THE EXTREME MICROLENSING EVENT OGLE-2007-BLG-224: TERRESTRIAL PARALLAX OBSERVATION OF A THICK-DISK BROWN DWARF

By several measures OGLE-2007-BLG-224 was the most extreme microlensing event (EME) ever observed, having a substantially higher magnification, shorter-duration peak, and faster angular speed across the sky than any previous well observed event. These extreme features suggest an extreme lens. Fortunately, the observations themselves had extreme characteristics, and these permit one to test the nature of the lens.

OGLE-2007-BLG-224 (R.A. = 18:05:41, decl. =−28:45:36) was announced as a probable microlensing event by the OGLE collaboration (Udalski 2003) on 2007 May 9 and independently by the MOA collaboration (Bond et al. 2002) on May 12 as MOA-2007-BLG-163. At discovery, it was already recognized to be quite short, Einstein timescale t_E ∼ 7 days, and was consistent with peaking at high magnification, although with very low probability of doing so. Such high-mag events (typically defined as A_max>100) are extremely sensitive to planets, and hence planet-detection groups attempt to predict these rare events so as to intensively monitor them over their peak. This is notoriously difficult, especially for short events, because so little information is available before peak. Indeed, four of the five high-mag events that have to date yielded planet detections had much longer-than-average Einstein timescales, t_E>40 days (Udalski et al. 2005; Gould et al. 2006; Gaudi et al. 2008a; Bennett et al. 2008; Dong et al. 2009). Nevertheless, 20 hours before peak, OGLE issued an alert calling this a "possible high-magnification event," and 10 hours later, by combining OGLE and MOA data, including points from MOA just 12 hours before peak, the μFUN collaboration was able to predict A_max>50 and on this basis issued a general alert advocating intensive observations.

As a result, on the night of the peak, the μFUN Bronberg 0.35 m telescope (South Africa) obtained 754 unfiltered images over 6.5 hours ending at UT 03:43 just 10 minutes before peak, during which the magnified flux increased by a factor of 38. The μFUN SMARTS 1.3 m telescope (Chile) obtained a total of 304 images (52 in I band, 8 in V, and 244 in H) over 5.5 hours beginning 38 minutes before peak and the OGLE 1.3 m Warsaw telescope obtained 62 images (57 in I and 5 in V) over 6.9 hours beginning 25 minutes before peak. The RoboNet 2 m Liverpool Telescope obtained eight R images whose number and timing were determined by an automated program (Snodgrass et al. 2008; Tsapras et al. 2009) that queries several photometry databases and attempts to optimize observations. Critically, two of these observations were about 35 minutes before peak and two others were 25 minutes after peak.

Additional observations were obtained by the MOA 1.8 m telescope (New Zealand), the μFUN 0.4 m Auckland, 0.35 m Farm Cove, and 0.4 m Vintage Lane telescopes (New Zealand), the μFUN 1.0 m Mt. Lemon telescope (Arizona), the PLANET 1.0 m Canopus (Tasmania), 0.6 m (Perth), 1.5 m Boyden (South Africa) and 1.54 m Danish (Chile) telescopes, as well as the RoboNet Faulkes North 2 m (Hawaii), and the Faulkes South 2 m (New South Wales) telescopes. These observations helped in the determination of the event's overall parameters, but not in the characterization of the peak, which is the central focus of this Letter.

Normally, microlensing events yield only one physical characteristic parameter, the Einstein timescale, t_E, which is a degenerate combination of three physical parameters of the system, i.e., the lens mass M, the lens-source relative proper motion in the Earth frame, ${\mbox{\boldmath $\mu $}}_{\rm geo}$, and the lens-source relative parallax π_rel = AU/D_l − AU/D_s,

$$\begin{equation} t_{\rm E}= {\theta _{\rm E}\over \mu _{\rm geo}}; \quad \theta _{\rm E}= {\pi _{\rm rel}\over \pi _{\rm E}}; \quad \pi _{\rm E}^2 = {\pi _{\rm rel}\over \kappa M}, \end{equation} \tag{ 1 }$$

where D_l and D_s are the lens and source distances and κ = 4G/(c²AU) ∼ 8.1 mas M⁻¹_☉. Here, $\pi _{\rm E}={\rm AU}/\tilde{r}_{\rm E}$ is the "microlens parallax," the ratio of the radius of the Earth's orbit to the Einstein radius projected on the observer plane, $\tilde{r}_{\rm E}$. See Figure 1 of Gould (2000b) for a geometric derivation of the relations between (π_E, θ_E) and (M, π_rel).

Hence, if the lens is unseen, its mass and distance can be determined only by measuring both θ_E and π_E (Gould 1992). It is quite rare that either of these parameters can be measured, and only three times (out of >4000 events) have both been well measured without seeing the lens itself (An et al. 2002; Jaroszynski et al. 2005; Kubas et al. 2005). However, as pointed out more than a decade ago, EMEs present a unique opportunity to measure both parameters (Gould 1997).

2.1. Angular Einstein Radius, θ_E, from Finite-Source Effects

2.2. Projected Einstein Radius from Terrestrial Parallax, π_E

Second, and more dramatically, EMEs are subject to "terrestrial parallax" effects (Hardy & Walker 1995; Holz & Wald 1996). If a microlensing event is observed from two different locations, the source-lens relative trajectory will appear different: there will be a different impact parameter, u₀, and a different time of closest approach, t₀. Since the projected Einstein radius $\tilde{r}_{\rm E}={\rm AU}/\pi _{\rm E}$ is typically of order AU, the second observer should typically be in solar orbit to notice a significant effect, and indeed one such space-based measurement has been made (Dong et al. 2007). However, the main way that microlens parallax has been measured in the past is to take advantage of the moving platform of the Earth, but usually the event must last a large fraction of a year for this to work (Poindexter et al. 2005). For EMEs, the relevant spatial scale and timescales are reduced by a factor A_max. For example, if the projected velocity of the lens is 100 km s⁻¹ in the westward direction, then t₀ will be about 80 s later in Chile than South Africa. Measuring the peak time of a normal microlensing event (which typically lasts t_E ∼ 30 days) to this precision is virtually impossible. But since the peaking timescale of this event is roughly the source crossing time, t_* ≡ ρ t_E = 8.5 minutes, such measurements become quite practical. Indeed, the event passed both South Africa and the Canaries about 1 minute earlier than Chile, with both time differences accurate to a few seconds (See Figure 1). In practice, we simultaneously account for the difference in impact parameters and peak times at all locations (An et al. 2002), as well as the Earth's orbital motion (which turns out be negligible), to measure both the microlens parallax π_E = 1.97 ± 0.13 and the direction of lens-source relative motion, 52 ± 5° south of west (see Figure 2). The parallax measurement can also be expressed in terms of the offsets, ${\bf \bDelta t} \equiv (\Delta t_0,t_{\rm E}\Delta u_0)$, from which it is ultimately derived:

$$\begin{eqnarray} &&{\bDelta t}_{12}=(-18.1,54.0)s\pm (5.8,2.5)s\nonumber \end{eqnarray}$$

$$\begin{eqnarray} &&{ \bDelta t}_{23}=(-43.1,-52.0)s\pm (2.6,7.0)s\nonumber \end{eqnarray}$$

$$\begin{equation} {\bDelta t}_{31}=(61.2,-2.0)s\pm (4.3,5.2)s, \end{equation} \tag{ 2 }$$

where 1 = South Africa, 2 = Canaries, 3 = Chile.

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2.3. Mass, Distance, and Transverse Velocity

The determination of π_E and θ_E yield the mass and relative parallax

$$\begin{eqnarray} M &=& {\theta _{\rm E}\over \kappa \pi _{\rm E}} = 0.056\,{\pm}\, 0.004\;M_\odot\nonumber\\ \pi _{\rm rel} &=& \theta _{\rm E}\pi _{\rm E} = 1.78\,{\pm}\, 0.13\;{\rm mas} \end{eqnarray} \tag{ 3 }$$

Assuming (as is consistent with its color and flux) that the source is in the Galactic bulge $(\pi _s = 125\;{\mu \rm as})$, the lens parallax and distance are π_l = π_rel + π_s = 1.90 mas, D_l = AU/π_s = 525 ± 40 pc, respectively.

The projected velocity of the lens in the Earth frame is $\tilde{v}_{\rm geo}= \mu _{\rm geo}({\rm AU}/\pi _{\rm rel})= 127\;{\rm km}\;{\rm s}^{-1}$. To find the projected velocity in the frame of the Sun, we must remove the motion of the Earth around the Sun (23 km s⁻¹, almost due east). We then find $\tilde{v}_{\rm hel}= 112\;{\rm km}\;{\rm s}^{-1}$ at 61° south of west. This means that the lens is moving against the direction of Galactic rotation, just 1° out of the Galactic plane (toward Galactic south). Taking account of the motion of the Sun relative to the local standard of rest (Dehnen & Binney 1998) as well as the small mean motion (and its uncertainty) of the source, we find that the lens is moving at $\tilde{v}_{\rm hel}= 113\pm 21\;{\rm km}\;{\rm s}^{-1}$ relative to the Galactic disk at its location, almost directly counter to Galactic rotation. This motion is quite consistent with the kinematics of the Galactic thick disk, which has an asymmetric drift of 43 km s⁻¹ and a dispersion of 49 km s⁻¹ in the direction of Galactic rotation (Casertano et al. 1990). (It is also consistent with Galactic halo stars, but with a probability more than 100 times smaller.) Moreover, since the inferred mass is below the threshold for burning hydrogen, the lens is almost certainly a brown dwarf. While nearby brown dwarfs of this mass have been detected (e.g., Burgasser et al. 2006; Faherty et al. 2009), these are mostly quite young and so still retain the heat generated during their collapse from a cloud of gas. The thick disk is of order 11 Gyr old, and hence brown dwarfs have had substantial time to cool. Only those very near the hydrogen burning limit are easy to see, and then only if they are relatively nearby.

Hubble Space Telescope (HST) data were taken in V, I, J, and H bands Δt₁ = 29 days after peak when the source was magnified by a factor A = 1.005, and again almost exactly one year later, Δt₂ = 1.08 years. At the first epoch, the source and lens were virtually coincident, being separated by only μ_geoΔt₁ ∼ 4 mas, i.e., <0.1 pixels, while at the second epoch they were separated by μ_helΔt₂ ∼ 47 mas ∼ 1 pixel, where μ_hel = 43 mas yr^-1 is the heliocentric proper motion. These observations confirm that the excess flux (above the source flux predicted from the microlensing fit) is consistent with zero, but unfortunately not with very high precision because an unrelated star lying 150 mas from the source degrades the measurements. We discuss the prospect for future observations of the lens flux below.

We now ask, given a standard Galactic model (Han & Gould 2003; Gould 2000a), how likely it is that detailed information on a t_E = 7 day (but otherwise unconstrained) microlensing event toward this line of sight (l = 2.37,  b = −3.71) would turn out to imply a foreground (D_l < 4 kpc) thick-disk star rather than a star in the Galactic bulge?  The chance is just 1/235. Hence, either we were extremely lucky to have found this object, or brown dwarfs are more common in the thick disk than our standard model for the mass function would predict. Specifically, our model assumes a relatively flat power-law mass function for low-mass stars and brown dwarfs with dN/dlog  M ∝ M^−0.3 from M = 0.7 M_☉ down to M = 0.03 M_☉. This model is consistent with results from observations of nearby thin disk brown dwarfs (Pinfield et al. 2006; Metchev et al. 2008), and thus our detection would imply that brown dwarfs must be an order of magnitude more common in the thick disk than in the thin disk, in order that the a priori probability of detecting this event be ≳10%. This possibility should be considered seriously, since the prevalence of old brown dwarfs is essentially unconstrained by any data, owing to their faintness.

In this light, we note that two other sets of investigators have concluded that they must have been "lucky" unless old-population brown-dwarfs are more common than generally assumed. First, Burgasser et al. (2003) discovered a halo brown dwarf, probably within 20 pc of the Sun, a volume that contains only about seven halo stars over the entire mass range from the hydrogen-burning limit to a solar mass (Gould 2003). Yet the survey in which this object was discovered would only be sensitive to halo brown dwarfs in an extremely narrow mass range just below this limit (Burgasser 2004). Second, Gaudi et al. (2008b) analyzed a microlensing event of a nearby (1 kpc), bright (V = 11) source serendipitously discovered by an amateur astronomer hunting for comets, finding that it was most likely a low-mass star or brown dwarf moving at roughly 100 km s⁻¹. Based on the low rate of such events (and the non-systematic character of the search), they concluded that they were "probably lucky... but perhaps not unreasonably so" to have found this event (see also Fukui et al. 2007). Finally, Faherty et al. (2009) found 14 high-velocity objects in a sample of 332 M, L, and T dwarfs, which are consistent with thick-disk or halo kinematics. Only one of these has J − K < 0, which would be indicative of an old, low-mass brown dwarf (Burrows et al. 2001), and with v_tan = 140 km s⁻¹ is most likely a halo brown dwarf, but could be in the high-velocity tail of the thick disk. At absolute magnitude M_J = 15.9, it must be very close to the hydrogen-burning limit M>0.07 M_☉ if it is as old as the thick disk and halo: ≳11 Gyr. As this object was found within 10 pc, it is yet another "lucky find" (compare to, e.g., Burgasser 2004). While the evidence from each of these studies is marginal, collectively they point to the need for closer investigation of the frequency of old brown dwarfs.

Brown dwarfs are very blue in H – K and somewhat red in J – H, so H is the most favorable band to observe them. In the heliocentric frame, the lens is moving away from the source at μ_hel = 43 mas yr^-1. Hence, just three years after the event, the lens should be well removed from the source in Keck telescope H-band images (given its 40 mas adaptive-optics point spread function). Equivalent angular resolution with HST would require waiting four times longer, although it would profit from the much fainter sky as seen from space as well as its better defined point-spread function. From Burrows et al. (2001, Figures 1, 8, 9, and 24) and Burrows et al. (1997, Figure 23) one finds that the absolute magnitude of an 11 Gyr old, M = 0.056 M_☉ brown dwarf is M_H = 17.0, implying H = 25.7 at 525 pc (assuming extinction A_H = 0.1). By comparison, the source is H_s = 17.5. In principle, the lens could be younger, in which case it would be brighter and so easier to detect. However, such high-velocity young stars are extremely rare, and there is no known mechanism for preferentially accelerating brown dwarfs to this speed.

If the lens is indeed in the thick disk, this would be a challenging but not impossible observation, and would permit a unique test of models of old brown dwarfs by comparison with an object of known mass and well constrained age. The astrometry associated with this measurement would yield the lens-source relative proper motion ${\mbox{\boldmath $\mu $}}_{\rm hel}$, which would test both the magnitude of the microlens-based proper motion and the direction of the microlens parallax, thereby confirming and refining (or contradicting) the microlens-based mass estimate (Gould et al. 2004).

Looking further ahead, the space-based James Webb Space Telescope (launch currently scheduled for 2013) will be able to take a spectrum of this object, thereby testing more detailed atmospheric models.

We thank C. S. Kochanek, S. Poindexter, and S. Kozlowski for help with modeling the HST point-spread function. We acknowledge the following support: NSF AST-0757888 (A.G., S.D.); NASA NNG04GL51G (D.D., A.G., R.P.); Polish MNiSW N20303032/4275 (A.U.); HST-GO-11311 (K.S.); NSF AST-0206189, NASA NAF5-13042 (D.P.B.); Korea Science and Engineering Foundation grant 2009-008561 (C.H.) Korea Research Foundation grant 2006-311-C00072 (B.-G.P.) Deutsche Forschungsgemeinschaft (C.S.B.); PPARC/STFC, EU FP6 programme "ANGLES" (Ł.W., N.J.R.); PPARC/STFC (RoboNet); Dill Faulkes Educational Trust (Faulkes Telescope North); Grants JSPS18253002 and JSPS20340052 (MOA); Marsden Fund of New Zealand (I.A.B., P.C.M.Y.); Foundation for Research Science and Technology of New Zealand.