OGLE-2016-BLG-0263Lb: Microlensing Detection of a Very Low-mass Binary
Companion through a Repeating Event Channel
C. Han
1
, A. Udalski
2,23
, A. Gould
3,4,5,24
, I. A. Bond
6,25
,
and
M. D. Albrow
7
, S.-J. Chung
3,8
, Y. K. Jung
9
, Y.-H. Ryu
3
, I.-G. Shin
9
, J. C. Yee
9
, W. Zhu
4
, S.-M. Cha
3,10
, S.-L. Kim
3,8
,
D.-J. Kim
3
, C.-U. Lee
3,8
, Y. Lee
3,10
, B.-G. Park
3,8
(The KMTNet Collaboration),
J. Skowron
2
, P. Mróz
2
, P. Pietrukowicz
2
, S. Kozłowski
2
, R. Poleski
2,4
, M. K. Szymański
2
, I. Soszyński
2
, K. Ulaczyk
2
,
M. Pawlak
2
(The OGLE Collaboration),
F. Abe
11
, Y. Asakura
11
, R. Barry
12
, D. P. Bennett
12,13
, A. Bhattacharya
12,13
, M. Donachie
14
, P. Evans
14
, A. Fukui
15
, Y. Hirao
16
,
Y. Itow
11
, N. Koshimoto
16
,M.C.A.Li
14
, C. H. Ling
3
, K. Masuda
11
, Y. Matsubara
11
, Y. Muraki
11
, M. Nagakane
16
, K. Ohnishi
17
,
C. Ranc
12
, N. J. Rattenbury
14
, To. Saito
18
, A. Sharan
14
, D. J. Sullivan
19
, T. Sumi
16
, D. Suzuki
12,20
, P. J. Tristram
21
, T. Yamada
22
,
T. Yamada
16
, and A. Yonehara
22
(The MOA Collaboration)
1
Department of Physics, Chungbuk National University, Cheongju 28644, Korea
2
Warsaw University Observatory, Al. Ujazdowskie 4, 00-478 Warszawa, Poland
3
Korea Astronomy and Space Science Institute, Daejon 34055, Korea
4
Department of Astronomy, Ohio State University, 140 W. 18th Ave., Columbus, OH 43210, USA
5
Max Planck Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany
6
Institute of Natural and Mathematical Sciences, Massey University, Auckland 0745, New Zealand
7
University of Canterbury, Department of Physics and Astronomy, Private Bag 4800, Christchurch 8020, New Zealand
8
Korea University of Science and Technology, 217 Gajeong-ro, Yuseong-gu, Daejeon 34113, Korea
9
Smithsonian Astrophysical Observatory, 60 Garden St., Cambridge, MA 02138, USA
10
School of Space Research, Kyung Hee University, Yongin 17104, Korea
11
Institute for Space-Earth Environmental Research, Nagoya University, Nagoya 464-8601, Japan
12
Code 667, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
13
Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA
14
Department of Physics, University of Auckland, Private Bag 92019, Auckland, New Zealand
15
Okayama Astrophysical Observatory, National Astronomical Observatory of Japan, 3037-5 Honjo, Kamogata, Asakuchi, Okayama 719-0232, Japan
16
Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
17
Nagano National College of Technology, Nagano 381-8550, Japan
18
Tokyo Metropolitan College of Aeronautics, Tokyo 116-8523, Japan
19
School of Chemical and Physical Sciences, Victoria University, Wellington, New Zealand
20
Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, Kanagawa 252-5210, Japan
21
University of Canterbury Mt. John Observatory, P.O. Box 56, Lake Tekapo 8770, New Zealand
22
Department of Physics, Faculty of Science, Kyoto Sangyo University, 603-8555 Kyoto, Japan
Received 2017 May 2; revised 2017 August 7; accepted 2017 August 8; published 2017 September 5
Abstract
We report the discovery of a planet-mass companion to the microlens OGLE-2016-BLG-0263L. Unlike most low-
mass companions that were detected through perturbations to the smooth and symmetric light curves produced by
the primary, the companion was discovered through the channel of a repeating event, in which the companion itself
produced its own single-mass light curve after the event produced by the primary had ended. Thanks to the
continuous coverage of the second peak by high-cadence surveys, the possibility of the repeating nature due to
source binarity is excluded with a 96% confidence level. The mass of the companion estimated by a Bayesian
analysis is
MM4.1
p
2.5
6.5
J
=
-
+
. The projected primary-companion separation is
a
6.5
1.9
1.3
=
^
-
+
au. The ratio of the
separation to the snow-line distance of
a
a 15.4
sl
~
^
corresponds to the region beyond Neptune, the outermost
planet of the solar system. We discuss the importance of high-cadence surveys in expanding the range of
microlensing detections of low-mass companions and future space-based microlensing surveys.
Key words: brown dwarfs – gravitational lensing: micro – planetary systems
1. Introduction
A microlensing signal of a very low-mass companion such
as a planet is usually a brief perturbation to the smooth and
symmetric lensing light curve produced by the single mass of
the primary lens. Short durations of perturbations combined
with the nonrepeating nature of lensing events imply that
microlensing detections of low-mass companions require high-
cadence observations. During the first decade of microlensing
surveys, when the survey cadence was not sufficiently high to
detect short companion signals, lensing experiments achieved
The Astronomical Journal, 154:133 (9pp), 2017 October https://doi.org/10.3847/1538-3881/aa859a
© 2017. The American Astronomical Society. All rights reserved.
23
The OGLE Collaboration.
24
The KMTNet Collaboration.
25
The MOA Collaboration.
1
the required observational cadence by employing a strategy in
which lensing events were detected by wide-field surveys, and
a fraction of these events were monitored using multiple
narrow-field telescopes (Gould & Loeb 1992; Udalski et al.
2005; Beaulieu et al. 2006).
Thanks to the instrumental upgrade of existing surveys and
the addition of new surveys, the past decade has witnessed a
great increase of the observational cadence of lensing surveys.
By entering the fourth phase survey experiment, the Optical
Gravitational Lensing Experiment (OGLE) group substantially
increased the observational cadence by broadening the field of
view (FOV) of their camera from 0.4
deg
2
to 1.4
deg
2
(Udalski
et al. 2015). In addition, the Korea Microlensing Telescope
Network (KMTNet) group started a microlensing survey in
2015 using three globally distributed telescopes, each of which
is equipped with a camera having 4
deg
2
FOV (Kim et al.
2016). Furthermore, the Microlensing Observation in Astro-
physics (MOA) group (Bond et al. 2001; Sumi et al. 2003)
plans to add a new infrared telescope (T. Sumi 2017, private
communication) into the survey. With the elevated sampling
rate, microlensing surveys have become increasingly capable
of detecting short signals without the need for follow-up
observations, e.g., OGLE-2012-BLG-0406Lb (Poleski et al.
2014b), OGLE-2015-BLG-0051/KMT-2015-BLG-0048Lb
(Han et al. 2016), OGLE-2016-BLG-0954Lb (Shin et al.
2016), and OGLE-2016-BLG-0596Lb (Mróz et al. 2017).
One very important merit of high-cadence microlensing surveys
is the increased rate of detecting very low-mass companions.
Currently, more than 2000 lensing events are being detected every
season. Due to the limited resources, however, only a handful of
events can be monitored by follow-up observations. In principle,
follow-up observations can be started at the early stage of
anomalies, but implementing this strategy in practice is challen-
ging due to the difficulty in detecting short anomalies in their
early stages. By contrast, high-cadence surveys are capable of
continuously and densely sampling the light curves of all
microlensing events, and thus the rate of detecting very low-
mass companions is expected to be greatly increased.
Another important advantage of high-cadence surveys is that
they open an additional channel of detecting very low-mass
companions. By definition, under the survey+follow-up
strategy, events can only be densely monitored by follow-up
observations once they have been alerted by surveys.
Furthermore, follow-up resources are limited, so in practice
those observations have been confined to those located in the
narrow region of separations from the host star, the so-called
“lensing zone” (Gould & Loeb 1992; Griest & Safizadeh
1998). In contrast, high-cadence surveys are able to densely
monitor events not only during the lensing magnification but
also before and after it, and this allows low-mass companions
to be detected via the “repeating-event” channel. The signal
through the repeating-event channel is produced by a
companion with a projected separation that is substantially
larger than the Einstein radius of the primary star, and it occurs
when the source trajectory passes the effective magnification
regions of both the primary star and the companion
(Di Stefano
& Scalzo 1999). Thus, the two lenses (primary and companion)
act essentially independently and appear to give rise to two
separate microlensing events with different timescales (related
by the square root of their mass ratio) but the same source star.
Therefore, the channel is important because it expands the
region of microlensing detections of low-mass companions
to larger separations. Under the assumption of power-law
distributions of host-planet separations, Han (2007) estimated
that planets detectable by high-cadence surveys through the
repeating channel will comprise ∼3%–4% of all planets.
In this paper, we report the discovery of a planet-mass binary
companion through the repeating-event channel. In Section 2,
we describe the survey observations that led to the discovery of
the companion. In Section 3, we explain the procedure of
analyzing the observed lensing light curve and present the
physical parameters of the lens system. We discuss the
importance of the repeating-event channel in Section 4.
2. Observation and Data
The low-mass binary companion was discovered from the
observation of the microlensing event OGLE-2016-BLG-
0263. In Figure 1,wepresentthelightcurveoftheevent.
The event occurred on a star located toward the Galactic
bulge field with equatorial coordinates
R.A ., decl.
J2000
=(
)
17 59 34. 9, 31 49 07. 0
hm
s
¢ -
()
that are equivalent to the Galac-
tic coordinates
lb,0.95,4.06=-
-
(
)( )
. The lensing-
induced brighte ni ng of the sourc e star was ide nti fied o n
2016 March 1 (
H
JD HJD 2450000 7448.7¢= - =
) by the
Early Warning System of the OGLE survey (Udalskietal.
1994; Udalski 2003) using the 1.3 m Warsaw telescope at the
LasCampanasObservatoryinChile. Observations by the
OGLE survey w ere conducted with an ∼1 day cadence, and
most images were taken in the standard Cousins I band with
occasiona l observati on s in the J ohns on V ba nd for col or
measurement. After being identified, the event fo llowe d a
standard point-source point-lens (PSPL) light c urve, peaked at
H
JD 7470¢~
, and gradually r eturned to the baseline magni-
tude of
I
16.9~
.
However, after returning to baseline, the source began to
brighten again. The anomaly was noticed on 2016 May 30
(
H
JD 7538~
) and announced to the microlensing community for
possible follow-up observations, although none were conducted.
The anomaly, which continued for about 10 days, appears to be an
independent PSPL event with a short timescale. The time between
the first and second peaks of the light curve is ∼73 days.
The event was also in the footprint of the KMTNet and
MOA surveys. The KMTNet survey utilizes three globally
distributed 1.6 m telescopes that are located at the Cerro Tololo
Figure 1. Light curve of OGLE-2016-BLG-0263. The curve superposed on the
data points represents the best-fit binary-lens model. The arrow denotes the
time when the event was first discovered. The lower panel shows the residual
from the model.
2
The Astronomical Journal, 154:133 (9pp), 2017 October Han et al.
Interamerican Observatory in Chile (KMTC), the South
African Astronomical Observatory in South Africa (KMTS),
and the Siding Spring Observatory in Australia (KMTA).
Similar to the OGLE observations, most of the KMTNet data
were acquired using the standard Cousins I-band filter with
occasional V-band observations. The event was in the BLG34
field for which observations were carried out with an ∼2.5 hr
cadence. The MOA survey uses the 1.6 m telescope located at
the Mt.John University Observatory in New Zealand. Data
were acquired in a customized R-band filter with a bandwidth
corresponding to the sum of the Cousins R and I bands. The
event was independently found by the MOA survey and
dubbed MOA-2016-BLG-075.
Photometry of the images was conducted using pipelines
based on the difference imaging analysis method (Alard &
Lupton 1998;Woźniak 2000) and customized by the individual
groups: Udalski (2003) for OGLE, Albrow et al. (2009) for
KMTNet, and Bond et al. (2001) for MOA. In order to analyze
the data sets acquired by different instruments and reduced by
different photometry pipelines, we readjust the error bars of the
individual data sets. Following the usual procedure described in
Yee et al. (2012), we normalize the error bars by
k ,1
0
2
min
2
12
sss=+() ()
where
0
s
is the error bar estimated from the photometry
pipeline,
min
s
is a term used to adjust error bars for consistency
with the scatter of the data set, and k is a normalization factor
used to make the
2
c
per degree of freedom unity. The
2
c
value
is computed based on the best-fit solution of the lensing
parameters obtained from modeling (Section 3). In Table 1,we
list the error-bar adjustment factors for the individual data sets.
We note that the OGLE data used in our analysis were
rereduced for optimal photometry and the error bars were
estimated according to the prescription described in Skowron
et al. (2016), although one still needs a nonunity (
k 1
¹
)
scaling factor to make
dof 1
2
c =
.
3. Analysis
The light curve of OGLE-2016-BLG-0263 is characterized
by two peaks in which the short second one occurred well after
the first one. The light curve of such a repeating event can be
produced in two cases. The first case is a binary-source (BS)
event in which the double peaks are produced when the lens
passes close to both components of the source separately, one
after another (Griest & Hu 1992; Sazhin & Cherepash-
chuk 1994; Han & Gould 1997). The other case is a binary-
lens (BL) event, where the source approaches both components
of a widely separated BL, and the source flux is successively
magnified by the individual lens components (Di Stefano &
Mao 1996). The degeneracy between BS and BL perturbations
was first discussed by Gaudi (1998). In order to investigate the
nature of the second peak, we test both the BS and BL
interpretations.
3.1. BS Interpretation
The light curve of a repeating BS event is represented by the
superposition of the PSPL light curves involved with the
individual source stars, i.e.,
A
AF AF
FF
AAq
q1
.2
F
F
BS
1 0,1 2 0,2
0,1 0,2
12
=
+
+
=
+
+
()
Here
F
i
0,
represents the baseline fluxes of the individual source
components and
qFF
F
0,2 0,1
=
is the flux ratio between the
source components. The lensing magnification involved with
each source component is represented by
A
u
uu
uu
tt
t
2
4
;,3
i
i
i
i
i
i
i
2
2
12
0,
2
0,
E
2
12
=
+
+
=+
-
⎡
⎣
⎢
⎢
⎛
⎝
⎜
⎞
⎠
⎟
⎤
⎦
⎥
⎥
()
()
where
t
i
0,
is the time of the closest lens-source approach,
u
i0,
is
the lens-source separation at that moment, and
t
E
is the Einstein
timescale. For the basic description of the light curve of a BS
event, therefore, one needs six lensing parameters, including
t
0,1
,
t
0,2
,
u
0,1
,
u
0,2
,
t
E
, and q
F
(Hwang et al. 2013). The light
curve is then modeled as
Ft FA t t u t u t q F;, ,, ,, , , 4
jk sj k
F
bj, BS 0,1 0,1 0,2 0,2 E ,
=+() ( ) ()
where
FF,
sj bj,,
(
)
are specified separately for each observatory
but there is a single q
F
for all observatories using a single band
(e.g., the I band).
We model the observed light curve based on the BS
parameters. Since the light curve of a BS event varies smoothly
with the changes of the lensing parameters, we search for the
best-fit parameters by
2
c
minimization using a downhill
approach. For the downhill approach, we use the Markov
chain Monte Carlo (MCMC) method. We set the initial values
of
t
0,1
and
t
0,2
based on the times of the first and second peaks,
respectively, while the initial values of
u
0,1
and
u
0,2
are
determined based on the peak magnifications of the individual
peaks. Since both PSPL curves of the individual peaks share a
common timescale,
26
we set the initial value of
t
E
as that
estimated based on the PSPL fitting of the light curve with the
first peak. The initial value of the flux ratio q
F
is guessed based
on the values of
u
i0,
.
In Table 2, we present the parameters of the best-fitBS
solution. Also presented is the ratio of the source flux F
s
to that
of the blend F
b
that is estimated from the OGLE data set. The
uncertainties of the lensing parameters are estimated based on
the scatter of points on the MCMC chain. According to the
solution, the second peak was produced by the lens approach-
ing very close to the second source, which is approximately 30
times fainter than the primary source star. In Figure 2 ,we
present the model light curve (dotted curve) superposed on the
observed data points. At first glance, the model appears to
describe the overall shape of the second peak. However, careful
inspection of the model light curve and the residual reveals that
the fit is inadequate not only in the rising and falling parts but
also near the peak part of the light curve.
Table 1
Error-bar Correction Factors
Data Set k
min
s
OGLE 1.452 0.001
MOA 1.212 0.001
KMT (CTIO) 1.204 0.001
KMT (SAAO) 1.806 0.001
KMT (SSO) 1.300 0.001
26
In the Appendix, we discuss the possibility of different timescales due to the
orbital motion of the source.
3
The Astronomical Journal, 154:133 (9pp), 2017 October Han et al.
We check whether the fit can be further improved with
higher-order effects. The trajectory of the lens with respect to
the source might deviate from rectilinear due to the orbital
motion of the Earth around the Sun. We check this so-called
“microlens-parallax” effect (Gould 1992) by conducting
additional modeling. Accounting for microlens-parallax effects
requires including two additional parameters of
NE,
p
and
EE,
p
,
which represent the components of the microlens parallax
vector
E
p
projected onto the sky along the north and east
equatorial coordinates, respectively. The direction of
E
p
corresponds to that of the relative lens-source motion in the
Earth’s frame. The magnitude of
E
p
is
ErelE
ppq=
, where
DDau
rel
S
1
L
1
p =-
--
()
is the relative lens-source parallax and
D
L
and
D
S
represent the distances to the lens and source,
respectively. From the modeling with parallax effects, we find
that the improvement of the fit is very minor with
4.4
2
c
D
~
.
3.2. BL Interpretation
Unlike the case of a BS event, the light curve of a BL event
cannot be described by the superposition of the two light curves
involved with the individual lens components because the lens
binarity induces a region of discontinuous lensing magnifica-
tions, i.e., caustics. As a result, the lensing parameters needed
to describe a BL event are different from those of a BS event.
Basic description of a BL event requires six principal
parameters. The first three of these parameters, t
0
, u
0
, and
t
E
,
are the same as those of a single-lens event. The other three
parameters describe the BL, including the projected separation
s (normalized to
E
q
), the mass ratio q between the binary
components, and the angle between the source trajectory and
the binary axis, α. Light curves produced by binary lenses are
often identified by characteristic spike features that are
produced by the source crossings over or approaches close to
caustics. In this case, the caustic-involved parts of the light
curve are affected by finite-source effects. To account for finite-
source effects, one needs an additional parameter,
E
*
r
qq=
,
where
*
q
is the angular source radius. For OGLE-2016-BLG-
0263, however, the light curve does not show any feature
involved with a caustic, and thus we do not include ρ as a
parameter.
Binary lenses form caustics of three topologies (Schneider &
Weiss 1986; Erdl & Schneider 1993), which are usually
referred to as “close,”“resonant,” and “wide.” For a “resonant”
binary, where the projected binary separation is equivalent to
the angular Einstein radius, i.e.,
s
1~
, the caustics form a
single big closed curve with six cusps. For a “close” binary
with
s
q13
4
12
<-
(Dominik 1999), the caustic consists of
two parts, where one four-cusp caustic is located around the
barycenter of the BL and two small three-cusp caustics are
positioned away from the barycenter. For a “wide” topology
with
s
q13
2
12
>+
(Dominik 1999), there exist two four-
cusp caustics that are located close to the individual lens
components.
A repeating BL event is produced by a wide BL, and the
individual peaks of the repeating event occur when the source
approaches the four-cusp caustics of the wide BL. The caustic
has an offset of
xqs q1
D
~+(
)
with respect to each lens
position toward the other lens component (Di Stefano &
Mao 1996; An & Han 2002). In the very wide binary regime
with
s
1
, each of the two caustics is approximated by the
tiny astroidal Chang–Refsdal caustic with an external shear
qs q1
2
g
=+[( )
]
(Chang & Refsdal 1984) and the offset
x 0
D
, implying that the position of the caustic approaches
that of the lens components. In this regime, the light curves
involved with the individual BL components are described by
two separate PSPL curves, and the light curve of the repeating
event is approximated by the superposition of the two PSPL
curves, i.e.,
Ft FAt At F
Sbobs 1 2
=++() [ () ()]
, where
F
obs
is the
observed flux and A
1
and A
2
represent the lensing magnifications
involved with the individual lens components. To be noted is
that the timescales of the two PSPL curves of a repeating
event are proportional to the square root of the masses of the
lens components, i.e.,
tt mm q
E,2 E,1 2 1
12 12
==()
, while the
timescales of the two PSPL curves of a repeating BS event are
the same because both PSPL curves are produced by a
common lens.
To test the BL interpretation, we conduct BL modeling of the
observed light curve. Similar to the BS case, we set the initial
values of the lensing parameters based on the time of the major
peak for t
0
, the peak magnification of the major event for u
0
,
the duration of the major event for
t
E
, the ratio of the time gap
between the two peaks to the event timescale for
s
tt
E
~D
,
the ratio between the timescales of the first and second events
for
qtt
E,2 E,1
2
~ ()
, and
0a ~
for a repeating BL event. Based
on these initial values, we search for a BL solution using the
Table 2
Best-fit Binary-source Solution
Parameter Value
2
c
2598.8
t
0,1
(HJD) 2457470.441±0.028
t
0,2
(HJD) 2457543.426±0.028
u
0,1
0.646±0.032
u
0,2
0.095±0.004
t
E
(days) 15.33±0.50
q
F
I
,
0.037±0.002
q
FR,
0.036±0.002
FF
sb
2.452/0.219
Figure 2. Enlarged view of the light curve around the second peak. Superposed
on the data points are the model light curves obtained from binary-lens (solid)
and binary-source (dotted) analysis. The lower panels show the residual from
the individual models.
4
The Astronomical Journal, 154:133 (9pp), 2017 October Han et al.
MCMC downhill approach. To double-check the result, we
conduct a grid search for a solution in the parameter space of
sq,,a
(
)
. From this, we confirm that the solution found based
on the initial values of the lensing parameters converges with
the solution found by the grid search.
Although the binary-lensing model does not suffer from the
degeneracy in the s and q parameters, it is found that there
exists a degeneracy in the source trajectory angle α. This
degeneracy occurs because a pair of solutions with source
trajectories passing the lens components on the same, (+, +),
solution and the opposite, (+, −), solution sides with respect to
the binary axis results in similar light curves (see Figure 3). For
OGLE-2016-BLG-0263, we find that the (+, +) solution is
slightly preferred over the (+, −) solution by
7.8
2
c
D
=
.
In Table 3, we present the best-fit BL parameters along with
the
2
c
value of the fit. Since the degeneracy between the (+, +)
and (+, −) solutions is quite severe, we present both solutions.
Because the difference between the source trajectory angles of
the two solutions is small, it is found that the lensing
parameters of the two solutions are similar to each other.
Two factors to be noted are that the binary separation,
s
4.7~
,
is substantially greater than the Einstein radius and that the
mass ratio between the lens components,
q 0.0
3
~
, is quite
small. We present the model light curve of the best-fitBL
solution, i.e., the (+, +) solution, in Figure 1 for the whole
event and Figure 2 for the second peak.
In Figure 3, we present the lens system geometry that shows
the source trajectory (line with an arrow) with respect to the
lens components ( blue dots). The upper and lower panels are
for the (+, + ) and (+, −) solutions, respectively. The tiny red
cuspy closed curves near the individual lens components
represent the caustics. We note that all lengths are scaled to the
angular Einstein radius corresponding to the total mass of the
BL. The two dotted circles around the individual caustics
represent the Einstein rings corresponding to the masses of the
individual BL components with radii
r
q11
1
12
=+[( )]
and
r
qq1
2
12
=+[( )]
. From the geometry, one finds that the
source trajectory approached both lens components and the two
peaks in the lensing light curve were produced at the moments
when the source approached the caustics near the individual
lens components. In the regime with a small mass ratio,
q 1
,
the caustics located close to the higher- and lower-mass lens
components are often referred to as “central” and “planetary”
caustics, respectively. The small central caustic is located
very close to the higher-mass lens component, and its size
as measured by the width along the binary axis is
qs s4 0.006
12
~-~
-
()
(Chung et al. 2005). The compara-
tively larger planetary caustic is located on the side of the
lower-mass lens component with a separation from the heavier
lens component of
ss14.6~- ~
. The size of the planetary
caustic is related to the separation and mass ratio of the BL by
qss4 1 0.03
12 2 12
~-~[( ) ]
(Han 2006). Since the distance
to each caustic from the source trajectory is much greater than
the caustic size, the light curve involved with each lens
component appears as a PSPL curve.
3.3. Comparison of Models
Knowing that both BS and BL interpretations can explain the
repeating nature of the lensing light curve, we compare the two
models in order to find the correct interpretation of the event.
For this, we construct the cumulative distribution of the
2
c
difference between the two models.
Figure 4 shows the constructed
2
c
D
distribution, where
2
BS
2
B
L
2
ccc
D
= –
. The distribution shows that the BL inter-
pretation describes the observed light curve better than the BS
interpretation does. The biggest
2
c
D
occurs during the second
peak. This can also be seen in Figure 2, where the residuals
from both models around the second peak are presented. The
total
2
c
difference is
160
2
c
D
~
. To show the statistical
significance of the difference between the two models, we
conduct an F-test for the residuals from the models in the
region around the second peak. From this, we find F = 1.78.
This corresponds to an
96%~
probability that the two models
have different variances, suggesting that they can be distin-
guished with a significant confidence level.
We note that the unambiguous discrimination between the
two interpretations was possible due to the continuous coverage
of the second peak using the globally distributed telescopes.
One may note large gaps in the observations from Chile
(
7
537 HJD 7546<¢<
) and Australia (
7
540 HJD 7551<¢<
),
Figure 3. Lens system geometry that shows the source trajectory (line with an
arrow) with respect to the binary-lens components (blue dots). Here M
1
and M
2
denote the heavier- and lower-mass components of the binary lens. The dotted
circles represent the boundary of effective lensing magnification, and the size
of each circle corresponds to the Einstein radius corresponding to the mass of
each lens component. The tiny close curves at the centers of the dotted circles
represent the caustics. The inset shows the enlarged view of the caustic located
close to M
2
.
Table 3
Best-fit Binary-lens Solution
Parameter (+, +) Solution (+, −) Solution
2
c
2438.2 2446.0
t
0
(HJD) 2457470.433± 0.036 2457470.432±0.036
u
0
0.581±0.027 0.599±0.031
t
E
(days) 16.24±0.45 15.92±0.51
s 4.72±0.12 4.86±0.15
q (10
−2
) 3.06±0.08 2.97±0.09
α (rad) 0.095±0.002 0.163±0.003
FF
sb
2.419/0.254 2.543/0.131
5
The Astronomical Journal, 154:133 (9pp), 2017 October Han et al.