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Astronomy & Astrophysics manuscript no. pap c
ESO 2019
January 24, 2019
Two new free-floating or wide-orbit planets from microlensing
Przemek Mróz?1, Andrzej Udalski1, David P. Bennett2,3, Yoon-Hyun Ryu4, Takahiro Sumi5, Yossi
Shvartzvald6, and,
Jan Skowron1, Radosław Poleski1,7, Paweł Pietrukowicz1, Szymon Kozłowski1, Michał K. Szymański1,
Łukasz Wyrzykowski1, Igor Soszyński1, Krzysztof Ulaczyk1,8, Krzysztof Rybicki1, Patryk Iwanek1
(The OGLE Collaboration),
Michael D. Albrow9, Sun-Ju Chung4,10, Andrew Gould4,11,7, Cheongho Han12 , Kyu-Ha Hwang4,
Youn Kil Jung4, In-Gu Shin13, Jennifer C. Yee13, Weicheng Zang14, Sang-Mok Cha4,15, Dong-Jin Kim4,
Hyoun-Woo Kim4, Seung-Lee Kim4,10, Chung-Uk Lee4,10, Dong-Joo Lee4, Yongseok Lee4,15 ,
Byeong-Gon Park4,10, Richard W. Pogge7(The KMTNet Collaboration),
Fumio Abe16, Richard Barry2, Aparna Bhattacharya2,3, Ian A. Bond17, Martin Donachie18,
Akihiko Fukui19,20 , Yuki Hirao3,5, Yoshitaka Itow16, Kohei Kawasaki5, Iona Kondo5, Naoki Koshimoto21,22,
Man Cheung Alex Li18, Yutaka Matsubara16 , Yasushi Muraki16, Shota Miyazaki5, Masayuki Nagakane5,
Clément Ranc2, Nicholas J. Rattenbury18 , Haruno Suematsu5, Denis J. Sullivan23, Daisuke Suzuki24,
Paul J. Tristram25 , Atsunori Yonehara26 (The MOA Collaboration),
Dan Maoz27, Shai Kaspi27 , and Matan Friedmann27 (The Wise Group)
(Affiliations can be found after the references)
Received 2018 XX XX / Accepted 2018 YY YY
ABSTRACT
Planet formation theories predict the existence of free-floating planets that have been ejected from their parent systems. Although
they emit little or no light, they can be detected during gravitational microlensing events. Microlensing events caused by rogue
planets are characterized by very short timescales tE(typically below two days) and small angular Einstein radii θE(up to several
µas). Here we present the discovery and characterization of two ultra-short microlensing events identified in data from the Optical
Gravitational Lensing Experiment (OGLE) survey, which may have been caused by free-floating or wide-orbit planets. OGLE-
2012-BLG-1323 is one of the shortest events discovered thus far (tE= 0.155 ±0.005 d, θE= 2.37 ±0.10 µas) and was caused by an
Earth-mass object in the Galactic disk or a Neptune-mass planet in the Galactic bulge. OGLE-2017-BLG-0560 (tE= 0.905±0.005 d,
θE= 38.7±1.6µas) was caused by a Jupiter-mass planet in the Galactic disk or a brown dwarf in the bulge. We rule out stellar
companions up to a distance of 6.0 and 3.9 au, respectively. We suggest that the lensing objects, whether located on very wide
orbits or free-floating, may originate from the same physical mechanism. Although the sample of ultrashort microlensing events is
small, these detections are consistent with low-mass wide-orbit or unbound planets being more common than stars in the Milky
Way.
Key words. Planets and satellites: detection, Gravitational lensing: micro
1. Introduction
Theories of planet formation predict the existence of free-
floating (rogue) planets that are not gravitationally teth-
ered to any host star. These objects could have formed
in protoplanetary disks around stars, as “ordinary” plan-
ets, and could have been ejected as a result of various
mechanisms, including planet-planet dynamical interac-
tions (e.g., Rasio & Ford 1996; Weidenschilling & Marzari
1996; Marzari & Weidenschilling 2002; Chatterjee et al.
2008; Scharf & Menou 2009; Veras et al. 2009), ejections
from multiple-star systems (e.g., Kaib et al. 2013; Suther-
land & Fabrycky 2016), stellar flybys (e.g., Malmberg et al.
2011; Boley et al. 2012; Veras & Moeckel 2012), dynamical
interactions in stellar clusters (e.g., Hurley & Shara 2002;
Spurzem et al. 2009; Parker & Quanz 2012; Hao et al. 2013;
Liu et al. 2013), or the post-main-sequence evolution of the
?Corresponding author: pmroz@astrouw.edu.pl
host star(s) (e.g., Veras et al. 2011, 2016; Kratter & Perets
2012; Voyatzis et al. 2013).
It is believed that low-mass planets are more likely to be
scattered to wide orbits or ejected than giant, Jupiter-mass
planets. Calculations of Ma et al. (2016), which are based on
the core accretion theory of planet formation, predict that
most free-floating planets should be of Earth mass. Rogue
planets are more likely to form around FGK-type stars,
because they are scattered into wide orbits following close
encounters with gas giant planets, which are more likely
to form around massive stars. The typical total ejected
mass is about 5−20 M⊕and about 10-20% of all plane-
tary systems should give rise to rogue planets. Similarly,
Barclay et al. (2017), using N-body simulations of terres-
trial planet formation around solar-type stars, estimated
that about 2.5 terrestrial-mass planets are ejected per star
in the Galaxy during late-stage planet formation, but these
numbers strongly depend on the adopted initial conditions.
Article number, page 1 of 8
arXiv:1811.00441v2 [astro-ph.EP] 23 Jan 2019
A&A proofs: manuscript no. pap
Free-floating planetary-mass objects can also be formed
by the fragmentation of gas clouds, in a way similar to that
in which stars form. Star formation processes are believed to
extend down to 1−4MJup (Boyd & Whitworth 2005; Whit-
worth & Stamatellos 2006). This parameter space cannot
be probed with the current surveys of young stellar clus-
ters and star-forming regions, which are unable to detect
objects less massive than 5−6MJup (Peña Ramírez et al.
2012; Lodieu et al. 2013; Mužić et al. 2015). Free-floating
planetary-mass objects may also form from small molecular
cloudlets that have been found in H II regions, although it
is unclear whether these clouds may contract (Gahm et al.
2007; Grenman & Gahm 2014).
Gravitational microlensing is the only method that en-
ables us to find Earth-mass free-floating planets. A gravita-
tional microlensing event occurs when a lens (free-floating
planet or star) is very closely aligned with a distant source
star, with the angular separation smaller than the Einstein
radius of the lens θE= 5 µas pM/10 M⊕pπrel /0.1 mas
(here, Mis the lens mass, πrel =πl−πsis the relative lens-
source parallax, and πland πsare parallaxes to the lens and
source, respectively). The gravitational field of the lens can
focus light rays of the source, causing a transient bright-
ening of the source to an Earth-based observer. As typical
lens-source proper motion in the direction of the Galactic
center is µrel = 5 mas/yr, timescales of microlensing events
due to Earth-mass lenses are very short tE=θE/µrel ≈
10−3yr ≈0.4d.
Because angular radii of giant source stars in the Galac-
tic bulge ρ∗= 6 µas(R/10 R) (πs/0.125 mas) are compa-
rable to angular Einstein radii of planetary-mass lenses,
light curves of giant-source events attributed to free-floating
planets should exhibit strong finite source effects (as each
point on the source surface is magnified by a different
amount). Detection of the finite source effects in the light
curve allows us to measure θE, which can place additional
constraints on the mass of the lens. Direct calculations of
the lens mass require additional information on πrel, but the
parallax measurement is challenging for such short events
(see Introduction in Mróz et al. 2018).
Microlensing events on timescales shorter than 2d have
been traditionally attributed to unbound planets. A statis-
tical analysis of 474 events discovered by the Microlensing
Observations in Astrophysics (MOA) group led to the claim
of an excess of events on timescales of 1–2d (corresponding
to Jupiter-mass lenses) and the suggestion that they are
caused by a sizable population of Jupiter-mass wide-orbit
or free-floating planets (Sumi et al. 2011). The analysis of a
larger data set collected during the years 2010–2015 of the
fourth phase of the Optical Gravitational Lensing Experi-
ment (OGLE-IV) did not confirm these findings (Mróz et al.
2017). Mróz et al. (2017) found a 95% upper limit on the
frequency of Jupiter-mass rogue planets in the Milky Way
of 0.25 per star. They detected, however, a few very short
events (tE<0.5d), which could be attributed to Earth-
and super-Earth-mass free-floating planets. Their sampling
was, however, insufficient to detect finite source effects. See
Mróz et al. (2017) and Mróz et al. (2018) for a detailed
discussion.
The only known ultrashort microlensing event that ex-
hibited prominent finite source effects, OGLE-2016-BLG-
1540, was identified by Mróz et al. (2018) in the OGLE
data from the 2016 observing season. This event was likely
caused by a Neptune-mass free-floating planet, as inferred
15.30
15.32
15.34
15.36
15.38
15.40
15.42
15.44
15.46
Magnitude
OGLE
MOA
Wise
OGLE-2012-BLG-1323
tE= 0.155 ±0.005 d
ρ= 5.03 ±0.07
6157 6158 6159 6160 6161 6162 6163 6164 6165
HJD - 2450000
−0.04
−0.02
0.00
0.02
0.04
Residual
13.95
14.10
14.25
14.40
14.55
14.70
14.85
15.00
Magnitude
OGLE
KMT CTIO
KMT SAAO
KMT SSO
OGLE-2017-BLG-0560
tE= 0.905 ±0.005 d
ρ= 0.901 ±0.005
7856 7857 7858 7859 7860 7861 7862 7863
HJD - 2450000
−0.04
−0.02
0.00
0.02
0.04
Residual
Fig. 1. Light curves of two ultrashort microlensing events. Up-
per panel: OGLE-2012-BLG-1323. Lower panel: OGLE-2017-
BLG-0560. Both events show strong finite-source effects, which
allows us to measure their angular Einstein radii.
from the measurement of the angular Einstein radius. En-
couraged by this discovery, we searched for short-timescale
microlensing events in the OGLE data from the 2017 sea-
son and complemented them with photometric observations
from the Korea Microlensing Telescope Network (KMT-
Net). We also searched for short-duration microlensing
events with giant sources in the archival OGLE data col-
lected during the 2010–2015 period.
Here we report the discovery and characterization of two
microlensing events, OGLE-2012-BLG-1323 and OGLE-
2017-BLG-0560, which can be attributed to free-floating
planets. We show that, although the sample of these events
is small, these detections are consistent with terrestrial-
mass wide-orbit or unbound planets being more common
than stars in the Milky Way.
2. Observations
Microlensing event OGLE-2017-BLG-0560 was announced
on 2017 April 16 by the OGLE Early Warning System
(Udalski 2003). This event was located at equatorial co-
ordinates of R.A. = 17h51m51s
.33, Dec. = −30◦2703100
.4
(J2000.0) in the field BLG534, which was observed with
Article number, page 2 of 8
Mróz et al.: Two new free-floating planet candidates from microlensing
Table 1. Short-timescale microlensing events exhibiting finite source effects
Parameter OGLE-2012-BLG-1323 OGLE-2017-BLG-0560 OGLE-2016-BLG-1540
Microlensing model:
t0(HJD0)6161.107 ±0.008 7859.523 ±0.003 7606.726 ±0.002
tE(days) 0.155 ±0.005 0.905 ±0.005 0.320 ±0.003
u00.63+0.64
−0.44 0.105+0.031
−0.045 0.53 ±0.04
ρ5.03 ±0.07 0.901 ±0.005 1.65 ±0.01
Is15.43 ±0.05 14.91 ±0.05 14.76 ±0.05
fs1.00 (fixed) 1.00 (fixed) 1.00 (fixed)
Source star:
IS,014.09 ±0.06 12.47 ±0.05 13.51 ±0.09
(V−I)S,01.73 ±0.02 2.31 ±0.02 1.67 ±0.02
(V−K)S,03.77 ±0.03 4.73 ±0.06 3.67 ±0.03
Teff (K) 3800 ±200 3600 ±200 3900 ±200
Γ(limb darkening, Iband) 0.40 0.41 0.36
Λ(limb darkening, Iband) 0.30 0.28 0.34
θ∗(µas) 11.9±0.5 34.9±1.5 15.1±0.8
Physical parameters:
θE(µas) 2.37 ±0.10 38.7±1.6 9.2±0.5
µrel,geo (mas yr−1)5.6±0.3 15.6±0.7 10.5±0.6
Notes. HJD0=HJD–2450000. fs=Fs/(Fs+Fb)is the blending parameter. Parameters for OGLE-2016-BLG-1540 are shown for
comparison and are taken from Mróz et al. (2018).
a cadence of 60 minutes. The OGLE survey operates from
Las Campanas Observatory, Chile, and uses a dedicated 1.3
m Warsaw Telescope, equipped with a mosaic CCD camera
with a field of view of 1.4 deg2(see Udalski et al. 2015 for
details of the survey).
This event was also observed by three identical 1.6 m
telescopes from the KMT Network (Kim et al. 2016), which
are located at the Cerro Tololo Inter-American Observatory
(CTIO; Chile), the South African Astronomical Observa-
tory (SAAO; South Africa), and the Siding Spring Obser-
vatory (SSO; Australia). The event was located in the two
overlapping fields BLG01 and BLG41, each observed with
a cadence of 30 minutes. For the modeling, we used obser-
vations collected between March 7 and May 26, 2017.
The second event analyzed in this paper, OGLE-2012-
BLG-1323, was also discovered by the OGLE Early Warn-
ing System, on 2012 August 21. This event is located at
equatorial coordinates of R.A. = 18h00m18s
.51, Dec. =
−28◦3500100
.7(J2000.0) in the field BLG512, which was
monitored with a cadence of 20 minutes. This event was
not previously identified as a free-floating planet candidate
(Mróz et al. 2017), owing to its extremely low amplitude
(below 0.1 mag).
We supplement OGLE observations with the data from
the MOA (Bond et al. 2001) and Wise groups (Shvartz-
vald et al. 2016). MOA observations were collected using
the 1.8 m telescope at Mt. John University Observatory in
New Zealand (Sumi et al. 2013). Wise observations were
taken with the 1 m telescope at Wise Observatory in Israel
equipped with the LAIWO camera.
All data were taken in the Iband except for MOA data;
the MOA group uses a custom wide filter, which is effec-
tively the sum of the standard Rand Ifilters. Photometry
was extracted using custom implementations of the differ-
ence image analysis technique: Woźniak (2000; OGLE), Al-
brow (2017; KMTNet and Wise), and Bond et al. (2001;
MOA).
3. Light curve modeling
Light curves of both events are well described by the
extended-source point-lens model (Fig. 1), which is defined
by four parameters: t0(time of the closest lens-source ap-
proach), u0(impact parameter in Einstein radius units), tE
(event timescale), and ρ=θ∗/θE(normalized radius of the
source, i.e., the ratio of the angular radius of the source θ∗
to the angular Einstein radius θE). Two additional parame-
ters (for each observatory and filter) are needed to describe
the source star flux (Fs) and unmagnified flux of the blend
(Fb). When the blend flux is allowed to vary, the best-fit
solutions are characterized by negative blending (Fb<0).
We therefore, following the approach of Mróz et al. (2018),
kept Fb= 0 constant, but we also added in quadrature 0.05
mag to the uncertainty of the source brightness.
The best-fit parameters and their uncertainties are
shown in Table 1. The uncertainties are estimated us-
ing the Markov chain Monte Carlo technique (Foreman-
Mackey et al. 2013) and represent 68% confidence intervals
of marginalized posterior distributions.
To describe the brightness profile of the source star,
we adopted the square-root limb-darkening law, described
by two parameters Γand Λ(which are filter-dependent;
Yoo et al. 2004). If allowed to vary, Γand Λare strongly
correlated. We thus kept limb-darkening coefficients con-
stant, using the limb-darkening models of Claret & Bloe-
men (2011) (see Table 1 for their numerical values). We used
ATLAS models and assumed a solar metallicity, microtur-
bulent velocity of 2km/s, and surface gravity of log g= 2.0
(Γand Λare weakly dependent on log gif log g≤2.0), as
is appropriate for giant sources.
The archival light curve of OGLE-2017-BLG-0560 shows
low-amplitude (0.02 mag), semi-regular variability that is
typical of OGLE small amplitude red giants (Wray et al.
2004). The strongest pulsation period in the 2017 data is
18.9 d. As the effective duration of the event (3 days) is
much shorter than the pulsation period, we expected that
Article number, page 3 of 8
A&A proofs: manuscript no. pap
the inferred model parameters should not be strongly influ-
enced by the variability of the source. Additional modeling,
in which we assume that the flux of the source varies sinu-
soidally with a period of 18.9 d, results in almost identical
microlensing parameters (within the error bars) to those of
the model with the constant source.
We also searched for terrestrial parallax signal (Gould
et al. 2009; Yee et al. 2009; Freeman et al. 2015) in the light
curve of OGLE-2012-BLG-1323, but the χ2improvement
was insignificant (∆χ2= 1) and the limits on the microlens
parallax were very poor. We did not fit the parallax model
to the light curve of OGLE-2017-BLG-0560 because of the
low-level variability of the source.
Finally, we also searched for possible binary lens mod-
els. Short-duration events may be caused by close binary
lenses (when the projected separation s, in Einstein radius
units, is much smaller than 1), when the source crosses a
small triangle-shaped caustic that is far (∼1/s) from the
center of mass. The expected light curves are asymmetric,
unless the source is larger than the caustic. In that case the
light curve may superficially look like an extended-source
point-lens event, except that it has a more extended tail.
We found that the best-fitting close binary models are dis-
favored by ∆χ2of several hundred for OGLE-2012-BLG-
1323 and even more for OGLE-2017-BLG-0560. The latter
event has a large amplitude (≈1mag), but the peak mag-
nification in close binary models is usually much lower than
that, unless the source is small (ρ < 0.001) and the light
curve is asymmetric. We cannot rule out that the lens is a
wide-orbit planet; we discuss these cases in Section 4.3.
4. Physical parameters
4.1. Source stars
Model parameters can be translated into physical param-
eters of the lens provided that the angular radius of the
source star is known. Here we use a standard technique
(Yoo et al. 2004) of measuring the offset of the source from
the centroid of red clump giants in the calibrated color–
magnitude diagram in a 20×20region around the event
(about 5 pc ×5 pc at the Galactic center distance; Figure 2).
Because we lack color observations collected during the two
events, our best estimate for the color of the source is the
color of the baseline star. This is further supported by the
lack of evidence for blending in the I-band light curves and
the low probability of bright unmagnified blends. As the
intrinsic color (Bensby et al. 2011) and dereddened bright-
ness of the red clump (Nataf et al. 2013) are known toward
a given direction, we are able to calculate the dereddened
color and brightness of the source. Subsequently, we use
color–color (Bessell & Brett 1988) and color–surface bright-
ness (CSB) (Kervella et al. 2004) relations for giants to mea-
sure the angular radius of the source star1. We also use the
1As both sources are very red, it is important to determine how
well the empirical CSB relations are calibrated in this range.
The relation of Kervella et al. (2004) was derived for giants with
colors 0.9<(V−K)0<2.5, but it agrees well with the earlier
relation by Fouque & Gieren (1997), which is valid in a wider
color range. Groenewegen (2004) published a CSB relation for
M giants (3.2<(V−K)0<6.1), which gives angular radii
that are systematically 10% lower than those based on Kervella
et al. (2004): θ∗= 10.9±0.7µas (OGLE-2012-BLG-1323) and
θ∗= 29.8±1.9µas (OGLE-2017-BLG-0560). Adams et al. (2018)
color–temperature relations of Houdashelt et al. (2000a,b)
and Ramírez & Meléndez (2005) to estimate the effective
temperature of the source. The angular Einstein radius is
θE=θ∗/ρ and the relative lens-source proper motion (in
the geocentric frame) is µrel,geo =θE/tE. The heliocentric
correction (v⊕,⊥πrel/au, where v⊕,⊥is the Earth’s velocity
projected on the sky), which should be added vectorially,
is of the order of 3πrel yr−1and is negligible unless the lens
is nearby (closer than 1 kpc from the Sun). The physical
parameters of the source star and lens are given in Table 1.
4.2. Proper motion of source stars
Because source stars are bright and lenses contribute little
(if any) light, the absolute proper motions of the sources can
be found in the second Gaia data release (DR2) (Gaia Col-
laboration et al. 2016, 2018). We recall, however, that the
Gaia performance in the crowded regions of the Galactic
center is poor, especially for faint sources. Figure 3 shows
proper motions of stars located within 40of the sources. In
both cases source proper motions are consistent with those
of Galactic bulge stars (represented by red clump and red
giant branch stars), although proper motions measured rel-
ative to the mean velocity of the bulge are high. This con-
tributes to the high relative lens-source proper motion of
OGLE-2017-BLG-0560 and its very short timescale.
4.3. Constraints on the host star
If the trajectory of the source passed near a putative host
star, we would detect additional anomalies in the light
curves of both events. As we have not found any, we are
able to provide only lower limits on the projected star-
planet separation, using the method of Mróz et al. (2018).
In short, the description of a binary lens requires three ad-
ditional parameters: mass ratio q, separation s(in Einstein
radius units), and angle αbetween the source trajectory
and binary axis. We consider a 0.3Mhost located ei-
ther in the Galactic disk (πrel = 0.1mas) or in the bulge
(πrel = 0.01 mas), which corresponds to θE,host = 0.49 mas
or 0.16 mas, respectively. Then, for each pair of mass ratio
q=pθE/θE,host and separation s, we simulate 180 OGLE
light curves (spanning from 2010 March 4 through 2017 Oc-
tober 30) with uniformly distributed α, and calculate the
fraction of light curves that show signatures of the putative
host star (see Fig. 4). For OGLE-2012-BLG-1323 we find a
90% lower limits of 11.8au for the disk case (4.9 Einstein
radii of the host) and 6.0 au for the bulge host (4.5 Einstein
radii of the host). The formal 90% limits for OGLE-2017-
BLG-0560 are 9.3 au and 3.9 au, respectively, but the sensi-
tivity to additional anomalies in the light curve is reduced,
owing to low-level variability of the source.
5. Discussion
The two microlensing events presented in this paper and
OGLE-2016-BLG-1540 (Mróz et al. 2018) share a number
of similarities (Table 1). All events occurred on bright gi-
ant stars (with estimated angular radii of 9.2−34.9µas)
recently published a new CSB relation for giants (−0.01 <(V−
I)0<1.74), from which we find θ∗= 11.5±0.9µas (OGLE-2012-
BLG-1323) and θ∗= 32.3±2.3µas (OGLE-2017-BLG-0560), in
good agreement with our determination.
Article number, page 4 of 8
Mróz et al.: Two new free-floating planet candidates from microlensing
0.5 1.0 1.5 2.0 2.5 3.0 3.5
V−I(OGLE-IV)
12
13
14
15
16
17
18
19
20
I(OGLE-IV)
OGLE-2012-BLG-1323 red clump
source
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
V−I(OGLE-IV)
13
14
15
16
17
18
19
20
21
I(OGLE-IV)
OGLE-2017-BLG-0560 red clump
source
Fig. 2. OGLE-IV color–magnitude diagrams for stars in 20×20regions around OGLE-2012-BLG-1323 and OGLE-2017-BLG-0560.
Sources are marked with blue squares and are likely located in the Galactic bulge. If sources were M dwarfs, they would have
absolute I-band magnitudes of 9.75 (OGLE-2012-BLG-1323) and 13.90 (OGLE-2017-BLG-0560) (Pecaut & Mamajek 2013) and
would be located at a distance of 140 pc and 16 pc, respectively, which contradicts the Gaia DR2 parallaxes (0.15 ±0.14 mas and
0.23 ±0.19 mas, respectively).
−20−15−10−505101520
µE[mas/yr]
−20
−15
−10
−5
0
5
10
15
20
µN[mas/yr]
main sequence
giants
source
OGLE-2012-BLG-1323
−20−15−10−505101520
µE[mas/yr]
−20
−15
−10
−5
0
5
10
15
20
µN[mas/yr]
main sequence
giants
source
OGLE-2017-BLG-0560
Fig. 3. Gaia DR2 proper motions of stars within 40of OGLE-2012-BLG-1323 (left) and OGLE-2017-BLG-0560 (right). Blue
contours correspond to the main-sequence stars (Galactic disk population) and red contours to giants (bulge population). Solid
contours enclose 68% and 95% of all objects. The source is marked with a black dot. The black dashed circle corresponds to the
relative source-lens proper motion of 5.6 mas/yr (left) and 15.6 mas/yr (right).
and their relative lens-source proper motions are high
(5.6−15.6mas/yr). All three events show prominent fi-
nite source effects, which led to the measurement of the
angular Einstein radius. The fact that all three events oc-
curred on bright, large sources is surprising as less than 3%
of all known events are found with sources brighter than
I= 16 mag. Moreover, the microlensing event rate Γis
proportional to the area of the sky swept by the Einstein
ring: Γ∝θEµrel. The high lens-source relative proper mo-
tion makes an event more likely to be found, but events
with µrel >10 mas yr−1are very rare (Han et al. 2017).
Article number, page 5 of 8
A&A proofs: manuscript no. pap
1 2 3 4 5 6 7 8 9 10
Separation (Einstein radii of the host)
0.0
0.2
0.4
0.6
0.8
1.0
Probability of detecting the host star
OGLE-2012-BLG-1323
OGLE-2017-BLG-0560
Fig. 4. Probability of detecting the putative host star as a func-
tion of star-planet separation. Solid curves correspond to the
lens located in the Galactic bulge (πrel = 0.01 mas) and dashed
curves to the lens in the Galactic disk (πrel = 0.1mas).
Strong finite source effects make the duration of an event
longer, especially if ρ1, which makes giant source events
easier to detect. The typical timescale t∗of such an event
is comparable to the time needed for the lens to cross the
chord of the source:
t∗= 2tEρs1−u0
ρ2
.(1)
Monitoring of giant-star microlensing events, as advocated
by the Hollywood strategy of Gould (1997), is therefore a
promising way of studying free-floating planets.
On the other hand, the peak magnification Apeak in the
absence of blending declines with the source size (Gould &
Gaucherel 1997):
Apeak ≈1 + 2
ρ2(forρ1).(2)
The OGLE Early Warning System alerts events that
brighten by at least 0.06 mag (Udalski 2003), which cor-
responds to ρ.6, but the search algorithm of Mróz et al.
(2017) is sensitive to lower magnifications. Equation (1) also
explains why the impact parameter of OGLE-2012-BLG-
1323 is poorly measured (cf. Table 1): for large sources
(ρ= 5) changing the impact parameter from u0= 0 to
u0= 1 leads to an increase in tEof only 2%, which is al-
ready included in the reported uncertainties.
The mass of the lens depends on the angular Einstein
radius θEand the relative parallax πrel:
M=θ2
E
κπrel
.(3)
For both events, the masses cannot be unambiguously de-
termined because the microlens parallaxes cannot be mea-
sured. For lenses located in the Galactic disk (πrel ≈
0.1mas) the masses are 2.3M⊕and 1.9MJup for OGLE-
2012-BLG-1323 and OGLE-2017-BLG-0560, respectively.
If the lenses are located in the Galactic bulge (πrel ≈
0.01 mas), they have higher masses of about 23 M⊕or
20 MJup, respectively.
The mass of the lens can be further constrained by
employing the Bayesian analysis. If we assume a Galac-
tic model and a mass function of lenses, we can estimate
the mass of the lens that most likely reproduces the ob-
servations (Einstein radius and proper motion) given the
model. However, as we probe extreme events, we must be
cautious that the inferred masses will depend on priors
that may be derived from data on objects whose proper-
ties lie well beyond the range of those being probed. We
used the Galactic model of Bennett et al. (2014) and two
planetary mass functions as the prior. The first mass func-
tion (dN/dM ∝M−1.3), taken from Sumi et al. (2011),
overpredicts the number of short-timescale events (Mróz
et al. 2017). The second function (dN/dM ∝M−1.8) is
steeper, which is consistent with the findings of Clanton &
Gaudi (2016) and Suzuki et al. (2016), and better describes
the event timescale distribution of Mróz et al. (2017). The
posterior distributions favor Galactic bulge lenses, but the
allowed range of masses is very broad (see Table 2). The
median masses of the Bayesian results,
M= (0.038,1.5,100) MJup,
when combined with the angular Einstein radius values in
Table 1,
θE= (2.37,9.2,38.7) µas,
correspond to lens-source relative parallaxes of
πrel = (0.019,0.007,0.002) mas
for the three events OGLE-2012-BLG-1323, OGLE-2016-
BLG-1540, and OGLE-2017-BLG-0560, respectively.
The ultrashort timescale event OGLE-2012-BLG-1323
(tE= 0.155 ±0.005 d) is almost certainly caused by a
planetary-mass object (Earth- to super-Earth-mass), while
the mass of OGLE-2016-BLG-1540 (tE= 0.320±0.003 d) is
poorly constrained. The rate of events due to brown dwarfs
and stars with timescales shorter than 0.32 d (0.155 d) is
just 10−5(5×10−7) of the total event rate (Mróz et al.
2017).
It is not possible to determine, without further high-
resolution follow-up observations, whether these planets are
free-floating or are located at very wide orbits. Owing to
their high relative lens-source proper motions, such searches
will be possible in the near future with current instruments
or next-generation telescopes (Gould 2016). As the sources
are bright, separations of ∼100 mas are required to resolve
the putative host stars; such separations will be reached in
the late 2020s.
Presently, there are no observational constraints on the
frequency of bound Earth- and super-Earth-mass wide-
orbit planets as their detection is challenging with the cur-
rent techniques. For example, Poleski et al. (2014) found
a4MUranus planet at projected separation of 5.3 Einstein
radii and Sumi et al. (2016) discovered a Neptune analog at
projected separation of 2.4 Einstein radii. Planet-formation
theories, such as the core accretion model (Ida & Lin 2004),
predict very few low-mass planets at wide orbits because
the density of solids and gas in a protoplanetary disk is very
low at such large separations. It is believed that Uranus and
Article number, page 6 of 8
Mróz et al.: Two new free-floating planet candidates from microlensing
Table 2. Posterior distributions for the lens mass calculated from the Bayesian analysis
Percentile 2.3th 15.9th 50.0th 84.1th 97.7th
Prior 1:
OGLE-2012-BLG-1323 1.2M⊕5.0M⊕12M⊕47M⊕480M⊕
OGLE-2017-BLG-0560 5.7MJup 24MJup 100MJup 0.40M0.75M
OGLE-2016-BLG-1540 22M⊕110M⊕1.5MJup 47MJup 58MJup
Prior 2:
OGLE-2012-BLG-1323 3.8M⊕7.8M⊕30M⊕240M⊕990M⊕
OGLE-2017-BLG-0560 1.1MJup 13MJup 77MJup 0.35M0.74M
OGLE-2016-BLG-1540 32M⊕120M⊕2MJup 40MJup 53MJup
Notes. We use the Galactic model of Bennett et al. (2014) and the planetary mass function dN/dM ∝M−1.8(prior 1) or
dN/dM ∝M−1.3(prior 2).
Neptune formed closer to the Sun, near Jupiter and Saturn,
and were subsequently scattered into wide orbits (Thommes
et al. 1999, 2002). Likewise, multiple protoplanets of up to a
few Earth masses can be scattered to wide orbits and even-
tually ejected by growing gas giants (e.g., Chatterjee et al.
2008; Izidoro et al. 2015; Bromley & Kenyon 2016; Silsbee
& Tremaine 2018). From the point of view of microlensing
observations, these objects, whether bound or free-floating,
are in practice indistinguishable.
While making statistical inferences out of such a small
sample of events is risky, we show that these detections
are consistent with low-mass lenses being common in the
Milky Way, unless it is just a coincidence that the events
occurred on bright giant stars. According to models pre-
sented by Mróz et al. (2017), about 2.8×10−3of all events
should be caused by Earth- and super-Earth-mass lenses
(on timescales tE<0.5d) if there were one such object per
each star. About 50 events with giant sources brighter than
I= 16 are found in OGLE high-cadence fields annually,
thus we expect to find 2.8×10−3×50 = 0.1very short
microlensing events with giant sources annually (about one
event during the entire OGLE-IV time span) if the proba-
bility of detection is the same for events due to free-floating
planets and stars. In reality, the detection efficiency for
bright events on timescales of O(1 d) is a factor of 2−4
lower than for stellar events (Mróz et al. 2017). Thus, our
findings support the conclusions of Mróz et al. (2017) that
such Earth-mass free-floating (or wide-orbit) planets are
more common than stars in the Milky Way.
Acknowledgements. P.M. acknowledges support from the Foundation
for Polish Science (Program START) and the National Science Center,
Poland (grant ETIUDA 2018/28/T/ST9/00096). The OGLE project
has received funding from the National Science Center, Poland, grant
MAESTRO 2014/14/A/ST9/00121 to A.U. Work by A.G. was sup-
ported by AST-1516842 from the US NSF. I.G.S. and A.G. were sup-
ported by JPL grant 1500811. A.G. received support from the Euro-
pean Research Council under the European Union’s Seventh Frame-
work Programme (FP 7) ERC Grant Agreement n. [321035]. This
research has made use of the KMTNet system operated by the Ko-
rea Astronomy and Space Science Institute (KASI) and the data
were obtained at three host sites of CTIO in Chile, SAAO in South
Africa, and SSO in Australia. Work by C.H. was supported by a grant
(2017R1A4A1015178) from the National Research Foundation of Ko-
rea. The MOA project is supported by JSPS KAKENHI Grant Num-
bers JSPS24253004, JSPS26247023, JSPS23340064, JSPS15H00781,
and JP16H06287. This research was supported by the I-CORE pro-
gram of the Planning and Budgeting Committee and the Israel Sci-
ence Foundation, Grant 1829/12. D.M. and A.G. acknowledge support
from the US-Israel Binational Science Foundation.
References
Adams, A. D., Boyajian, T. S., & von Braun, K. 2018, MNRAS, 473,
3608
Albrow, M. 2017, MichaelDAlbrow/pyDIA: Initial Release on Github.
Barclay, T., Quintana, E. V., Raymond, S. N., & Penny, M. T. 2017,
ApJ, 841, 86
Bennett, D. P., Batista, V., Bond, I. A., et al. 2014, ApJ, 785, 155
Bensby, T., Adén, D., Meléndez, J., et al. 2011, A&A, 533, A134
Bessell, M. S. & Brett, J. M. 1988, PASP, 100, 1134
Boley, A. C., Payne, M. J., & Ford, E. B. 2012, ApJ, 754, 57
Bond, I. A., Abe, F., Dodd, R. J., et al. 2001, MNRAS, 327, 868
Boyd, D. F. A. & Whitworth, A. P. 2005, A&A, 430, 1059
Bromley, B. C. & Kenyon, S. J. 2016, ApJ, 826, 64
Chatterjee, S., Ford, E. B., Matsumura, S., & Rasio, F. A. 2008, ApJ,
686, 580
Clanton, C. & Gaudi, B. S. 2016, ApJ, 819, 125
Claret, A. & Bloemen, S. 2011, A&A, 529, A75
Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013,
PASP, 125, 306
Fouque, P. & Gieren, W. P. 1997, A&A, 320, 799
Freeman, M., Philpott, L. C., Abe, F., et al. 2015, ApJ, 799, 181
Gahm, G. F., Grenman, T., Fredriksson, S., & Kristen, H. 2007, AJ,
133, 1795
Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, A&A,
616, A1
Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A,
595, A1
Gould, A. 1997, in Variables Stars and the Astrophysical Returns of
the Microlensing Surveys, ed. R. Ferlet, J.-P. Maillard, & B. Raban,
125
Gould, A. 2016, Journal of Korean Astronomical Society, 49, 123
Gould, A. & Gaucherel, C. 1997, ApJ, 477, 580
Gould, A., Udalski, A., Monard, B., et al. 2009, ApJ, 698, L147
Grenman, T. & Gahm, G. F. 2014, A&A, 565, A107
Groenewegen, M. A. T. 2004, MNRAS, 353, 903
Han, C., Udalski, A., Sumi, T., et al. 2017, ApJ, 843, 59
Hao, W., Kouwenhoven, M. B. N., & Spurzem, R. 2013, MNRAS, 433,
867
Houdashelt, M. L., Bell, R. A., & Sweigart, A. V. 2000a, AJ, 119,
1448
Houdashelt, M. L., Bell, R. A., Sweigart, A. V., & Wing, R. F. 2000b,
AJ, 119, 1424
Hurley, J. R. & Shara, M. M. 2002, ApJ, 565, 1251
Ida, S. & Lin, D. N. C. 2004, ApJ, 604, 388
Izidoro, A., Morbidelli, A., Raymond, S. N., Hersant, F., & Pierens,
A. 2015, A&A, 582, A99
Kaib, N. A., Raymond, S. N., & Duncan, M. 2013, Nature, 493, 381
Kervella, P., Bersier, D., Mourard, D., et al. 2004, A&A, 428, 587
Kim, S.-L., Lee, C.-U., Park, B.-G., et al. 2016, Journal of Korean
Astronomical Society, 49, 37
Kratter, K. M. & Perets, H. B. 2012, ApJ, 753, 91
Liu, H.-G., Zhang, H., & Zhou, J.-L. 2013, ApJ, 772, 142
Lodieu, N., Dobbie, P. D., Cross, N. J. G., et al. 2013, MNRAS, 435,
2474
Ma, S., Mao, S., Ida, S., Zhu, W., & Lin, D. N. C. 2016, MNRAS,
461, L107
Malmberg, D., Davies, M. B., & Heggie, D. C. 2011, MNRAS, 411,
859
Marzari, F. & Weidenschilling, S. J. 2002, Icarus, 156, 570
Article number, page 7 of 8
A&A proofs: manuscript no. pap
Mróz, P., Ryu, Y.-H., Skowron, J., et al. 2018, AJ, 155, 121
Mróz, P., Udalski, A., Skowron, J., et al. 2017, Nature, 548, 183
Mužić, K., Scholz, A., Geers, V. C., & Jayawardhana, R. 2015, ApJ,
810, 159
Nataf, D. M., Gould, A., Fouqué, P., et al. 2013, ApJ, 769, 88
Parker, R. J. & Quanz, S. P. 2012, MNRAS, 419, 2448
Peña Ramírez, K., Béjar, V. J. S., Zapatero Osorio, M. R., Petr-
Gotzens, M. G., & Martín, E. L. 2012, ApJ, 754, 30
Pecaut, M. J. & Mamajek, E. E. 2013, ApJS, 208, 9
Poleski, R., Skowron, J., Udalski, A., et al. 2014, ApJ, 795, 42
Ramírez, I. & Meléndez, J. 2005, ApJ, 626, 465
Rasio, F. A. & Ford, E. B. 1996, Science, 274, 954
Scharf, C. & Menou, K. 2009, ApJ, 693, L113
Shvartzvald, Y., Maoz, D., Udalski, A., et al. 2016, MNRAS, 457, 4089
Silsbee, K. & Tremaine, S. 2018, AJ, 155, 75
Spurzem, R., Giersz, M., Heggie, D. C., & Lin, D. N. C. 2009, ApJ,
697, 458
Sumi, T., Bennett, D. P., Bond, I. A., et al. 2013, ApJ, 778, 150
Sumi, T., Kamiya, K., Bennett, D. P., et al. 2011, Nature, 473, 349
Sumi, T., Udalski, A., Bennett, D. P., et al. 2016, ApJ, 825, 112
Sutherland, A. P. & Fabrycky, D. C. 2016, ApJ, 818, 6
Suzuki, D., Bennett, D. P., Sumi, T., et al. 2016, ApJ, 833, 145
Thommes, E. W., Duncan, M. J., & Levison, H. F. 1999, Nature, 402,
635
Thommes, E. W., Duncan, M. J., & Levison, H. F. 2002, AJ, 123,
2862
Udalski, A. 2003, Acta Astron., 53, 291
Udalski, A., Szymański, M. K., & Szymański, G. 2015, Acta Astron.,
65, 1
Veras, D., Crepp, J. R., & Ford, E. B. 2009, ApJ, 696, 1600
Veras, D. & Moeckel, N. 2012, MNRAS, 425, 680
Veras, D., Mustill, A. J., Gänsicke, B. T., et al. 2016, MNRAS, 458,
3942
Veras, D., Wyatt, M. C., Mustill, A. J., Bonsor, A., & Eldridge, J. J.
2011, MNRAS, 417, 2104
Voyatzis, G., Hadjidemetriou, J. D., Veras, D., & Varvoglis, H. 2013,
MNRAS, 430, 3383
Weidenschilling, S. J. & Marzari, F. 1996, Nature, 384, 619
Whitworth, A. P. & Stamatellos, D. 2006, A&A, 458, 817
Woźniak, P. R. 2000, Acta Astron., 50, 421
Wray, J. J., Eyer, L., & Paczyński, B. 2004, MNRAS, 349, 1059
Yee, J. C., Udalski, A., Sumi, T., et al. 2009, ApJ, 703, 2082
Yoo, J., DePoy, D. L., Gal-Yam, A., et al. 2004, ApJ, 603, 139
1Warsaw University Observatory, Al. Ujazdowskie 4, 00-478
Warszawa, Poland
2Code 667, NASA Goddard Space Flight Center, Greenbelt,
MD 20771, USA
3Department of Astronomy, University of Maryland, College
Park, MD 20742, USA
4Korea Astronomy and Space Science Institute, Daejon 34055,
Republic of Korea
5Department of Earth and Space Science, Graduate School of
Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
6IPAC, Mail Code 100-22, Caltech, 1200 E. California Blvd.,
Pasadena, CA 91125, USA
7Department of Astronomy, Ohio State University, 140 W.
18th Ave., Columbus, OH 43210, USA
8Department of Physics, University of Warwick, Coventry
CV4 7AL, UK
9University of Canterbury, Department of Physics and As-
tronomy, Private Bag 4800, Christchurch 8020, New Zealand
10 Korea University of Science and Technology, Daejeon 34113,
Republic of Korea
11 Max-Planck-Institute for Astronomy, Königstuhl 17, 69117
Heidelberg, Germany
12 Department of Physics, Chungbuk National University,
Cheongju 28644, Republic of Korea
13 Harvard-Smithsonian Center for Astrophysics, 60 Garden
St., Cambridge, MA 02138, USA
14 Physics Department and Tsinghua Centre for Astrophysics,
Tsinghua University, Beijing 100084, China
15 School of Space Research, Kyung Hee University, Yongin,
Kyeonggi 17104, Republic of Korea
16 Institute for Space-Earth Environmental Research, Nagoya
University, Nagoya 464-8601, Japan
17 Institute of Natural and Mathematical Sciences, Massey Uni-
versity, Auckland 0745, New Zealand
18 Department of Physics, University of Auckland, Private Bag
92019, Auckland, New Zealand
19 Department of Earth and Planetary Science, Graduate
School of Science, The University of Tokyo, 7-3-1 Hongo,
Bunkyo-ku, Tokyo 113-0033, Japan
20 Instituto de Astrofísica de Canarias, Vía Láctea s/n, E-38205
La Laguna, Tenerife, Spain
21 Department of Astronomy, Graduate School of Science, The
University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-
0033, Japan
22 National Astronomical Observatory of Japan, 2-21-1 Osawa,
Mitaka, Tokyo 181-8588, Japan
23 School of Chemical and Physical Sciences, Victoria Univer-
sity, Wellington, New Zealand
24 Institute of Space and Astronautical Science, Japan
Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo,
Sagamihara, Kanagawa, 252-5210, Japan
25 University of Canterbury Mt. John Observatory, P.O. Box
56, Lake Tekapo 8770, New Zealand
26 Department of Physics, Faculty of Science, Kyoto Sangyo
University, 603-8555 Kyoto, Japan
27 School of Physics and Astronomy and Wise Observatory, Tel-
Aviv University, tel-aviv 6997801, Israel
Article number, page 8 of 8
