1 Introduction

Microlensing Discovery of a Tight, Low Mass-ratio Planetary-mass Object around an Old, Field Brown Dwarf


Observations of accretion disks around young brown dwarfs have led to the speculation that they may form planetary systems similar to normal stars. While there have been several detections of planetary-mass objects around brown dwarfs (2MASS 1207-3932 and 2MASS 0441-2301), these companions have relatively large mass ratios and projected separations, suggesting that they formed in a manner analogous to stellar binaries. We present the discovery of a planetary-mass object orbiting a field brown dwarf via g ravitational microlensing, OGLE-2012-BLG-0358Lb. The system is a low secondary/primary mass ratio (0.080 0.001), relatively tightly-separated ( AU) binary composed of a planetary-mass object with 1.9 0.2 Jupiter masses orbiting a brown dwarf with a mass 0.022 . The relatively small mass ratio and separation suggest that the companion may have formed in a protoplanetary disk around the brown dwarf host, in a manner analogous to planets.

Subject headings:
planetary systems – brown dwarfs – gravitational lensing: micro

1. Introduction

Brown dwarfs (BDs) are sub-stellar objects that are too low in mass to sustain hydrogen fusion reactions in their cores. Although still a matter of debate, the most popular theory about the origin of BDs is that they form via direct collapse similar to stars, perhaps aided by turbulent fragmentation (see Luhman (2012) for a review). This theory is supported by observational evidence showing that several medium-sized BDs are girdled by disks of material (Luhman et al., 2005; Apai et al., 2005; Ricci et al., 2012). The existence of accretion disks around these failed stars naturally leads to the speculation that BDs may also harbor planetary systems analogous to those found in abundance around stars.

There have been several detections of planetary-mass objects around brown dwarfs: 2MASS 1207-3932B with (Chauvin et al., 2004) and 2MASS 0441-2301B with (Todorov et al., 2010). However, these systems have relatively large mass ratios of for 2MASS 1207-3932 and – 0.5 for 2MASS 0441-2301, more akin to binary stellar systems. Furthermore, they have relatively large separations ( AU for 2MASS 0441-2301 and AU for 2MASS 1207-3932), likely near or beyond the outer edges of the accretion disks observed around BDs (Luhman et al., 2007; Ricci et al., 2012, 2013). Therefore, it seems unlikely that these companions formed from the protoplanetary disk material via either of the popular giant planet formation mechanisms of core accretion (Pollack et al., 1996) or disk fragmentation (Kuiper, 1951; Cameron, 1978; Boss, 1997; Durisen et al., 2007). Rather, these are more likely to have formed like stellar binaries, through the process of gravitational fragmentation of massive primordial disk (Lodato et al., 2005). Thus, according to a classification system based on their formation, they are not bona fide planets.

Figure 1.— Light curve the microlensing event OGLE-2012-BLG-0358. The lower 2 panels show the residuals from the best-fit standard binary-lens model and from the model considering the parallax effect. The letters after the individual telescopes represent the pass bands of observation.

In this paper, we report a microlensing discovery of a tight, low mass-ratio planetary-mass object orbiting an old, field BD that we suggest may have formed in a protoplanetary disk. Microlensing is the astronomical phenomenon wherein the brightness of a star is magnified by the bending of light due to the gravity of an intervening object (lens) positioned between the background star (source) and an observer. This discovery was possible, in spite of the extremely low luminosity of the BD, because the lensing phenomenon occurs regardless of the lens brightness.

2. Observation

The BD planetary system was discovered in the microlensing event OGLE-2012-BLG-0358. The event occurred in 2012 observing season on a star located in the Galactic Bulge field with equatorial coordinates , which corresponds to the Galactic coordinates . It was first discovered by the Optical Gravitational Lensing Experiment (OGLE: Udalski (2003)) group in April 2012. During its early phase, the light curve of the event appeared to be a high-magnification event produced by a single mass. Since high-magnification events are prime targets for planet detections, the event was additionally observed by other groups including the Microlensing Follow-Up Network (FUN: Gould et al. (2006)), Microlensing Observations in Astrophysics (MOA: Bond et al. (2001); Sumi et al. (2003)), and RoboNet (Tsapras et al., 2009). As the event approached its peak, it was noticed that the light curve deviated from a standard single-lens light curve and the anomaly became obvious as the light curve peaked again  5 days after the first peak. Continued observations by the OGLE group revealed that the event produced another extended weak bump. In Table 1, we list the telescopes used for observation.

In Figure 1, we present the light curve of the event. It is characterized by two strong peaks centered at Heliocentric Julian Date (HJD)2456537.5 and 2456542.5 and an extended weak bump centered at HJD 2456065. A strong peak in a lensing light curve occurs when a source star approaches close to or crosses the tip of a caustic produced by a lens composed of multiple objects. The caustic represents the envelope of light rays refracted by a curved surface and it is commonly visible as a curved region of bright light appearing when light shines on a drinking glass. For a gravitational lens composed of two masses, caustics form a single or multiple sets of closed curves each of which is composed of concave curves that meet at cusps.

group telescope
OGLE 1.3 m Warsaw, Las Campanas, Chile
MOA 0.6 m Boller & Chivens, Mt. John, New Zealand
FUN 1.3 m SMARTS, Cerro Tololo Inter-American (CTIO), Chile
FUN 0.4 m Auckland, New Zealand
FUN 0.36 m Klein Karoo Observatory (KKO), South Africa
FUN 0.3 m Perth Extrasolar Survey Telescope (PEST), Australia
FUN 0.4 m Turitea, New Zealand
RoboNet 2.0 m Faulkes North Telescope (FTN), Hawaii, USA
RoboNet 2.0 m Faulkes South Telescope (FTS), Australia
RoboNet 2.0 m Liverpool Telescope (LT), Canary Islands, Spain
Table 1Telescopes
Figure 2.— Geometry of the lens system. The closed figures composed concave curves represent the caustic and the line with an arrow is the source trajectory. and represent the binary lens components, where M1 is the heavier one. Greyscale represents the lensing magnification where brighter tone denotes higher magnifications. All lengths are scaled by the Einstein radius corresponding to the total mass of the binary lens.

3. Modeling

With the signature of lens multiplicity, we conduct binary-lens modeling of the observed light curve. Basic description of a binary-lens light curve requires 7 lensing parameters. Three of these parameters describe the lens-source approach, including the time of the closest source approach to a reference position of the binary lens, , the separation between the source and the reference position, (normalized by the angular Einstein radius ), and the time scale for the source to cross (Einstein time scale ). The Einstein ring denotes the image of a source in the event of perfect lens-source alignment, and its radius is commonly used as the length scale of lensing phenomena. Another three lensing parameters describe the binary nature of the lens, including the projected separation, (normalized by ), and the mass ratio, , between the binary components, and the angle between the source trajectory and the binary axis, (source-trajectory angle). The last parameter is the normalized source radius , where is the angular source radius. This parameter is needed to precisely describe the parts of a lensing light curve involved with caustic crossings or approaches of the source during which the lensing light curve is affected by the finite size of the source star. In our modeling of finite-source effects, we additionally consider the limb-darkening variation of the source star surface by modeling the surface brightness profile as a standard linear law.

We search for a solution of lensing parameters that best describes the observed light curve by minimizing in the parameter space encompassing wide ranges of binary separations and mass ratios. For minimization, we use the Markov Chain Monte Carlo method. In order to properly combine data sets obtained from different observatories, we readjust photometric errors of the individual data sets first by adding a quadratic error term so that the cumulative distribution of ordered by magnifications matches to a standard cumulative distribution of Gaussian errors and then by rescaling errors so that per degree of freedom becomes unity for each data set. We eliminate data points with large errors and obvious outlyers to minimize their effect on modeling.

From the initial search for solutions obtained from modeling based on the standard binary-lensing parameters (standard model), we find a solution of a binary lens with a projected separation and a mass ratio . See Table 2 for the complete solution. Although the model describes the main feature of the two strong peaks, it is found that there exist long-term residuals in the wings of the light curve including the extended weak bump as shown in the bottom panel of Figure 1. This suggests the need to consider higher-order effects.

parameters model
standard parallax () parallax () orbit + parallax xallarap ( yr)
2347.81/1592 1598.22/1590 1596.24/1590 1595.17/1588 1601.53/1588
(HJD’) 6040.240.01 6040.330.01 6040.330.01 6057.490.10 6040.330.01
0.1080.001 0.0980.001 -0.0980.001 -0.8320.002 0.0980.001
(days) 24.380.07 26.470.11 26.460.11 25.640.08 26.460.12
1.6870.002 1.6960.003 1.6960.003 1.7000.002 1.6960.003
() 9.8100.071 12.5310.154 12.4860.159 12.2810.118 12.4870.179
5.5440.001 -0.7210.001 0.7220.001 -5.4270.002 5.5620.001
() 2.640.01 2.360.01 2.370.01 2.380.01 2.360.01
- -1.420.06 1.490.07 1.450.03 -
- -0.340.04 -0.190.06 -0.380.02 -
yr - - - 0.050.01 -
yr - - - -0.040.01 -
- - - - -2.180.03
- - - - 0.190.11
(deg) - - - - 247.82.0
(deg) - - - - 10.31.9

Note. – HJD’=HJD-2450000. We note that the lensing parameters t0 and u0 are measured with respect to the center of the caustic located on the planet side.

Table 2Lensing Parameters

There exist several causes of long-term deviations in lensing light curves. The first is the change of the observer¡¯s position caused by the orbital motion of the Earth around the Sun (Gould, 1992; Alcock et al., 1995). This “parallax effect” causes the source trajectory to deviate from rectilinear, resulting in long-term deviations. The second is the positional change of the lens caused by the orbital motion of the binary lens (Dominik, 1998; Albrow et al., 2000; Bennett et al., 2010; Penny et al., 2011; Shin et al., 2011, 2012; Skowron et al., 2011). In addition to causing the source trajectory to deviate from rectilinear, the “lens orbital effect” causes further deviation in lensing light curves by deforming the caustic over the course of the event. The last cause of the deviation is the change of the source position caused by its orbital motion, if the source is a binary (Han & Gould, 1997; Dominik, 1998). Since this affects lensing light curves similarly to the parallax effect, it is often referred to as the “xallarap effect”, which is parallax spelled backward.

Considering that the parallax effect requires 2 parameters and , that represent the two components of the lens parallax vector projected onto the sky along the north and east equatorial coordinates, respectively. The magnitude of the parallax vector corresponds to the relative lens-source parallax, , scaled to the Einstein radius of the lens, i.e., (Gould, 2004). To first order approximation, the lens orbital motion is described by 2 parameters and that represent the change rates of the normalized binary separation and the source trajectory angle, respectively (Albrow et al., 2000). Modeling the xallarap effect requires 5 parameters: the components of the xallarap vector, and , the orbital period , inclination and the phase angle of the source orbital motion. The magnitude of the xallarap vector corresponds to the semi-major axis of the source’s orbital motion with respect to the center of mass normalized by the projected Einstein radius onto the source plane (Dong et al., 2009).

4. Result

We test models considering the higher-order effects, and the results are summarized in Table 2. From the comparison of the results, we find the following results. First, it is found that the parallax effect substantially improves the fit as shown by the residuals in Figure 1. We find that the improvement is compared to the standard binary-lens model. Second, when we additionally consider the lens orbital effect, on the other hand, the improvement of the fit is meager. Finally, we find that considering the xallarap effect yields solutions as good as the parallax solution for source orbital periods yrs. This is expected because it is known that xallarap effects can mimic parallax effects (Smith et al., 2003; Dong et al., 2009). However, the xallarap solutions are excluded because they result in masses of the source companion bigger than 3 and this contradicts to the upper limit set by the observed blended light. Therefore, we conclude that the dominant effect for the long-term deviation is the parallax effect. Finally, since the source lies very near the ecliptic, it is subject to the “ecliptic degeneracy”, which has almost identical parameters except (Skowron et al., 2011).

In Figure 1, we present the best-fit model (parallax model in Table 2) curve that is overplotted on the observed light curve. In Figure 2, we also present the geometry of the lens system for the best-fit solution. It is found that the lens consists of binary components with a projected separation bigger than the Einstein radius corresponding to the total mass of the binary. For such a binary lens, there exist two sets of 4-cusp caustics, where one small set is located close to the heavier lens component (primary) and the other bigger set is located toward the lower-mass lens component (companion). The event was produced by the source trajectory passing the tips of the caustic located on the companion side. The strong peaks at HJD2456537.5 and 2456542.5 were produced at the moments of the source crossings over the caustic tips, while the extended weak bump centered at HJD2456065 was produced as the source passed through the magnification zone of the primary lens. Despite the relatively short time scale days of the event, clear detection of the parallax effect was possible due to combination of the large value of the lens parallax combined with the good coverage of the extended bump that continued for almost 2 months after the main peaks.

Detecting the parallax effect is important for the determinations of the physical lens parameters because the lens parallax is related to the mass and the distance to the lens by and , respectively. Here , is the parallax of the source star, and is the distance to the source star. The source is in the Galactic bulge and thus its distance is known. Considering the mass distribution of the Galactic bulge and the projected source location, we estimate that kilo-parsecs, corresponding to milli-arcseconds.

parameter for for
total mass () 0.0240.002 0.0240.002
primary mass () 0.0230.002 0.0220.002
companion mass () 1.890.19 1.850.19
projected separation (AU) 0.890.03 0.870.03
distance (kilo-parsec) 1.790.12 1.760.13
height above plane (parsec) 1067 1067
velocity, rotation direction (km s) -28 -598
velocity, vertical direction (km s) 176 -166
Table 3Physical Parameters

For the full characterization of the physical parameters, it is needed to additionally determine the Einstein radius, which is given by . The normalized source radius is measured by analyzing the caustic-crossing parts of the light curve that are affected by finite-source effects. The angular source radius is estimated from the source type that is determined based on its de-reddened color and brightness. For this, we first calibrate the color and brightness by using the centroid of bulge giant clump as a reference (Yoo et al., 2004), for which the de-reddened brightness at the Galactocentric distance (Nataf et al., 2013) and color (Bensby et al., 2011) are known. We then translate into color by using the color-color relations (Bessell & Brett, 1988) and then find using the relation between the and the angular radius (Kervella et al., 2004). Figure 3 shows the location of the source star in the color-magnitude diagram of stars in the same field obtained by the OGLE III experiment. It is found that the source is a K-type giant with an angular radius micro-arcseconds. The estimated Einstein radius is milli-arcseconds. Combined with the measured Einstein time scale , the relative lens-source proper motion is milli-arcseconds per year.

In Table 3, we present the determined physical parameters of the lens. The mass of the companion is twice that of the Jupiter. The mass of the primary is . This is firmly below the hydrogen-burning limit of and thus the primary is a BD. The lens is located at a distance kilo-parsecs from the Earth toward the Galactic center. Then the projected separation between the lens components is AU.

We also show the height above the Galactic plane and the tranverse velocity in the directions of Galactic rotation and Galactic north pole, respectively. To find the latter two, we measure the source proper motion mas yr relative to the Galactic bar, and correct for the bar proper-motion gradient (Gould & Yee, 2013). These kinematic variables are the only ones that differ significantly between the two solutions resulting from the ecliptic degeneracy with and . However, both sets of as well as are consistent with a lens age in the range 1 – 10 Giga-years, i.e., much older than BDs of this mass found in imaging studies.

Figure 3.— Location of the lensed source star in the color-magnitude diagram (marked in blue dot) relative to the centroid of the red clump (red dot). The magnitude and color are instrumental scale of the OGLE III data photometry.

5. Discussion

The properties of the OGLE-2012-BLG-0358L system are relatively extreme compared to other binaries with BD hosts. In particular, the separation is a factor and times smaller than those of 2MASS 1207-3932 and 2MASS 0441-2301, respectively, and the mass ratio of is a factor and times smaller than the mass ratios of these systems. Systems with such extreme properties may be difficult to form via conventional binary BD formation mechanisms (e.g, Bate (2012)), suggesting an alternative scenario where the companion formed in the protoplanetary disk of the host BD. Surveys for disks around young BD have found some systems with inferred disk masses up to and even slightly exceeding (Harvey et al., 2012), although these are relatively rare and the inferred masses are subject to considerably uncertainty. Such massive disks are likely to be near the limit of stability (e.g., Lodato et al. (2005)), arguing for a gravitational instability formation scenario rather than core accretion. On the other hand, the relatively close separation may pose a challenge for gravitational instability. Clearly, additional theoretical work is needed to explore the viability of planet formation in BD protoplanetary disks, either by the gravitational instability or core accretion mechanism. For this, it is essential to find more binaries with BD hosts in wide ranges of mass ratios and separations.

Microlensing surveys for exoplanets are well-suited to detect planetary companions to very faint, low-mass stars and old BDs, systems which are difficult to discover via other methods. The last two decades have witnessed tremendous progress in microlensing experiments, which have enabled a nearly 10-fold increase in the observational cadence, resulting in an almost 100-fold increase in the event detection rate. With this observational progress, the number of BD events with precisely measured physical parameters is rapidly increasing (Shin et al, 2013; Choi et al., 2013). Furthermore, a new survey based on a network of multiple telescopes equipped with large format cameras is planned to achieve an even higher cadence of more than 100 per day. Hence, starting from the system reported in this work, many additional BD hosts will be surveyed via microlensing. The discovery of additional, close separation, BD/planet systems with even more extreme mass ratio systems from these surveys will provide important empirical constraints on the ubiquity and mechanisms of planet formation around these hosts.

Work by CH was supported by Creative Research Initiative Program (2009-0081561) of National Research Foundation of Korea. 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. TS acknowledges the support JSPS 24253004. TS is supported by the grant JSPS23340044. YM acknowledges support from JSPS grants JSPS23540339 and JSPS19340058. AG and BSG acknowledge support from NSF AST-1103471. BSG, AG, and RWP acknowledge support from NASA grant NNX12AB99G. SDong¡¯s research was performed under contract with the California Institute of Technology funded by NASA through the Sagan Fellowship Program. KA, DB, MD, KH, MH, SI, CL, RS, YT are supported by NPRP grant NPRP-09-476-1-78 from the Qatar National Research Fund (a member of Qatar Foundation). MD is a Royal Society University Research Fellow. KH is a Royal Society Leverhulme Trust Senior Research Fellow. CS received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 268421. The research leading to these results has received funding from the European Community’s Seventh Framework Programme (/FP7/2007-2013/) under grant agreement no. 229517.


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