MICROLENSING DISCOVERY OF A POPULATION OF VERY TIGHT, VERY LOW MASS BINARY BROWN DWARFS

Brown dwarfs (BDs) are collapsed objects with masses below the minimum mass required to fuse hydrogen of ∼0.08 M_☉. Direct imaging surveys have found that isolated BD systems to be fairly ubiquitous in the field as well as in young clusters (see Luhman 2012 for a review), with frequencies rivaling those of their more massive hydrogen-fusing stellar brethren. However, it is unclear whether BDs simply represent the low-mass extension of the initial collapsed object mass function (IMF), and thus formed via the same processes as stars, or if their formation requires additional physical mechanisms.

The minimum mass of the IMF potentially provides an important discriminant between various models of BD formation, with very low mass BD binary systems being particularly important in this regard. This is because predictions for the multiplicity properties of low-mass BDs—frequency, mass ratio, and separation as a function of total system mass and age—differ significantly depending on the formation scenario. However, the currently available observational samples are strongly influenced by detection biases and selection effects. For example, although BD surveys in young stellar associations allow for detections of low-mass BD systems, these associations are typically fairly distant, making it difficult to detect tight BD binaries. Conversely, field BD binaries can be resolved to much smaller separations, but low-mass, old field BDs are quite faint and thus difficult to detect. As a result, the current sample of binary BDs is not only small in number but also substantially incomplete, particularly in the regime of low mass and small separation. A further complication is that direct mass measurements are available only for a subset of tight field BD binaries. Mass estimates of other systems must rely on comparison with models, resulting in substantial systematic uncertainties.

Gravitational microlensing is well suited to fill the gap. Microlensing is the astronomical phenomenon wherein the brightness of a star is magnified by the bending of light caused by the gravity of an intervening object (lens) located between the background star (source) and an observer. Since this effect occurs regardless of the lens brightness, microlensing is suitable for detecting faint objects such as BDs (Paczyński 1986). For a lensing event produced by a binary lens with well-resolved brightness variation of the lensed star, it is possible to precisely measure the physical parameters of the lensing object including the mass and distance. Here we report the discovery and characterization of two binary BD systems, both of which have very low mass and tight separation, thus constituting a new population.

These BD binaries were discovered in microlensing events OGLE-2009-BLG-151/MOA-2009-BLG-232 and OGLE-2011-BLG-0420. The events occurred on stars located in the Galactic bulge field with equatorial and Galactic coordinates $({\rm R.A.},{\rm decl.})_{2000}=(17^{\rm h} 54^{\rm m} 22\buildrel{\mathrm{s}}\over{.}34, -29^\circ 03^{\prime } 20{\buildrel{\prime\prime}\over{.}} 8)$, (l, b)₂₀₀₀ = (088, −170) and $({\rm R.A.},{\rm decl.})_{2000}=(17^{\rm h} 50^{\rm m} 56\buildrel{\mathrm{s}}\over{.}18, -29^\circ 49^{\prime } 30{\buildrel{\prime\prime}\over{.}} 2)$, (l, b)₂₀₀₀ = (35984, −145), respectively.

OGLE-2009-BLG-151/MOA-2009-BLG-232 was first discovered by the Optical Gravitational Lensing Experiment (OGLE; Udalski 2003) group and was independently discovered by the Microlensing Observations in Astrophysics (MOA; Bond et al. 2001; Sumi et al. 2003) group in 2009 observation season. OGLE-2011-BLG-0420 was detected by the OGLE group in the 2011 season. Both events were additionally observed by follow-up observation groups including Microlensing Follow-Up Network (μFUN; Gould et al. 2006), Probing Lensing Anomalies NETwork (PLANET; Beaulieu et al. 2006), RoboNet (Tsapras et al. 2009), and Microlensing Network for the Detection of Small Terrestrial Exoplanets (MiNDSTEp; Dominik et al. 2010). In Table 1, we list the survey and follow-up groups along with their telescope characteristics. Data reductions were carried out using photometry codes developed by the individual groups.

Figure 1 displays the light curves of the individual events. OGLE-2009-BLG-151/MOA-2009-BLG-232 is characterized by two strong spikes flanking a "U"-shaped trough, which is typical for caustic-crossing binary-lens events. Caustics denote positions on the source plane where the lensing magnification of a point source diverges (Petters et al. 2001). When a caustic is formed by an astronomical object composed of two masses, it forms a single set or multiple sets of closed curves each consisting of concave curves that meet at cusps. When a source star crosses the caustic, its brightness is greatly enhanced, causing strong deviation from the smooth and symmetric single-lens light curve. The light curve of OGLE-2011-BLG-0420, on the other hand, appears to be smooth and symmetric, which are the characteristics of a lensing event caused by a single mass. From the fit based on the single-lens model, however, the light curve exhibits noticeable deviations near the peak, which indicates the existence of a companion to the lens. According to the classification scheme of binary signatures in lensing light curves set by Ingrosso et al. (2009), the deviations of OGLE-2009-BLG-151/MOA-2009-BLG-232 and OGLE-2011-BLG-0420 are classified as Classes II and I, respectively.

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With known binary signatures, we conduct binary-lens modeling of the observed light curves. For a single lens, the light curve is described by three parameters: the time of closest lens–source approach, t₀; the lens–source separation (normalized by the Einstein-ring radius, θ_E) at that time, u₀; and the Einstein timescale, t_E, which represents the time required for the source to cross θ_E. The Einstein ring denotes the image of a source in the event of perfect lens–source alignment, and so is used as the length scale of lensing phenomena. Binary lenses require three additional parameters: the mass ratio, q; the projected separation (normalized by θ_E) between the binary components, s; and the angle between the source trajectory and the binary axis, α (source trajectory angle).

In addition to the basic lensing parameters, it is often necessary to include additional parameters to precisely describe subtle light curve features caused by various second-order effects. For both events, the lensing-induced magnification lasted for several months, which comprises a significant fraction of Earth's orbital period around the Sun (1 year). Then, the apparent motion of the source with respect to the lens deviates from rectilinear (Gould 1992) due to the change of the observer's position caused by Earth's orbital motion. This parallax effect causes long-term deviation in the lensing light curves. Consideration of the parallax effect requires two additional parameters, π_{E, N} and π_{E, E}, which are the two components of the lens parallax vector π_E, projected on the sky along the north and east equatorial coordinates, respectively. The orbital motion of the lens also affects lensing light curves. The lens orbital motion causes the projected binary separation and the source trajectory angle to change over the course of a lensing event. These require two additional lensing parameters of the change rates of the binary separation, ds/dt, and the source trajectory angle, dα/dt. Finally, finite-source effects become important whenever the magnification varies very rapidly with the change of the source position, so that different parts of the source are magnified by different amounts. Such a rapid magnification variation occurs near caustics and thus finite-source effects are important for binary-lens events involved with caustic crossings or approaches. This requires one more parameter, the normalized source radius ρ_* = θ_*/θ_E, where θ_* is the angular source radius. Measuring the deviation caused by the parallax and finite-source effects is important to determine the physical parameters of the lens. By measuring the finite-source effect, the Einstein radius is determined by θ_E = θ_*/ρ_* once the source radius is known. With the measured lens parallax and the Einstein radius, the mass and distance to the lens are determined as M_tot = θ_E/(κπ_E) and D_L = AU/(π_Eθ_E + π_S), respectively (Gould 1992; Gould et al. 2006). Here κ = 4G/(c²AU), AU is an astronomical unit, π_S = AU/D_S, and D_S ∼ 8 kpc is the source distance.

We model the observed light curves by minimizing χ² in the parameter space. We investigate the existence of possible degenerate solutions because it is known that light curves resulting from different combinations of lensing parameters often result in similar shapes (Griest & Safazadeh 1998; Dominik 1999; An 2005). In modeling finite-source effects, we additionally consider the limb-darkening variation of the source star surface (Witt 1995) by modeling the surface profile as a standard linear law. For χ² minimization, we use the Markov Chain Monte Carlo method. Photometric errors of the individual data sets are rescaled so that the χ² per degree of freedom becomes unity for each data set. We eliminate data points with large errors and those lying beyond 3σ from the best-fit model to minimize their effect on modeling.

Table 2 gives the solutions of the lensing parameters found from modeling. In Figure 2, we also present the geometry of the lens system where the source trajectory with respect to the positions of the binary lens components and the caustic are shown. For OGLE-2009-BLG-151/MOA-2009-BLG-232, we find that the two strong spikes were produced by the source crossings of a big caustic formed by a binary lens with the projected separation between the lens components (s ∼ 1.14) being similar to the Einstein radius of the lens. We find that including the second-order effects of lens parallax and orbital motions improves the fit by Δχ² = 213. OGLE-2011-BLG-0420 is also a caustic-crossing event, but the projected binary separation (s ∼ 0.29) is substantially smaller than the Einstein radius. For such a close binary lens, the caustic is small. For OGLE-2011-BLG-0420, the caustic is so small that the source size is similar to that of the caustic. Hence, the lensing magnification is greatly attenuated by the severe finite-source effect, and thus the deviation during the caustic crossings is weak. We find that there exists an alternative solution with s > 1 caused by the well-known close/wide binary degeneracy, but the degeneracy is resolved with Δχ² = 27. The parallax and lens orbital effects are also clearly measured with Δχ² = 403. From 10 years of OGLE data, we find that OGLE-2011-BLG-0420S (source star) is extremely stable, but OGLE-2009-BLG-151/MOA-2009-BLG-232S exhibits irregular <1% variations, typically on timescales of a few hundred days. Because these can affect the parallax measurement, we restrict the modeling to t₀ ± 300 days to minimize the impact of variations while still retaining enough baseline to ensure a stable fit. We also include a "slope" parameter for the source flux to account for the remaining variability. We find only slight differences in final results if we repeat this procedure with longer baselines. Therefore, it is unlikely but not impossible that source variability affects the OGLE-2009-BLG-151/MOA-2009-BLG-232 parallax measurement. By contrast, the results for OGLE-2011-BLG-0420 are very robust.

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Since ρ_* and π_E are well measured (Table 2), it is possible to determine M_tot and D_L for both systems. The only missing ingredient is the angular source radius θ_*, which is needed to find θ_E = θ_*/ρ_*. This is determined from the de-reddened color and brightness of the source star. For the calibration of the color and brightness, we use the centroid of bulge giant clump as a reference (Yoo et al. 2004) because its de-reddened brightness I_{0, c} = 14.45 at the Galactocentric distance (Nataf et al. 2012) and the color (V − I)_{0, c} = 1.06 (Bensby et al. 2011) are known. We then translate V − I into V − K color by using the relation. Once the V − K color is known, the angular source radius θ_* is obtained the relation between the V − K color and the angular radius provided by Kervella et al. (2004). In Table 3, we list the measured de-reddened colors (V − I)₀, magnitudes I₀, angular radii, types of the source stars, and the measured Einstein radii of the individual events. Figure 3 shows the locations of the lensed stars of the individual events on the color–magnitude diagrams.

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The derived physical quantities for the OGLE-2009-BLG-151/MOA-2009-BLG-232L and OGLE-2011-BLG-0420L binaries are listed in Table 4. Here the letter "L" at the end of each event indicates the lens of the event. The total system masses are M_tot = (0.025 ± 0.001) M_☉ and (0.034 ± 0.002) M_☉, respectively, well below the hydrogen-burning limit. The projected separations and mass ratios are d_⊥ = (0.31 ± 0.01) AU and q = 0.419 ± 0.006 for OGLE-2009-BLG-151/MOA-2009-BLG-232L, and d_⊥ = (0.19 ± 0.01) AU and q = 0.377 ± 0.009 for OGLE-2011-BLG-0420L. It is worth emphasizing the high precisions (<10%) with which the total system masses and individual component masses are determined.

Figure 4 compares OGLE-2009-BLG-151/MOA-2009-BLG-232L and OGLE-2011-BLG-0420L to a sample of low-mass binaries in the field and in young associations from Faherty et al. (2011), Basri & Martín (1999), Burgasser et al. (2008, 2012), and Lane et al. (2001). The only known BD binaries with comparable total masses are Oph 16225-240515 with M_tot ∼ 0.032 M_☉ (Jayawardhana & Ivanov 2006) and 2MASSJ1207334-393254 (Chauvin et al. 2004) with M_tot ∼ 0.028 M_☉. However, these two systems are both young (5 Myr and 8 Myr, respectively) and have very wide separations of hundreds of AU. Indeed, OGLE-2009-BLG-151/MOA-2009-BLG-232L and OGLE-2011-BLG-0420L are the tightest known BD binaries with substantially lower mass than previously known field BD binaries. Both systems have mass ratios of ∼0.4, apparently consistent with the trend found from old field BDs, which tend to have a preference for larger mass ratios (see Figure 3 of Burgasser et al. (2007)), although it is important to stress that the selection effects in microlensing and direct imaging surveys are very different.

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Burgasser et al. (2007) suggested that field low-mass binaries with M_tot = 0.05–0.2 M_☉ may exhibit an empirical lower limit to their binding energies of Gm₁m₂/a ∼ 2.5 × 10⁴² erg (see Figure 5). Although OGLE-2009-BLG-151/MOA-2009-BLG-232L and OGLE-2011-BLG-0420L are substantially lower in mass than these BD binaries, they are also considerably tighter. Therefore, with binding energies of ∼7 × 10⁴² erg and 2 × 10⁴³ erg, they are consistent with the extrapolation of the minimum binding energy limit down to total system masses of M_tot ∼ 0.02 M_☉.

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Although we are unable to provide an estimate of the space density of such tight, low-mass BD binaries, or even an estimate of their frequency relative to more massive stellar binaries, the discovery of two systems among the relatively small sample of binary lensing events with precise mass estimates strongly suggests that very low mass, very tight BD binaries are not rare. Thus, these detections herald a much larger population of such systems. We can therefore conclude that BD binaries can robustly form at least down to system masses of ∼0.02 M_☉, providing a strong constraint for formation models.

The discoveries of the binary BDs reported in this paper demonstrate the importance of microlensing in BD studies. The microlensing method has various advantages. First, it enables us to detect faint old populations of BDs that could not be studied by the conventional method of imaging surveys and the sensitivity extends down to planetary mass objects (Sumi et al. 2011). It also allows one to detect BDs distributed throughout the Galaxy. Therefore, microlensing enables us to study BDs based on a sample that is not biased by the brightness and distance. Second, in many cases of microlensing BDs, it is possible to precisely measure the mass, which is not only the most fundamental physical parameter but also a quantity enabling to unambiguously distinguish BDs from other low-mass populations such as low-mass stars. While mass measurements by the conventional method require long-term and multiple stage observation of imaging, astrometry, and spectroscopy by using space-borne or very large ground-based telescopes, microlensing requires simple photometry by using 1 m class telescopes. Despite the observational simplicity, the mass can be measured with uncertainties equivalent to or smaller than those of the measurement by conventional methods. Finally, microlensing can expand the ranges of masses and separations in the binary BD sample that is incomplete below ∼0.1 M_☉ in mass and ∼3 AU in separation. Microlensing sensitivity to binary objects peaks when the separation is of the order of the Einstein radius. Considering that the Einstein radius corresponding to a typical binary BD is <1 AU, microlensing method will make it possible to study binary BDs with small separations.

The number of microlensing BDs is expected to increase in the future with the upgrade of instruments in the existing survey experiments and the advent of new surveys. The OGLE group recently upgraded its camera with a wider field of view to significantly increase the observational cadence. The Korea Microlensing Telescope Network (KMTNet), now being constructed, will achieve 10 minute sampling of all lensing events by using a network of 1.6 m telescopes on three different continents in the Southern hemisphere with wide-field cameras. Furthermore, there are planned lensing surveys in space including EUCLID and WFIRST. With the increase of the microlensing event rate combined with the improved precision of observation, microlensing will become a major method to study BDs.

Work by C. Han was supported by the research grant of Chungbuk National University in 2011. 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. The MOA experiment was supported by grants JSPS22403003 and JSPS23340064. This work is based in part on data collected by MiNDSTEp with the Danish 1.54 m telescope at the ESO La Silla Observatory, which is operated based on a grant from the Danish Natural Science Foundation (FNU). The MiNDSTEp monitoring campaign is powered by ARTEMiS (Dominik et al. 2008). 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 de Belgique—Actions de recherche concertées—Académie universitaire Wallonie-Europe. 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), member of the Qatar Foundation, for support by grant NPRP 09-476-1-078. C.S. has received funding from FP7/2007-2013 under grant agreement No. 268421. K.H. is supported by a Royal Society Leverhulme Trust Senior Research Fellowship. A.G. and B.S.G. acknowledge support from NSF AST-1103471. B.S.G., A.G., and R.W.P. acknowledge support from NASA grant NNX12AB99G. Work by J.C.Y. is supported by a National Science Foundation Graduate Research Fellowship under grant No. 2009068160. S.D.'s research was performed under contract with the California Institute of Technology funded by NASA through the Sagan Fellowship Program. T.S. was supported by the grant JSPS23340044. Y.M. acknowledges support from JSPS grants JSPS23540339 and JSPS19340058. T.C.H. and C.U.L. acknowledge the support of KASI grant 2012-1-410-02 and KRCF.