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OGLE-2016-BLG-1190Lb: The First Spitzer Bulge Planet Lies Near the Planet/Brown-dwarf Boundary

December 2017
The Astronomical Journal 155(1):40

Authors:

We report the discovery of OGLE-2016-BLG-1190Lb, which is likely to be the first Spitzermicrolensing planet in the Galactic bulge/bar, an assignation that can be confirmed by two epochs of high-resolution imaging of the combined source–lens baseline object. The planet's mass, M_p = 13.4 ± 0.9 M_J , places it right at the deuterium-burning limit, i.e., the conventional boundary between "planets" and "brown dwarfs." Its existence raises the question of whether such objects are really "planets" (formed within the disks of their hosts) or "failed stars" (low-mass objects formed by gas fragmentation). This question may ultimately be addressed by comparing disk and bulge/bar planets, which is a goal of the Spitzer microlens program. The host is a G dwarf, M_(host) = 0.89 ± 0.07 M⊙, and the planet has a semimajor axis a ~ 2.0 au. We use Kepler K2 Campaign 9 microlensing data to break the lens-mass degeneracy that generically impacts parallax solutions from Earth–Spitzerobservations alone, which is the first successful application of this approach. The microlensing data, derived primarily from near-continuous, ultradense survey observations from OGLE, MOA, and three KMTNet telescopes, contain more orbital information than for any previous microlensing planet, but not quite enough to accurately specify the full orbit. However, these data do permit the first rigorous test of microlensing orbital-motion measurements, which are typically derived from data taken over <1% of an orbital period.

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OGLE-2016-BLG-1190Lb: The First Spitzer Bulge Planet Lies

Near the Planet/Brown-dwarf Boundary

Y.-H. Ryu

, J. C. Yee

, A. Udalski

, I. A. Bond

, Y. Shvartzvald

5,60

, W. Zang

6,7

, R. Figuera Jaimes

8,9

, U. G. Jørgensen

W. Zhu

, C. X. Huang

12,13,14

, Y. K. Jung

and

M. D. Albrow

, S.-J. Chung

1,16

, A. Gould

1,11,17

, C. Han

, K.-H. Hwang

, I.-G. Shin

, S.-M. Cha

1,19

, D.-J. Kim

H.-W. Kim

, S.-L. Kim

1,16

, C.-U. Lee

1,16

, D.-J. Lee

, Y. Lee

1,19

, B.-G. Park

1,16

, R. W. Pogge

(KMTNet Collaboration),

S. Calchi Novati

20,21

, S. Carey

, C. B. Henderson

, C. Beichman

, B. S. Gaudi

(Spitzer team),

P. Mróz

, R. Poleski

3,11

, J. Skowron

, M. K. Szymański

, I. Soszyński

, S. Kozłowski

, P. Pietrukowicz

, K. Ulaczyk

M. Pawlak

(OGLE Collaboration),

F. Abe

, Y. Asakura

, R. Barry

, D. P. Bennett

, A. Bhattacharya

, M. Donachie

, P. Evans

, A. Fukui

, Y. Hirao

Y. Itow

, K. Kawasaki

, N. Koshimoto

,M.C.A.Li

, C. H. Ling

, K. Masuda

, Y. Matsubara

, S. Miyazaki

Y. Muraki

, M. Nagakane

, K. Ohnishi

, C. Ranc

, N. J. Rattenbury

, To. Saito

, A. Sharan

, D. J. Sullivan

, T. Sumi

D. Suzuki

25,32

, P. J. Tristram

, T. Yamada

, A. Yonehara

(MOA Collaboration),

G. Bryden

, S. B. Howell

, S. Jacklin

(UKIRT Microlensing Team),

M. T. Penny

11,61

, S. Mao

6,37,38

, Pascal Fouqué

39,40

, T. Wang

(CFHT-K2C9 Microlensing Survey group),

R. A. Street

, Y. Tsapras

, M. Hundertmark

10,42

, E. Bachelet

, M. Dominik

8,62

,Z.Li

, S. Cross

, A. Cassan

K. Horne

, R. Schmidt

, J. Wambsganss

, S. K. Ment

, D. Maoz

, C. Snodgrass

, I. A. Steele

(RoboNet Team),

and

V. Bozza

21,47

, M. J. Burgdorf

, S. Ciceri

,G.D’Ago

, D. F. Evans

, T. C. Hinse

, E. Kerins

, R. Kokotanekova

52,53

P. Longa

, J. MacKenzie

, A. Popovas

, M. Rabus

, S. Rahvar

, S. Sajadian

, J. Skottfelt

, J. Southworth

, and

C. von Essen

(MiNDSTEp Team)

Korea Astronomy and Space Science Institute, Daejon 34055, Korea

Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA

Warsaw University Observatory, Al. Ujazdowskie 4, 00-478 Warszawa, Poland

Institute of Natural and Mathematical Sciences, Massey University, Auckland 0745, New Zealand

Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA

Physics Department and Tsinghua Centre for Astrophysics, Tsinghua University, Beijing 100084, China

Department of Physics, Zhejiang University, Hangzhou, 310058, China

Centre for Exoplanet Science, SUPA School of Physics & Astronomy, University of St Andrews, North Haugh, St Andrews KY16 9SS, UK

European Southern Observatory, Karl-Schwarzschild-Str. 2, D-85748 Garching bei München, Germany

Niels Bohr Institute & Centre for Star and Planet Formation, University of Copenhagen, Øster Voldgade 5, DK-1350—Copenhagen K, Denmark

Department of Astronomy, Ohio State University, 140 W. 18th Avenue, Columbus, OH 43210, USA

Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Dunlap Institute for Astronomy and Astrophysics, University of Toronto, Toronto, ON M5S 3H4, Canada

Centre of Planetary Science, University of Toronto, Scarborough Campus Physical & Environmental Sciences, Toronto, M1C 1A4, Canada

University of Canterbury, Department of Physics and Astronomy, Private Bag 4800, Christchurch 8020, New Zealand

Korea University of Science and Technology, 217 Gajeong-ro, Yuseong-gu, Daejeon 34113, Republic of Korea

Max-Planck-Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany

Department of Physics, Chungbuk National University, Cheongju 28644, Korea

School of Space Research, Kyung Hee University, Yongin, Kyeonggi 17104, Korea

IPAC, Mail Code 100-22, Caltech, 1200 E. California Boulevard, Pasadena, CA 91125, USA

Dipartimento di Fisica “E. R. Caianiello,”Università di Salerno, Via Giovanni Paolo II, I-84084 Fisciano (SA), Italy

Spitzer Science Center, MS 220-6, California Institute of Technology, Pasadena, CA, USA

NASA Exoplanet Science Institute, California Institute of Technology, Pasadena, CA 91125, USA

Institute for Space-Earth Environmental Research, Nagoya University, Nagoya 464-8601, Japan

Code 667, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA; david.bennett@nasa.gov

Department of Physics, University of Auckland, Private Bag 92019, Auckland, New Zealand

Okayama Astrophysical Observatory, National Astronomical Observatory of Japan, 3037-5 Honjo, Kamogata, Asakuchi, Okayama 719-0232, Japan

Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan

Nagano National College of Technology, Nagano 381-8550, Japan

Tokyo Metropolitan College of Aeronautics, Tokyo 116-8523, Japan

School of Chemical and Physical Sciences, Victoria University, Wellington, New Zealand

The Astronomical Journal, 155:40 (24pp), 2018 January https://doi.org/10.3847/1538-3881/aa9be4

Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, Kanagawa 252-5210, Japan

University of Canterbury Mt. John Observatory, P.O. Box 56, Lake Tekapo 8770, New Zealand

Department of Physics, Faculty of Science, Kyoto Sangyo University, 603-8555 Kyoto, Japan

Kepler & K2 Missions, NASA Ames Research Center, PO Box 1, M/S 244-30, Moffett Field, CA 94035, USA

Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235, USA

National Astronomical Observatories, Chinese Academy of Sciences, A20 Datun Road, Chaoyang District, Beijing 100012, China

Jodrell Bank Centre for Astrophysics, Alan Turing Building, University of Manchester, Manchester M13 9PL, UK

CFHT Corporation, 65-1238 Mamalahoa Highway, Kamuela, Hawaii 96743, USA

Université de Toulouse, UPS-OMP, IRAP, Toulouse, France

Las Cumbres Observatory Global Telescope Network, 6740 Cortona Drive, Suite 102, Goleta, CA 93117, USA

Zentrum für Astronomie der Universität Heidelberg, Astronomisches Rechen-Institut, Mönchhofstr. 12-14, D-69120 Heidelberg, Germany

Sorbonne Universités, UPMC Univ Paris 6 et CNRS, UMR 7095, Institut d’Astrophysique de Paris, 98 bis bd Arago, F-75014 Paris, France

School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel

Planetary and Space Sciences, Department of Physical Sciences,The Open University, Milton Keynes, MK7 6AA, UK

Astrophysics Research Institute, Liverpool John Moores University, Liverpool CH41 1LD, UK

Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Napoli, Italy

Universität Hamburg, Faculty of Mathematics, Informatics and Natural Sciences, Department of Earth Sciences,

Meteorological Institute, Bundesstraße 55, 20146 Hamburg, Germany

Department of Astronomy, Stockholm University, AlbaNova University Center, SE-106 91 Stockholm, Sweden

INAF-Osservatorio Astronomico di Capodimonte, Salita Moiariello 16, I-80131, Napoli, Italy

Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK

Max Planck Institute for Solar System Research, Justus-von-Liebig-Weg 3, D-37077 Göttingen, Germany

School of Physical Sciences, Faculty of Science, Technology, Engineering and Mathematics,

The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK

Unidad de Astronomía, Fac. de Ciencias Básicas, Universidad de Antofagasta, Avda. U. de Antofagasta 02800, Antofagasta, Chile

Instituto de Astrofísica, Pontiﬁcia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, 7820436 Macul, Santiago, Chile

Department of Physics, Sharif University of Technology, PO Box 11155-9161 Tehran, Iran

Department of Physics, Isfahan University of Technology, 841568311 Isfahan, Iran

Centre for Electronic Imaging, Department of Physical Sciences, The Open University, Milton Keynes, MK7 6AA, UK

Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark

Received 2017 August 22; revised 2017 November 15; accepted 2017 November 17; published 2017 December 28

Abstract

We report the discovery of OGLE-2016-BLG-1190Lb, which is likely to be the ﬁrst Spitzer microlensing planet in

the Galactic bulge/bar, an assignation that can be conﬁrmed by two epochs of high-resolution imaging of the

combined source–lens baseline object. The planet’s mass, M

=13.4±0.9 M

, places it right at the deuterium-

burning limit, i.e., the conventional boundary between “planets”and “brown dwarfs.”Its existence raises the

question of whether such objects are really “planets”(formed within the disks of their hosts)or “failed stars”(low-

mass objects formed by gas fragmentation). This question may ultimately be addressed by comparing disk and

bulge/bar planets, which is a goal of the Spitzer microlens program. The host is a G dwarf,

host

=0.89±0.07 M

, and the planet has a semimajor axis a∼2.0 au. We use Kepler K2 Campaign 9

microlensing data to break the lens-mass degeneracy that generically impacts parallax solutions from Earth–Spitzer

observations alone, which is the ﬁrst successful application of this approach. The microlensing data, derived

primarily from near-continuous, ultradense survey observations from OGLE, MOA, and three KMTNet telescopes,

contain more orbital information than for any previous microlensing planet, but not quite enough to accurately

specify the full orbit. However, these data do permit the ﬁrst rigorous test of microlensing orbital-motion

measurements, which are typically derived from data taken over <1% of an orbital period.

Key words: gravitational lensing: micro

1. Introduction

The discovery of the Spitzer microlensing planet OGLE-

2016-BLG-1190Lb is remarkable in ﬁve different respects.

First, it is the ﬁrst planet in the Spitzer Galactic-distribution

sample that likely lies in the Galactic bulge, which would break

the trend from the three previous members of this sample.

Second, it is precisely measured to be right at the edge of the

brown-dwarf desert. Since the existence of the brown-dwarf

desert is the signature of different formation mechanisms for

stars and planets, the extremely close proximity of OGLE-

2016-BLG-1190Lb to this desert raises the question of whether

it is truly a “planet”(by formation mechanism)and therefore

reacts back upon its role tracing the Galactic distribution of

planets, just mentioned above. Third, it is the ﬁrst planet to

enter the Spitzer “blind”sample whose existence was

recognized prior to its choice as a Spitzer target. This seeming

contradiction was clearly anticipated by Yee et al. (2015a)

when they established their protocols for the Galactic

distribution experiment. The discovery therefore tests the

well-deﬁned, but intricate, procedures devised by Yee et al.

(2015a)to deal with this possibility. Fourth, it is the ﬁrst planet

(and indeed the ﬁrst microlensing event)for which the well-

known microlens-parallax degeneracy has been broken by

observations from two satellites. Finally, it is the ﬁrst

microlensing planet for which a complete orbital solution has

been attempted. Although this attempt is not completely

successful in that a one-dimensional degeneracy remains, it is

an important benchmark on the road to such solutions.

In view of the diverse origins and implications of this

discovery, we therefore depart from the traditional form of

NASA Postdoctoral Program Fellow.

Sagan Fellow.

Royal Society University Research Fellow.

The Astronomical Journal, 155:40 (24pp), 2018 January Ryu et al.

introductions and begin by framing this discovery with four

semi-autonomous introductory subsections.

1.1. Microlens Parallax from One and Two Satellites

When Refsdal (1966)ﬁrst proposed measuring microlens

parallaxes using a satellite in solar orbit, a quarter century

before the ﬁrst microlensing event, he already realized that this

measurement would be subject to a fourfold degeneracy, and

further, that this degeneracy could be broken by observations

from a second satellite. See also Gould (1994b)and Calchi

Novati & Scarpetta (2016). The microlens parallax is a vector,

pmpp

ºº ();, 1

rel

Erel

whose amplitude is the ratio of the lens–source relative parallax

p=-

()DDau LS

rel 11

to the Einstein radius θ

, and whose

direction is that of the lens–source relative proper motion

rel.

As illustrated in Figure1 of Gould (1994b; compare to

Figure1 of Yee et al. 2015b)observers from Earth and a

satellite will see substantially different light curves. By

comparing the two light curves, one can infer the vector offset

within the Einstein ring of the source as seen from the two

observers. Combining this vector offset with the known

projected offset of the satellite and Earth, one can then infer

However, this determination is in general subject to a

fourfold degeneracy. Although the component of the vector

offset in the direction of the lens–source motion

rel gives rise

to an offset in peak times of the event and can therefore be

determined unambiguously, the component transverse to this

motion must be derived from a comparison of the impact

parameters, which leads to a fourfold ambiguity. That is, the

impact parameter is a signed quantity but only its magnitude

can be readily determined from the light curve.

By far, the most important aspect of this degeneracy is that the

source may be either on the same or opposite sides of the lens as

seen from the two observatories. The parallax amplitude π

will

be smaller in the ﬁrst case than in the second, which will directly

affect the derived lens mass Mand π

rel

(Gould 1992,2004),

kp ppqk==º



()MG

;;

au 8.1 mas .2

rel

rel E E 2

By contrast, the remaining twofold degeneracy only impacts

the inferred direction of motion, which is usually of little

physical interest.

The ﬁrst such parallax measurement was made by Dong &

Udalski et al. (2007)by combining Spitzer and ground-based

observations of OGLE-2005-SMC-001 toward the Small

Magellanic Cloud. Subsequently, more than 200 events were

observed toward the Galactic bulge in 2014 and 2015 as part of

a multiyear Spitzer program (Gould et al. 2013,2014),of

which more than 70 have already been published. A key issue

in the analysis of these events has been to break this fourfold

degeneracy, in particular the twofold degeneracy that impacts

the mass and distance estimates. Although in some cases (Yee

et al. 2015b; Zhu et al. 2015)this degeneracy has been broken

by various fairly weak effects, in the great majority of cases,

the degeneracy was broken only statistically (Calchi Novati

et al. 2015a; Zhu et al. 2017b).

Although such statistical arguments are completely adequate

when the derived conclusions are themselves statistical, they

are less satisfactory for drawing conclusions about individual

objects. Hence, for the 2016 season, Gould et al. (2015b)

speciﬁcally proposed observing some events with Spitzer that

lie in the roughly 4 deg

observed by Kepler during its K2

Campaign 9, in addition to the regular Spitzer targets drawn

from a much larger ∼100 deg

area (Gould et al. 2015a).

Contrary to the expectations of Refsdal (1966)and Gould

(1994b),Spitzer,Kepler, Earth, and the microlensing ﬁelds all

lie very close to the ecliptic, so that the projected positions of

the sources as seen from the three observatories are almost

colinear. This means that it is almost impossible to use Kepler

to fully break the fourfold degeneracy. Nevertheless, this

conﬁguration does not adversely impact Kepler’s ability to

break the key twofold degeneracy that impacts the mass and

distance determinations, which turns out to be quite important

in the present case. (See also Zhu et al. 2017c for the case of a

single-lens event.)

1.2. Planets at the Desert’s Edge

The term “brown-dwarf desert”was originally coined by Marcy

&Butler(2000)to describe the low frequency of “brown dwarfs”

in Doppler (radial velocity, RV)studies relative to “planets”of

somewhat lower mass. Since the sensitivity of the surveys rises

with mass, this difference cannot be due to selection effects. Later,

Grether & Lineweaver (2006)quantiﬁed this desert as the

intersection of two divergent power laws, subsequently measured

as ~-

Nd M Mln 0.3 for “planets”and ~

Nd M Mln 1for

“stars.”We placed all these terms in quotation marks because they

are subject to three different deﬁnition systems that are not wholly

self-consistent. By one deﬁnition system, planets, brown dwarfs,

and stars are divided by mass at 13 M

and 0.08 M

. By a second,

they are divided at deuterium and hydrogen burning. And in a third

system, they are divided by formation mechanism: in-disk

formation for planets, gravitational collapse for stars, and [either

or both]for brown dwarfs.

The ﬁrst deﬁnition has the advantage that mass is something

that can in principle be measured. The second system is

valuable because it permits a veneer of physical motivation on

what is actually an arbitrary boundary. In fact, no plausible

mechanism has ever been advanced as to how either deuterium

burning or hydrogen burning can have any impact on the mass

function of the objects being formed. In particular, hydrogen

burning commences in very low-mass stars long after they have

become isolated from their sources of mass accretion. The third

deﬁnition speaks to a central scientiﬁc question about these

various types of objects: where do they come from?

Unfortunately, for ﬁeld objects, there is precious little

observational evidence that bears on this question. Up until

now, the key input from observations is statistical: far from the

boundaries, planets and stars follow divergent power laws,

which almost certainly reﬂect different formation mechanisms

(Grether & Lineweaver 2006). However, near the boundary, in

particular in the brown-dwarf desert and on its margins, there is

no present way to map individual objects onto a formation

mechanism even if their masses were known. Moreover, using

the RV technique, i.e., the traditional method for ﬁnding

brown-dwarf companions at few astronomical unit separations,

there is no way to precisely measure the masses (unless, by

extreme chance, the system happens to be eclipsing).

If the divergent power laws (as measured well away from

their boundaries)represent different formation mechanisms,

then most likely these power laws continue up to and past these

nominal boundaries, so that “brown dwarfs”as deﬁned by mass

The Astronomical Journal, 155:40 (24pp), 2018 January Ryu et al.

represent a mixture of populations as deﬁned by formation, and

high-mass “planets”do as well.

Microlensing opens several different laboratories for disen-

tangling formation mechanism from mass, at least statistically.

First, as pointed out by Ranc et al. (2015)and Ryu et al. (2017),

microlensing can probe to larger orbital radii than RV for both

massive planets and brown dwarfs and so determine whether

the independent mode of planet formation “dies off”at these

radii and, if so, how this correlates to the behavior of brown

dwarfs. Second, it can probe seamlessly to the lowest-mass

hosts of brown dwarfs, even into the brown-dwarf regime itself.

This is a regime that is progressively less capable of forming

brown dwarfs from disk material, although it may be proﬁcient

at forming Earth-mass planets (Shvartzvald et al. 2017b).

Third, since microlensing is most directly sensitive to the

companion/host mass ratio q, it can precisely measure

the distribution of this parameter, even for samples for which

the individual masses are poorly known.

The minimum in

this distribution can then be regarded as the location of the

mean boundary between two formation mechanisms averaged

over the microlensing host-mass distribution. Shvartzvald et al.

(2016)found that this minimum was near q∼0.01, which

corresponds to M

comp

∼5M

Jup

for characteristic microlensing

hosts, which are typically in the M dwarf regime. This tends to

indicate that this boundary scales as a function of the host mass.

Another path open to microlensing is probing radically

different star-forming environments, in particular the Galactic

bulge. Thompson (2013), for example, has suggested that

massive-planet formation via the core-accretion scenario was

strongly suppressed in the Galactic bulge by the high-radiation

environment. This would not impact rocky planets but would

lead to a dearth of Jovian planets and super-Jupiters if these

indeed formed by this mechanism. Of particular note in this

regard is that adaptive optics observations by Batista et al.

(2014)indicated that MOA-2011-BLG-293Lb (Yee et al. 2012)

is a 5 M

object orbiting a solar-like host in the Galactic bulge.

This might be taken as evidence against Thompson’s

conjecture. However, another possibility is that MOA-2011-

BLG-293Lb formed at the low-mass end of the gravitational-

collapse mode that produces most stars, which was perhaps

more efﬁcient in the high-density, high-radiation environment

that characterized early star formation in the bulge. In this case,

we would expect the companion mass function in the Galactic

bulge to be rising toward the deuterium-burning limit, in sharp

contrast to the mass function in the solar neighborhood, which

is falling in this range. That is, high-mass planets (near the

deuterium-burning limit)would be even more common than the

super-Jupiter found by Batista et al. (2014).

1.3. Construction of Blind Tests in the Face

of “Too Much”Knowledge

Yee et al. (2015a)proposed measuring the Galactic

distribution of planets by determining individual distances to

planetary (and non-planetary)microlenses from the combined

analysis of light curves obtained from ground-based and Spitzer

telescopes. Because the lenses are usually not directly detected,

such distance measurements are relatively rare in the absence of

space-based microlens parallax (Refsdal 1966; Gould 1994b)

and, what is more important, heavily biased toward nearby

lenses.

As Yee et al. (2015a)discuss in considerable detail, it is by

no means trivial to assemble a Spitzer microlens parallax

sample (Gould et al. 2013,2014,2015a,2015b,2016)that is

unbiased with respect to the presence or absence of planets.

Calchi Novati et al. (2015a)showed how the cumulative

distribution of planetary events as a function of distance toward

the Galactic bulge could be compared to that of the parent

sample to determine whether planets are relatively more

frequent in the Galactic disk or bulge. However, this

comparison depends on the implicit assumption that there is

no bias toward the selection of planetary events. In fact, it

would not matter if the planetary sample were biased, provided

that this bias were equal for planets in both the Galactic disk

and bulge. However, particularly given the constraints on

Spitzer target-of-opportunity selection, it is essentially impos-

sible to ensure such a uniform bias without removing this bias

altogether.

Hence, Yee et al. (2015a)developed highly articulated

protocols for selecting Spitzer microlens targets that would

ensure that the resulting sample was unbiased. We will review

these procedures in some detail in Section 5.1. However, from

the present standpoint, the key point is that however exactly the

sample is constructed, it must contain only events with

“adequately measured”microlens parallaxes. Yee et al.

(2015a)did not specify what was “adequate”because this

requires the study of real data. Zhu et al. (2017b)carried out

such a study based on a sample of 41 Spitzer microlensing

events without planets, which meant that these authors could

not be biased—even unconsciously—by a “desire”to get more

planets into the sample. In addition, they speciﬁcally did not

investigate how their criteria applied to the two Spitzer

microlens planets that were previously discovered (Udalski

et al. 2015b; Street et al. 2016)until after these criteria were

decided. The Zhu et al. (2017b)criteria, as they apply to non-

planetary events, are quite easy to state once the appropriate

deﬁnitions are in place (Section 5.2). A crucial point, however,

is that for planetary events, these same criteria must be applied

to the point-lens event that would have been observed in the

absence of planets.

Thus, although in some cases it may be quite obvious

whether a planetary event should or should not be included in

the sample, it is also possible that this assignment may require a

rather detailed analysis.

The Spitzer microlens planetary event OGLE-2016-BLG-

1190 does in fact require quite detailed analysis to determine

whether it belongs in the Spitzer Galactic distribution of planets

sample. OGLE-2016-BLG-1190 was initially chosen for

Spitzer observations based solely on the fact that it had an

anomaly that was strongly suspected to be (and was ﬁnally

conﬁrmed as)planetary in nature. At ﬁrst sight, this would

seem to preclude its participation in an “unbiased sample.”

Nevertheless, Yee et al. (2015a)had anticipated this situation

and developed protocols that enable, under some circum-

stances, the inclusion of such planets without biasing the

sample. We show that OGLE-2016-BLG-1190 in fact should

be included under these protocols. This then sets the stage for

whether its parallax is “adequately measured”according to the

Zhu et al. (2017b)criteria, or rather whether the corresponding

As a result, in microlensing statistical studies, the planet/brown-dwarf

boundary is often deﬁned by q. For example, Suzuki et al. (2016; following

Bond et al. 2004)and Shvartzvald et al. (2016)use q=0.03 and q=0.04,

respectively, which would correspond to the conventional 13 M

jup

limit for

stars of mass M;0.4 M

and M;0.3 M

, respectively.

The Astronomical Journal, 155:40 (24pp), 2018 January Ryu et al.

point-lens event would have satisﬁed them. We address this

point for the ﬁrst time here as well.

1.4. Full Kepler Orbits in Microlensing

When microlensing planet searches were ﬁrst proposed (Mao

& Paczyński 1991; Gould & Loeb 1992), it was anticipated that

only the planet–star mass ratio qand projected separation

(scaled to the Einstein radius θ

)swould be measured. Even

the mass Mof the host was thought to be subject only to

statistical estimates, while orbital motion was not even

considered. It was quickly realized, however, that it was at

least in principle possible to measure both θ

(Gould 1994a)

and the microlens parallax π

(Gould 1992),

qkp p p

kkººº



()MM

;;

au 8.14 mas ,3

2rel E

2rel

and that this could then yield both the lens mass M=θ

/κπ

and the lens–source relative parallax π

rel

=θ

The fact that linearized orbital motion was measurable was

discovered by accident during the analysis of the binary

microlensing event MACHO-97-BLG-41 (Albrow et al. 2000).

In a case remarkably similar to the one we will be analyzing

here, the source ﬁrst passed over an outlying caustic of a close

binary and later went over the central caustic. From the analysis

of the latter, one could determine (s,q)and “predict”the

positions of the two outlying caustics. These differed in both

coordinates from the caustic transit that had actually been

observed. The difference was explained in terms of binary

orbital motion, and the linearized orbital parameters were thus

measured. This was regarded at the time as requiring very

special geometry because the typical duration of caustic-

induced effects is a few days whereas the orbital period of

systems probed by microlensing is typically several years. In

fact, however, orbital motion began to be measured or

constrained in many planetary events, mostly with quite

generic geometries, including the second microlensing planet

OGLE-2005-BLG-071Lb (Udalski et al. 2005; Dong et al.

2009). A fundamental feature of microlensing that enables such

measurements is that the times of caustic transits can often be

measured with precisions of better than one minute. Still, it did

not seem possible to measure full orbits. Nevertheless,

Skowron et al. (2011)signiﬁcantly constrained all seven

Kepler parameters for the binary system OGLE-2009-BLG-

020L, albeit with huge errors and strong correlations. These

measurements were later shown to be consistent with RV

follow-up observations by Yee et al. (2016). Subsequently,

Shin et al. (2011,2012)fully measured all Kepler parameters

for several different binaries.

To date, and with one notable exception, such complete

Kepler solutions have been more of interest in terms of

establishing the principles and methods of making the

measurements than anything they are telling us about nature.

The exception is OGLE-2006-BLG-109La,b, the ﬁrst two-

planet system found by microlensing (Gaudi et al. 2008;

Bennett et al. 2010). Due to the very large caustic from one of

the planets, together with a data rate that was very high and

continuous for that time, Bennett et al. (2010)were able to

introduce one additional dynamical parameter relative to the

standard two-dynamical parameter approach of Albrow et al.

(2000). This allowed them to make RV predictions for the

system that could be tested with future 30 m class telescopes.

However, if the method for measuring complete Kepler

orbits can be extended from binaries to planets (as we begin to

do here), then it will permit much stricter comparison between

RV and microlensing samples, which has so far been possible

only statistically, (e.g., Gould et al. 2010; Clanton &

Gaudi 2014a,2014b,2016). In particular, we provide here

the ﬁrst evidence for a non-circular orbit of a microlensing

planet.

2. Observations

2.1. Ground-based Observations

OGLE-2016-BLG-1190 is at (R.A., decl.)=(17:58:52.30,

−27:36:48.8), corresponding to (l,b)=(2.63, −1.84). It was

discovered and announced as a probable microlensing event by

the Optical Gravitational Lensing Experiment (OGLE)Early

Warning System (Udalski et al. 1994; Udalski 2003)at UT

17:37 on 2016 June 27. OGLE observations were at a cadence

of Γ=3hr

−1

using their 1.3 m telescope at Las Campanas,

Chile.

The event was independently discovered on July 6 by the

Microlensing Observations in Astrophysics (MOA)collabora-

tion as MOA-2016-BLG-383 based on Γ=4hr

−1

observa-

tions using their 1.8 m telescope at Mt. John, New Zealand.

The Korea Microlensing Telescope Network (KMTNet; Kim

et al. 2016)observed this ﬁeld from its three 1.6 m telescopes at

CTIO (Chile), SAAO (South Africa), and SSO (Australia),in

its two slightly offset ﬁelds BLG03 and BLG43, with a

combined cadence of Γ=4hr

−1

The great majority of observations were in the Iband for

OGLE and KMTNet and a broad RI band for MOA, with

occasional V-band observations made solely to determine

source colors. All reductions for the light-curve analysis were

conducted using variants of difference image analysis (DIA;

Alard & Lupton 1998), speciﬁcally Woźniak (2000)and

Albrow et al. (2009).

In addition to these high-cadence, near-continuous survey

observations, OGLE-2016-BLG-1190 was observed in two

lower-cadence surveys that were speciﬁcally motivated to

support microlensing in the Kepler microlensing (K2 C9)ﬁeld

(Henderson et al. 2016), in which it lies. These surveys,

respectively by the 3.6 m Canada–France–Hawaii Telescope

(CFHT)and the 3.8 m United Kingdom Infrared Telescope

(UKIRT)are both located at the Mauna Kea Observatory in

Hawaii. The CFHT observations were carried out equally in the

g,r, and ibands, but only the latter two are incorporated in the

ﬁt because the gdata are too noisy. The UKIRT observations

were in the Hband; these are used here solely for the purpose

of measuring the H-band source ﬂux, and so the (I−H)

source

color.

Finally, two follow-up groups started to monitor the event

shortly after the public announcement (just before peak)of an

anomaly by the MOA group. These were RoboNet and

MiNDSTEp. Both observatories began observing immediately,

i.e., just after peak, from SAAO using the LCO 1 m and from

the Danish 1.5 m at La Silla, Chile, respectively.

In the latter case, the observations were triggered auto-

matically by the SIGNALMEN algorithm (Dominik et al.

2007)after it detected an anomaly at HJD′=7581.0, with the

observations themselves beginning 0.73 days later. The

observations were taken by the EMCCD camera at 10 Hz

The Astronomical Journal, 155:40 (24pp), 2018 January Ryu et al.

(Skottfelt et al. 2015)in Vand I, but only the I-band data were

used in the analysis.

2.2. Spitzer Observations

At UT 02:44, June 29, Y.H.R. sent a message to the Spitzer

team reporting his “by eye”detection of an anomaly at HJD′

(≡HJD−2450000)∼7500, which he had tentatively mod-

eled as being due to a brown-dwarf (BD)or planetary

companion. That is, the putative anomaly had occurred about

69 days previously, and indeed 67 days before the OGLE alert.

Since this anomaly alert was also 12 days before peak, when

the event was only 0.3 mag above baseline, it was impossible at

that time to accurately estimate the basic parameters of the

event. Based on this alert (and subsequent additional modeling

using KMTNet data), the Spitzer team initiated regular cadence

(Γ∼1 day

−1

)observations at the next upload, leading to a total

of 19 observations during 7578<HJD′<7596. The data

were reduced using specially designed software for microlen-

sing (Calchi Novati et al. 2015b). We note that it was the

promptness of the OGLE alert that enabled the recognition of

the much earlier anomaly in time to trigger Spitzer observations

over the peak of the event.

Table 1speciﬁes the number of data points and ﬁlter(s)of

each observatory, as well as its contribution to the total χ

the best model (described in Section 3.4).

3. Analysis

Figures 1and 2show the light curve of all the data together

with a best-ﬁtting model. Ignoring the model for the moment,

the data show two clear isolated deviations from a smooth

point-lens model: an irregular bump at HJD′∼7500 and an

asymmetric peak at HJD′∼7581. Figure 1shows the overall

light curve together with two zooms featuring the regions

around the these two anomalies, while Figure 2shows a further

zoom of the ﬁrst anomaly. In addition, the data from the Spitzer

spacecraft show a clear parallax effect, i.e., although the data

are taken contemporaneously with the ground-based data, the

light curves observed from the two locations are clearly

different. The ﬁnal model for the light curve must account for

all of these effects: the two deviations from the point lens and

the parallax effect seen from Spitzer.

The nature of the two deviations can be understood through

the ground-based data alone. The two deviations could be

caused by the same planet or, in principle, by two different

companions to the host star. As we will show in Section 3.1,a

single planet that explains the central-caustic perturbation at

HJD′∼7581 actually predicts the existence of the planetary-

caustic perturbation at HJD′∼7500 if the source trajectory is

slightly curved. Such a curvature implies that we observe the

orbital motion of the planet, and since orbital motion is

partially degenerate with the parallax effect, in Section 3.2 we

proceed with ﬁtting the ground-based and Spitzer data together

with both effects. In that section, we show that the prediction of

the planetary-caustic crossing is remarkably precise. Thus, for

our ﬁnal ﬁts in Section 3.4, we model the light curve using a

full Keplerian prescription for the orbit.

3.1. Ground-based Model

The simplest explanation for the ground-based light curve is

that both deviations could be due to a single companion. All

companions that are sufﬁciently far from the Einstein ring

produce two such sets of caustics, one set of outlying

“planetary”caustic(s)and one “central”caustic. For wide-

separation companions (s>1), the second caustic lies directly

on the binary axis. For close companions (s<1), there are two

caustics that are symmetric about this axis, but for low-mass

companions, (q=1), these caustics lie close to the binary

axis. Thus, a planetary companion can generate two well-

separated deviations provided that the angle of the source

trajectory relative to the binary axis satisﬁes α∼0orα∼π.If

this is the true explanation, then the central-caustic crossing

should be consistent with a source traveling approximately

along the binary axis of that caustic. If the central-caustic

crossing is not consistent with such a conﬁguration, e.g., it

would require a source traveling perpendicular to the binary

axis, that would be evidence that the two deviations were due

to two separate companions. To test whether there is any

evidence for the latter hypothesis, we begin by excising the

data from the isolated, ﬁrst anomaly and ﬁtting the rest of the

ground-based light curve.

Such binary lens ﬁts require a minimum of six parameters

,s,q,α). The ﬁrst three are the standard point-lens

parameters (Paczyński 1986), i.e., the time of lens–source

closest approach, the impact parameter normalized to the

angular Einstein radius θ

, and the Einstein crossing time,

º()t,4

rel

where

rel is the lens–source relative proper motion and

=∣∣

rel rel . While for point lenses the natural reference point

for (t

)is the (single)lens, for binary lenses it must be

speciﬁed. We choose the so-called center of magniﬁcation

(Dong et al. 2006,2009). The remaining three parameters are

the companion–star separation s(normalized to θ

), their mass

ratio q, and the angle αof their orientation on the sky relative

rel. If the source comes close to or passes over the caustics,

then one also needs to specify ρ≡θ

/θ

, where θ

is the

source angular radius. We note that for s<1, the center of

magniﬁcation is conveniently the same as the center of mass.

We model the light curve using inverse ray shooting (Kayser

et al. 1986; Schneider & Weiss 1988; Wambsganss 1997)when

the source is close to a caustic, and multipole approximations

(Pejcha & Heyrovský 2009; Gould 2008)otherwise. We

initially consider an (s,q,α)grid of starting points for Markov

Chain Monte Carlo (MCMC)searches, with the remaining

Table 1

Observatory

Data set Number χ

Filter

OGLE 3293 3290.161 I

KMTC (BLG03)1510 1508.821 I

KMTC (BLG43)1437 1435.652 I

KMTS (BLG03)1770 1768.444 I

KMTS (BLG43)1713 1712.087 I

KMTA (BLG03)1108 1107.140 I

KMTA (BLG43)1136 1135.246 I

MOA 2089 2088.061 RI

MiNDSTEp 37 36.908 I

RoboNet 40 40.068 i

CFHT 67 66.870 i

CFHT 74 73.962 r

Spitzer 14 10.453 L

The Astronomical Journal, 155:40 (24pp), 2018 January Ryu et al.

parameters starting at values consistent with a point-lens

model. Then, (s,q)are held ﬁxed while the remaining

parameters are allowed to vary in the chain. We then start

new chains at each of the local minima in the (s,q)χ

surface,

with all parameters allowed to vary.

We ﬁnd that the light curve excluding the early caustic-

crossing data can be explained by a planet with parameters:

a=-()( ) ()sq, , 0.60, 0.016, 0.01 . 5

As expected for a light curve generated by a single, low-mass

companion, αis indeed close to zero. For such central-caustic

events, we usually expect two solutions related by the well-

known close-wide «-

(

)ss

1degeneracy (Griest & Saﬁza-

deh 1998; Dominik 1999). Thus, we might also expect a

second solution with parameters (s,q,α)=(1.67, 0.016,

−0.01). However, although the central caustics of both the

s<1 and s>1 solutions are quite similar, the planetary

caustic lies on the opposite side of the host as the planet for

s<1 and on the same side for s>1. As a result, because

α∼0, the s>1 solution would produce a large planetary-

caustic crossing after the central-caustic crossing, which we do

not observe. Therefore, the s<1 solution is the only one that

can explain the light curve.

Nevertheless, at ﬁrst sight, it does not appear that the s<1

solution can explain the planetary-caustic crossing at

HJD′∼7500. The s<1 caustic geometry is characterized

by two caustics on opposite sides of this axis. For (s,q)=(0.6,

0.016), the angle between each caustic and the binary axis is

f∼16°(see Equation (12)). Thus, given that the source

trajectory is very close to the planet–star axis (a

∣

∣1),it

would appear that the source would pass between the two

caustics (e.g., the source travels along the x-axis between the

Figure 1. Light curve of OGLE-2016-BLG-1190. The data points are colored as indicated by observatory in the top panel, which shows the full light curve. Fluxes f

from observatory i(including Spitzer)are aligned to the OGLE scale by ¢=- +()()ffffff

iibissib

,obs ,obs , ,ogle , ,ogle . Models are shown for ground-based and Spitzer

data in black and green, respectively. Vertical dashed and solid lines indicate the subjective and objective selection dates for Spitzer observations, respectively. Open

and ﬁlled circles for Spitzer data (green)show observations initiated by the subjective and objective selection, respectively. Lower panels show zooms of the

planetary-caustic crossing (left)and central-caustic cusp approach (right).

The Astronomical Journal, 155:40 (24pp), 2018 January Ryu et al.

red caustics in Figure 3), whereas we clearly see in the data

(Figure 1)that the source must pass over a caustic at HJD′

∼7500.

However, this apparent contradiction can be resolved if the

planet (and so caustics)moved during the ∼80 days between

the times of the ﬁrst perturbation and the second (when this

geometry is determined). Naively, we expect motion of order

dα/dt∼17°/(80 days)∼0°.2 day

−1

. This kind of motion was

indeed the resolution of the ﬁrst such puzzle for MACHO-97-

BLG-41 (Bennett et al. 1999; Albrow et al. 2000; Jung

et al. 2013).

Hence, we conclude that the two perturbations are likely

caused by a single companion, with the proviso that we must

still check that the form of the planetary-caustic perturbation

“predicted”by the central-caustic crossing is consistent with

the observed perturbation and that the amplitude of internal

motion is consistent with a gravitationally bound system.

3.2. Linearized Orbital Motion and the Microlens Parallax

Given our basic understanding of the anomaly from the

ground-based data, we can proceed with modeling the full data

set including Spitzer data. The ground-based modeling implies

that the orbital-motion effect plays a prominent role, so we

allow for linearized motion of the lens system, i.e., we add two

variables corresponding to the velocity of the lens projected

onto the plane of the sky, dα/dt and ds/dt. Including the

Spitzer data requires also including the parallax effect. The

combination of these two effects implies the possibility of up to

eight degenerate solutions: two solutions because with orbital

motion the source can pass through either planetary caustic,

multiplied by four solutions due to the well-known satellite

parallax degeneracy (Refsdal 1966; Gould 1994b).

We begin by describing the color–magnitude diagram (CMD)

analysis in Section 3.2.1 because it is used to derive the color–

color relation needed to combine the Spitzer and ground-based

data. Then, we give a qualitative evaluation of the Spitzer

parallax in Section 3.2.2. In this section, we show that the color–

color constraint plays an important role in measuring the parallax

even though the Spitzer light curve partially captures the peak of

the event. In Section 3.2.3, we present the full model of the event

including linearized orbital motion and parallax. This modeling

demonstrates that the orbital-motion parameters that are derived

after excluding the ±10 days of data around the planetary-caustic

crossing are very similar to those derived from the full data set.

Furthermore, the information from this restricted data set

eliminates one of the two possible directions of orbital motion.

Finally, in Section 3.3, we show that two of the parallax solutions

can be eliminated by two separate arguments. First, they are

inconsistent with Kepler K2 Campaign 9 microlensing observa-

tions. Second, they imply physical effects that are not observed.

This leaves us with only two solutions, both of which carry the

same physical implications for interpreting the light curve.

3.2.1. CMD and Spitzer–Ground Color–Color Relation

In order to derive the VIL color–color relations needed to

incorporate the Spitzer data, we must place the source on a

CMD. We conduct this analysis by ﬁrst using the OGLE V/I

CMD and then conﬁrm and reﬁne the result using H-band data

from UKIRT.

The middle panel of Figure 4shows an instrumental CMD

based on OGLE-IV data. The clump centroid is at

(

)()VII, 2.89, 16.35

clump,O IV . The source is shown at

-= 

(

)(

)

VII, 2.57 0.06, 21.35 0.01

s,O IV , with the

color derived by regression (i.e., independent of model)and

the magnitude obtained from the (ﬁnal)modeling. Also shown

in this ﬁgure are two points related to the blended light, which

are not relevant to the present discussion but will be important

later. The key point here is that the source lies 0.32 mag

Figure 2. Further zoom of the lower-left panel of Figure 1, focusing on the data

approaching and within the planetary caustic. The caustic entrance is well-

deﬁned by the KMTA and MOA data, with residuals that are consistent with

the errors and that show no signiﬁcant systematic trends.

Figure 3. Geometry of the source and lens system based on ground-based data

modeled with linearized orbital motion. The caustic structure is shown at two

epochs, HJD′=7500 (blue)and 7582 (red)when, according to Figure 1, the

source has just entered the planetary caustic and just passed the central caustic,

respectively. A model that failed to include orbital motion and whose trajectory

angle αwas determined solely by modeling the source passage over the central

caustic, would miss the (red)caustics.

The Astronomical Journal, 155:40 (24pp), 2018 January Ryu et al.

blueward of the clump in the instrumental OGLE-IV system,

which corresponds to 0.30 mag in the standard Johnson–

Cousins system (Udalski et al. 2015a).

The top panel of Figure 4shows an Iversus (I−H)CMD,

which is formed by cross-matching OGLE-IV I-band to UKIRT

H-band aperture photometry. The magnitude of the clump is the

same as in the middle panel, I

clump

=16.35±0.05. To ensure

that the (I−H)color of the clump is on the same system as the

(V−I)color, we make a VIH color–color diagram in the lower

panel based on cross-matched stars and then identify the

intersection of the resulting track with the measured (V−I)

color to obtain (I−H)

clump

=2.78±0.02. Also shown is the

position of the source. Its magnitude is the same as that in the

middle panel. We determine (I−H)

=2.29±0.03 from a

point-lens model that excludes all data within three days of the

anomalies. This permits a proper estimate of the error bars and is

appropriate because the UKIRT data end 3.5 days before the

anomaly at peak. Hence, the source lies 0.49 mag blueward of the

clump in (I−H). To derive the inferred offset in (V−I),

we consult the color–color relations of Bessell & Brett (1988).

We adopt (V−I)

0,clump

=1.08 from Bensby et al. (2013),which

implies (I−H)

0,clump

=1.32 based on Table3 of Bessell & Brett

(1988), and hence (I−H)

0,s

=0.83±0.03. Then, using Table2

of Bessell & Brett (1988),weobtain(V−I)

0,s

=0.75±0.03,

i.e., 0.33 mag blueward of the clump. (Note that while we made

speciﬁc use of the color of the clump in this calculation, the ﬁnal

result, i.e., the offset from the clump in (V−I), is basically

independent of the choice of clump color.)Thus, the results of the

two determinations are consistent. Although the formal error of

the I/H-based determination is smaller than the one derived

qfrom OGLE-IV V/Idata, there are more steps. Hence, we assign

equal weight to the two determinations and adopt (V−I)

=

0.77±0.04.

To infer the I−Lsource color from the measured

(

)VI 2.57

s,O IV , we employ the method of Shvartzvald

et al. (2017b). In brief, this approach applies the VIL color–

color relations of Bessell & Brett (1988)to a VIL cross-

matched catalog of giant stars to derive an offset (including

both instrumental zero point and extinction)between the

intrinsic and observed (I−L)color. Note that in this approach,

explicit account is taken of the fact that the source is a dwarf

while the calibrating stars are giants. We thereby derive

(I−L)

=1.82±0.06, where here Lis the Spitzer instru-

mental magnitude.

From the CMD, we can also derive the angular source size

(required to determine the Einstein radius θ

=θ

/ρ).We

adopt a dereddened clump magnitude I

0,clump

=14.35 (Nataf

et al. 2013). Using this and the measurements reported above,

we derive [(V−I),I]

0,s

=(0.77±0.04, 19.35±0.05). Using

the VIK color–color relations of Bessell & Brett (1988)and the

color/surface-brightness relations of Kervella et al. (2004), this

yields (e.g., Yoo et al. 2004)

qm=

*() ()0.455 0.030 as, 6

where the error is dominated by scatter in the surface brightness

at ﬁxed color (as estimated from the scatter of spectroscopic

color at ﬁxed photometric color; Bensby et al. 2013).By

combining this with the ρmeasured from the ﬁnal model

(Section 3.4), we derive

== 

*() ()0.49 0.04 mas. 7

3.2.2. Spitzer Parallax

Heuristically, space-based microlens parallaxes are derived

from the difference in (t

)as seen by observers on Earth and

in space, separated in projection by ^

D(Refsdal 1966;

Gould 1994b). The vector microlens parallax

Eis deﬁned

(Gould 1992,2000; Gould & Horne 2013)as

º().8

Erel

rel

Observers separated by ^

Dwill detect lens–source separations

in the Einstein ring ptb

ºD D = ^

()uD,au

E, where

tbDº -Dº -

Å()

tuu,,9

0,sat 0,

and where the subscripts indicate parameters as determined

from the satellite and ground. Hence, from a series of such

measurements (which of course are individually sensitive to the

Figure 4. Instrumental color–magnitude diagrams in (I−H,I)(top)and

(V−I,I)(middle), together with the VIH color–color diagram (bottom), which

are derived by matching OGLE-IV instrumental Vand Iwith UKIRT H

(aligned to 2MASS). The clump centroid is marked in red, while the source is

marked in magenta. For the (V−I,I)(middle)panel, the blended light is

shown in green. Because the blend is displaced from the source by 0 5, only

6% of its light can be due to the lens. This ﬂux upper limit shown, in blue (with

arbitrary (V−I)color), restricts the lens mass to M

1M

To avoid ambiguity and possible confusion by cursory readers, we quote the

ﬁnally adopted values of the θ

and θ

in Equations (6)and (7), rather than the

values derived from the intermediate modeling described thus far, which differ

very slightly.

The Astronomical Journal, 155:40 (24pp), 2018 January Ryu et al.

magniﬁcation and not to (t

)directly), one can infer the

vector microlens parallax

ptb=DD



() ()

au ,, 10

where Δβis generally subject to a fourfold degeneracy,

bD= -

 Å

∣∣ ∣∣ ()uu,11

,0,sat0,

due to the fact that in most cases microlensing is sensitive only

to the absolute value of u

, whereas u

is actually a signed

quantity.

This heuristic picture is somewhat oversimpliﬁed because ^

is changing with time, which also means that t

is not identical

for the two observers. Hence, in practice, one ﬁts directly for

E, taking account of both the orbital motion of the satellite and

Earth (and hence, automatically, the time variable ^

D(t)).

Nevertheless, in most cases (including the present one), the

changes in ^

Dare quite small, p

^

∣

∣Dddttau

EE , which

means that this simpliﬁed picture yields a good understanding

of the information ﬂow.

This qualitative picture can be used to show that the color

constraints play an important role in this event, despite the fact

that the peak is nearly captured in the Spitzer observations. As

can be seen from Figure 1, in this case Spitzer observations

begin roughly at peak. In general, it is quite rare that Spitzer

observes a full microlensing light curve. This is partly because

the maximum observing window is only 38 days, but mainly

because the events are only uploaded to Spitzer three to nine

days after they are recognized as interesting (Figure1of

Udalski et al. 2015b), which is generally after they are well on

their way toward peak. Yee et al. (2015a)argue that with color

constraints, even a fragmentary light curve can give a good

parallax measurement. In this case, we have much more than a

fragment, but as we show below, including the color

constraints leads to a much stronger constraint on the parallax

measurement.

If, as in the present case for Spitzer data, the peak of the light

curve is not very well-deﬁned, a free, ﬁve-parameter (t

), point-lens ﬁt would not constrain these parameters very

well. However, in a parallax ﬁt, we effectively know t

, which

we approximate here as identical to the ground, t

=94 days.

After applying this constraint on t

,ﬁtting the Spitzer data

alone yields t

0,sat

=7579.5±1.4 days and u

0,sat

=0.059±

0.021, which would lead to a parallax error of σ(π

)∼

0.021 au/D

⊥

∼0.016, and so a fractional parallax error of

σ(π

)/π

∼40% for the small parallax solutions. Note that this

would not imply that the parallax is “unmeasured”: the fact that

the parallax is measured to be small (0.06 and with relatively

small errors)would securely place the lens in or near the bulge,

which is signiﬁcant information on its location.

However, by including the color constraint, we can reduce

this uncertainty to <10%, giving a solid measurement of the

parallax. First, one should note that the above ﬁt to the Spitzer

light curve yields a Spitzer source ﬂux of f

=0.22±0.11 (in

the instrumental Spitzer ﬂux system). On the one hand, this is

perfectly consistent with the prediction based on the ground

solution and the VIL color–color relation f

s,Spitz

=0.245±

0.015, which is an important check on possible systematic

errors. On the other hand, the errors on the ﬁt value of f

s,Spitz

are

an order of magnitude larger than the one derived from the VIL

relation. This means that the color–color relation can signiﬁcantly

constrain the ﬁt. Imposing this additional constraint, we then ﬁnd

0,sat

=7579.3±0.8 days and u

0,sat

=0.0635±0.0029, sub-

stantially improving the constraints on u

0,sat

. This reduces the

parallax error to about 6% for the Δβ

and Δβ

−−

solutions and

to about 4% for the Δβ

+−

and Δβ

−+

solutions. See Section 3.3.

3.2.3. Modeling Orbital Motion

We now proceed with a simultaneous, 11 geometric-

parameter

,q,α

,ρ,π

E,N

,π

E,E

,ds/dt,dα/dt)

ﬁt to the ground- and space-based data. The ﬁrst nine

parameters have been described above. The last two are a

linearized parameterization of orbital motion, with α(t)≡α

+

(dα/dt)(t−t

),s(t)≡s

+(ds/dt)(t−t

As discussed above, we expect a total of eight solutions: four

from the satellite parallax degeneracy (Equation (11)) and two

from the two planetary caustics. However, we found to our

surprise that only one direction of angular orbital motion was

permitted for each of the four parallax-degenerate solutions,

i.e., the source trajectory could pass through one of the

planetary caustics but not the other. These solutions are given

in Table 2.

To understand why only one direction of angular orbital

motion is permitted, we stepped back and performed a series of

tests. In the ﬁrst test, we ﬁt for the above 11 parameters but, as

in Section 3.1, with the data surrounding the planetary

perturbation at t

=HJD′∼7500 removed (speciﬁcally

7490 <HJD′<7510). That is, we removed the information

that we had previously believed was responsible for the

measurement of orbital motion. Thus, we are testing whether

information from the immediate neighborhood of the planetary

caustic is required to predict the time and position of the

planetary-caustic crossing.

From the light curve (Figure 1), we can see that the midpoint

of the two caustic crossings of the planetary caustic is

∼7500.375. From the modeling with the full data set, we

know the ylocation of the caustic η

c,0

(Han 2006). Therefore, if

the orbital motion is constrained by the restricted data set, it

should predict a planetary caustic close to this location. We

conduct this test in a rotated frame for clarity. For each MCMC

sample in the ﬁt to the restricted data set, we predict the

position of the center of the planetary caustic, ﬁrst in the

unrotated frame according to Han (2006),

xh =- 



⎛

⎝

⎜

⎡

⎣

⎢

⎤

⎦

⎥

⎞

⎠

⎟

() ()ss

s,1,1

1.12

We then rotate by an angle f=dα/dt(t

−t

)to obtain

¢¢



(

),, and ﬁnally convert this result to the observational

plane,

xh=+

¢¢

()()( ) ()tt t t,,0,. 13

xy 0E

The result is shown in Figure 5along with the “observed”

position of the caustic (t

)=(7500.375, 1.0)derived from

,η

c,0

There are two main points to note about this ﬁgure. The ﬁrst

is that the ﬁt to the main light curve alone, primarily the

central-caustic approach, measures the orbital-motion para-

meters well enough to “predict”the position of the caustic to

Together with, as always, two ﬂux parameters (f

)for each observatory,

for the source ﬂux and blended ﬂux, respectively.

The Astronomical Journal, 155:40 (24pp), 2018 January Ryu et al.

within a few σ. Second, this error bar is quite small, about two

days in one direction (roughly aligned with time)and 0.5 days

in the transverse direction. From the inset, which zooms out to

the scale of Figure 3, one can see that the offset between the

predicted and observed planetary-caustic crossing is tiny

compared to the movement of the caustics that is illustrated in

Figure 3.

This test demonstrates that the orbital motion can be

determined quite precisely without data from the planetary

caustic, but it does not in itself tell us what part of the light

curve this information is coming from. In principle, it could be

coming from the cusp approach at the peak of the light curve or

it could be coming from subtle features in the light curve that

lie 10 or more days from the planetary crossing and that are

induced by the planetary caustic itself. Or, it could be some

combination. In particular, one suspects that a signiﬁcant

amount of information must come from the central caustic

because information from the “extended neighborhood”of the

planetary caustic would not distinguish between the positive

and negative values of dα/dt that are required for the source to

cross, respectively, the lower and upper planetary caustics

shown in Figure 3.

Hence, for our second test, we remove all data

7240<HJD′<7567. Here we are directly testing what

information is available from the central-caustic region. As

shown in Table 3(bottom row), the measurement of the orbital

parameters ds/dt and dα/dt is quite crude compared to either

the previous test or the full data set (ﬁrst two rows).

Nevertheless, dα/dt is detected at 4σ. Moreover, in order for

the direction of revolution to be in the opposite sense, so that

the source would transit the other caustic in Figure 3,dα/dt

should have the negative of its actual value, i.e.,

a+

dt 1.4

. Hence, the value measured after excluding

all data 7240<HJD′<7567 differs from the one required for

opposite revolution by 7.4σ. That is, it is the source passage by

the central caustic that ﬁxes the direction of the planet’s

revolution about the host. Then, as can be seen by comparison

of the second and ﬁfth lines of Table 3, it is the light curve in

the general vicinity of the planetary caustic that permits a

precise prediction of the orbital motion when the data

immediately surrounding the caustic are removed.

To further explore the origin of the orbital information, we

show in Table 3two additional cases, with data deleted in the

intervals 7495<HJD′<7567 and 7490<HJD′<7567.

Comparing the last three lines of Table 3, one sees that the

light curve from more than 10 days before the crossing

contributes greatly to the measurement of transverse motion,

and that the light curve from the following ﬁve days contributes

Table 2

Best-ﬁt Solutions for Parallax+Orbital Motion (Two-parameter)Models

Parameters (−,+)(+,−)(+,+)(−,−)

/dof 14283.479/14252 14292.586/14252 14296.670/14252 14302.523/14252

(HJD

′

)7582.161±0.007 7582.160±0.007 7582.167±0.007 7582.167±0.007

(10

−2

)−1.747±0.023 1.717±0.023 1.667±0.021 −1.667±0.022

(days)95.747±0.958 97.354±1.006 100.161±0.952 100.192±0.983

s0.604±0.002 0.603±0.002 0.603±0.002 0.604±0.002

q(10

−2

)1.414±0.019 1.393±0.019 1.360±0.017 1.354±0.018

α(rad)0.033±0.005 −0.033±0.005 −0.028±0.005 0.030±0.005

ρ(10

−3

)0.908±0.050 0.873±0.050 0.860±0.045 0.868±0.046

E,N

0.065±0.003 −0.063±0.002 0.038±0.002 −0.037±0.002

E,E

0.004±0.006 0.011±0.007 0.008±0.006 0.011±0.007

ds/dt (yr

−1

)−0.278±0.018 −0.286±0.019 −0.332±0.018 −0.320±0.018

dα/dt (yr

−1

)−1.417±0.030 1.402±0.030 1.394±0.030 −1.385±0.030

Figure 5. “Predicted”(small circles)vs. “observed”(large blue circle)position

of source crossing of planetary caustic within the Einstein ring. The predictions

are from an MCMC chain created by ﬁtting both ground-based and Spitzer data

to a model with linearized orbital motion, but with the data points in the

neighborhood of the observed planetary-caustic crossing omitted. Points are

colored by (black, red, green)for Δχ

<(1, 4, 9). The abscissa of the

prediction for each chain element is the time that the source should have

crossed the center of the planetary caustic. The ordinate is that of the center of

the caustic at this time, multiplied by t

. The abscissa of the “observed”

position is the midtime of the two caustic crossings shown in the lower-left

panel of Figure 1. The ordinate is that of the source position at this time,

multiplied by t

. Even without any “knowledge”of the source crossing, the

model predicts its position very accurately. Inset shows zoom-out on the same

scale as Figure 3.

Table 3

Orbital Motion with Deleted Data

Deleted Data ds/dt dα/dt

None −0.278±0.018 −1.417±0.030

7490–7510 −0.211±0.056 −1.548±0.056

7495–7567 −0.234±0.102 −1.156±0.115

7490–7567 −0.195±0.210 −1.192±0.282

7240–7567 −0.361±0.224 −1.720±0.423

The Astronomical Journal, 155:40 (24pp), 2018 January Ryu et al.

even more. On the other hand, it is mostly the data after the

crossing that contributes to the measurement of ds/dt.

A very important implication of Table 3is that the orbital

motion that is predicted based on the the subtle light curve

features away from the planetary-caustic crossings yield

accurate results. That is, of the eight hypothetical cases,

(2 parameters)×(4 tests), the predictions of orbital motion are

within 1σof the true value for six cases, and at 2.0σand 2.3σin

the remaining two. This provides evidence that such measure-

ments are believable within their own errors in other events

(i.e., the overwhelming majority)for which there is no way of

conﬁrming the results.

These results have important implications for microlensing

observations with WFIRST (Spergel et al. 2013)and,

potentially, Euclid (Penny et al. 2013)because their Sun-angle

constraints will very often restrict the light-curve coverage

much more severely compared to those obtained from the

ground.

3.3. Only the Two “Large Parallax”Solutions Are Allowed

The high precision of the two-parameter orbital-motion

measurement motivates us to attempt to model full Keplerian

motion. However, before moving on to this added level of

complexity, we ﬁrst note that only two of the four solutions

permitted by the parallax degeneracy are allowed. We present