2.4 m MDM telescope.

The analysis of Gould et al. (2006) indicated a super-Earth mass planet with Mp = 13 M® orbiting a star of M* ~ 0.49M©. Such a planet, like OGLE-2005-BLG-390Lb, would be invisible to other planet detection methods. High magnification events also place tight constraints on the presence of additional planets, and in the case of OGLE-2005-BLG-169, Jupiter-mass planets can be exclude from the separation range 0.6-18 AU and Saturn-mass planets can be excluded from the range 1-11 AU.

The precise masses of the host star and planet have not yet been determined because the host star has not been detected. Thus, the lens system properties can only be determined by a Bayesian analysis, as was done for OGLE-2005-BLG-390Lb in Fig. 3.15. This analysis uses the parameters from the microlensing light curve, including the Einstein radius crossing time of = 43 ± 1.3 days, the source radius crossing time of i* = 0.019 ± 0.01 days, and the lens-source relative proper motion of yU,rei = 8.4 ± 0.6mas/yr. The results of this analysis are presented in Fig. 3.17. These have assumed a Han-Gould model for the Galactic bar (Han & Gould, 1995), a double-exponential disk with a scale height of 325 pc, and a scale length of 3.5kpc, as well as other Galactic model parameters as described in Bennett & Rhie (2002).

Fig. 3.17. OGLE-2005-BLG-169 lens property figure. Bayesian probability densities for the properties of the planet and its host star if it is a main sequence star, (a) The masses of the lens star and its planet (M* and Mp respectively), (b) the separation, (c) their distance from the observer (Dl); and (d) the I-band brightness of the host star. The dashed vertical lines indicate the medians, and the shading indicates the central 68.3% and 95.4% confidence intervals. All estimates follow from a Bayesian analysis assuming a standard model for the disk and bulge population of the Milky Way, the stellar mass function of Bennett & Rhie (2002).

Because this model is different from the Galactic model used by Gould et al. (2006), the resulting parameters differ slightly from their results. We find a lens system distance of Dl = 2.7 ® kpc, a three dimensional star-planet separation of a = 3.3 _n'q AU and main sequence stellar and planetary masses of M, =0.52 M© and Mp = 14 Me. If we assume that white dwarfs have an a priori probability to host planets that is equal to that of main sequence stars (at the separations probed by microlensing), then there is a 35% probability that the host star is a white dwarf. The possibility of a brown dwarf host star is excluded by the light curve limits on the microlensing parallax effect (Gould et al., 2006).

Fig. 3.17(d) shows the probability distribution of the /-band magnitude of the planetary host star compared to the source star at I = 20.58 ± 0.10. The implied planetary host star brightness distribution has a median and 1-a range of /¡ens = 21.9 , but the most interesting feature of this figure is that the probability of a main sequence lens fainter than I = 23 vanishes. This is because the mass-distance relation, eq. 3.17 ensures that the lens star will be nearby and at least at bright as I = 23, even if it is at the bottom of the main sequence at M* = 0.08M©. In fact, the microlensing parallax constraint from the light curve yields a lower limit for the lens star mass of M* ^ 0.14M©. Thus, the planetary host star must be at least 16% of the brightness of the combined lens plus source star blended image, and this implies that it will be detectable if it is not a stellar remnant. Plus, the relatively rapid relative proper motion, = 8.4 ± 0.6mas/yr, of OGLE-2005-BLG-169L, implies that the lens-source separation is already detectable with HST (Bennett et al., 2007a), as discussed in Sect. 3.4.1.

One of the most interesting consequences of the discoveries of OGLE-2005-BLG-390Lb and 169Lb is that super-Earth planets of ~ 5-15M© are likely to be quite common. Gould et al. (2006) combined these detections with null results from very high magnification events (Abe et al., 2004; Dong et al., 2006) plus samples of lower magnification events (Albrow et al., 2001; Gaudi et al., 2002) to solve for the fraction, /se, of stars with planets of mass ratio ~ 8 x 10~5 at the separations of 1.5-4 AU, where microlensing is most sensitive. They found that the median and 90% confidence level upper and lower limits are fse = 0.38 , based on the two planets discovered and the accumulated null results. The 90% c.l. lower limit is fse > 16%. This is significantly higher than the fraction of F, G, and K stars with Jupiter-mass planets in this 1.5-4 AU separation range. This fraction of stars with Jupiters at this separation can be estimated from Butler et al. (2006) to be /j ^ 3%. Thus, these cool, super-Earth planets appear to represent the most common type of exoplanet yet discovered. This would seem to confirm the prediction of the core-accretion theory that ~ 10M© planets form much more frequently than gas giants, like Jupiter (Ida & Lin, 2004; Laughlin, Bodenheimer & Adams, 2004), although this may not be incompatible with the disk instability theory (Boss, 2006).

The final event that we will present is OGLE-2006-BLG-109, which is much more complicated than the other events (Gaudi et al. 2007; Bennett et al. 2007, both in preparation). The light curve for this event is shown in Fig. 3.18, while the central caustic configuration is shown in Fig. 3.19. This is the first microlensing event with

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Fig. 3.18. Two views of the OGLE-2006-BLG-109 light curve, which is the first multiplanet microlensing event with a planet of slightly less than a Jupiter mass (q = 1.35 x 10~3 at ~ 2.7 AU and a planet of slightly more than a Saturn mass (q = 4.9 x 10~4) at - 5.4AU. The signal is dominated by the Saturn-mass planet because it is close to the Einstein ring at d = 1.4, and there are two pairs of caustic crossing features (at t = 3822.5, 3822.9 and t = 3830.2, 3831.2) and a cusp approach (at t = 3834.1) due to the Saturn-mass planet. The Jupiter-mass planet planet is further from the Einstein ring at d = 0.63, so its signal is limited to the highest magnification part of the light curve and is responsible for the cusp approach feature at t = 3831.65. Both planetary orbital motion and microlensing parallax must be included to obtain an acceptable model for this event.

two detected planets, and it also shows clear signals of planetary orbital motion and microlensing parallax. These effects are detectable because the Saturn-mass planet has a projected separation that is close to the Einstein ring, which causes its caustic to become quite extended. Its effects are visible for 11 days.

Another notable feature of OGLE-2006-BLG-109 is that the lens is > 5 times brighter than the source. It is detectable (although not completely resolved) in the best seeing (0.7") OGLE images and is clearly visible in K and ff-band adaptive optics images from the Keck telescope. As a result, there are two methods to determine the lens star mass: the combination of the Oe determination from the finite source effects and the microlensing parallax effect yields the lens mass via eq. 3.19, while the lens star detection give the lens mass with the help of mass-luminosity relations, as discussed in Sect. 3.4.1. However, one complication is that there is some degeneracy in the effects of microlensing parallax and the planetary orbital motion on the microlensing light curve. On the other hand, the planetary orbital motion parameters yield information about the orbits that haven't been detected before in a microlensing event. So, this event will yield much more information about the OGLE-2006-BLG-109L planetary system than was anticipated for any planetary microlensing event.

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Fig. 3.19. The central caustic OGLE-2006-BLG-109 configuration for is shown at 3-day intervals from t = 3820 (shortly before the first caustic crossing) through t = 3835 (a day after the final cusp approach). The time-order of the different color caustic curves is red, magenta, green, black, cyan, blue. The grey curve is the source trajectory, which is curved due to the microlensing parallax effect (i.e. the orbital motion of the Earth) and the small circle that the source trajectory in the left, close-up panel shows the source star radius.

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Fig. 3.19. The central caustic OGLE-2006-BLG-109 configuration for is shown at 3-day intervals from t = 3820 (shortly before the first caustic crossing) through t = 3835 (a day after the final cusp approach). The time-order of the different color caustic curves is red, magenta, green, black, cyan, blue. The grey curve is the source trajectory, which is curved due to the microlensing parallax effect (i.e. the orbital motion of the Earth) and the small circle that the source trajectory in the left, close-up panel shows the source star radius.

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