Observations from Australasia using the Gravitational Microlensing Technique
Philip Yock
, PASA, 17 (1), 35.

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Contents Page: Volume 17, Number 1

Extra-Solar Planets

The study of extra-solar planetary systems is one of the more intriguing applications of the gravitational microlensing technique. This application was first proposed by Mao and Paczynski (1991). Several refinements have since been discussed (Gould & Loeb 1992; Bennett & Rhie 1996; Gaudi & Gould 1997; Wambsgnass 1997; Griest & Safizadeh 1998; Gaudi, Naber & Sackett 1998; Di Stefano & Scalzo 1999). The technique may be likened to Rutherford scattering, as shown in Figure 8. Whereas Rutherford used $\alpha$ particles to probe atomic structure, gravitational microlensers use photons to probe planetary structure, by searching for deviations from the light curve produced by a single lens. The technique is promising because, as is indicated in the figure, the region that is probed in microlensing lies a few AU from the parent star. In contrast, the complementary Doppler technique enjoys greatest sensitivity for planets at orbital radii <1 AU (Marcy & Butler 1998). Applications of the microlensing technique by the PLANET, MOA and MPS groups to events OGLE-98-BLG-14, MACHO-98-BLG-35 and MACHO-97-BLG-41 respectively are described below.

**Figure 8:** Comparison of Rutherford scattering and gravitational microlensing. The longitudinal scale has been compressed in the lower illustration. Note that the probe is decelerated by electrons in Rutherford scattering, but deflected by planets in gravitational microlensing.
$\begin{figure} \begin{center} \psfig{file=fig8.eps,height=7cm} \end{center} \end{figure}$

OGLE-98-BLG-14

The PLANET group made approximately 600 observations of OGLE-98-BLG-14 over a period of $\sim100$ days (Albrow et al. 1999b). The resulting light curve did not differ appreciably from that of a single lens, even though the estimated detection efficiency for a Jupiter-like planet in the event was $\sim$ 60%. Thus, although Jupiter analogues could not be ruled out in this event, the detection efficiency was high enough to ensure that future non-detections in similar events would suffice to constrain the abundance of Jupiter-like planets in the galactic bulge. A significant result was obtained for OGLE-98-BLG-14 on the presence of planets heavier than Jupiter. It was found that 'super-Jupiters' with planet-to-star mass ratios

$\epsilon>10^{-2}$ and orbital radii in the range (0.4-2.4)R_E could be excluded with 95% confidence. Here R_E denotes the Einstein radius for the event¹.

MACHO-98-BLG-35

A significant refinement to the original proposal for planet hunting by Mao and Paczynski (1991) was made by Griest and Safizadeh (1998). They found that in microlensing events with high peak amplification, >20, a planet always perturbs the light curve near its peak. This happens because the planet produces a small, stellar caustic around the lens, and the source approaches this caustic at the time of peak magnification. The perturbation to the light curve calculated by Griest and Safizadeh is detectable with high probability for Jupiter-like planets, and, depending on the geometry of the event, detectable with finite probability for lighter planets. Because the time of peak magnification of a microlensing event is generally known in advance, the finding by Griest and Safizadeh appeared to offer a systematic strategy for detecting planets. An opportunity arose to test the above strategy with event MACHO-98-BLG-35. This reached a peak magnification $\sim80$ . The peak of the event was monitored by the MPS and MOA groups (Rhie et al. 1999). Their light curves are shown in Figure 9. These include the best fit to the data assuming a lens with and without a planet. The parameters for the best fit with a planet were obtained with a planet mass ratio

$\epsilon =7\times 10^{-5}$ and an orbit radius of 1.35R_E. Assuming a typical value for the lens mass

$\sim0.3M_{\odot}$ , these parameters correspond to a planet with mass between about that of Earth and about twice that of Neptune at an orbit radius of a few AU. The formal significance of the detection is at the $\sim4.5\sigma$ level.

**Figure 9:** Peak structure of event MACHO-98-BLG-35 as determined by the MPS and MOA groups (Rhie et al. 1999). The error bars are those returned by the DoPHOT point-spread-function fitting routine (Schechter, Mateo & Saha 1993) with 1% added in quadrature to allow for possible flat fielding and similar errors that are not included in the DoPHOT routine. The pale curve is the best fit to the data for a lens without a planet, and the heavy curve is the best fit for a lens with a single planet with mass fraction
$\epsilon =7\times 10^{-5}$ and orbit radius = 1.35 Einstein radii.
$\begin{figure} \begin{center} \psfig{file=fig9.ps,height=9cm} \end{center} \end{figure}$

Figure 10 shows the same data as Figure 9 but plotted as a ratio to the best fit single lens light curve. Fig. 11 shows exclusion regions, at the $6.3\sigma$ confidence level, for planets with various masses. These were calculated by comparing the observed light curves for the event with expected light curves for a dense sampling of possible planetary configurations (Rhie et al. 1999). A Solar System analogue is excluded at the 90% confidence level. In 88% of the cases, a Jupiter-like planet would have been detected, and in 19% of the cases a Saturn-like planet would have been detected. Peale (1997) has proposed the existence of planetary systems in which Jupiter and Saturn are replaced with Neptune-like planets. It is possible that this observation represents the first detection of such a system.

**Figure 10:** The same data as in Figure 9 but plotted as a ratio to the best fit to the data for a lens without a planet.
$\begin{figure} \begin{center} \psfig{file=fig10.ps,height=8cm} \end{center} \end{figure}$

The light curves of the MPS and MOA groups for the peak of MACHO-98-BLG-35, shown above in Figs. 9 and 10, include measurements made at larger-than-normal air masses, up to air mass = 3. The data of both groups were examined for associated deleterious effects. In the case of the MPS data this was explicitly reported in the primary publication (Rhie et al. 1999). In the case of the MOA data, light curves of nearby stars of similar colour, crowdedness and magnitude were examined using the same DoPHOT point-spread-function fitting routine that had been used for MACHO-98-BLG-35. It was found that the formal DoPHOT error bars tended to overestimate the statistical errors of check stars, but that a slowly varying systematic error <1.0% could have been present. This appeared to be too slowly varying and too small to account for the putative planetary deviation seen at UT $\approx$ 4.6 on Fig. 10. It was allowed for by Rhie et al. (1999) by adding 1% in quadrature to the formal DoPHOT errors.

**Figure 11:** Exclusion regions at the 6.3 $\sigma$ level of confidence for event MACHO-98-BLG-35 in the lens plane for planets with various mass-fractions ranging from Earth-mass (
$\epsilon = 3 \times 10^{-6}$ ) to three times the mass of Jupiter (

$\epsilon = 3 \times 10^{-3}$ ). The data are from Rhie et al. (1999). The exclusion region for an Earth-mass planet is the dark, nearly-circular region at the Einstein radius (r = 1 R_E). The exclusion regions for heavier planets are successively larger regions surrounding this. The horizontal axis denotes the track of the source star, from right to left.
$\begin{figure} \begin{center} \psfig{file=fig11.ps,height=18cm} \end{center} \end{figure}$

The PLANET collaboration also observed MACHO-98-BLG-35 near its peak (Greenhill 1999). It is hoped that their data will be used to check the above interpretation of the event.

MACHO-97-BLG-41

The microlens event MACHO-97-BLG-41 was monitored by several groups because the light curve showed anomalous behaviour at an early stage, not dissimilar to that expected for a Jupiter-like planet (Glanz 1997). Recently, three analyses of the event have been reported. The MACHO and GMAN groups reported that single-lens and (static) binary-lens models could not reproduce their data (Alcock et al. 1999). Subsequently, the MPS group in association with a Wise Observatory team proposed a model of the event in which the lens is assumed to be a planet orbiting a binary star (Bennett et al. 1999). According to this model, the mass ratio of the binary star system is 3.8:1 and the stars are most likely to be a late K dwarf and an M dwarf with a separation of about 1.8 AU. A planet of about 3 Jupiter masses orbits this system at a distance of about 7 AU. Most recently, the PLANET group reported that their dataset, and those of the MACHO, GMAN, MPS and Wise groups, can be accounted for by a rotating binary lens in the Galactic disk with total mass

$M \sim 0.3 M_{\odot}$ (M-dwarf binary system) and period $P \sim 1.5$ yr. (Albrow et al. 1999c). The last proposal does not require the additional complication of a planet, and would seem appealing on the basis of Occam's Razor. Still further data for the event are available that were not included in the above modeling. It will be interesting to see if a global analysis can pin down the parameters of this interesting event more tightly. Several hundred observations were made of each of the above three events, OGLE-98-BLG-14, MACHO-98-BLG-35 and MACHO-97-BLG-41. For the first and last of these, the crucial observations extended over a period of about 100 days. For the high magnification event, MACHO-98-BLG-35, observations were made over a considerably shorter period without loss of sensitivity. This would appear to confirm the relatively good potential of the high magnification technique of Griest and Safizadeh (1998).