Microlensing Planet Detections

Table 3.1 summarizes the properties of the planets discovered by microlensing to date, including four published microlensing exoplanet discoveries (Bond et al., 2004; Udalski et al., 2005; Beaulieu et al., 2006; Gould et al., 2006) plus a 2-planet system that will soon be published (Gaudi et al. 2007, Bennett et al. 2007, both in preparation). The microlensing discoveries are compared to other known exoplanets in Fig. 3.9.

The first planet discovered by microlensing is shown in Fig. 3.10. The light curve is plotted in units of the source star flux, which is determined by the best microlensing model to the event, because the star field is too crowded to determine the unmagnified stellar flux directly. This event was first discovered by the OGLE group and announced via their "early warning system" as event OGLE-2003-BLG-235 on 2003 June 22. On 2003 July 21, the alert system of the MOA-I microlensing survey detected this event and reported it as MOA-2003-BLG-53. The MOA detection came later because the MOA-I telescope had only a 0.61 m aperture and has worse seeing conditions than are typical at the 1.3 m OGLE telescope in Chile. However, the MOA telescope had a larger field-of-view (FOV), and this enabled them to image each of their survey fields ~ 5 times per clear night. As a result, MOA was able to detect the second caustic crossing for this event, and arrange for the additional observations that caught the caustic crossing endpoint (thanks to first author, Ian Bond, who was monitoring the photometry in real time).

The naming convention for planets discovered is that the name from the first team to find the microlensing event is used for the event, so in this case OGLE-

Exoplanet Discovery Potential

Exoplanet Discovery Potential

Fig. 3.9. The sensitivity of various exoplanet detection methods is plotted in the mass vs. semi-major axis plane. Doppler radial velocity detections are shown in black, with 1-sided error bars for the m sin i uncertainty. Planets first detected by transits are shown in blue, and the microlensing planet discoveries are shown in red. The gold, cyan and green shaded regions show the sensitivity of the radial velocity method and NASA's Kepler and SIM missions, respectively. The light red and red curves show the sensitivity of current and future microlensing planet search programs, and the purple curve gives the sensitivity of the proposed Microlensing Planet Finder (MPF) mission.

Fig. 3.9. The sensitivity of various exoplanet detection methods is plotted in the mass vs. semi-major axis plane. Doppler radial velocity detections are shown in black, with 1-sided error bars for the m sin i uncertainty. Planets first detected by transits are shown in blue, and the microlensing planet discoveries are shown in red. The gold, cyan and green shaded regions show the sensitivity of the radial velocity method and NASA's Kepler and SIM missions, respectively. The light red and red curves show the sensitivity of current and future microlensing planet search programs, and the purple curve gives the sensitivity of the proposed Microlensing Planet Finder (MPF) mission.

2003-BLG-235 takes precedence over MOA-2003-BLG-53. When referring to the lens system, we add a suffix "L", and when referring to the source, we add an "S". For a lens or source system that is multiple, we add an additional capital letter suffix for a stellar mass object or a lower case letter for a planetary mass companion. So, 0GLE-2006-BLG-109LA, 0GLE-2006-BLG-109Lb, and 0GLE-2006-BLG-109Lc, refer to the star and two known planets of the 0GLE-2006-BLG-109 lens system. This convention provides names for multiple components of the source star system. For example, 0GLE-2022-BLG-876Sb would refer to a planetary companion to the source star which would be difficult, but not impossible (Graff & Gaudi, 2000; Lewis, 2001) to detect.

It is interesting to note that this event was discovered by a procedure that differs from both the alert-plus-follow up strategy suggested by Gould & Loeb (1992) and the high magnification strategy suggested by Griest & Safizadeh (1998). Instead, the planetary deviation was detected in the observations of one of the survey teams, and identified in time to obtain additional data to confirm the planetary nature of

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Fig. 3.10. The OGLE-2003-BLG-235/MOA-2003-BLG-53 light curve with OGLE data in red and MOA data in blue. The top-left panel presents the complete data set during 2003 (main panel) and the 2001-2003 OGLE data (inset). The median errors in the OGLE and MOA points are indicated in the legend. The bottom panel is the same as the top panel, but with the MOA data grouped in 1 day bins, except for the caustic crossing nights, and with the inset showing MOA photometry during 2000-2003. The binary- and single-lens fits are indicated by the solid black and cyan dashed curves, respectively. The right panel shows the light curve and models during caustic traverse. These models are the single-lens case (cyan, long-dashed curve), the best binary lens with q > 0.03 (magenta, short-dashed line), the planetary lens with caustic entry before day 2835 (green, dotted, line), and the best overall fit with q = 0.0039(black, solid line). The insets show the second caustic crossing and a region of the declining part of the light curve where the best-fit nonplanetary binary-lens model fails to fit the data. MOA data on days other than the caustic entry and exit (days 2835 ± 0.5 and 2842 ± 0.5) are placed in 1 day bins.

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Fig. 3.10. The OGLE-2003-BLG-235/MOA-2003-BLG-53 light curve with OGLE data in red and MOA data in blue. The top-left panel presents the complete data set during 2003 (main panel) and the 2001-2003 OGLE data (inset). The median errors in the OGLE and MOA points are indicated in the legend. The bottom panel is the same as the top panel, but with the MOA data grouped in 1 day bins, except for the caustic crossing nights, and with the inset showing MOA photometry during 2000-2003. The binary- and single-lens fits are indicated by the solid black and cyan dashed curves, respectively. The right panel shows the light curve and models during caustic traverse. These models are the single-lens case (cyan, long-dashed curve), the best binary lens with q > 0.03 (magenta, short-dashed line), the planetary lens with caustic entry before day 2835 (green, dotted, line), and the best overall fit with q = 0.0039(black, solid line). The insets show the second caustic crossing and a region of the declining part of the light curve where the best-fit nonplanetary binary-lens model fails to fit the data. MOA data on days other than the caustic entry and exit (days 2835 ± 0.5 and 2842 ± 0.5) are placed in 1 day bins.

the light curve deviation. We will return to this strategy later in the discussion of future microlensing projects given in Sect. 3.6.1.

Another notable feature of this event is that the lens star has been identified in HST images (Bennett et al., 2006). As indicated in Fig. 3.7, there is an extra source of light superimposed at the location of the source star. This is very likely to be the lens star, and if so, the HST photometry implies that a fraction, flens = 0.18 ± 0.05, of the total source plus lens flux comes from the lens. During the microlensing event, the lens and source were separated by < 0.1 mas, but by the time of the HST images, At = 1.78 years after peak magnification, the lens-source separation should have grown to At^rel = 5.9 ± 0.7mas. (/i,rel = 3.3 ± 0.4mas/yr was determined from eq. 3.16 with input parameters from the light curve model.) This separation, plus the mass-distance relation, eq. 3.17, enable to derivation of the curves shown in the bottom left panel of Fig. 3.7. These show the amplitude for the offset of the centroids of the blended lens plus source images in different color bands. The HST data indicate a marginal detection of this color-dependent centroid shift at a level consistent with the assumption that the excess flux is due to the lens.

Star-Planet^ Separation J

Star-Planet^ Separation J

Microlensing Source

Fig. 3.11. Bayesian probability densities for the properties of the planet, OGLE-2003-BLG-235Lb, and its host star if it is a main sequence star. (a) The masses of the lens star and its planet (Mt 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).

Fig. 3.11. Bayesian probability densities for the properties of the planet, OGLE-2003-BLG-235Lb, and its host star if it is a main sequence star. (a) The masses of the lens star and its planet (Mt 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).

With this marginal detection of the color-dependent centroid shift, we can't be absolutely sure that the lens star has been detected because it is possible that the excess flux could be due to a companion to the source star. It is straight forward to deal with this uncertainty with a Bayesian analysis (Bennett et al., 2006), and the results of such an analysis are shown in Fig. 3.11. The resulting most likely parameter values for the event parameters are a host star mass of M* = 0.63 +0 09M©, a planet mass of Mp = 2.6 +0 ' 8MJup, and an orbital semi-major axis of a = 4.3 +0 ' 8 AU. The distance to the lens system is DL = 5.8 +0 ' 7 kpc, and the lens star magnitude is

The light curve of the second planet discovered by microlensing, OGLE-2005-BLG-71Lb, is shown in Fig. 3.12 (Udalski et al., 2005). This was a moderately high magnification event that would have reached a maximum magnification of Amax ~ 42 if the lens star had no planets. Because of the d ^ 1/d ambiguity discussed in Sect. 3.4, this event has two models that explain the major features of the light curve quite well. Fig. 3.3 shows the magnification patterns for these models, and for the trajectory of the lens, which is nearly perpendicular to the lens axis, the

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Fig. 3.12. The OGLE-2005-BLG-71 light curve showing the planetary anomaly near the peak. The triple peak (two large symmetric peaks surrounding a small peak) indicates that the source passed three cusps of a caustic, the middle one being weak (insets). The interval between peaks (and so cusps) is At = 3 days, implying that the companion mass must be small.

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Fig. 3.12. The OGLE-2005-BLG-71 light curve showing the planetary anomaly near the peak. The triple peak (two large symmetric peaks surrounding a small peak) indicates that the source passed three cusps of a caustic, the middle one being weak (insets). The interval between peaks (and so cusps) is At = 3 days, implying that the companion mass must be small.

light curves for these different models are quite similar. From Udalski et al. (2005) the physically interesting parameters of the best fit models are tE = 70.9 ± 3.3, q = 7.1 ±0.3 x 10^3, and d = 1.294±0.002 for the "wide" model and tE = 73.9±3.5, q = 6.7 ± 0.3 x 10~3, and d = 0.758 ± 0.002 for the "close" model. However, the x2 difference between these two models is A\2 = XciOSe — Xwide = 22.0, so the "wide" model is strongly preferred.

OGLE-2005-BLG-71Lb was the first planet discovery with significant contributions from amateur astronomers, with critical observations near the two strong cusp approach peaks by Grant Christie of the Auckland Observatory and Jennie McCormick of the Farm Cove Observatory.

With a mass ratio of q = 7.1 ±0.3 x 10~3, OGLE-2005-BLG-71Lb must certainly be a gas giant planet, but without further information such as measurement of finite

Fig. 3.13. The observed light curve of the OGLE-2005-BLG-390 microlensing event and best-fit model plotted as a function of time. The data set consists of 650 data points from PLANET Danish (red points), PLANET Perth (blue), PLANET Canopus (Hobart, cyan), RoboNet Faulkes North (green), OGLE (black), and MOA (brown). The top left inset shows the OGLE light curve extending over the previous 4 years, whereas the top right one shows a zoom of the planetary deviation, covering a time interval of 1.5 days. The solid curve is the best binary lens model described in the text with q = 7.6 ± 0.7 x 10~B, and a projected separation of d = 1.610 ± 0.008Re■ The dashed grey curve is the best binary source model that is rejected by the data, and the dashed orange line is the best single lens model.

source effects, the detection of the lens star or a measurement of the microlensing parallax effect, we cannot determine the properties of the host star or the planetary mass with much precision. Fortunately, we are able to detect the lens star in a set of HST images, and the light curve yields weak detections of both a finite source size and the microlensing parallax effect. So, we expect to determine the host star and planet masses and to convert their separation into physical units, but this analysis is not yet complete (Dong et al 2007, in preparation).

The first low-mass planet discovered by microlensing was OGLE-2005-BLG-390Lb (Beaulieu et al., 2006), led by the PLANET Collaboration. This planet is currently tied with G1 581c (Udry et al., 2007) as the lowest mass exoplanet orbiting a normal star yet to be discovered1. This event was detected through a planetary caustic deviation, and the amplitude of the deviation was significantly reduced by the finite angular size of the clump giant source star. If the planet were smaller by a factor of ~ 2, it would not have been detected in this event. As originally pointed xThe minimum mass of Mp > 5.03M® is often quoted for G1 581c, but the Mp sin i ambiguity of the radial velocity method implies that the median predicted mass is Mp = 5.5M®. This is the appropriate number to compare to other detection methods.

Microlensing Source

Fig. 3.13. The observed light curve of the OGLE-2005-BLG-390 microlensing event and best-fit model plotted as a function of time. The data set consists of 650 data points from PLANET Danish (red points), PLANET Perth (blue), PLANET Canopus (Hobart, cyan), RoboNet Faulkes North (green), OGLE (black), and MOA (brown). The top left inset shows the OGLE light curve extending over the previous 4 years, whereas the top right one shows a zoom of the planetary deviation, covering a time interval of 1.5 days. The solid curve is the best binary lens model described in the text with q = 7.6 ± 0.7 x 10~B, and a projected separation of d = 1.610 ± 0.008Re■ The dashed grey curve is the best binary source model that is rejected by the data, and the dashed orange line is the best single lens model.

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Caustic Exoplanets
Fig. 3.14. Comparison of the OGLE-2005-BLG-390Lb planetary caustic (the black diamond shaped curve) with the source star size (black circle). The black line with the arrow show the motion of the source star.

out in Bennett & Rhie (1996) and discussed in Sect. 3.3.3, a microlensing search for Earth-mass planets should focus on events with main sequence source stars.

The OGLE-2005-BLG-390Lb light curve deviation does not show the characteristic features of a fold caustic crossing, like OGLE-2003-BLG-235, or of a cusp approach, like OGLE-2005-BLG-71. This is because the planetary caustic is smaller than the source star's angular radius of 9* = 5.3 ± 0.7pas, as shown in Fig. 3.14. Because the light curve does not show these characteristic binary-microlensing features, we must consider a non-planetary explanation for the light curve involving the lensing of a binary source star by a single star lens. Gaudi (1998). However, as the Fig. 3.13 shows, a binary source model is a poor fit to the data, as it fails to account for the Perth and Danish data near the end of the perturbation. Formally, the binary source model increases the fit x2 by A\2 = 46.25 with one fewer degree of freedom. These data are also sufficient to avoid a possible degeneracy in the planetary parameters for such events that occurs when the wings of the deviation are poorly sampled (Gaudi & Gould, 1997).

The microlensing model for this event directly determines the planet-star mass ratio, q = 7.6 ± 0.7 x 10~5, the projected planet-star separation, d = 1.610 ± 0.008, the Einstein radius crossing time, tE = 11.03 ± 0.11 days, and the source radius crossing time, i* = 0.282 x 0.010 days. With the value for 9* mentioned above, this yields the angular Einstein radius, 9E = 0.21 ± 0.03 mas, from eq. 3.16 and the mass-distance relation from eq. 3.17. This mass-distance relation can be combined with a standard Galactic model in a Bayesian analysis to estimate the probability distribution of the lens system parameters (Alcock et al., 1995, 1996; Poindexter et al., 2005; Dominik, 2006). The results of such an analysis are shown in Fig. 3.15 following the method of Dominik (2006), and nearly identical results are obtained using the Galactic model and mass function parameters of Bennett & Rhie (2002). This analysis gives a 95% probability that the planetary host star is a main-sequence

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Fig. 3.15. Bayesian probability densities for the properties of the planet and its host star: (a), the masses of the lens star and its planet (M* and Mp respectively), (b), their distance from the observer Dl, (c), the three dimensional separation or semi-major axis a of an assumed circular planetary orbit; and (d), the orbital period O of the planet. The bold, curved line in each panel is the cumulative distribution, with the percentiles listed on the right. The dashed vertical lines indicate the medians, and the shading indicates the central 68.3% confidence intervals, while dots and arrows on the abscissa mark the expectation value and standard deviation. The medians of these distributions yield a Mp = 5.5 M® planetary companion at a separation of d = 2.6 AU from a M* = 0.22 Mq Galactic Bulge M-dwarf at a distance of Dl = 6.6±l.Okpc from the Sun. The median planetary period is O = 9 years.

star, a 4% probability that it is a white dwarf, and a probability of,l% that it is a neutron star or black hole. The median parameters shown in Fig. 3.15 imply that the planet receives radiation from its host star that is only 0.1% of the radiation that the Earth receives from the Sun, so the probable surface temperature of the planet is 50 K, similar to the temperature of Neptune.

As discussed in Sect. 3.4.1, the lens star mass can be determined directly if the lens star is detected. However, this will be quite difficult for OGLE-2005-BLG-390L, because the source is a giant star. For the median mass and distance to the lens system, the lens star would be fainter than the source by a factor of 2000 in the ^-band. So, the detection of the lens star may require many years for the relative proper motion of prei = 6.8mas/yr, and the development of new instruments for large ground-based or space telescopes.

OGLE-2005-BLG-169 was the third published event from the 2005 season and the second low-mass planet found by microlensing (Gould et al., 2006). This was a very high magnification event, with a peak magnification of Amax ^ 800, and

OGLE (Chile) iiFUN (Chile) juFUN (MDM, Arizona) juFUN (Auckland, NZ) RoboNet (Hawaii)

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