MOA-2010-BLG-523: "FAILED PLANET" = RS CVn STAR^*

High-magnification microlensing events provide a powerful tool for planet detection, partly because planets are more likely to perturb these events and partly because their high magnification (hence high signal-to-noise ratio, S/N) allows even very small perturbations to be detected. However, non-microlensing flux variations are also enhanced in these events. In this paper, we report on the discovery of an apparent planet candidate that turned out instead to be a highly magnified active star and discuss methods by which we identified and excluded this interloper.

Stars are intrinsically variable, and starspots can induce substantial light-curve variations in cool stars. However, for most G and K dwarfs this variability is manifested at a low level because magnetic activity decays quickly with age. Late M dwarfs can remain active for a Hubble time, but they are faint and will not be common microlensing sources. There is, however, an important sub-population of highly active RS CVn stars (Hall 1976) that are intrinsically luminous.

Magnetic activity is governed by the Rossby number (Noyes et al. 1984), R_O ≡ P/t_c, where P is the rotation period and t_c is the convective overturn timescale. Greater rotation (smaller P) induces faster buildup of magnetic fields. Deeper convection (bigger t_c) permits the fields to build up for a longer time before they propagate to the surface. In the R_O regime of interest here, the observed rms photometric variability A_r is a very steep function of 1/R_O (Hartman et al. 2009):

$$\begin{equation} A_r \propto R_O^{-3.5\pm 0.5}; \qquad R_O\equiv {P\over t_{\rm c}}. \end{equation} \tag{ 1 }$$

As stars leave the main sequence they will develop deep surface convection zones as they become cooler, but they will also expand substantially and slow down due to angular momentum conservation. Hence, some special circumstance is required to induce or permit relatively rapid rotation. There are three potential mechanisms. First, a K dwarf may find itself in a close binary (either by birth or through three-body interactions) and thus be spun up by tides. Second, an F or G dwarf may find itself in a wider binary that is not initially tidally interacting. But as the dwarf evolves into a K subgiant, its expanding radius enables tidal interactions with its companion that then spin up the subgiant. Finally, stars in a narrow range of masses, 1.25 M_☉ ≲ M ≲ 1.5 M_☉ (typically F dwarfs), can spend most of their lives spinning fairly rapidly because of their shallow convection zones and so are still spinning when they evolve into K subgiants. The lower mass limit is required for fast rotation to survive. Above the upper mass limit, stars evolve so rapidly through the Hertzsprung gap that they spend almost no time as subgiants. The resulting single-star RS CVn subgiants therefore span a narrow range of ages, 7 Gyr ≳ t ≳ 3 Gyr.

Here we report the detection of the first spectroscopically confirmed RS CVn star in the Galactic bulge. The detection was beyond serendipitous. It resulted from intensive spectroscopic and photometric observations of an extremely rare high-magnification microlensing event of a subgiant source. Only about 1 bulge subgiant per 100 million is so magnified each year. The intensive photometry was carried out to find planets (orbiting the lenses), while the high-resolution spectrum of MOA-2010-BLG-523S was obtained to study chemical abundances of bulge dwarfs and subgiants.

MOA-2010-BLG-523S is a subgiant, with a temperature T ∼ 5123 K and surface gravity log g = 3.6 (Bensby et al. 2011, 2013).⁶⁷ As such, either the second or the third mechanism of forming RS CVn stars should apply. That is, it is either in a binary that was "tidally activated" by the growth of the primary as it evolved along the subgiant branch, or it is an isolated, retired F dwarf. The mere existence of an isolated RS CVn star would be evidence for intermediate-age bulge stars. Of course, with just one detection, one could not make a reliable estimate of the fraction of bulge stars that are of intermediate age. But there are other lines of evidence for such a population, including age estimates of microlensed dwarfs and subgiants (Bensby et al. 2011) and asymptotic giant branch (AGB) stars (Cole & Weinberg 2002; van Loon et al. 2003; Uttenthaler et al. 2007). Thus, it would be of considerable interest to distinguish between the single-star and binary-star scenarios. Unfortunately, we find that both scenarios are plausible, given the available evidence, and so no definitive statement can be made regarding a putative intermediate-age population.

A major focus of this paper is the secure identification of the microlensed subgiant as an RS CVn star. However, the process of this discovery is of independent scientific interest. The event became a focus of attention because of deviations from standard microlensing seen over the peak. The I-band light curve was quite well fit by a planetary model and hence was far "along the road" to being published as a microlensing planet, in which case it would have been only the 14th such planet. It was really only very small discrepancies that led to the gradual unraveling of this picture and the recognition that the deviations at peak are most likely due to magnified starspots rather than a planet orbiting the lens star. The fact that irregular variability due to spots can be fit by planetary microlensing is sobering. As we discuss in Section 6, it implies that great care is required to securely identify microlensing planets in high-magnification events for cases of low-amplitude signals that lack clear microlensing signatures.

Microlensing event MOA-2010-BLG-523 ((R.A., Decl.) = (17:57:08.9, −29:44:58) (l, b) = (0.59, −2.58)) was alerted by the Microlensing Observations in Astrophysics (MOA; Bond et al. 2001; Sumi et al. 2011) collaboration at UT 08:46, 2010 August 21, and again 26.5 hr later as a potential high-magnification event that would peak at A_max ∼ 70 in 4 hr. In fact, the event continued to rise for another 36 hr, which triggered much more intensive observations. At UT 16:51 August 23, the Microlensing Follow Up Network (μFUN) issued a high-magnification alert, predicting a peak at UT 02:00–04:00, and on this basis contacted the Very Large Telescope (VLT) bulge-dwarf spectroscopy group, advocating observations in that time interval. At the same time, μFUN organized its own continuous photometric observations using the 1.3 m SMARTS telescope at CTIO to begin shortly after twilight. Very importantly in the present context, these observations were carried out with the ANDICAM camera, which is equipped with an optical/infrared (IR) dichroic, so that it can take images simultaneously in, e.g., I and H bands.

While the prediction of peak time turned out to be correct, VLT was unable to observe the event exactly when requested due to a conflict with technical activities, but it did make a 2 hr exposure (split in 4 × 30 minutes) with UVES on VLT beginning near twilight (UT 23:56). The main information on this spectrum has already been reported by Bensby et al. (2011).

There are two other very important data sets coming from the Optical Gravitational Lens Experiment (OGLE; Udalski et al. 1994; Udalski 2003). The event itself was monitored by OGLE-IV, which began operations in 2010 March. However, during 2010, OGLE-IV was in commissioning phase and so did not issue alerts. The data were first reduced in 2010 November. Unfortunately, the target falls in a gap between chips in the new 32-chip OGLE-IV camera, meaning that the target was captured only when small pointing errors moved the target onto a chip, which occurred about 1/3 of the time. Due to the high quality of OGLE data (and despite the reduced coverage), it was already evident that the source was a low-amplitude variable, and indeed it was checked (and confirmed) at the time of the image reductions that these variations were not due to chip-edge effects. Hence, A.U. had already suggested at this time that "the analysis of this object may be more complicated than expected."

The target also appears in OGLE-III, which took microlensing data from 2002 to 2009. In addition, it was in a field that was the subject of a special high-cadence 46 day campaign in 2001 whose aim was to find transiting planets, during which it was observed 786 times.

In addition, there were several other data sets, which in particular define the falling wing of the light curve extremely well. These include the RoboNet 2.0 m Faulkes North Telescope (SDSS-i) in Hawaii, the PLANET 1.0 m Canopus Telescope (I) in Tasmania (Australia), the PLANET 0.6 m telescope (I) in Perth, Australia, and the following μFUN telescopes: Auckland 0.4 m (I), Farm Cove 0.36 m (unfiltered), Kumeu 0.36 m (I), and Molehill 0.3 m (unfiltered; all in New Zealand). The 0.6 m University of Canterbury B&C telescope intensively observed both wings of the light curve. Like the MOA 1.8 m telescope, it is located at Mt. John, New Zealand. Finally, the MiNDSTEp 1.5 m telescope (I) in La Silla, Chile, obtained data including a few points over the crucial peak region.

As will be discussed in Section 6, a complete analysis of the microlensing event MOA-2010-BLG-523 is complicated by spots on the surface of the source (called MOA-2010-BLG-523S). However, it is possible to derive reasonably robust estimates of all the microlensing parameters required to constrain the source properties without detailed modeling of these complexities.

We begin by simply excising the data within 0.8 days of the peak and fitting the rest of the light-curve flux F to the standard Einstein–Liebes–Refsdal–Paczyński (Einstein 1936; Liebes 1964; Refsdal 1964; Paczyński 1986) five-parameter form

$$\begin{eqnarray} F(t) &=& f_{\rm s} A(u[t]) + f_{\rm b}; \quad u^2 = u_0^2+ {(t-t_0)^2 \over t_{\rm E}^2}; \nonumber\\ A &=& {u^2 + 2\over u\sqrt{u^2+4}}. \end{eqnarray} \tag{ 2 }$$

Here A is the magnification, u is the projected source–lens separation in units of the Einstein radius, u₀ is the impact parameter, t₀ is the time of closest approach, t_E is the Einstein crossing time, f_s is the source flux, and f_b is any blended flux that does not participate in the event but is within the same point-spread function (PSF) as the source. If there is more than one observatory, then each requires its own (f_s, f_b). We find

$$\begin{equation} t_0= 5432.603\pm 0.002; \quad t_{\rm E}=18.5\pm 0.5\,{\rm days};\quad u_0\lesssim 0.002 \end{equation} \tag{ 3 }$$

and for the OGLE observatory

$$\begin{equation} I_{\rm s} = 19.33 \pm 0.03; \quad {f_{\rm b}\over f_{\rm s}} = 0.03\pm 0.03. \end{equation} \tag{ 4 }$$

(All times are given in HJD' = HJD − 2,450,000.)

Inspection of the relatively flat-peaked light curve shows that the lens crossed directly over the source and that the source crossing time is (crudely) of order t_* ∼ 0.15 days, implying a source size (normalized to the Einstein radius) ρ ≡ t_*/t_E ∼ 0.008. Hence, because u₀ ≪ ρ (and noting that A → u⁻¹ for u ≪ 1), we can approximate the peak predicted magnification as

$$\begin{equation} A_{\rm max}= \langle r^{-1}\rangle \rightarrow {2\over \rho } \biggl [1 + \biggl ({3\pi \over 8} - 1\biggr)\Gamma \biggr ], \end{equation} \tag{ 5 }$$

where 〈rⁿ〉 is the nth moment of the source surface brightness, and where we have assumed a linearly limb-darkened (and unspotted) source in making the evaluation, in which case the moments can generally be evaluated:

$$\begin{equation} \langle r^n\rangle = {\rho ^n\over n/2 + 1}(1 - \alpha _n\Gamma); \quad \alpha _n = 1 - {(3/2)!(1 + n/2)!\over (3/2 + n/2)!}. \end{equation} \tag{ 6 }$$

Here Γ is the "natural" form of the linear limb-darkening coefficient, defined by surface brightness S(r)∝1 − Γ[1 − (3/2)(1 − (r/ρ)²)^1/2] (Albrow et al. 1999). It is related to the standard form u by Γ = 2u/(3 − u). It is more "natural" in the sense that there is no net flux associated with the limb-darkening term, which results in simpler formulae when written in terms of Γ. This includes not just the moment Equations (6), but all formulae without exception. For example, the limb-darkening term in the standard formula for ellipsoidal variation (Morris 1985), (15 + u)/(3 − u), becomes simply (5 + 3Γ).

We adopt Γ_I = 0.477 from Claret (2000), by applying the stellar parameters measured by Bensby et al. (2011): T = 5123 K, [Fe/H] = +0.06, log g = 3.6, and ξ = 1.68 km s⁻¹. Hence, A_max = 2.17/ρ. We evaluate A_max by taking the ratio of observed flux at peak to the fit value of f_s and get very nearly the same answer, whether using the average of the two OGLE peak points or a median estimate of CTIO near-peak points: A_max = 265. We thereby derive

$$\begin{equation} \rho = {2.17/A_{\rm max}} = 0.0082 \pm 0.0003, \end{equation} \tag{ 7 }$$

where the error is derived from the 3% error in f_s and a 3% error in the peak flux due to spots.

4.1. Baseline Variability

As we will argue below, the rms variability of the source is about 3%. This is to be compared with the photometric errors, which are typically close to 10%. If the source were a strictly periodic variable, then the period could easily be identified by folding the light curve, despite the low S/N of individual points. The situation is more complex for a quasi-periodic variable (as would be expected for a rotating spotted star). We are therefore quite fortunate that the source lies in a 2001 OGLE transit-campaign field, which was observed 786 times on 32 separate nights during a 46 day window. Binning the data by day, we therefore achieve errors of 0.02, which is comparable to the amplitude of the signal. The result is shown in Figure 1. The light curve gives the clear impression of variability with a period of order 12 days.

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We then use all the OGLE-III data to test for a quasi-periodic signal. If this is a spotted star, we expect that the underlying physical mechanism (rotation of the star) will be strictly periodic, but that the phase of the variations will drift over time as spots appear and disappear. As discussed above, except during the transit campaign, we are compelled to fold the data to pick up any signal at all. On the other hand, if we fold data over an interval that is too long, the result will suffer from destructive interference between different phase regimes. We therefore consider separate fits to the data for each of the nine seasons, 2001–2009. In each trial, we hold the period fixed at a common value for all seasons. Hence, there are 28 parameters [Period + 9 × (phase, amplitude, zero-point)]. At P = 10.914 ± 0.055 days, there is an improvement of Δχ² = 69 relative to a fit for constant magnitude in each season (9 parameters), i.e., 19 fewer parameters; see Figure 2.

We find that the phases are not consistent from one season to the next, suggesting that the variations are not strictly periodic. To further test this, we fit for a single phase and amplitude together with a zero-point offset for each season. This produces an improvement (relative to no periodic variations) of only 30 for 3 dof. Clearly, the quasi-periodic variations are favored over strictly periodic variations.

4.2. Source Is the Variable

4.3. Calcium H&K Emission

4.4. Microturbulence Parameter ξ

Figure 4 shows the microturbulence parameter ξ plotted against temperature for 26 microlensed dwarfs and subgiants as found by Bensby et al. (2010, 2011). MOA-2010-BLG-523S has one of the largest ξ. Moreover, it is well above the upper envelope of points on the low-temperature part of the diagram. This high "microturbulence" may reflect real turbulent motions on the surface of the star (as would be expected for an active star) but may in part reflect rotational motion. Since microturbulence represents a Gaussian velocity distribution that adds to the line in quadrature with other effects, like instrumental resolution, unmodeled rotational motion, it will contribute to ξ as

$$\begin{equation} \Delta \xi ^2 = {\langle r^2\rangle \over \langle r^0\rangle } {(v\sin i)^2\over 2} = {1 - 0.2\Gamma \over 4}(v\sin i)^2 \quad (u\gg \rho), \end{equation} \tag{ 8 }$$

where vsin i is the projected rotational motion.

In fact, Equation (8) applies to sources that are not differentially magnified, which is of course the usual case, but not the present one. If the lens were directly aligned with the source, then

$$\begin{equation} \Delta \xi ^2 = {\langle r^1\rangle \over \langle r^{-1}\rangle } {(v\sin i)^2\over 2} \simeq {1 - 0.3\Gamma \over 6}(v\sin i)^2 \quad (u=0), \end{equation} \tag{ 9 }$$

i.e., roughly 2/3 of the non-differentially magnified case. For the actual geometry at the time of VLT spectra and I-band limb darkening, we find below that Δξ² = 0.2(vsin i)². Hence, the measured ξ places an upper limit on vsin i,

$$\begin{equation} v\sin i \lesssim \sqrt{5}\xi = 3.8\,{\rm km}\,{\rm s}^{-1}. \end{equation} \tag{ 10 }$$

4.5. Lithium

4.6. Radial Velocity

4.7. Source Size

Bensby et al. (2011) derive an equivalent (V − I)₀ = 0.86 color from their spectroscopic solution (primarily from the temperature, but also taking into account the metallicity and gravity). We find from the microlens solution in Section 3 that the unmagnified source flux is ΔI = 3.18 mag fainter than the clump. From the color–magnitude diagram of the neighboring field, there appears to be very little differential reddening. Hence, ΔI ≃ ΔI₀. Based on the measured metallicity distribution of bulge stars, Nataf et al. (2012) estimate that the absolute magnitude of the clump is M_{I, cl} = −0.12. Therefore, the absolute magnitude of the source is

$$\begin{equation} M_{I,\rm s} = M_{I,\rm cl} + \Delta I - 5\log {D_{\rm s}\over D_{\rm cl}} = 3.06 - 5\log {D_{\rm s}\over D_{\rm cl}}, \end{equation} \tag{ 11 }$$

where the last term is the ratio of the distances to the source and the clump. We then apply standard techniques (Yoo et al. 2004) to evaluate the source radius, first using Bessell & Brett (1988) to convert (V − I) → (V − K) and then using Kervella et al. (2004) to obtain the K-band surface brightness from the (V − K) color. Finally, we find

$$\begin{equation} R_{\rm s} = 2.15\,R_\odot {D_{\rm s}\over D_{\rm cl}}. \end{equation} \tag{ 12 }$$

Note in particular that this derivation is independent of any assumption about the Galactocentric distance R₀ or the geometry of the Galactic bar, etc. Subgiants would be expected to have R_s ≳ 2 R_☉. Hence, the source cannot lie substantially closer than the bulge because it would then be too small to be a subgiant (as indicated by its spectroscopic gravity).

4.8. Consistency of Spectrum with Stellar Rotation

If the source is rotating with a period P = 10.9 days, as seems indicated by the quasi-periodic variability seen in Figures 1 and 2, then the surface velocity is v = 2πR_s/P = 10.0 km s⁻¹(R_s/2.15 R_☉). The upper limit vsin i ≲ 3.8 km s⁻¹ (Equation (10)) then implies i ≲ 22°. This is a plausible value since randomly oriented stars will be uniformly distributed in cos i. That is, 7% of the stars have i < 22°, which is small but not implausibly so.

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4.9. Consistency with Maoz–Gould Effect

Maoz & Gould (1994) predicted that microlensing of rotating stars would generate an apparent RV shift, which would change during the course of the event. Their principal point was that the magnitude of this effect falls off only linearly with relative source–lens separation z ≡ u/ρ, compared to the quadratic falloff of photometric effects:

$$\begin{equation} \hspace{-10pt}\Delta v = {\langle r^2 \rangle \over \langle r^0 \rangle }{v\sin i\over 2 z}\sin \phi = {1 - 0.2\,\Gamma \over 4z}v\sin i\sin \phi \quad (z\gg 1), \end{equation} \tag{ 13 }$$

where ϕ is the angle between the source–lens separation and the projected spin axis.

The Bensby et al. (2011) spectrum is actually composed of four 30-minute exposures, centered on HJD − 2,455,432 = (0.510, 0.531,0.552, 0.573). Because the lens came very close to source center, we will adopt z = (t − t₀)/t_*. As we discuss in Section 6, t₀ is not very accurately predicted by the light curve with the peak data removed and is actually approximately t₀ = 5432.66 (compared to t₀ = 5432.60 found in Section 3). Therefore, at the four epochs, z = (1.00, 0.86, 0.72, 0.58). We find numerically that the pre-factor in Equation (13) at these four epochs is (0.294, 0.333, 0.311, 0.266). Thus, the maximum predicted relative shift is only 0.067vsin isin ϕ < 0.31 km s⁻¹. Based on cross-correlation, the four spectra are consistent at this level.

We search for local analogs of MOA-2010-BLG-523S in order to better understand its nature and, to this end, begin by summarizing its characteristics.

5.1. Summary of Characteristics

5.2. Comparison by Rossby Number to M37 Sample

5.3. Comparison to Isaacson & Fischer Sample

As discussed in Section 4.3, Isaacson & Fischer (2010) found only three stars with comparable or greater S_HK in their sample of 234 subgiants. These are Hipparcos stars HIP 5227, 8281, and 97501, which have (V − K) = 2.43, 2.56, and 2.59, respectively. They are thus considerably redder than MOA-2010-523S, which has (V − I)₀ = 0.86 estimated from its spectrum (Bensby et al. 2011), corresponding approximately to (V − K)₀ = 1.92. They are also about 1–1.5 mag more luminous than the subgiants in the Bensby et al. (2011) sample shown in Figure 4. Indeed, stars of this color and luminosity would not be deliberately selected for the Bensby et al. (2011) "dwarf and subgiant" program and are excluded from the analysis if they are observed by accident (J. A. Johnson et al. 2013, in preparation). Based on their V/K photometry, Hipparcos distances, combined with the Kervella et al. (2004) surface brightness relations, these three stars have radii of 5.4, 5.9, and 7.0 R_☉, respectively.

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All three of these stars are spectroscopic binaries, and at least the first two are broadly consistent with being tidally synchronized. Their binary periods are, respectively, 27.3 and 30.1 days (Eker et al. 2008), which would imply surface velocities of 10 km s⁻¹ in both cases, while Isaacson & Fischer (2010) report vsin i of 14 and 6.2 km s⁻¹, respectively. However, D. Fischer (2011, private communication) notes that the profile of the first star is contaminated by lines from a companion, which she estimates to broaden the vsin i determination by 20%–30%, making both stars quite consistent with tidal synchronization. D. Fischer also notes that the third star (HIP 97501) is a clear double-lined spectroscopic binary, so that its binary nature is not in doubt even though the three RV measurements by Isaacson & Fischer (2010) show a scatter of only 0.2 km s⁻¹.

A plausible scenario for these stars is that their moderately close companions only started to spin them up when they began to expand their envelopes as they approached the giant branch. In particular, for the first two, their known periods (P ∼ 30 days) are too long for tidal synchronization while the stars were on the main sequence. However, as they evolved along the subgiant branch, they were clearly tidally spun up, as evidenced by both their vsin i and their calcium H&K activity.

Because MOA-2010-BLG-523S is a much smaller star, a much closer companion would be required to tidally couple with it. On the other hand, its period is much shorter. Since tidal amplitudes scale ∝R³/P², a companion in an 11 day period could provide tidal interactions only a factor of ∼2 smaller than these local analogs. Because MOA-2010-BLG-523S's period is shorter and its phase of subgiant evolution is longer, it would have many more periods to tidally synchronize. Hence, tidal spin-up by a binary companion is a very plausible explanation for its variability and the strength of its calcium lines.

5.4. Comparison to Kepler Sample

Due to its predicted high magnification, MOA-2010-BLG-523 was monitored almost continuously over peak by the 1.3 m SMARTS telescope, although there were short gaps to check on another, possibly interesting, event. These data, by themselves, display a significant "bump" near peak. Moreover, the time of the observed peak is asymmetrically offset from that expected based on the MOA data (roughly a half-day on either side of peak) by about 1.5 hr. Such bumps and asymmetries are just the type of features we look for to identify planetary anomalies due to central caustics in high-magnification events. Within 2 days, preliminary models were circulated, and within 4 days, a planetary model was found that matched all the major light-curve features; see Figure 5.

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In accord with standard microlensing practice, one person (J.C.Y.) was assigned to systematically review all the evidence and propose a final model, which would then be vetted by all groups contributing data. Her report stated that the observed deviations were most likely due to either systematics in the data or stellar variability and so most likely implied that there was no planet or, in any case, that it was impossible to reliably claim a planet. Note that none of the evidence presented here that MOA-2010-BLG-523S is an RS CVn star entered into J.C.Y.'s reasoning or report.

Rather, J.C.Y. was led to question the planetary model because of three features. First, the model source crossing time was almost exactly half the naive time derived from inspection of the light curve. To enable this, the model has the source pass the planet–star axis almost exactly at right angles, so that it passes the middle (weak) cusp almost exactly at peak; see Figure 5. Second, one of the three predicted features of the peak light curve takes place in a small gap in the data. Third, another feature is somewhat more pronounced in the model than in the data. Each of these is, by itself, quite plausible and within the range of microlensing experience, but together they were suspicious.

Hence, J.C.Y. sought confirmation of the planetary signal in other data sets. Unfortunately, the two other Chile observatories that might have taken such data (OGLE and La Silla) had very sparse coverage. She therefore investigated the CTIO ANDICAM H-band data, which are normally of substantially lower quality than the I-band data and so are usually used only for special purposes, such as comparison with high-resolution post-event H-band imaging (e.g., Janczak et al. 2010) or when I-band data are saturated (e.g., Dong et al. 2009). In this case, the H-band data showed a smooth peak, which is clearly inconsistent with the "bump" seen in the I band; see Figure 6. (Note, however, that the H-band peak is still asymmetrically offset by 1.5 hr compared to the time expected based on data in the wings.)

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It is in principle possible to have "sharper" features in the I band than in the H band due to limb-darkening effects. This is contrary to the general expectation that microlensing is achromatic since in general relativity geodesics do not depend on wavelength. This exception occurs when the lens resolves the source because limb darkening is more severe in bluer passbands, making the light profile more compact. Nevertheless, the amplitude of the difference seen in this event is much too big to be explained by this effect. The relative difference in effective source sizes is

$$\begin{equation} \sqrt{\langle [r(H)]^2\rangle \over \langle [r(I)]^2\rangle }-1 =\sqrt{1 - 0.2\Gamma _H\over 1 - 0.2\Gamma _I}-1 \sim 0.1(\Gamma _I-\Gamma _H) <0.02, \end{equation} \tag{ 14 }$$

whereas the difference in timescales of the observed deviations is a factor of ∼2. Hence, there is no plausible reason for the difference in the I and H bands over the peak. Moreover, J.C.Y. found that the other part of the "planetary signal," the asymmetry in the light curve (both I and H bands), can be fit by "xallarap" (orbital motion of the source about a companion) with periods of 3–15 days.

The path to gathering the evidence summarized in Section 4 was circuitous. First, in response to J.C.Y.'s report, A.U. reiterated that the source (or at least some star in the aperture) was a variable with an 11 day period and a 1% amplitude. This variability had previously been ignored in the analysis due to the fact that the "planetary" deviation had a much shorter timescale. Then A.G. learned from stellar-interiors expert M.H.P. that RS CVn stars were found very frequently at T ∼ 5250 K. M.H.P. then suggested that the Rossby number scalings from Hartman et al. (2009) could explain the observed variability. In the meantime, it was found that variability at fixed period but random phase (characteristic of spots) is strongly favored over a strictly periodic signal. These results were consistent with an RS CVn star, so one would expect to see the strong calcium H&K emission characteristic of such stars in the UVES spectrum. However, Bensby et al. (2011) had not remarked upon this because the blue spectral channel is rarely if ever examined for stars in this program because they are very heavily reddened. A check of the blue channel indeed showed strong H&K lines. These lines proved to be easily detectable in this case, not only because they are intrinsically strong, but also because the spectrum was taken at I ∼ 13.3, which is substantially brighter than is typical for the Bensby et al. (2011) sample (see their Figure 1).

In brief, the contradiction between the optical and IR light curves proved to be the crucial turning point in debunking the "planet," even though a more detailed investigation of the available data provides overwhelming evidence that this was a microlensed RS CVn star.

This history argues for caution in the interpretation of planetary signals, particularly when they are both of small amplitude and without the discontinuous slopes characteristic of caustic crossings (e.g., Gould et al. 2006). One may counter in this case that RS CVn stars are extremely rare, but the fact remains that this "rare event" occurred within the first dozen or so microlensing planets. Such rare events in small samples remind us to be vigilant about our assumptions.

We note that the misinterpretation of microlensed spots as planetary signals was suggested more than a decade ago by Heyrovský & Sasselov (2000), who specifically cautioned on the difficulty of distinguishing spots from planets in high-magnification events and even suggested intensive multi-band photometry as a means to tell the difference. As they remarked, such multi-band (optical/IR) photometry had already been advocated by Gaudi & Gould (1997) as a means to better characterize planetary perturbations. This earlier paper (see also Gould & Welch 1996) was the motivation to build the optical/IR dichroic camera ANDICAM (DePoy et al. 2003), whose I/H observations of MOA-2010-BLG-523 proved crucial in demonstrating that the deviations were due to spots rather than a planet. There were several other early investigations of the interpenetration of spots and binary or planetary microlensing. Han et al. (2000) argued that spots might be easier to study in binary-lens than single-lens microlensing because the caustics were more likely to transit the source. And Rattenbury et al. (2002) made a broader investigation of whether spots could in fact be mistaken for planets, arguing that this was really only possible in the rare events (such as MOA-2010-BLG-523) in which the lens passes very close to or over the source. However, to our knowledge, there are no previously published observations of microlensed spots.

Finally, we comment on the implications of this "false planet" for the detection of planets in variable-source events in general and the possibility of variable-star contamination of the Gould et al. (2010) high-magnification planet-frequency statistical study in particular.

In their analysis of MOA-2010-BLG-073, Street et al. (2013) showed that the source star was variable, but that it was still possible to reliably detect and characterize a low-mass companion (in that case, at the boundary between planets and brown dwarfs). Hence, variability by itself is not grounds for removing a source from planet searches. Indeed, regular variability can aid in characterizing an event (Assef et al. 2006). The single most important difference between MOA-2010-BLG-073 and MOA-2010-BLG-523 is that the former had a large, well-mapped perturbation, which was well away from the peak that defined the primary event; see Figure 1 of Street et al. (2013). The major problem was then to remove the long-term (200 days) trend from the data, rather than confirming the planetary (or rather, low-q) nature of the perturbation.

As we have stressed, identification of the perturbation as planetary (not variability induced) is more difficult when it is superposed on the peak in a high-magnification event. Hence, it is appropriate to review the six planet detections that went into the Gould et al. (2010) statistical analysis of 13 high-magnification events. First note that in contrast to MOA-2010-BLG-523, there was no evidence that any of these 13 events (or in particular the five with planets) were variables. For three of the Gould et al. (2010) planets (OGLE-2006-BLG-109Lb,c and OGLE-2007-BLG-349Lb), the signatures are extremely strong and obviously due to planets. The signatures are more subtle for the other three planets, but in each case compelling. For both MOA-2007-BLG-400Lb and MOA-2008-BLG-310Lb, the signatures occur exactly when the source limb passes over the center of magnification of the system, which is what is predicted for small central caustics. For OGLE-2005-BLG-169Lb, there is a discontinuous change in the slope of the light curve, which is characteristic of microlensing caustic crossings but is almost never seen in stellar variables. Inspection of Figure 5 shows that such a break is predicted by the planetary model of MOA-2010-BLG-523 (at HJD' ∼ 5432.67) but is conveniently lodged in a short gap in the data. This was one of the three "features" that originally alerted J.C.Y. to problems in the planetary interpretation.

As we have emphasized, it will be quite rare that an RS CVn star is magnified sufficiently to get a high-S/N spectrum of the heavily extincted Ca H&K lines. Nevertheless, there are other paths toward identifying bulge RS CVn stars. Udalski et al. (2012) found optical counterparts to X-ray sources from the Jonker et al. (2011) Galactic Bulge Survey (GBS) catalog, including 81 spotted stars, which are very probably RS CVn stars. However, because the underlying X-ray catalog is confined to 1 < |b| < 2, it is likely that a large fraction of these are in the disk.

There are two relatively straightforward ways to distinguish between bulge and disk membership. First, a subset of 7 of these 81 stars are eclipsing. All but one of these are relatively bright, 12.7 < I < 15.2, and so it should be possible to obtain spectra and thus measure their distances using the method of eclipsing binaries. Even the faintest of these, at I = 17.4, is not beyond reach. A large fraction of the remainder could be put on a clump-centric color–magnitude diagram (Nataf et al. 2011). In most cases, this should clearly distinguish between bulge and foreground stars. Unfortunately, the extinction map of Nataf et al. (2012) does not reach most of the Udalski et al. (2012) stars because this map is based on OGLE-III data, whereas the GBS survey is restricted to low-latitude fields that are only covered by OGLE-IV. However, it should be possible to apply the clump-centric method to these OGLE-IV fields as well.

The evidence presented in Sections 4 and 5 that MOA-2011-BLG-523S is an RS CVn star is overwhelming. This star shows quasi-periodic variations (the form expected for spots) with a period of P = 10.9 days. The amplitude of variation (few percent) is consistent with what one would expect from its inferred Rossby number. It exhibits very strong calcium H&K emission, such as is seen in only 3 out of a sample of 234 local subgiants. All three are spectroscopic binaries, and two are known to have periods of P ∼ 30 days, which, given their radii and measured vsin i, implies that they are tidally spun up. MOA-2010-BLG-523S has high microturbulence measured compared to the 26 microlensed dwarfs and subgiants, particularly among stars of similar temperature.

Unfortunately, it is not possible to say definitively whether MOA-2010-BLG-523S is in a binary or not. Its period relative to its radius is suggestive of being in the same class of tidally spun-up binaries that includes the three calcium-active subgiants just mentioned. But its temperature is near the range of active subgiants found from Kepler seismology, the great majority of which must be single stars (or widely separated, non-interacting binaries). If a strong case could be made that this was not a binary, then from the lithium measurement (Section 4.5) this would be evidence for an intermediate-age population. But this is not the case. The fact that the peak is offset from the time expected from the wings by 1.5 hr strongly suggests "xallarap" (orbital motion of the source due to a binary companion). However, the irregular character of the light curve, probably due to microlensed spots, compromises our ability to make a rigorous microlensing fit for xallarap.

The I-band light curve is well fitted by a planetary-lens model. The path to discovering that this is a coincidence and that the light-curve anomaly is due to spots was quite circuitous, as described in Section 6. This argues for caution in the interpretation of planetary microlensing events in which the deviations are small and lack features that are obviously due to a two-body lens.

A.G. and J.C.Y. acknowledge support from NSF AST-1103471. Work by J.C.Y. was supported by an SNSF Graduate Research Fellowship under grant No. 2009068160. A.G., B.S.G., L.-W.H., and R.W.P. acknowledge support from NASA grant NNX12AB99G. Work by C. Han was supported by Creative Research Initiative Program (2009-0081561) of National Research Foundation of Korea. T.B. was funded by grant No. 621-2009-3911 from The Swedish Research Council. Work by S. Dong was performed under contract with the California Institute of Technology (Caltech) funded by NASA through the Sagan Fellowship Program. T.C.H. acknowledges support from the Korea Research Council for Science and Technology (KRCF) via the KRCF Young Scientist Research Fellowship Program. Work by B. Shappee and J. van Saders was supported by National Science Foundation Graduate Research Fellowships. The MOA project acknowledges grants 20340052 and 22403003 from JSPS. T. Sumi acknowledges support from JSPS23340044. The OGLE project has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007–2013)/ERC grant agreement No. 246678 to A.U. M.H. acknowledges support by the German Research Foundation (DFG). D.R. (boursier FRIA), F.F. (boursier ARC), and J. Surdej acknowledge support from the Communauté française Belgique Actions de recherche concertées—Académie universitaire Wallonie-Europe. C.S. received funding from the European Union Seventh Framework Programme (FPT/2007–2013) under grant agreement 268421. The Danish 1.54 m telescope is operated based on a grant from the Danish Natural Science Foundation (FNU). K.A., D.M.B., M.D., K.H., M.H., C.L., C.S., R.A.S., and Y.T. are thankful to the Qatar National Research Fund (QNRF) by grant NPRP-09-476-1-078.