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The First Cold Neptune Analog Exoplanet: MOA-2013-BLG-605Lb

November 2015

November 2015

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arXiv

Authors:

Takumu Sumi

LINE Corp

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We present the discovery of the first Neptune analog exoplanet, MOA-2013-BLG-605Lb. This planet has a mass similar to that of Neptune or a super-Earth and it orbits at $9\sim 14$ times the expected position of the snow-line, $a_{\rm snow}$, which is similar to Neptune's separation of $ 11\,a_{\rm snow}$ from the Sun. The planet/host-star mass ratio is $q=(3.6\pm0.7)\times 10^{-4}$ and the projected separation normalized by the Einstein radius is $s=2.39\pm0.05$. There are three degenerate physical solutions and two of these are due to a new type of degeneracy in the microlensing parallax parameters, which we designate "the wide degeneracy". The three models have (i) a Neptune-mass planet with a mass of $M_{\rm p}=21_{-7}^{+6} M_{\rm earth}$ orbiting a low-mass M-dwarf with a mass of $M_{\rm h}=0.19_{-0.06}^{+0.05} M_\odot$, (ii) a mini-Neptune with $M_{\rm p}= 7.9_{-1.2}^{+1.8} M_{\rm earth}$ orbiting a brown dwarf host with $M_{\rm h}=0.068_{-0.011}^{+0.019} M_\odot$ and (iii) a super-Earth with $M_{\rm p}= 3.2_{-0.3}^{+0.5} M_{\rm earth}$ orbiting a low-mass brown dwarf host with $M_{\rm h}=0.025_{-0.004}^{+0.005} M_\odot$. The 3-D planet-host separations are 4.6$_{-1.2}^{+4.7}$ AU, 2.1$_{-0.2}^{+1.0}$ AU and 0.94$_{-0.02}^{+0.67}$ AU, which are $8.9_{-1.4}^{+10.5}$, $12_{-1}^{+7}$ or $14_{-1}^{+11}$ times larger than $a_{\rm snow}$ for these models, respectively. The Keck AO observation confirm that the lens is faint. This discovery suggests that Neptune-like planets orbiting at $\sim 11\,a_{\rm snow}$ are quite common. They may be as common as planets at $\sim 3\,a_{\rm snow}$, where microlensing is most sensitive, so processes similar to the one that formed Uranus and Neptune in our own Solar System may be quite common in other solar systems.

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arXiv:1512.00134v1 [astro-ph.EP] 1 Dec 2015

The First Cold Neptune Analog Exoplanet:

MOA-2013-BLG-605Lb

T. Sumi1,2, A. Udalski3,4, D.P. Bennett5,6,2, A. Gould7, R. Poleski3,4,7, I.A. Bond8,2,

N. Rattenbury9,2, R. W. Pogge7T. Bensby10, J.P. Beaulieu11 , J.B. Marquette11 ,

V. Batista11 , S. Brillant12

and

F. Abe13, A. Bhattacharya5, M. Donachie9, M. Freeman9, A. Fukui14, Y. Hirao1, Y. Itow13,

N. Koshimoto1, M.C.A. Li9, C.H. Ling8, K. Masuda13, Y. Matsubara13 , Y. Muraki13 ,

M. Nagakane1, K. Ohnishi15, To. Saito16, A. Sharan9, D.J. Sullivan17, D. Suzuki5,

P.,J. Tristram18, A. Yonehara19,

(The MOA Collaboration)

M.K. Szyma´nski3, K. Ulaczyk3, S. Koz lowski 3, L. Wyrzykowski3, M. Kubiak3, P.

Pietrukowicz3, G. Pietrzy´nski3, I. Soszy´nski3,

(The OGLE Collaboration)

– 2 –

ABSTRACT

We present the discovery of the ﬁrst Neptune analog exoplanet, MOA-2013-

BLG-605Lb. This planet has a mass similar to that of Neptune or a super-Earth

and it orbits at 9 ∼14 times the expected position of the snow-line, asnow, which

is similar to Neptune’s separation of 11 asnow from the Sun. The planet/host-star

mass ratio is q= (3.6±0.7)×10−4and the projected separation normalized by the

1Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka

560-0043, Japan,

e-mail: sumi@ess.sci.osaka-u.ac.jp

2Microlensing Observations in Astrophysics (MOA)

3Warsaw University Observatory, Al. Ujazdowskie 4, 00-478 Warszawa,Poland; udalski, msz, mk, pietrzyn,

soszynsk, szewczyk, kulaczyk@astrouw.edu.pl

4Optical Gravitational Lens Experiment (OGLE)

5Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA; bennett@nd.edu

6Laboratory for Exoplanets and Stellar Astrophysics, NASA/Goddard Space Flight Center, Greenbelt,

MD 20771, USA

7Department of Astronomy, Ohio State University, 140 W. 18th Ave., Columbus, OH 43210, USA

8Institute of Information and Mathematical Sciences, Massey University, Private Bag 102-904, North

Shore Mail Centre, Auckland, New Zealand; i.a.bond,c.h.ling,w.sweatman@massey.ac.nz

9Department of Physics, University of Auckland, Private Bag 92019, Auckland, New Zealand;

n.rattenbury,mli351,p.yock@auckland.ac.nz; asha583,mdon849@aucklanduni.ac.nz

10Lund Observatory, Department of Astronomy and Theoretical physics, Box 43, SE-221 00 Lund, Sweden

11UPMC-CNRS, UMR7095, Institut d’Astrophysique de Paris, F-75014 Paris, France

12European Southern Observatory (ESO), Karl-Schwarzschildst. 2, D-85748 Garching, Germany

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

abe,itow,kmasuda,ymatsu@stelab.nagoya-u.ac.jp

14Okayama Astrophysical Observatory, National Astronomical Observatory of Japan, 3037-5 Honjo, Kamo-

gata, Asakuchi, Okayama 719-0232, Japan

15Nagano National College of Technology, Nagano 381-8550, Japan

16Tokyo Metropolitan College of Aeronautics, Tokyo 116-8523, Japan

17School of Chemical and Physical Sciences, Victoria University, Wellington, New Zealand

18Mt. John University Observatory, P.O. Box 56, Lake Tekapo 8770, New Zealand

19Department of Physics, Faculty of Science, Kyoto Sangyo University, 603-8555 Kyoto, Japan

– 3 –

Einstein radius is s= 2.39 ±0.05. There are three degenerate physical solutions

and two of these are due to a new type of degeneracy in the microlensing parallax

parameters, which we designate “the wide degeneracy”. The three models have

(i) a Neptune-mass planet with a mass of Mp= 21+6

−7M⊕orbiting a low-mass

M-dwarf with a mass of Mh= 0.19+0.05

−0.06M⊙, (ii) a mini-Neptune with Mp=

7.9+1.8

−1.2M⊕orbiting a brown dwarf host with Mh= 0.068+0.019

−0.011M⊙and (iii) a

super-Earth with Mp= 3.2+0.5

−0.3M⊕orbiting a low-mass brown dwarf host with

Mh= 0.025+0.005

−0.004M⊙. The 3-D planet-host separations are 4.6+4.7

−1.2AU, 2.1+1.0

−0.2

AU and 0.94+0.67

−0.02 AU, which are 8.9+10.5

−1.4, 12+7

−1or 14+11

−1times larger than asnow

for these models, respectively. The Keck AO observation conﬁrm that the lens

is faint. This discovery suggests that Neptune-like planets orbiting at ∼11 asnow

are quite common. They may be as common as planets at ∼3asnow, where

microlensing is most sensitive, so processes similar to the one that formed Uranus

and Neptune in our own Solar System may be quite common in other solar

systems.

Subject headings: gravitational lensing – Galaxy: bulge – stars: variables: other

1. Introduction

The formation of the ice giants Uranus and Neptune is not well understood. In the

favored core accretion theory, the gas giant planets like Jupiter and Saturn are believed

to form through the accumulation of small icy planetesimals into solid cores of about

5-15 M⊕in the region beyond the snow-line at asnow ≈2.7(Mh/M⊙) (Ida & Lin 2004;

Laughlin, Bodenheimer & Adams 2004; Kennedy, Kenyon & Bromley 2006), where the pro-

toplanetary disk is cold enough for ices (especially water-ice) to condense. However, such

a scenario is unable to form smaller ice giants like Uranus and Neptune at their current

orbital positions, due to the low density of planetesimals and slow evolution in these orbits

(Pollack et al. 1996).

One idea is that Uranus and Neptune formed in the Jupiter-Saturn region between ∼5

and ∼17 AU, then migrated outwards to the current position (Fernandez 1984; Thommes, Duncan & Levison

1999; Helled & Bodenheimer 2013). The distribution of such cold ice-giant planets in other

solar systems is important for understanding the formation of our own cold ice giants. Also,

in our own Solar System, the distribution of Kuiper Belt objects (KBOs) is dominated by

gravitational interactions with Neptune. Since KBOs hold large amounts of water and other

volatiles needed for life, it could be that exo-neptunes play an important role in the devel-

opment of life in some exoplanetary systems, whether or not they play this role in our own

– 4 –

Solar System.

In the 20 years since the ﬁrst exoplanet discovery (Mayor & Queloz 1995), there have

been repeated discoveries of planets that are quite diﬀerent from those in our own So-

lar System. However, the detection of planets similar to those in our own Solar System

has been more diﬃcult. Only Jupiter analogs have been detected orbiting solar type stars

(Wittenmyer et al. 2014), while Jupiter/Saturn (Gaudi et al. 2008; Bennett et al. 2010) and

Venus/Earth analogs (Burke et al. 2014; Quintana et al. 2014) have been found orbiting

low-mass stars. Very cold, low-mass planets have yet to be explored (see the distribution of

known exoplanets as of 2015 Oct. 6 1in Figure 1). Cold ice-giants like Uranus and Neptune

are very diﬃcult to detect with the radial velocity and transit methods owing to their long

orbital periods (80-160 years), low orbital velocities and low transit probabilities. The direct

imaging method can detect wide-orbit planets if they are self-luminous, but otherwise, they

will be far too faint to detect, especially if they are as small as Uranus and Neptune.

Recently, low-mass stars (i.e. M-dwarfs) have attracted more interest in exoplanet search

programs because of their high detectability of habitable or cold low-mass planets.

Kepler ’s 150,000 targets contain about 3000 red dwarfs and more than a hundred plan-

etary systems have been found orbiting these stars (Morton & Swift 2013). These results

show that smaller planets are more common than larger planets around M-dwarfs, and plan-

ets with radii of ∼1.25 R⊕are the most common planets in these systems. Dressing & Charbonneau

(2013) estimated an occurrence rate of ∼0.5 habitable zone Earth size planets per M-dwarf,

and Quintana et al. (2014) found an Earth-radius habitable planet around a ∼0.5 M⊙M-

dwarf. That smaller planets are more common than larger planets around M-dwarfs may be

related to the fact that only small mass proto-planetary disks have been found around such

low mass stars (Kennedy & Kenyon 2008). The TRENDS high-contrast imaging survey, in

combination with radial velocity measurements, indicates that 6.5% ±3.0% of M-dwarf stars

host one or more massive companions with 1 < m/MJ<13 and 0 < a < 20 AU, however

this survey is not sensitive to cold ice planets (Montet et al. 2014; Clanton & Gaudi 2014).

The gravitational microlensing method is also sensitive to planets around M-dwarfs and

even brown dwarfs because it does not rely on the light from the host stars. Microlens-

ing relies upon random alignments between background source stars and foreground lens

star+planet systems, and more massive lens stars are only favored by the factor √Mwhile

smaller masses have shorter timescales which can also bias against detection. So M-dwarf

lens stars dominate microlensing events. Contrary to the other methods, microlensing is sen-

sitive to low-mass planets down to an Earth-mass (Bennett & Rhie 1996) orbiting beyond

1http://exoplanet.eu

– 5 –

the snow-line, as shown in Fig. 1. Microlensing is therefore complementary to the other

planet detection techniques. Statistical analyses of microlensing samples indicate that the

planet abundance beyond the snow line is about a factor ∼7 larger than the abundance of

close-in planets. Neptune mass planets are more abundant than gas giants around M-dwarfs,

and one or more planets per star in total are predicted just beyond the snow-line (Sumi et al.

2010; Gould et al. 2010; Cassan et al. 2012).

In about half of the planetary systems found by microlensing, the mass of the host

and planets and their projected separation have been measured by microlensing paral-

lax in combination with the ﬁnite source eﬀect (Bennett et al. 2008; Gaudi et al. 2008;

Muraki et al. 2011; Kains et al. 2013; Tsapras et al. 2014; Udalski et al. 2015a) and/or direct

detection of the lens ﬂux by high resolution imaging by adaptive optics (AO) (Bennett et al.

2010; Kubas et al. 2012; Batista et al. 2014, 2015) or the Hubble Space Telescope (HST)

(Bennett et al. 2006, 2015; Dong et al. 2009b). The probability distribution of physical

mass and separations of other events have been estimated using a Bayesian analysis as-

suming a Galactic model. Among the planetary systems with mass measurements, three of

them have very low mass hosts, less than 0.2M⊙and each system has a planetary mass

ratio q < 0.01. These three systems are MOA-2007-BLG-192L (Mh= 0.084+0.015

−0.012M⊙,

Mp= 3.2+5.2

−1.8M⊕) (Bennett et al. 2008; Kubas et al. 2012), MOA-2010-BLG-328L (Mh=

0.11 ±0.01M⊙, Mp= 9.2±2.2M⊕) (Furusawa et al. 2013), and OGLE-2013-BLG-0723LB

(Mh= 0.031 ±0.003M⊙, Mp= 0.69 ±0.06M⊕) (Udalski et al. 2015b). Neptune analog

planets are still diﬃcult to detect even by microlensing.

Recently, Poleski et al. (2014) found a planet in a Uranus-like orbit with mass of ∼4

MUranus at ∼18 AU around ∼0.7 M⊙star. This is ∼9 times the snow-line of the host. While

their mass estimates are based on a Bayesian analysis and have large uncertainties, their

detection demonstrated the ability to detect planets in these orbits with microlensing.

In this paper, we present the detection and the mass measurement of the ﬁrst Neptune

analog MOA-2013-BLG-605Lb via microlensing. We detected the microlensing parallax ef-

fect which yield the mass measurement of the lens system in combination with the ﬁnite

source eﬀect.

Microlensing parallax can be measured when one observes an event simultaneously from

two diﬀerent locations, either with a telescope on Earth and a space telescope, (Refsdal 1966;

Udalski et al. 2015a) or with two ground-based telescopes, referred to as terrestrial parallax

(Gould et al. 2009). It is known that there is a four-fold degeneracy in these parallax mea-

surements, (Refsdal 1966; Gould 1994). Two elements of this four-fold degeneracy correspond

to two diﬀerent magnitudes of the measured parallax. As a result, the physical parameters of

the lens diﬀers between these two degenerate solutions. The other two degenerate solutions

– 6 –

in the four-fold degeneracy just arise from a symmetry in the lensing geometry. The physi-

cal parameters of the lens are the same between these two degenerate solutions, except the

projected velocities which can be used to distinguish among solutions (Calchi Novati et al.

2015). Most commonly, parallax measurements have been made by observing an event from

an accelerated observatory; speciﬁcally from ground-based observations of an event which

is long enough for Earth to move signiﬁcantly in its orbit around the Sun. This is referred

to as orbital parallax (Gould 1992). There is also an analogous four-fold discrete degener-

acy for orbital parallax, termed the “jerk parallax” degeneracy and their mirror solutions

(Gould 2004; Park et al. 2004). For the binary lens case, there is an approximate degeneracy

in the parallax parameters, known as the “ecliptic degeneracy” (Skowron et al. 2013). In

this work on event MOA-2013-BLG-605, we report a new type of degeneracy in parallax

model solutions, which is speciﬁc to widely separated binary lenses. The details of this new

degeneracy are presented in section §4.

We describe the observations of, and photometric data for, event MOA-2013-BLG-605

in sections §2 and §3. The light curve modeling is described in section §4. In section §5

and §6 we present the physical parameters of the lens system and constraints by the Keck

AO observation. We discuss, in section §7, the manner in which we might measure the lens

mass in the future and we present an overall discussion and our conclusions in section §8.

2. Observation

The Microlensing Observations in Astrophysics (MOA; Bond et al. 2001; Sumi et al.

2003) collaboration carries out a microlensing survey toward the Galactic bulge from the

Mt. John University Observatory in New Zealand. The MOA-II survey (Sumi et al. 2011)

is a very high cadence photometric survey of the Galactic bulge with the 1.8 m MOA-II

telescope equipped with a 2.2 deg2ﬁeld-of-view (FOV) CCD camera. The 2013 MOA-II

observing strategy called for the 6 ﬁelds (∼13 deg2) with the highest lensing rate to be

observed with a 15 minute cadence, while the next 6 best ﬁelds were observed with a 47

minute cadence, and 8 additional ﬁelds were observed with a 95 minutes cadence. Most

MOA-II observations use the custom MOA-red wide band ﬁlter, which corresponds to the

sum of the standard Cousins Rand I-bands. MOA-II issues ∼600 alerts of microlensing

events in real time each year.2

The Optical Gravitational Lensing Experiment (OGLE; Udalski, Szyma´nski and Szyma´nski

2015) also conducts a microlensing survey toward the Galactic bulge with the 1.3 m Warsaw

2https://it019909.massey.ac.nz/moa/

– 7 –

telescope at the Las Campanas Observatory in Chile. The fourth phase of OGLE, OGLE-

IV started its high cadence survey observations in 2010 with a 1.4 deg2FOV mosaic CCD

camera. OGLE observes bulge ﬁelds with cadences ranging from one observation every 20

minutes for 3 central ﬁelds to less than one observation every night for the outer bulge ﬁelds.

Most observations are taken in the standard Kron-Cousin I-band with occasional observa-

tions in the Johnson V-band. OGLE-IV issues ∼2000 microlensing event alerts in real time

each year.3

The microlensing event MOA-2013-BLG-605 was discovered at (R.A., decl.)(2000)=

(17:58:42.85, -29:23:53.66) [(l, b) = (1.0583◦, -2.695◦)], in MOA ﬁeld gb9, which is mon-

itored every 15 min, and it was announced by the MOA Alert System on 2013 Aug 30

(HJD′≡HJD−2450000 ∼6535). Figure 2 shows the light curve. At the time of its dis-

covery, MOA recognized this event as a possible free-ﬂoating plant candidate (Sumi et al.

2011) as the best ﬁt single lens light curve had an Einstein radius crossing time of light curve

tE= 0.73 ±0.10 days. (See Figure 2.) Nearly four weeks later, the OGLE Early Warning

System (EWS) system (?) detected this event being magniﬁed again with longer timescale

due to the lensing eﬀect of the host star. The OGLE EWS system announced this event as

OGLE-2013-BLG-1835 on 2013 Sep 25 (HJD′∼6560), as shown in the top panel of Figure

2. The initial short magniﬁcation by the planet at HJD′∼6535 was conﬁned by the OGLE

survey data. Actually, it should have triggered the OGLE discovery alert but due to unfor-

tunate deeply hidden bug in the EWS software this did not happen. The later magniﬁcation

by the host was observed by MOA, as well as OGLE.

Follow-up observations of the stellar part of the light curve in the V,Iand H-bands were

obtained by the µFUN collaboration using the CTIO 1.3 m SMARTS telescope. These data

were taken mainly to extract the source color. We use the average of these CTIO and OGLE

V−Icolor measurements. CTIO H-band measurements are used to drive H-band source

magnitude, which is very important for comparison to the AO observations (see Section 6).

3. Data Reduction

The MOA images were reduced with MOA’s implementation (Bond et al. 2001) of the

diﬀerence image analysis (DIA) method (Tomany & Crotts 1996; Alard & Lupton 1998;

Alard 2000). In the MOA photometry, we found that there were systematic errors that

correlate with the seeing and airmass, as well as the motion, due to diﬀerential refraction,

of a nearby, possibly unresolved star. There is also a potential systematic error due to the

3http://ogle.astrouw.edu.pl/ogle4/ews/ews.html

– 8 –

relative proper motion of a nearby star or stars, which we model as linear function in time.

We ran a detrending code to measure these eﬀects in the 2011, 2012 and 2014 data, and we

removed these trends with additive corrections to the full 2011-2014 data set. (The MOA

data from 2006-2010 indicate no signiﬁcant photometric variations, but they are not included

in the light curve analysis.) This detrending procedure improved the ﬁt χ2by ∆χ2= 0.073

per data point in the baseline, so it has reduced the systematic photometry errors signiﬁ-

cantly. This investigation of the systematics is necessary to have conﬁdence in the modeling

of the light curve with high order eﬀects in the following section.

The OGLE data were reduced with the OGLE DIA (Wo´zniak 2000) photometry pipeline

(Udalski, Szyma´nski and Szyma´nski 2015). In this event, the center of the magniﬁed source

star is slightly shifted from the center of the apparent star identiﬁed in the reference image,

due to blending with one or more unresolved stars. So the OGLE data have been re-reduced

with a centroid based diﬀerence images, just as the MOA pipeline does (Bond et al. 2001).

The number of data points used for the light curve modeling are 9675, 5514 and 64

for MOA-Red, OGLE-Iand OGLE-Vpassbands, respectively. The photometric errorbars

provided by the photometry codes give approximate estimates of the absolute photometric

uncertainty of each measurement, and we regard them as an accurate representation of the

relative uncertainty for each measurement. This is adequate for determining the best light

curve model, but in order to determine the uncertainties on the model parameters, it is

important to have more accurate error bars. We accomplish this with the method presented

in Yee et al. (2012). We rescale the errors using the formula, σ′

i=kpσ2

i+e2

min, where σi

and σ′

iare original and renormalized errorbars in magnitudes. The parameters kand emin

are selected so that the cumulative χ2distribution sorted by the magniﬁcation of the best

model is a straight line of slope 1 and χ2/dof∼1. This procedure yields k= 1.092313

and emin = 0.012662 for MOA-Red, k= 1.387059 and emin = 0.010938 for OGLE-Iand

k= 1.571492 and emin = 0.0 for OGLE-V. Note that the changes of the ﬁnal best ﬁt model

due to this error renormalization are negligible.

4. Light curve modeling

We search for the best ﬁt models of the standard (static), the parallax, the parallax

with the linear orbital motion of the planet, the keplerian orbital motion, with the keplerian

prior, the Galactic kinematic constraint and the Galactic density prior using Markov Chain

Monte Carlos (MCMC) (Verde et al. 2003). The best ﬁt models are shown in Table 1-6 and

their physical parameters are in Tables 7-12, respectively (see Section 5).

– 9 –

4.1. Standard (static) model

In a point-source point-lens (PSPL) microlensing model, there are three parameters, the

time of peak magniﬁcation t0, the Einstein radius crossing time tE, and the minimum impact

parameter u0. The standard binary lens model has four more parameters, the planet-host

star mass ratio q, the projected separation normalized by Einstein Radius s, the angle of

the source trajectory relative to the binary lens axis α, and the ratio of the angler source

radius to the angler Einstein radius ρ=θ∗/θE.ρcan only be measured for events that show

ﬁnite source eﬀects. The measurement of ρis important because it allows us to determine

the angular Einstein radius θE=θ∗/ρ since the angular source radius, θ∗, can be estimated

from its color and extinction-corrected apparent magnitude (Kervella et al. 2004).

We use linear limb-darkening models for the source star using the coeﬃcients, u=

0.5863, 0.7585 and 0.6327 for the I,Vand MOA-Red bands, respectively (Claret 2000).

The MOA-Red value is the mean of the Rand I-band values. These values were selected

from Claret (2000) for a K2 type source star with T= 5000 K, logg= 4.0 and log[M/H] = 0,

based on the extinction corrected, best ﬁt source V−Icolor and brightness (see Section 5).

The best ﬁt standard model parameters are shown in Table 1. The mass ratio of

q∼3×10−4and separation of s∼2.3 indicate that the companion is a relatively low mass

planet at wide separation.

4.2. Parallax model with a New Type of Degeneracy

There are higher order eﬀects that require additional parameters. The orbital motion

of the Earth can cause the apparent lens-source relative motion to deviate from a constant

velocity, and apparent lens-source separation and orientation. This eﬀect is known as the

microlensing parallax eﬀect (Gould 1992; Alcock et al. 1995; Smith, Mao & Wo´zniak 2002),

and it can be described by the microlensing parallax vector πE= (πE,N, πE,E). The direction

of πEis the direction of the lens-source relative motion projected on the sky (geocentric

proper motion at a ﬁxed time), and the amplitude of the microlensing parallax vector,

πE= AU/˜rE, is the inverse of the Einstein radius, projected to the observer plane. Because

the Galactic bulge is close to the ecliptic plane, there is an approximate degeneracy in

the parallax parameters, known as the “ecliptic degeneracy,” where models with similar

parameters but with (u0, α, πE,N) = −(u0, α, πE,N) produce nearly indistinguishable light

curves. This corresponds to a reﬂection of the lens plane with respect to the geometry of

Earth’s orbit, (Smith, Mao & Paczy´nski 2003; Skowron et al. 2013).

We found the four degenerate parallax models as shown in Table 1. The light curves

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of these four models are almost identical, which is shown in Figure 2. The caustics, critical

curves and source trajectory of these models are shown in Figure 3. The “P” scripts indicate

models with microlensing parallax. The ”+” and ”−” subscripts refer to two diﬀerent 2-

fold degeneracies in the parallax models. The ﬁrst “±” subscript refers to the sign of the u0

parameter, and refers to the “ecliptic degeneracy” mentioned above, but the second “±” sub-

script refers to a new parallax degeneracy, the wide degeneracy, that is particular to events

like this, with a wide separation planet detected through a crossing of the planetary caustic.

The light curve measurements indicate the angle, α(tpcc ), between the source trajectory and

lens axis at the time of the planetary caustic crossing, tpcc. Due to the reﬂection symmetry

of the lens system, the light curve constrains α(tpcc) up to a reﬂection symmetry, as shown in

Figure 3. If there were no microlensing parallax, we could use α(tpcc) to predict the closest

approach of the source to the center-of-mass, u0, and therefore the peak magniﬁcation of the

the stellar part of the microlensing light curve. But, when the microlensing parallax eﬀect is

included, the angle αcan vary in time, so that α(tpcc)6=α(t0). For a wide-separation plan-

etary event, like MOA-2013-BLG-605, the light curve basically constrains the microlensing

parallax through the three parameters, α(tpcc), u0, and t0, which is essentially the time of the

stellar peak magniﬁcation (cf. An & Gould 2001). As a result, the conﬁgurations shown in

the upper and lower panels of Figure 3 yield nearly identical light curves as shown in Figure

2, even though the source passes through in between the two masses in the upper panels

and below or above the masses in the bottom two panels. The lower panels imply a larger

curvature of the source trajectory, and therefore, a larger microlensing parallax signal. (Note

that the model parameter α0and s0given in Table 1-6 are the αand svalues at a ﬁxed time

tﬁx = 6573.045, following the convention of Geocentric microlensing parallax parameters.)

Fig. 4 shows the ∆χ2distribution of the parallax parameters from the best ﬁt MCMC

models. The best ﬁt values are compared to that of other models in Figure 5. In late

September, the Earth’s acceleration is in the East-West (E-W) direction, so for a typical

event, we would expect a better constraint on parallax in the E-W direction, i.e, a smaller

error for πE,E. However, in this case, the planetary signal plays a big role in the parallax

signal. The angle and timing of caustic entry for a given u0value – which is constrained by

the main peak corresponding to the host star – constrain the parallax parameters.

For all these models, qand sare similar to that of the standard model, so the companion

is a cold low mass planet. For all 4 degenerate solutions, the model parameters of greatest

interest are all very similar, except for the microlensing parallax. The ecliptic degeneracy

yields nearly identical physical parameters, except that the direction of the lens-source rela-

tive motion is diﬀerent. Potentially, this angle can be measured with follow-up observations

(Bennett et al. 2015; Batista et al. 2015). In contrast to the ecliptic degeneracy, the wide de-

generacy implies diﬀerent amplitudes, πE, of the microlensing parallax vector, which implies

– 11 –

diﬀerent lens system masses, as discussed in Section 5 below.

Thus, this wide degeneracy presents us with two diﬀerent classes of physical models,

P±∓ and P±±, where the P±± models have larger πEimplying smaller lens system masses

and distance (see Section 5 and Table 7).

These four parallax models are preferred over the standard πE= 0 model in both

the MOA-Red and OGLE-Ibands by (∆χ2

MOA,∆χ2

OGLE) = (−21.8,−11.5), (−21.6,−11.1),

(−21.9,−12.5) and (−23.6,−12.8) for theP+−, P−+, P++ and P−− models, respectively. In

total, the χ2diﬀerences range from ∆χ2=−33.3 to −37.1. Microlensing parallax signals

can sometimes be mimicked by the systematic errors in the light curve photometry, but a

consistent signal seen in both the MOA and OGLE data implies that the signal is likely to

be real.

4.3. Xallarap model

The xallarap eﬀect is a light curve distortion caused by the orbital motion of the source

star (Griest & Hu 1992; Han & Gould 1997), so it only occurs if the source star has a bi-

nary companion (Derue et al. 1999; Alcock et al. 2001). Xallarap can be represented by ﬁve

additional model parameters. The xallarap vector ξE= (ξE,N, ξE,E) is similar to the parallax

vector, πE, and represents the direction of the lens-source relative motion. The amplitude of

the xallarap vector, ξE=as/ˆrEis the semimajor axis of the source’s orbit, as, in units of the

Einstein radius projected on the source plane, ˆrE=θEDs. The other xallarap parameters

are the direction of the observer relative to the source orbital axis, with vector components

R.A.ξand decl.ξ, and the source binary orbital period, Tξ. For an elliptical orbit, two addi-

tional parameters are required, the orbital eccentricity, ǫand time of perihelion, tperi , which

we did not consider here as their inclusion did not improve the ﬁt of the model to the data.

We found xallarap models giving only marginally better χ2values compared to parallax

models for Tξ≥160 days and worse values of χ2for shorter values of Tξ. This is not surprising

as it is known that xallarap eﬀects can mimic parallax eﬀects (Smith, Mao & Paczy´nski

2003; Dong et al. 2009a). Including xallarap yields a slight improvement of ∆χ2∼ −5 for

160 ≤Tξ<200 days and ∆χ2∼ −9 at Tξ≥200 days. However, these models lead to

a xallarap amplitude of ξE≥0.26, which is larger than would be induced by a “normal”

main-sequence companion. Here ξEis expressed, making use of Kepler’s third law, by

ξE=as

ˆrE

=1AU

ˆrEMc

M⊙ M⊙

Mc+Ms

Tξ

1yr2

.(1)

These models require a source companion of mass Mc>6M⊙for Tξ≥160 days and

– 12 –

Mc>40M⊙for Tξ≥200 days. Such a heavy object would most likely be a stellar remnant

or a black hole – in either case, a rare object and thus an unlikely source companion. For

this reason we reject the inclusion of the xallarap in our models.

4.4. Orbital motion model

4.4.1. Linear Orbital Motion

The orbital motion of the planet around the host star causes a similar eﬀect as parallax.

To a ﬁrst-order approximation, the orbital motion of the planet is described by two parame-

ters, the rate of change, ω=dα/dt (radian yr−1), of the binary axis angle α, and the rate of

change ds/dt(yr−1), of the projected lens star and planet separation s(Dong et al. 2009a;

Batista et al. 2011), as follows,

s=s0+ds/dt(t−tﬁx), α =α0+ω(t−tﬁx),(2)

where, s0and α0are instantaneous value of sand αat the time tﬁx . We required the planet

to be bound. That is, the ratio of the projected kinetic energy and potential energy,

KE

PE ⊥

=(r⊥/AU)3

8π2(M/M⊙)"1

dt 2

+dα

dt 2#yr2,(3)

which is less than the ratio of kinetic to potential energy (KE/PE) in three dimensions,

was required to be less than unity in the MCMC calculations used to determine the model

parameter distributions. The four best linear orbital motion models (with scripts ”L”) that

correspond to each of four parallax models in Table 1, are shown in Table 2. One ﬁnds that

πEand its uncertainty signiﬁcantly increased, while the χ2only slightly improved. This is

because of the well known degeneracy between one component of the parallax vector, πE,⊥,

which is the perpendicular to the binary axis and close to πE,Nin this case, and the lens

orbital rotation on the sky, ω. As an example, ∆χ2distribution of πE,Nand ωfor the model

P+−L is shown in Figure 6.

Note that there are two additional degenerate models P±± L′which have smaller s0∼

1.97 and larger ds/dt ∼ −4.1 yr−1compared to the other models. Here, sof these models

are similar to others, s∼2.4, when the source crosses the planetary caustic. However these

models are disfavored with the full Keplerian orbit in the following analysis.

The physical parameters of the lens system of these models are shown in Table 8 (see

details in section §5). The host stars in these four models have a brown dwarf mass. Note

– 13 –

that (KE/PE)⊥of these models given in Table 8 are close to unity. The probability of having

such high value is quite low as it requires very large eccentricity of e∼1, seeing the orbital

plane face-on. If the parameters are not well constrained by the light curve, the density

distribution of the MCMC chain depends on the prior probability of the ﬁtting parameters

in MCMC. Although the linear approximation of the lens motion is good enough in most of

the cases, we inadvertently assumed the uniform prior on all microlensing ﬁtting parameters,

which is not correct.

4.4.2. Full Keplerian Orbit

To take the proper weighting on the orbital parameters, we adopt the full Keplerian

parameterization by Skowron et al. (2013). The advantage of the full Keplerian orbit is not

only being more accurate and allowing only bound orbital solutions, it also enables us to

introduce physically justiﬁed priors on the orbital parameters. In addition to the parameters

deﬁned above, we introduce the position and velocity along the line of sight, szin units of

rEand dsz/dt in yr−1. Then, the three dimensional position and velocity of the secondary

relative to its host can be described by (s0,0, sz) and s0(γk, γ⊥, γz) = (ds/dt, s0ω, dsz/dt).

We run MCMC ﬁtting using the microlensing parameters with these six instantaneous

Cartesian phase-space coordinates, in which we transform the “microlensing” parameters to

“Keplerian” parameters, i.e., eccentricity (e), time of periapsis (tperi), semi-major axis (a)

and three Euler angles, longitude of the ascending node (Ωnode), inclination (i), and argument

of periapsis (ωperi). By following Skowron et al. (2013), we assume ﬂat priors on values of

eccentricity, time of periapsis, log(a), and ωperi. Owing to the fact that orbital orientation is

random in space, we multiply the prior by |sin i|. We must multiply the Jacobian of the pa-

rameter transformation function, jkep =||∂(e, a, tperi ,Ωnode, i, ωperi)/∂(s0, α0, sz, γk, γ⊥, γz)||

(Eq. B6 in Skowron et al. 2013). So we adopt the Keplerian orbit prior of Pkep =jkep|sin i|a−1

and added the ∆χ2penalty of ∆χ2

kep =−2 ln(Pkep).

We ﬁrst show the results with full Keplerian orbit (with scripts “K”) without any priors

in Table 3 and Table 9. The results are almost same as the ones with the linear approximation

of the orbit. The large eccentricity of e∼1 seeing the orbital plane face-on (i∼0,180◦)

is as expected from the large (KE/PE)⊥in the linear orbit. The physical parameter of the

keplerian orbits, semi-major axis akep, period P,e, and iare not well constrained so that

they have very large asymmetric error bars in MCMC in Table 9. Here, when the best ﬁt

is outside of the 68% conﬁdence interval of MCMC chains, the error bar is designated as

“±0.0”. So the light curve shape itself does not constrain the parameters more than the

linear orbit model, except that it ruled out the models with smaller s0and larger ds/dt

– 14 –

corresponding to P±±L′. The best ﬁt parallax vectors are larger than that of the static

model as shown in Figure 5. Note that, the ratio of 3D kinetic to potential energy (KE/PE)

can be calculated in these full Keplerian orbit models as shown in Table 9. which are also

close to unity.

The results with the Keplerian orbit with the Keplerian prior (with scripts “Kp”) are

shown in Table 4, Table 10 and Figure 5. πEis reduced by a factor of 1/2∼2/3 because the

circular orbit is preferred by the Keplerian prior. So the lens masses increased, while the

hosts are still the high-mass and low-mass brown dwarfs. As for the models P±∓Kp, there

are other minima with a lower parallax value of πE∼0.2 with similar ﬁnal χ2whose host is

a low-mass M-dwarf. This is because Pkep prefers larger values of Dlby D6

l. But χ2values

from the light curves alone are larger than brown dwarf models. So there seems to be some

conﬂict between light curve and prior.

4.4.3. Stellar Kinematic constraint

In Table 10, the projected lens-source relative velocity ˜vt= (˜vt,l , ˜vt,b ) of these Kp

models in the Galactic coordinate diﬀers signiﬁcantly. Those of the M-dwarf models are

signiﬁcantly diﬀerent from the expected value from the Galactic kinematics as shown in

Fig. 7. Here we assume a source distance of Ds= 8kpc, the proper motion of the Galactic

center is µGC = 6.1 mas yr−1, the proper motion dispersion of stars in the bulge is σµ,GB = 3

mas yr−1, the velocity dispersions of the Galactic disk stars in the Galactic coordinates are

σDisk,l = 34 km s−1and σDisk,b = 18 km s−1. Then the expected average (˜vt,exp,l,˜vt,exp,b ) and

dispersion (˜σt,l,˜σt,b) of the lens projected velocity are calculated. The probability of having

observed ˜vtcan be given by

Pkin = exp "−(˜vt,l −˜vt,exp,l)2

2˜σ2

t,l #exp "−(˜vt,b −˜vt,exp,b)2

2˜σ2

t,b #.(4)

The ∆χ2penalty of ∆χ2

kin =−2 ln(Pkin) is about +16 and +15 for M-dwarf P+−Kpand

P−+Kpmodels respectively. On the other hand the penalty is +9, +4, +2 and +2 for brown

dwarf P+−Kp, P−+Kp, P++Kpand P−−Kpmodels, respectively. So the M-dwarf models are

less preferred.

Thus, we conducted MCMC runs by adding the penalty ∆χ2

kin. The results (with scripts

“Kpk”) are shown in Table 5, Table 11 and Figure 5. As expected, πEvalues for the M-dwarf

models increase to ∼0.3 to reduce the ∆χ2

kin and the total χ2value became similar or larger

than the brown dwarf models. In total, low-mass brown dwarf P±±O models are slightly

– 15 –

preferred over other models.

4.4.4. Galactic mass density prior

Finally, we applied the prior for the Galactic mass density model (Batista et al. 2011;

Skowron et al. 2013).

Pgal =ν(x, y, z)f(µ)[g(M)M]D4

lµ4

πE

,(5)

which is the microlensing event rate multiplied by the Jacobian of the transformation from

microlensing parameters to physical coordinates, jgal =||∂(Dl, M, µ)/∂(tE, θE,πE)||. Here

ν(x, y, z) is the local density of lenses, g(M) is the mass function. f(µ) is the two-dimensional

probability function for a given source-lens relative proper motion, µ=vt/Dl, which is set

to unity because it is already implemented in Pkin above. We adopt the Galactic model by

Han & Gould (1995) for ν(x, y, z) and adopt g(M)∝M−1by following Batista et al. (2011).

The results of MCMC runs by adding a penalty of ∆χ2

gal =−2 ln(Pgal) are shown (with

scripts “Kpkg”) in Table 6, Table 12 and Figure 5. The light curves, caustics, critical curves

and source trajectory of the models comprising both parallax and planetary orbital motion

with various diﬀerent priors are almost same as that of the parallax-only models shown in

Figure 2 and Figure 3. Overall, the lens masses slightly increased relative to that of Kpk

models because this Pgal prefers larger Dl, i.e., smaller πE.

In addition to above six models, there are two more minima for P±±Kpkg with a lower

parallax value of πE∼0.8 with similar ﬁnal χ2values. This is also because the prior Pgal

prefers larger Dland smaller πEvalues. These solutions happen to have similar πEvalues

with that of high-mass brown dwarf P±∓Kpkg models, hence the similar physical parameters.

As for the P±∓Kpkg models, there are two other minima which each have a much smaller

parallax value of πE∼0.035 and a smaller ﬁnal χ2=15107. This is because their large

values of Dl= 7 kpc are preferred by Pgal. These solutions have a very heavy host mass

of Mh∼1.7M⊙which would be quite rare. In addition, these solutions have a value of

χ2

lc ∼15224 which is larger than any other model with parallax, which conﬂict to the

preference by Pgal. Furthermore, these models have very bright H-band source magnitudes

Hs= 15.816 ±0.017 and Hs= 15.824 ±0.018 for P++ Kpkg and P−−Kpkg, respectively. These

are too bright compared to the Keck AO measurement of the target, H= 15.90 ±0.02, by

3σ(see Section 6). If we assume that the host is a main sequence star, then total brightness

of the source plus lens is expected to be brighter and ruled out by Keck measurements by

– 16 –

more than 4σ. For these reasons we do not consider these solutions to be real, and are not

listed amongst the other solutions in the Tables.

5. Lens properties

The lens physical parameters can be derived for this event because we could measure

both the parallax and ﬁnite source eﬀects in the light curve.

The OGLE-IV calibrated color magnitude diagram (CMD) in a 2′×2′region around

the event is shown in Figure 8. Figure 8 also shows the center of the Red Clump giants

(RCGs) (V−I, I )RC,obs = (2.047,15.73) ±(0.002,0.04) and the model independent OGLE

V−Isource color found by linear regression and the best ﬁt source Imagnitude of the

model P++Kp, (V−I, I)s= (1.985,18.13) ±(0.008,0.02). Isfor other models are almost

same, as shown in Table 1-6.

Assuming the source suﬀers the same dust extinction and reddening as the RCGs and

using the expected extinction-free RCG centroid (V−I, I)RC,0= (1.06,14.39) ±(0.06,0.04)

at this position (Bensby et al. 2013; Nataf et al. 2013), we estimated the extinction-free

color and magnitude of the source as (V−I , I)s,0= (1.00,16.80) ±(0.06,0.06). This color

measurement is consistent with the independent measurement of (V−I)s,0= 1.02 ±0.06 by

the CTIO 1m telescope. We use the average color of (V−I)s,0= 1.01 ±0.06 in the following

analyses. Here the errors in (V−I)s,0are dominated by the error in (V−I)RC,0. These

values are consistent with the source being a K2 subgiant (Bessell & Brett 1988).

Following Fukui et al. (2015), we estimated the source angular radius, θ∗, by using the

relation between the limb-darkened stellar angular diameter, θLD, (V−I) and Igiven by

Equation (4) of Fukui et al. (2015). This relation is derived from a subset of the interfer-

ometrically measured stellar radii in Boyajian et al. (2014), in which the dispersion of the

relation is ∼2% by using only stars with 3900K < Teﬀ <7000 K to improve the ﬁt for FGK

stars. This yield the source radius of θ∗=θLD/2 = 1.84 ±0.12 µas.

The spectrum of the source was taken by the VLT at a time when the source was

still magniﬁed, and which gives the source eﬀective temperature, Teﬀ = 4854 ±66 K, the

gravity, log g= 3.30 ±0.14, and the metallicity, [Fe/H]= −0.17 ±0.09 (Bensby et al. in

preparation). By using these values and the the relation by Casagrande et al. (2010), we

derive the extinction-free source colors, (V−I)s,0,spec = 1.036 ±0.047 and (V−H)s,0,spec =

2.244±0.078. Thus we get (I−H)s,0,spec = 1.208±0.091. The extinction-free H-band source

magnitude is given as Hs,0=Is,0−(I−H)s,0,spec = 15.59 ±0.11.

– 17 –

Then we got θ∗= 1.90±0.11 µas by using the relation between θLD ,Hs,0, (V−H)s,0and

[Fe/H], given by Equation (9) of Fukui et al. (2015), which is also driven in the same way as

Equation (4) of Fukui et al. (2015) but with the metallicity term. Note Hin the relation is

in Johnson magnitude system. Thus the observed H-band source magnitude which is in the

2MASS system, is converted to the Johnson system by following Fukui et al. (2015). This is

consistent with above value. The average of above values are,

θ∗= 1.87 ±0.12 µas,(6)

where we adopt the larger error from the estimate with (V−I, I ), conservatively. This value

is about the median of those from other models and diﬀerences from them are less than 2%,

thus we adopt this value for all models in the following analysis.

We also tested the traditional method as follows. Following Yoo et al. (2004), the dered-

dened source color and brightness (V-K,K)s,0= (2.2,15.6) are estimated using the observed

(V-I,I)s,0and the color-color relation of Kenyon & Hartmann (1995). By using this (V-K,

K)s,0relation and the empirical color/brightness-radius relation of Kervella et al. (2004), we

estimated the source angular radius, θ∗= 1.85 ±0.16 µas, where the error includes uncer-

tainties in the color conversion and the color/brightness-radius relations. This is consistent

with the above value.

The physical parameters of all models are listed in Table 7-12. The physical properties

of three models with realistic priors and constraint, i.e., Kp, Kpk , and Kpkg , are basically

same within the error bars. In the following analysis, we focus on the model Kpk.

The angular Einstein radii, and geocentric lens-source relative proper motion µgeo are

estimated, respectively, as follows,

θE=θ∗

ρ= 0.48 ±0.06 mas,(7)

µgeo =θE

= 8.4±1.2 mas yr−1.(8)

This µgeo is consistent with the typical value for disk lenses of µ∼5-10 mas yr−1.

The total mass and distance of the lens system can be given by M=θE/(κπE) and

Dl= AU/(πEθE+πs), where κ= 4G/(c2AU)=8.144 mas M−1

⊙,πs=AU/Dsand Ds∼8 kpc

is the distance to the source. Thus these quantities depend on the parallax parameter and

we have three groups of solutions in models, i.e, small πE∼0.3 (P±∓Kpk), medium πE∼0.8

(P±∓Kpk and P±± Kpk) and large πE∼2 (P±±Kpk). The distance to the system, Dl, the

– 18 –

mass of the host, Mh, and planet, Mp, and their projected separation, a⊥, of these solutions

are,

Dl= 3.6+0.6

−0.8kpc,1.8+0.4

−0.2kpc,or 0.85+0.13

−0.08 kpc,(9)

Mh=M

1 + q= 0.19+0.05

−0.06 M⊙,0.068+0.019

−0.011 M⊙,or 0.025+0.005

−0.004 M⊙,(10)

Mp=qM

1 + q= 21+6

−7M⊕,7.9+1.8

−1.2M⊕,or 3.2+0.5

−0.3M⊕,(11)

a⊥=sθEDl= 4.2+0.7

−0.9AU,2.1+0.4

−0.2AU,or 0.94+0.12

−0.09 AU,(12)

respectively. Here a⊥is the 2-dimensional (2D) projection of a 3D elliptical orbit having a

semi-major axis a. The expected 3D semi-major axis can be estimated by aexp =p3/2a⊥.

The best ﬁt 3D semi-major axis by the Keplerian orbit, akep, are in-between of these values

in the case of this event.

The semi-major axis akep normalized by the snow-line, asnow = 2.7(Mh/M⊙), are

akep

asnow

= 8.9+10.5

−1.4,12+7

−1,or 14+11

−1,(13)

The eﬀective temperature of the planet at the time of its formation based on the host mass

and host-planet separation are also given in the tables.

The small parallax models suggest that the planet has a mass similar to Neptune (17M⊕)

orbiting a very low mass M-dwarf in the Galactic disk. The planet is very cold as the

estimated separation is 8.9+10.5

−1.4times larger than the snow-line. This is comparable to

Neptune’s semi-major axis, i.e., 11 times larger than the Sun’s snow-line. This interpretation

of the planetary signal for MOA-2013-BLG-605Lb, therefore, suggests the planet is a Neptune

analog.

The medium parallax models correspond to a miniature Neptune (or large-mass “super-

Earth”) orbiting a high-mass brown dwarf host. The planet is even colder as the planetary

orbit radius is 12+7

−2times larger than the snow line, which is also similar to the Neptune.

The large parallax models correspond to three times the Earth-mass planet orbiting a

low-mass brown dwarf host. The planet is colder because the planetary orbit radius is 14+11

−1

times larger than the snow line.

– 19 –

These solutions of Kpk are compared to the planets found by other methods in Figure

1. As one can see in the right-hand panel of Figure 1, in either group of models, this planet

is the coldest low mass planet ever found and it is very similar to Neptune.

6. Keck AO Observations and Lens Mass constraint

We observed with the NIRC2 instrument mounted on KECK-II the microlensing target

MOA-2013-BLG-0605 on July 26, 2015. We used the Wide camera giving a pixel scale of

0.04 arcsec and a ﬁeld of view of 40 arcsec. We adopted a 5 position dithering pattern, and

did 30 exposures of 10 seconds each. We performed dark subtraction and ﬂatﬁelding in the

standard manner. We then stacked the frames using Swarp (Bertin et al. 2002), without

subtracting the background. The ﬁnal image is shown in Figure 9.

For absolute calibration, we used images from the VVV survey done with the VISTA

4m telescope at Paranal (Minniti et al. 2010). We extracted a 3 arcmin JHK band images

centred on the target. We computed a PSF model using PSFEX software (Bertin & Arnouts

1996), and measured ﬂuxes on the frames using SExtractor with this PSF model. We cross

identiﬁed the stars from the ﬁeld with 2MASS catalogues. We selected 300 stars that are

bright while not saturated on VVV, and derive the photometric zero points with an accuracy

of 0.004 mag. We then use the VVV catalogue to perform the astrometric calibration of the

KECK frame.

We then measure the ﬂuxes using SExtractor as described in (Batista et al. 2014). We

cross identiﬁed 39 stars in both the VVV and KECK image. We exclude the stars saturated

on the KECK, and derive the zero point of KECK photometry. In the non-AO PSF, there

are two stars, the source with H= 15.90 ±0.02 and a blend at ∼0.3 arcsec to the south

with H= 17.01 ±0.03. Here, these two stars are blended in the OGLE reference image

and the cataloged centroid is in-between of them. The actual source position during the

magniﬁcation on the OGLE diﬀerence image was precisely measured as shown by the red

cross in Figure 9. This clearly resolved the source and showed that the blend measured in

the ﬁtting process is not the lens.

By a linear regression of OGLE-I-band light curve and µFUN CTIO H-band light curve,

which are calibrated to the 2MASS scale, we got the source (I−H) color as,

(I−H)s= 2.256 ±0.016.(14)

By using this color and the best ﬁt Is,H-band source magnitude, Hsare calculated as shown

in Table 7-12. There is a trend that the smaller the parallax is, the brighter the source is.

The Hsof low-mass brown dwarf models are almost same as the Keck measurement of

– 20 –

H= 15.90 ±0.02 or only slightly brighter within 1σ. The Hsof high-mass brown dwarf and

most of M-dwarf models are within 2σ. The M-dwarf models, P−+Kp, P−+Kpk and P−+Kpkg

have Hs= 15.856 ±0.022, 15.856 ±0.024, and 15.845 ±0.026, which are 1.6, 1.7 and 2.1

σbrighter than the Keck measurement. Furthermore, these are 2.0, 2.0 and 2.4 σbrighter

when those include the lens (host) brightness (Kroupa & Tout 1997) of Hh= 20.96 ±0.24

(Mh= 0.28M⊙,Dl= 4.3kpc), 21.22 ±0.24 (Mh= 0.20M⊙,Dl= 3.5kpc) and 21.17 ±0.24

(Mh= 0.21M⊙,Dl= 3.7kpc), respectively. These results indicate that the lens is very

faint and not detected, which is consistent with the light curve solutions that the host is

a low-mass M-dwarf or a brown dwarf mentioned in Section 4. The low-mass brown dwarf

models are marginally preferred.

As mentioned in Section 4.4.4, there are two minima with a much smaller parallax value

of πE∼0.035 for the P±∓Kpkg models. In addition to the rarity of their heavy host mass

of ∼1.7M⊙which might be a stellar remnant, their source magnitudes Hs= 15.824 ±0.018

and Hs= 15.816 ±0.017 are 2.9σand 3.2σbrighter than the Keck measurement. So these

models are not likely real. If their host is a main sequence star, then total brightness of the

source plus lens are ruled out by Keck measurement by more than 4σ.

7. Future Mass Measurement

Let us consider the prospects for resolving the degeneracy and characterizing the host

and the planet. In the ﬁrst epoch of Keck AO observations, we could not detect any excess

light, which conﬁrmed the lens is faint. If the second epoch is taken by HST or AO ob-

servations, then we may directly detect the host (or possibly its companion). We can then

measure the lens mass and distance or place a stronger upper limit on the lens mass.

In Table 7-12, the geocentric proper motions are reported as |µgeo|=θE/tE= 8 ∼9

mas yr−1. The heliocentric proper motion is given by (Janczak et al. 2010),

µhel =µgeo +v⊕,⊥

πrel

AU,(15)

where v⊕,⊥= (v⊕,⊥,N , v⊕,⊥,E) = (−2.96,−8.24) km s−1is the velocity of the Earth projected

on the plane of the sky at the peak of the event. The estimated µhel = (µhel,N, µhel,E) of each

model is shown in Table 7-12, and they are about 8 ∼9 mas yr−1. Hence it is clear that

the lens will be separately resolved by HST or AO observations in 5-10 years’ time given

a diﬀraction limit of 50 mas. Or, if we do not see any luminous object, then the lens is a

sub-stellar object.

Not only the value but also the direction of expected relative proper motion would help

– 21 –

us to know if it was the lens or just an ambient star when we detect such star at 80mas from

the source 10 years later.

8. Discussion and Conclusion

There are three physical planetary solutions for the MOA-2013-BLG-605L system. One

comprises a Neptune-mass planet at a wide separation from a very low mass M-dwarf host

star, having a very similar temperature as Neptune when the planet was formed. The

second solution comprises a mini-Neptune around a high-mass brown dwarf which is even

colder than Neptune when it was formed. The third one is a super-Earth around a low-mass

brown dwarf.

These degenerate solutions may be resolved by future high resolution imaging of the

lens by the HST or ground-based telescopes using adaptive optics, after waiting a period of

time for the positions of the lens and the source to diverge. We may detect an M-dwarf lens

host star, but we do not expect to detect a brown dwarf host star by such direct imaging.

In either case, the host is one of the four least massive main sequence stars orbited

by a planet for which the planet’s mass was measured and for which the planet-host mass

ratio is q < 0.01. The other low host mass, low planet mass systems are MOA-2007-BLG-

192L (Mh= 0.084+0.015

−0.012M⊙,Mp= 3.2+5.2

−1.8M⊕r⊥= 0.66+0.51

−0.22 AU) (Bennett et al. 2008;

Kubas et al. 2012), MOA-2010-BLG-328L (Mh= 0.11 ±0.01M⊙, Mp= 9.2±2.2M⊕, r⊥=

0.92±0.16 AU) (Furusawa et al. 2013) and OGLE-2013-BLG-0723LB (Mh= 0.031±0.003M⊙, Mp=

0.69 ±0.06M⊕) (Udalski et al. 2015b).

These planets found around very low mass (∼0.1M⊙) hosts have relatively small masses

themselves, ranging from super-Earth mass to Neptune mass. In contrast, a roughly equal

number of giant planets and planets with Neptune-mass or less have been found across the

whole mass range of host stars. This may imply that the formation of gas giants is more

diﬃcult around very low mass stars compared to average K-M dwarf stars with masses of

∼0.5M⊙, which is the typical host star for microlensing planets. This is somewhat as

predicted by the core accretion model of planetary formation, but this work provides the

ﬁrst observational evidence supporting this prediction.

This could be the second exoplanet around a brown dwarf with a mass measurement hav-

ing a planetary mass-ratio q < 0.03 after OGLE-2013-BLG-0723LB (Udalski et al. 2015b).

There are three brown dwarf binaries where one of the components is in the planetary mass

regime (Choi et al. 2013; Han et al. 2013). However, their mass ratios are large q≥0.08,

suggesting that their formation may be considered more akin to binary formation than plan-

– 22 –

etary formation.

The separation of the planet is very wide, 8.9+10.5

−1.4, 12+7

−1or 14+11

−1times larger than the

snow line of ∼0.5(M/0.2M⊙) AU, ∼0.2(M/0.07M⊙) or ∼0.08(M/0.03M⊙) AU, respectively,

as seen in Figure 1. The eﬀective temperature of the planet when it was formed, based on

the host mass and the planet-host separation, is ∼26K, ∼13K or ∼7K, the coldest planet

found to date apart from those planets found by the direct imaging method, which can

presently only ﬁnd heavy gas-giant planets of more than a few Jupiter masses. The eﬀective

temperature of these heavy gas-giants are a few hundreds K or higher due to their internal

heat. In either interpretation, planet MOA-2013-BLG-605Lb is orbiting around one of the

least massive objects found to date at a very wide separation. The planet is the coldest

exoplanet discovered so far. This is the ﬁrst observed example of a Neptune-like exoplanet

in terms of mass and temperature, which are important factors in any planetary formation

theory.

The probability of detecting such wide separation low mass planets is very low, even

by microlensing. The probability of a source crossing the planetary caustic is proportional

to the size of the planetary caustic, wc∼4q1/2s−2∼0.01 (Han 2006), divided by half the

circle with radius of separation s, i.e., P∼4/πq1/2s−3∼1×10−3(s= 2.4). It is an order

of magnitude smaller than planets at s∼1, where ∼10 planets with Neptune-mass or less

have been found by microlensing. This may imply that such low-mass planets with masses

about that of Neptune at a≃10 asnow are as common as low-mass planets at a few times of

the snow line (Sumi et al. 2010; Gould et al. 2010; Cassan et al. 2012).

This conclusion may challenge the standard core accretion model and other formation

models (Ida & Lin 2004) which predict few Neptune-like planets at ∼10 asnow. More accurate

measurements of the abundance and distribution of Neptune-like ice-giant planets are very

important in the study of the formation of Neptune and in the study of planet formation

mechanisms in general. The microlensing exoplanet search by NASA’s WFIRST satellite

is expected to detect hundreds of neptune-like planets and will constrain further planetary

formation models.

TS acknowledges the ﬁnancial support from the JSPS, JSPS23103002,JSPS24253004

and JSPS26247023. The MOA project is supported by the grant JSPS25103508 and 23340064.

The OGLE project has received funding from the National Science Centre, Poland, grant

MAESTRO 2014/14/A/ST9/00121 to AU. DPB acknowledges support from NSF grants

AST-1009621 and AST-1211875, as well as NASA grants NNX12AF54G and NNX13AF64G.

Work by IAB and PY was supported by the Marsden Fund of the Royal Society of New

Zealand, contract no. MAU1104. NJR is a Royal Society of New Zealand Rutherford

– 23 –

Discovery Fellow. AS, ML and MD acknowledge support from the Royal Society of New

Zealand. AS is a University of Auckland Doctoral Scholar. AG was supported by NSF grant

AST 1103471 and NASA grant NNX12AB99G. J.P.B., S.B., J.B.M. gratefully acknowledges

support from ESO’s DGDF 2014. JPB & JB acknowledge the support of the Programme

National de Plan´etologie, CNRS, and from PERSU Sorbonne Universit´e.

REFERENCES

Alard C., 2000, A&AS, 144, 363

Alard C., Lupton R. H., 1998, ApJ, 503, 325

Alcock, C., et al. 1995, ApJ, 454, 125

Alcock, C., Allsman, R. A., Alves, D. R., et al. 2001, ApJ, 552, 259

An, J.H., Gould, A., 2001, ApJ, 563, L111

Batista, V., et al. 2011, ApJ, 529, 102

Batista, V., et al. 2014, ApJ, 780, 54

Batista, V., Beaulieu, J.-P., Bennett, D.P. et al. 2015, ApJ, submitted

Bessell, M. S., & Brett, J. M. 1988, PASP, 100, 1134

Bennett, D.P. & Rhie, S.H. 1996, ApJ, 472, 660

Bennett, D. P., Anderson, J., Bond, I. A., Udalski, & A., Gould, A. 2006, ApJ, 647, 171

Bennett, D. P., Bhattacharya, A., Anderson, J., et al. 2015, ApJ, submitted

Bennett, D. P., Bond, I. A., Udalski, A., et al. 2008, ApJ, 684, 663

Bennett, D. P., Rhie, S. H., Nikolaev, S., et al. 2010, ApJ, 713, 837

Bensby, T., Yee, J. C., Feltzing, S., et al. 2013, A&A, 549, A147

Berta, Z. K. ; Irwin, J., Charbonneau, D., 2013, ApJ, 775, 91

Bertin, E., & Arnouts, S. 1996, A&AS, 117, 393

– 24 –

Bertin, E., Mellier, Y., Radovich, M., Missonnier, G., Didelon, P., & Morin, B. 2002, in

ASP Conf. Ser. 281, Astronomical Data Analysis Software and Systems XI, ed. D. A.

Bohlender, D. Durand, & T. H. Handley (San Francisco, CA: ASP), 228

Bond I. A. et al., 2001, MNRAS, 327, 868

Borucki, W. J., Koch, D. G., Batalha, N., et a. 2012, ApJ, 745, 120

Boyajian, T. S., van Belle, G., & von Braun, K. 2014, AJ, 147, 47

Burke, Christopher J. et a. 2014, ApJS, 210, 19

Casagrande, L., Ram´ırez, I., Mel´endez, J., Bessell, M., & Asplund, M. , 2010, A&A, 512,

A54

Cassan, A., Kubas, D., Beaulieu, J.-P., et al. 2012, Nature, 481, 167

Clanton, C. & Gaudi, B.S., 2014, ApJ, 791, 91

Claret, A. 2000, A&A, 363, 1081

Choi, J.-Y., Han, C., Udalski, A., et al. 2013, ApJ, 768, 129

Derue, F., Afonso, C., et al. 1999, A&A, 351, 87

Dong, S., Gould, A., Udalski, A., et al. 2009a, ApJ, 695, 970

Dong, S., Bond, I. A., Gould, A., et al. 2009b, ApJ, 698, 1826

Dressing, C. D. & Charbonneau, D, 2013, ApJ, 767, 95

Fernandez, J. A.; Ip, W.-H. 1984, Icarus, 58, 109

Fukui, A. et al. 2015, ApJ, 809, 74

Furusawa, K. et al. 2013, ApJ, 779, 91

Gaudi, B. S., Bennett, D. P., Udalski, A., et al. 2008, Science, 319, 927

Gould, A. 1992, ApJ, 392, 442

Gould, A. 1994, ApJ, 421, L75

Gould, A. et al. 2009, ApJ, 698, L147

Gould, A., et al. 2010, ApJ, 720 1073

– 25 –

Gould, A. 2004, ApJ, 606, 319

Griest, K., & Hu, W. 1992, ApJ, 397, 362

Han, C. & Gould, A. 1995, ApJ, 449, 521

Han, C., 2006, ApJ, 638, 1080

Han, C., & Gould, A. 1997, ApJ, 480, 196

Han, C. & Gould, A. 2003, ApJ, 592, 172

Han, C., Jung, Y. K., Udalski, A., et al. 2013, ApJ, 778, 38

Helled, R. & Bodenheimer, P. 2014, ApJ, 789, 69

Ida, S., & Lin, D.N.C. 2004, ApJ, 616, 567

Janczak, J. et al. 2010, ApJ, 711, 731

Kains N. et al. 2013, A&A, 552, 70

Kennedy, G. M., Kenyon, S. J., & Bromley, B. C. 2006, ApJ, 650, L139

Kennedy, G. M., Kenyon, S. J., 2008, ApJ, 673, 502

Kenyon, S. J. & Hartmann, L., 1995, ApJS, 101, 117

Kervella, P., & Fouqu´e, P. 2008, A&A,491, 855

Kervella, P., Th´evenin, F., Di Folco, E., & S´egransan, D. 2004, A&A, 426, 297

Kroupa, P. & Tout, C. A., 1997, MNRAS, 287, 402

Kubas, D., Beaulieu, J. P., Bennett, D. P., et al. 2012, A&A, 540, 78

Laughlin, G., Bodenheimer, P., & Adams, F.C. 2004, ApJ, 612, L73

Malhotra, R., 1993, Nature, 365, 819

Mayor, M., & Queloz, D. 1995, Nature, 378, 355

Minniti, D., Lucas, P. W., Emerson, J. P., et al. 2010, New A, 15, 433

Montet, B. T., Crepp, J. R., Johnson, J. A., Howard, A. W., Marcy, G. W., 2014, ApJ, 781,

– 26 –

Morton, T. D. & Swift, J. J., 2014, ApJ, 791, 10

Muraki, Y., et al. 2011, ApJ, 741, 22

Nataf, D. M. et al. 2013, ApJ, 769, 88

Calchi Novati S., et al. 2015, accepted in ApJ. preprint (arXiv:1411.7378)

Park, B. -G. et al. 2004, ApJ, 609, 166

Refsdal, S. 1966, MNRAS, 134, 315

Poleski, R. et al., 2014, ApJ, 795, 42

Pollack, J. B., Hubickyj, O., Bodenheimer, P., et al. 1996, Icarus, 124, 62

Quintana, E.V., Barclay, T., Raymond, S.N. et al. 2014, Science, 344, 277

Skowron, J., Udalski, A., Gould, A., et al. 2011, ApJ, 738, 87

Smith, M. C., Mao, S., & Paczy´nski, B. 2003, MNRAS, 339, 925

Smith, M. C., Mao, S. & Wo´zniak, P. R., 2002, MNRAS, 332, 962

Sumi, T. et al., 2003, ApJ, 591, 204

Sumi, T. et al., 2010, ApJ, 710, 1641

Sumi, T. et al., 2011, Nature, 473, 349

Tsapras T. et al. 2014, ApJ, 782, 48

Tomany, A. B. & Crotts, A. P., 1996, AJ, 112, 2872

Thommes, E. W., Duncan, M. J. & Levison, H. F., 1999, Natur, 402, 635

Udalski,A., Szyma´nski, M.K. and Szyma´nski, G. 2015, Acta Astronomica, 65, 1

Udalski A. et al. 2015a, ApJ, 799, 237

Udalski A. et al. 2015b, ApJ, 812 47

Verde L., et al, 2003 ApJS, 148,195

Wittenmyer, R. A., et al. 2014, ApJ, 783, 103

Wo´zniak P. R., 2000, Acta Astronomica, 50, 421

– 27 –

Yee, J. C., Shvartzvald, Y., Gal-Yam, A., et al. 2012, ApJ, 755, 102

Yoo, J., et al, 2004a ApJ, 603, 139

This preprint was prepared with the AAS L

X macros v5.2.

– 28 –

Fig. 1.—: The distribution in planetary mass, Mp, versus the semi-major axis, a(left

panel) and anormalized by the snow-line (right panel) of discovered exoplanets by various

methods. Red circles indicate the microlensing planets. Microlensing planets for which mass

measurements have been made are indicated with ﬁlled circles. Microlensing planets where

the mass has been estimated by a Bayesian analysis are indicated with open circles. The

six model solutions for event MOA-2013-BLG-605Lb comprising parallax and the Keplerian

orbital motion with the Keplerian prior and the kinematic constraint (Kpk) are indicated by

purple ﬁlled circles. Black dots represent the radial velocity planets and blue ﬁlled squares

are transit planets. Cyan dots are transit planets found by Kepler. Magenta triangles

denote planets found via direct imaging. Green open squares denotes planets found via

timing measurements. Solar system planets are indicated by their initial. A green vertical

dashed line indicates the snow line. All models for MOA-2013-BLG-605Lb are very similar

to Neptune, when planet orbit radii are scaled to the snow line (right panel).

– 29 –

Fig. 2.—: Light curve of MOA-2013-BLG-605. Black, red and green points indicate MOA-

Red, OGLE-I and OGLE-V band data, respectively. Blue lines represent the best ﬁt parallax

model P++ which is almost identical to all models with parallax and orbital motion. Middle

and Bottom panels show the detail of the planetary signal and its residual from the best

model.

– 30 –

Fig. 3.—: Caustics (Red lines) of MOA-2013-BLG-605 of the best ﬁt parallax models, P+−,

P−+, P++ and P−− in top-left, top-right, bottom-left and bottom-right panel, respectively.

The ﬁgure of each model with a orbital motion and various priors are similar. Insets show

a close-up view around the planetary caustic. Blue circles indicate the best ﬁt source star

radius and position at HJD= 6534.6, just before crossing the planetary caustic. Blue lines

with arrows represent source star trajectories. The left and right black ﬁlled circles at y= 0

indicate the positions of primary and planet, respectively. The green lines show critical

curves.

– 31 –

Fig. 4.—: ∆χ2distribution of the parallax parameters from the best ﬁt parallax-only

models, without orbital motion, P++, P−+, P+−and P−−, from top to bottom. Black, red,

green, blue and orange dots indicate chains with ∆χ2<1, 4, 9, 16 and 25, respectively.

– 32 –

Fig. 5.—: The best ﬁt parallax parameters (πE,E,πE,N) of the parallax-only model (open

circles in the left panel) and the parallax with the orbital motion (ﬁlled circles) with the

Keplerian orbit (K), the Keplerian prior (Kp), kinematic constraint (Kpk) and the Galactic

prior (Kpkg) from the left to right panels, respectively. The black, red, green and blue color-

code correspond the models with the geometry of P+−, P−+, P++ and P−− , respectively.

– 33 –

Fig. 6.—: ∆χ2distribution of the parallax parameter πE,Nand orbital motion perimeter

ωfrom the best ﬁt MCMC models of the P+−L, the parallax with a linear orbital motion

model. Black, red, green, blue and orange dots indicate chains with ∆χ2<1, 4, 9, 16 and

25, respectively. Here ωis in rad day−1as actually used in the MCMC.

– 34 –

Fig. 7.—: Lens projected velocity ˜vt= (˜vl,˜vb) in the Galactic coordinate from the best ﬁt

with Keplerian orbit with the Keplerian prior. Top-left, top-right and bottom panels indicate

M-dwarf and brown dwarf P±∓Kpmodels and brown dwarf P±±Kpmodels, respectively.

Red circles are expected mean from the Galactic kinematics. Green error bars and circles

represent uncertainty due to the velocity dispersion of disk stars and bulge stars, respectively.

They are added in the quadrature in the total error shown in red error bars. Green bashed

line indicate the ecliptic North and East. The ˜vtof M-dwarf P±∓Kpmodels are signiﬁcantly

diﬀerent from the expected value from the Galactic kinematics.

– 35 –

Fig. 8.—: OGLE-IV calibrated Vand IColor magnitude diagram (CMD) within 2’×2’

around the event (green dots). A ﬁled square indicates the center of Red Clump Giants. The

source position shown by the ﬁlled circle, which is almost identical for all models, indicates

that the source star is a K2 sub-giant.

– 36 –

Fig. 9.—: H-band Keck AO image within 5”×5” around the event. The red cross indicates

the actual source position measured during the magniﬁcation on the OGLE diﬀerence image.

The brighter star at the cross is the source with H= 15.90 ±0.02 mag. The fainter star on

South is the blend with H= 17.01 ±0.02 mag. This shows that the blend measured in the

ﬁtting process is not the lens. The measured H-band ﬂux of the source shows that the lens

is very faint and not detected.

– 37 –

Table 1. Model Parameters. Standard and Parallax-only models.

Parameter Standard P+−P−+P++ P−−

t0(HJD′) 6573.056 6573.050 6573.050 6573.051 6573.052

0.008 0.009 0.009 0.009 0.010

tE(days) 20.47 19.93 20.04 20.10 20.15

0.13 0.32 0.29 0.32 0.28

u0(10−2) 7.563 7.932 -7.874 7.907 -7.890

0.099 0.186 0.175 0.185 0.164

q(10−4) 2.762 3.460 3.431 3.530 3.611

0.105 0.211 0.204 0.202 0.215

s2.304 2.391 2.384 2.393 2.395

0.010 0.019 0.018 0.020 0.017

α0(radian) 3.0996 3.1335 3.1534 2.9829 3.3035

0.0004 0.0077 0.0072 0.0084 0.0080

ρ(10−3) 3.37 3.88 3.85 3.91 3.95

0.10 0.15 0.14 0.15 0.14

πE,N0.000 -0.313 0.279 1.114 -1.144

0.000 0.076 0.071 0.086 0.082

πE,E0.000 -0.252 -0.261 -0.210 -0.249

0.000 0.107 0.100 0.104 0.104

πE0.000 0.401 0.382 1.134 1.170

0.000 0.088 0.082 0.084 0.088

Is(mag) 18.167 18.117 18.125 18.120 18.123

0.011 0.024 0.023 0.025 0.021

Ib(mag) 18.508 18.580 18.568 18.575 18.571

0.015 0.037 0.034 0.038 0.032

Hs(mag) 15.911 15.861 15.869 15.864 15.867

0.019 0.029 0.028 0.029 0.027

χ2

lc 15251.42 15217.49 15218.15 15216.43 15214.27

∆χ2

kep 0.00 0.00 0.00 0.00 0.00

∆χ2

kin 0.00 0.00 0.00 0.00 0.00

∆χ2

gal 0.00 0.00 0.00 0.00 0.00

χ215251.42 15217.49 15218.15 15216.43 15214.27

dof 15217 15215 15215 15215 15215

Note. — HJD′=HJD-2450000. The ﬁrst subscript of model P, “+” and

“−” indicate the models with u0>0 and u0<0, respectively. The second

subscript indicates the sign of impact parameter to the secondary lens, i.e,

“++” and “−− ” mean the source passes on the same side to the host and

planet. The 1σerror is given below each parameter. χ2

lc is the χ2from

the light curve alone. ∆χ2

kep, ∆χ2

kin and ∆χ2

gal are χ2penalty due to the

Keplerian, kinematic and the Galactic priors. Note that πEis not a ﬁt

parameter.

– 38 –

Table 2. Model Parameters. Linear orbit (L).

Parameter P+−L P−+L P++L P−−L P++ L′P−− L′

t0(HJD′) 6573.051 6573.051 6573.055 6573.055 6573.055 6573.055

0.006 0.009 0.010 0.010 0.010 0.010

tE(days) 19.95 19.90 21.33 21.24 21.25 21.22

0.32 0.22 0.31 0.33 0.35 0.34

u0(10−2) 7.869 -7.894 7.418 -7.452 7.455 -7.449

0.187 0.128 0.154 0.169 0.169 0.161

q(10−4) 3.614 3.422 4.183 4.913 2.805 2.846

0.201 0.260 0.355 0.474 0.491 0.220

s02.370 2.353 2.302 2.451 1.972 1.975

0.024 0.063 0.093 0.081 0.111 0.022

α0(radian) 3.1445 3.1444 2.9485 3.3412 2.9614 3.3222

0.0067 0.0076 0.0058 0.0144 0.0097 0.0126

ρ(10−3) 3.94 3.85 4.06 4.41 3.33 3.36

0.12 0.19 0.19 0.23 0.28 0.12

πE,N-1.528 1.420 3.731 -3.366 3.703 -3.326

0.194 0.226 0.213 0.340 0.283 0.318

πE,E-0.240 -0.191 0.070 -0.138 0.077 -0.143

0.106 0.074 0.092 0.114 0.112 0.111

πE1.546 1.433 3.732 3.369 3.704 3.330

0.194 0.225 0.213 0.337 0.284 0.317

ω(rad yr−1) -1.145 1.087 2.459 -1.974 2.550 -2.117

0.132 0.185 0.210 0.214 0.269 0.227

ds/dt -0.277 -0.403 -0.935 0.434 -4.104 -4.099

(yr−1) 0.376 0.588 0.921 0.829 1.049 0.244

sz0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000

dsz/dt 0.000 0.000 0.000 0.000 0.000 0.000

(yr−1) 0.000 0.000 0.000 0.000 0.000 0.000

Is(mag) 18.126 18.122 18.190 18.186 18.185 18.185

0.025 0.017 0.021 0.023 0.024 0.023

Ib(mag) 18.566 18.572 18.476 18.481 18.482 18.482

0.037 0.026 0.028 0.031 0.031 0.030

Hs(mag) 15.870 15.866 15.934 15.930 15.929 15.929

0.029 0.024 0.027 0.028 0.029 0.028

χ2

lc 15212.02 15214.89 15204.17 15204.36 15202.31 15202.52

∆χ2

kep 0.00 0.00 0.00 0.00 0.00 0.00

∆χ2

kin 0.00 0.00 0.00 0.00 0.00 0.00

∆χ2

gal 0.00 0.00 0.00 0.00 0.00 0.00

χ215212.02 15214.89 15204.17 15204.36 15202.31 15202.52

dof 15213 15213 15213 15213 15213 15213

Note. — Notation is ame as Table 1. The solutions P±± L′does not exist with the

full Keplerian orbit.

– 39 –

Table 3. Model Parameters. Full keplerian orbit (K).

Parameter P+−K P−+K P++K P−−K

t0(HJD′) 6573.051 6573.051 6573.054 6573.055

0.010 0.008 0.009 0.008

tE(days) 19.98 19.91 21.03 21.14

0.22 0.27 0.22 0.18

u0(10−2) 7.856 -7.886 7.553 -7.488

0.134 0.157 0.119 0.085

q(10−4) 3.789 3.663 4.216 5.197

0.196 0.211 0.335 0.317

s02.423 2.418 2.396 2.535

0.018 0.026 0.055 0.033

α0(radian) 3.1474 3.1410 2.9553 3.3528

0.0077 0.0075 0.0122 0.0080

ρ(10−3) 4.03 3.98 4.12 4.56

0.11 0.13 0.17 0.19

πE,N-1.509 1.413 3.389 -3.351

0.220 0.187 0.224 0.197

πE,E-0.252 -0.196 0.033 -0.114

0.112 0.081 0.084 0.103

πE1.530 1.427 3.389 3.353

0.219 0.181 0.225 0.194

ω(rad yr−1) -1.086 1.036 2.140 -1.744

0.179 0.130 0.155 0.156

ds/dt 0.304 0.293 0.241 1.431

(yr−1) 0.240 0.203 0.577 0.356

sz0.002 0.031 0.025 0.602

0.122 0.200 0.078 0.288

dsz/dt 0.108 0.005 -0.413 -0.695

(yr−1) 0.639 0.527 0.758 0.935

Is(mag) 18.127 18.123 18.171 18.180

0.017 0.020 0.015 0.012

Ib(mag) 18.563 18.571 18.501 18.489

0.026 0.030 0.020 0.016

Hs(mag) 15.871 15.867 15.915 15.924

0.023 0.026 0.022 0.020

χ2

lc 15212.20 15214.92 15204.70 15204.43

∆χ2

kep 0.00 0.00 0.00 0.00

∆χ2

kin 0.00 0.00 0.00 0.00

∆χ2

gal 0.00 0.00 0.00 0.00

χ215212.20 15214.92 15204.70 15204.43

dof 15211 15211 15211 15211

Note. — Notation is the same as for Table 1.

– 40 –

Table 4. Model Parameters. Full keplerian orbit with keplerian prior (Kp).

Parameter M-dwarf high-mass B-dwarf low-mass B-dwarf

P+−KpP−+KpP+−KpP−+KpP++KpP−− Kp

t0(HJD′) 6573.051 6573.052 6573.050 6573.049 6573.053 6573.053

0.009 0.009 0.009 0.009 0.008 0.009

tE(days) 19.93 19.93 20.01 20.08 20.38 20.63

0.27 0.19 0.31 0.26 0.19 0.16

u0(10−2) 7.942 -7.944 7.862 -7.816 7.816 -7.687

0.165 0.120 0.177 0.150 0.134 0.080

q(10−4) 3.420 3.330 3.436 3.401 3.838 4.010

0.165 0.118 0.132 0.160 0.185 0.155

s02.387 2.374 2.374 2.375 2.402 2.403

0.016 0.009 0.025 0.017 0.013 0.028

α0(radian) 3.1311 3.1540 3.1335 3.1540 2.9711 3.3154

0.0049 0.0048 0.0068 0.0037 0.0065 0.0042

ρ(10−3) 3.88 3.81 3.84 3.82 4.05 4.09

0.13 0.11 0.10 0.12 0.12 0.10

πE,N-0.005 0.030 -0.768 0.758 2.256 -2.244

0.050 0.040 0.177 0.118 0.104 0.117

πE,E-0.232 -0.216 -0.256 -0.225 -0.107 -0.221

0.085 0.075 0.090 0.084 0.090 0.070

πE0.232 0.218 0.809 0.790 2.259 2.255

0.086 0.072 0.147 0.104 0.103 0.115

ω(rad yr−1) 0.295 -0.256 -0.475 0.506 1.074 -1.031

0.030 0.012 0.121 0.137 0.047 0.090

ds/dt -0.001 -0.109 -0.122 -0.001 0.005 0.072

(yr−1) 0.011 0.144 0.222 0.049 0.046 0.295

sz0.365 1.458 1.031 0.027 0.098 0.256

0.613 0.782 1.006 0.110 0.076 0.484

dsz/dt 0.008 0.178 0.281 0.067 -0.100 -0.659

(yr−1) 0.066 0.319 0.516 0.629 0.405 0.875

Is(mag) 18.115 18.115 18.126 18.132 18.133 18.151

0.021 0.015 0.023 0.019 0.016 0.011

Ib(mag) 18.583 18.583 18.565 18.556 18.556 18.529

0.032 0.023 0.035 0.029 0.023 0.016

Hs(mag) 15.859 15.859 15.870 15.876 15.877 15.895

0.026 0.022 0.028 0.025 0.022 0.019

χ2

lc 15218.11 15218.29 15215.84 15217.62 15210.27 15207.90

∆χ2

kep -66.30 -66.44 -61.96 -62.08 -55.91 -55.95

∆χ2

kin 0.00 0.00 0.00 0.00 0.00 0.00

∆χ2

gal 0.00 0.00 0.00 0.00 0.00 0.00

χ215151.81 15151.85 15153.88 15155.54 15154.35 15151.95

dof 15211 15211 15211 15211 15211 15211

Note. — Notation is the same as for Table 1.

– 41 –

Table 5. Model Parameters. Kepler prior + kinematic constraint (Kpk)

Parameter M-dwarf high-mass B-dwarf low-mass B-dwarf

P+−Kpk P−+Kpk P+−Kpk P−+Kpk P++Kpk P−− Kpk

t0(HJD′) 6573.047 6573.054 6573.050 6573.051 6573.052 6573.054

0.009 0.009 0.009 0.008 0.009 0.010

tE(days) 20.20 19.83 19.96 19.93 20.41 20.52

0.16 0.23 0.10 0.24 0.32 0.28

u0(10−2) 7.797 -7.960 7.890 -7.905 7.804 -7.749

0.119 0.147 0.072 0.153 0.187 0.154

q(10−4) 3.526 3.124 3.557 3.400 3.812 4.054

0.176 0.120 0.131 0.158 0.189 0.279

s02.388 2.344 2.394 2.382 2.396 2.407

0.018 0.012 0.011 0.021 0.015 0.014

α0(radian) 3.1269 3.1568 3.1381 3.1516 2.9719 3.3182

0.0073 0.0058 0.0027 0.0059 0.0103 0.0102

ρ(10−3) 3.89 3.72 3.92 3.85 4.03 4.13

0.13 0.08 0.11 0.13 0.13 0.16

πE,N0.047 0.289 -0.891 0.793 2.242 -2.308

0.098 0.068 0.070 0.074 0.245 0.212

πE,E-0.315 -0.118 -0.259 -0.191 -0.108 -0.190

0.057 0.103 0.059 0.076 0.117 0.108

πE0.319 0.312 0.928 0.815 2.245 2.316

0.062 0.072 0.067 0.076 0.241 0.213

ω(rad yr−1) 0.302 0.040 -0.552 0.512 1.074 -1.065

0.036 0.030 0.065 0.069 0.162 0.141

ds/dt 0.047 -0.304 0.002 0.001 -0.001 0.049

(yr−1) 0.076 0.185 0.057 0.083 0.035 0.119

sz1.197 1.078 0.149 0.003 0.023 0.243

1.126 0.732 0.370 0.019 0.212 0.564

dsz/dt -0.095 0.658 -0.048 0.084 0.192 -0.493

(yr−1) 0.185 0.112 0.406 0.423 0.995 0.908

Is(mag) 18.135 18.112 18.122 18.120 18.135 18.142

0.014 0.018 0.007 0.019 0.025 0.020

Ib(mag) 18.552 18.588 18.571 18.574 18.552 18.542

0.020 0.028 0.011 0.029 0.036 0.029

Hs(mag) 15.879 15.856 15.866 15.864 15.879 15.886

0.021 0.024 0.018 0.025 0.030 0.026

χ2

lc 15218.49 15220.05 15215.31 15217.48 15210.26 15207.67

∆χ2

kep -65.62 -65.73 -61.27 -61.93 -55.94 -55.80

∆χ2

kin 13.53 5.89 7.81 4.03 1.91 1.88

∆χ2

gal 0.00 0.00 0.00 0.00 0.00 0.00

χ215166.40 15160.20 15161.85 15159.58 15156.24 15153.75

dof 15211 15211 15211 15211 15211 15211

Note. — Notation is the same as for Table 1.

– 42 –

Table 6. Model Parameters. Keplerian prior + kinematic+Galactic prior (Kpkg)

Parameter M-dwarf high-mass B-dwarf low-mass B-dwarf

P+−Kpkg P−+Kpkg P+−Kpkg P−+Kpkg P++Kpkg P−− Kpkg P++ Kpkg P−− Kpkg

t0(HJD′) 6573.048 6573.055 6573.051 6573.052 6573.052 6573.051 6573.052 6573.052

0.009 0.009 0.009 0.009 0.009 0.009 0.008 0.008

tE(days) 20.14 19.70 20.01 19.88 19.96 20.09 20.43 20.64

0.21 0.25 0.29 0.28 0.26 0.22 0.30 0.25

u0(10−2) 7.796 -8.042 7.860 -7.919 7.956 -7.897 7.778 -7.672

0.104 0.162 0.172 0.165 0.159 0.130 0.160 0.140

q(10−4) 3.514 3.137 3.436 3.364 3.379 3.307 3.754 3.969

0.070 0.082 0.146 0.155 0.203 0.196 0.240 0.274

s02.388 2.349 2.373 2.381 2.382 2.339 2.390 2.399

0.007 0.016 0.016 0.015 0.021 0.037 0.042 0.019

α0(radian) 3.1253 3.1563 3.1337 3.1528 2.9868 3.2979 2.9750 3.3119

0.0052 0.0063 0.0066 0.0068 0.0054 0.0057 0.0062 0.0103

ρ(10−3) 3.88 3.75 3.84 3.84 3.86 3.79 3.99 4.06

0.08 0.09 0.12 0.10 0.15 0.13 0.15 0.16

πE,N0.062 0.278 -0.768 0.755 0.785 -0.836 2.200 -2.201

0.069 0.063 0.142 0.112 0.042 0.114 0.110 0.168

πE,E-0.288 -0.087 -0.256 -0.166 -0.166 -0.241 -0.098 -0.211

0.069 0.076 0.090 0.098 0.097 0.093 0.088 0.092

πE0.295 0.291 0.810 0.773 0.802 0.870 2.202 2.211

0.072 0.059 0.138 0.110 0.049 0.115 0.108 0.169

ω(rad yr−1) 0.303 0.019 -0.474 0.485 -0.299 0.268 1.065 -1.025

0.034 0.011 0.101 0.050 0.071 0.072 0.076 0.067

ds/dt 0.033 -0.299 -0.120 -0.006 -0.082 -0.508 -0.006 0.087

(yr−1) 0.020 0.075 0.028 0.039 0.053 0.417 0.470 0.069

sz0.840 1.086 1.128 0.054 0.199 1.335 0.084 0.374

0.629 0.907 1.291 0.078 0.103 0.756 0.180 0.496

dsz/dt -0.093 0.648 0.255 0.256 0.972 0.891 0.108 -0.562

(yr−1) 0.188 0.238 0.324 0.371 0.203 0.548 0.923 0.674

Is(mag) 18.133 18.101 18.127 18.118 18.113 18.121 18.138 18.153

0.014 0.020 0.022 0.022 0.021 0.017 0.022 0.019

Ib(mag) 18.555 18.605 18.565 18.578 18.586 18.573 18.548 18.526

0.021 0.032 0.033 0.033 0.032 0.025 0.032 0.026

Hs(mag) 15.877 15.845 15.871 15.862 15.857 15.865 15.882 15.897

0.021 0.026 0.027 0.027 0.026 0.023 0.027 0.025

χ2

lc 15219.03 15220.81 15215.83 15217.93 15217.85 15215.74 15210.37 15208.07

∆χ2

kep -65.82 -65.90 -61.96 -62.20 -62.01 -61.58 -56.04 -56.06

∆χ2

kin 13.41 5.14 9.06 3.95 3.82 8.35 1.93 2.02

∆χ2

gal -38.35 -38.70 -30.50 -30.95 -30.60 -29.89 -21.33 -21.20

χ215128.27 15121.36 15132.43 15128.74 15129.06 15132.64 15134.94 15132.83

dof 15211 15211 15211 15211 15211 15211 15211 15211

Note. — Notation is the same as for Table 1.

– 43 –

Table 7. Lens physical parameters (Parallax only).

Parameter P+−P−+P++ P−−

θE(mas) 0.482±0.036 0.486±0.036 0.478±0.036 0.474±0.035

µgeo (mas yr−1) 8.61±0.67 8.63±0.67 8.47±0.66 8.38±0.64

µhel,N(mas yr−1) -6.83±0.52 6.19±0.49 7.98±0.65 -8.54±0.63

µhel,E(mas yr−1) -5.73±0.42 -6.22±0.46 -2.51±0.12 -2.75±0.14

Dl(kpc) 3.14+0.44

−0.48 3.22+0.43

−0.49 1.50+0.15

−0.10 1.47+0.14

−0.10

Mh(M⊙) 0.147+0.031

−0.037 0.156+0.030

−0.040 0.052+0.008

−0.005 0.050+0.007

−0.005

Mp(M⊕) 16.99+2.99

−3.59 17.83+2.93

−3.87 6.09+0.83

−0.45 5.98+0.75

−0.44

a⊥(AU) 3.62+0.51

−0.60 3.73+0.50

−0.61 1.71+0.15

−0.10 1.67+0.13

−0.11

a⊥/asnow 9.10+1.59

−0.83 8.85+1.61

−0.76 12.28+0.77

−0.78 12.44+0.83

−0.67

aexp (AU) 4.43+0.62

−0.73 4.57+0.61

−0.75 2.10+0.18

−0.12 2.04+0.16

−0.13

aexp/asnow 11.14+1.95

−1.01 10.84+1.97

−0.93 15.04+0.94

−0.95 15.24+1.01

−0.82

˜vt,l(km s−1) -208.5±35.3 71.7±34.9 63.1±4.9 -64.7±4.8

˜vt,b(km s−1) 46.7±31.7 228.9±33.8 62.2±3.0 -9.3±2.9

Teﬀ,exp (K) 20+5

−721+5

−710+1

−310+1

−3

Note. — aexp =p3/2a⊥is an expected 3D separation for the measured

projected separation, a⊥.asnow = 2.7(Mh/M⊙) is the snow-line. Teﬀ,exp is the

eﬀective temperature of the planet when it was formed based on the Mhand aexp .

– 44 –

Table 8. Lens physical parameters. Linear orbit (L)

Parameter P+−L P−+L P++L P− −L

θE(mas) 0.475±0.034 0.485±0.039 0.460±0.037 0.424±0.035

µgeo (mas yr−1) 8.48±0.63 8.69±0.72 7.69±0.64 7.11±0.61

µhel,N(mas yr−1) -8.83±0.63 8.17±0.72 6.61±0.64 -7.99±0.61

µhel,E(mas yr−1) -2.59±0.10 -2.37±0.10 -2.84±0.01 -2.77±0.03

Dl(kpc) 1.16+0.12

−0.17 1.22+0.40

−0.04 0.54+0.06

−0.05 0.64+0.08

−0.05

Mh(M⊙) 0.038+0.004

−0.006 0.042+0.015

−0.003 0.015+0.002

−0.000 0.015+0.005

−0.001

Mp(M⊕) 4.54+0.55

−0.74 4.74+1.79

−0.21 2.11+0.23

−0.23 2.53+0.36

−0.24

a⊥(AU) 1.31+0.11

−0.19 1.39+0.43

−0.05 0.58+0.05

−0.05 0.67+0.11

−0.04

a⊥/asnow 12.87+0.63

−0.46 12.40+1.17

−0.73 14.08+0.51

−1.73 16.05+0.24

−2.15

aexp (AU) 1.60+0.13

−0.23 1.70+0.53

−0.06 0.70+0.06

−0.06 0.82+0.13

−0.05

aexp/asnow 15.76+0.77

−0.56 15.19+1.43

−0.90 17.24+0.62

−2.12 19.66+0.30

−2.63

˜vt,l(km s−1) -47.1±6.1 53.5±8.2 24.4±1.1 -16.1±2.1

˜vt,b(km s−1) -7.2±3.6 49.8±4.8 23.3±0.6 1.7±1.2

Teﬀ,exp (K) 9+1

−39+2

−35+1

−15+1

−1

KE/PE⊥1.000 0.994 0.988 0.964

Note. — Notation is the same as for Table 7.

– 45 –

Table 9. Lens physical parameters. Keplerian orbit (K)

Parameter P+−K P−+K P++K P− −K

θE(mas) 0.464±0.032 0.469±0.034 0.454±0.035 0.410±0.031

µgeo (mas yr−1) 8.28±0.60 8.40±0.63 7.70±0.61 6.91±0.54

µhel,N(mas yr−1) -8.61±0.59 7.90±0.62 6.73±0.61 -7.76±0.54

µhel,E(mas yr−1) -2.59±0.10 -2.31±0.09 -2.60±0.01 -2.62±0.02

Dl(kpc) 1.20+0.39

−0.03 1.26+0.27

−0.08 0.60+0.06

−0.05 0.67+0.07

−0.05

Mh(M⊙) 0.037+0.014

−0.001 0.040+0.010

−0.004 0.016+0.003

−0.001 0.015+0.002

−0.001

Mp(M⊕) 4.70+1.69

−0.16 4.93+1.37

−0.23 2.31+0.28

−0.16 2.60+0.35

−0.17

a⊥(AU) 1.35+0.40

−0.03 1.43+0.28

−0.08 0.65+0.04

−0.04 0.69+0.05

−0.04

a⊥/asnow 13.39+0.51

−0.77 13.10+0.92

−0.53 14.72+0.53

−1.22 17.10+0.47

−1.29

aexp (AU) 1.65+0.49

−0.04 1.75+0.34

−0.09 0.80+0.05

−0.05 0.85+0.06

−0.05

aexp/asnow 16.40+0.63

−0.94 16.05+1.13

−0.65 18.03+0.64

−1.50 20.95+0.58

−1.58

akep (AU) 114+0

−112 117+0

−113 49+0

−44 44+0

−41

akep/asnow 1134+0

−1116 1069+0

−1035 1092+0

−1006 1080+0

−1022

P(yr) 6304+0

−6280 6260+0

−6217 2635+0

−2572 2362+0

−2331

e0.99+0.00

−0.52 0.99+0.00

−0.32 0.99+0.00

−0.15 0.98+0.00

−0.25

i177.7+0.0

−21.90.7+22.5

−0.04.7+7.8

−1.2161.6+8.5

−4.6

˜vt,l(km s−1) -47.8±7.0 53.6±6.7 26.5±1.4 -16.3±1.2

˜vt,b(km s−1) -6.9±4.2 50.1±3.9 24.7±0.8 1.4±0.7

Teﬀ,kep (K) 1.0+0.5

−0.61.1+0.5

−0.50.7+0.3

−0.20.7+0.3

−0.3

KE/PE⊥0.992 0.994 0.987 0.944

KE/PE 0.994 0.994 0.993 0.992

Note. — Notation is the same as for Table 7, except Teﬀ,kep is based on akep.

If the best ﬁt is outside of the 68% conﬁdence interval of MCMC chains, then

the error is designated as “±0.0”.

– 46 –

Table 10. Lens physical parameters. Keplerian orbit with Keplerian prior (Kp)

Parameter M-dwarf high-mass B-dwarf low-mass B-dwarf

P+−KpP−+KpP+−KpP−+KpP++KpP−− Kp

θE(mas) 0.482±0.035 0.491±0.034 0.487±0.034 0.489±0.035 0.462±0.033 0.458±0.031

µgeo (mas yr−1) 8.62±0.65 8.78±0.63 8.66±0.63 8.68±0.64 8.07±0.59 7.90±0.56

µhel,N(mas yr−1) -0.27±0.02 1.13±0.09 -8.47±0.60 8.08±0.62 7.41±0.59 -8.51±0.56

µhel,E(mas yr−1) -8.81±0.65 -8.88±0.63 -3.43±0.20 -3.14±0.18 -2.19±0.03 -2.57±0.05

Dl(kpc) 4.22+0.63

−0.97 4.31+0.80

−0.78 1.93+0.40

−0.23 1.95+0.45

−0.11 0.86+0.07

−0.06 0.86+0.04

−0.09

Mh(M⊙) 0.256+0.061

−0.094 0.276+0.095

−0.083 0.074+0.020

−0.012 0.076+0.018

−0.007 0.025+0.003

−0.002 0.025+0.002

−0.003

Mp(M⊕) 29.13+6.53

−9.98 30.68+10.12

−8.71 8.45+2.37

−1.18 8.62+2.61

−0.44 3.21+0.30

−0.27 3.33+0.19

−0.40

a⊥(AU) 4.86+0.75

−1.12 5.02+0.94

−0.92 2.23+0.42

−0.26 2.27+0.43

−0.13 0.95+0.04

−0.04 0.95+0.01

−0.09

a⊥/asnow 7.05+2.12

−0.86 6.73+1.72

−1.14 11.17+0.99

−0.79 11.07+0.80

−0.59 14.02+0.62

−0.53 14.13+0.64

−0.38

aexp (AU) 5.95+0.92

−1.38 6.15+1.15

−1.13 2.73+0.51

−0.31 2.78+0.53

−0.16 1.16+0.05

−0.05 1.16+0.01

−0.11

aexp/asnow 8.63+2.59

−1.05 8.24+2.10

−1.40 13.69+1.21

−0.97 13.55+0.98

−0.72 17.17+0.75

−0.66 17.31+0.78

−0.47

akep (AU) 4.92+1.72

−0.75 5.90+6.10

−1.30 2.43+3.49

−0.19 2.27+0.88

−0.22 0.95+0.09

−0.03 0.96+0.72

−0.01

akep/asnow 7.14+4.70

−0.77 7.90+9.22

−1.66 12.18+17.62

−1.22 11.08+3.86

−1.86 14.02+1.67

−0.50 14.21+12.66

−0.00

P(yr) 21.6+11.7

−1.827.2+51.5

−7.113.9+38.6

−1.612.4+7.1

−2.05.8+0.8

−0.25.9+8.3

−0.0

e0.00+0.24

−0.00 0.00+0.59

−0.00 0.00+0.62

−0.00 0.00+0.43

−0.00 0.00+0.09

−0.00 0.00+0.45

−0.00

i8.7+23.7

−0.8143.7+9.6

−13.2152.3+4.0

−24.43.2+49.0

−0.03.2+9.8

−0.0163.9+3.8

−18.9

˜vt,l(km s−1) -188.7±69.3 -144.1±67.2 -99.5±16.3 80.7±12.2 37.0±1.5 -28.6±1.7

˜vt,b(km s−1) 333.8±120.8 382.3±114.3 -8.2±10.6 91.8±7.8 33.1±0.9 -2.4±1.0

Teﬀ,kep (K) 33+12

−10 33+10

−20 14+2

−10 15+1

−47+1

−17+1

−3

KE/PE⊥0.495 0.394 0.432 0.499 0.498 0.464

KE/PE 0.500 0.500 0.500 0.500 0.500 0.500

Note. — Notation is the same as for Table 9.

– 47 –

Table 11. Lens physical parameters. Keplerian prior + kinematic constraint (Kpk)

Parameter M-dwarf high-mass B-dwarf low-mass B-dwarf

P+−Kpk P−+Kpk P+−Kpk P−+Kpk P++Kpk P−− Kpk

θE(mas) 0.481±0.035 0.503±0.034 0.477±0.033 0.486±0.035 0.464±0.033 0.452±0.034

µgeo (mas yr−1) 8.48±0.63 9.03±0.63 8.51±0.61 8.68±0.65 8.11±0.61 7.86±0.61

µhel,N(mas yr−1) 1.16±0.09 8.26±0.59 -8.45±0.59 8.19±0.63 7.44±0.61 -8.48±0.61

µhel,E(mas yr−1) -8.65±0.63 -3.69±0.24 -3.14±0.17 -2.72±0.15 -2.20±0.03 -2.47±0.05

Dl(kpc) 3.59+0.60

−0.39 3.55+0.20

−0.78 1.76+0.19

−0.15 1.92+0.28

−0.12 0.86+0.12

−0.06 0.85+0.08

−0.08

Mh(M⊙) 0.185+0.054

−0.034 0.198+0.007

−0.065 0.063+0.006

−0.006 0.073+0.014

−0.006 0.025+0.004

−0.003 0.024+0.004

−0.003

Mp(M⊕) 21.77+5.31

−3.34 20.58+0.56

−6.66 7.47+0.87

−0.77 8.28+1.35

−0.67 3.23+0.55

−0.29 3.24+0.38

−0.30

a⊥(AU) 4.13+0.74

−0.48 4.18+0.23

−0.96 2.01+0.15

−0.14 2.22+0.29

−0.12 0.95+0.11

−0.08 0.93+0.08

−0.08

a⊥/asnow 8.25+1.26

−1.09 7.83+1.79

−0.20 11.82+0.70

−0.44 11.25+0.76

−0.72 13.90+0.90

−0.44 14.34+0.73

−0.75

aexp (AU) 5.06+0.91

−0.59 5.12+0.29

−1.17 2.46+0.19

−0.17 2.72+0.35

−0.15 1.17+0.14

−0.09 1.14+0.09

−0.09

aexp/asnow 10.11+1.55

−1.34 9.59+2.20

−0.24 14.47+0.86

−0.54 13.78+0.93

−0.88 17.02+1.10

−0.54 17.57+0.89

−0.91

akep (AU) 4.62+4.71

−0.71 4.60+2.66

−1.18 2.01+1.10

−0.04 2.22+0.84

−0.17 0.95+0.32

−0.03 0.93+0.68

−0.01

akep/asnow 9.23+10.23

−1.47 8.63+7.94

−1.08 11.83+7.08

−0.33 11.26+3.37

−0.93 13.90+5.58

−0.78 14.42+10.92

−0.00

P(yr) 23.0+42.8

−4.522.2+24.9

−6.111.4+10.7

−0.312.2+6.7

−1.15.8+3.1

−0.25.8+7.4

−0.0

e0.00+0.48

−0.00 0.00+0.51

−0.00 0.00+0.38

−0.00 0.00+0.27

−0.00 0.00+0.30

−0.00 0.00+0.41

−0.00

i27.8+20.4

−13.183.4+4.1

−4.4175.9+0.0

−27.03.9+34.0

−0.04.3+28.4

−0.0167.7+0.0

−23.8

˜vt,l(km s−1) -92.4±26.5 177.3±53.3 -85.5±5.7 82.8±8.6 37.2±3.6 -27.7±2.9

˜vt,b(km s−1) 263.4±44.8 233.3±36.5 -9.2±3.6 86.1±5.3 33.2±2.0 -2.6±1.7

Teﬀ,kep (K) 25+5

−15 27+9

−813+1

−414+1

−47+1

−27+1

−3

KE/PE⊥0.439 0.086 0.498 0.498 0.497 0.480

KE/PE 0.500 0.500 0.500 0.500 0.500 0.500

Note. — Notation is the same as for Table 9.

– 48 –

Table 12. Lens physical parameters. Keplerian prior + kinematic + Galactic density prior (Kpkg)

Parameter M-dwarf high-mass B-dwarf low-mass B-dwarf

P+−Kpkg P−+Kpkg P+−Kpkg P−+Kpkg P++Kpkg P−− Kpkg P++ Kpkg P−−Kpkg

θE(mas) 0.482±0.033 0.498±0.034 0.487±0.035 0.487±0.034 0.485±0.036 0.493±0.036 0.469±0.035 0.461±0.035

µgeo (mas yr−1) 8.53±0.60 9.01±0.64 8.66±0.65 8.72±0.63 8.65±0.67 8.74±0.66 8.17±0.63 7.96±0.62

µhel,N(mas yr−1) 1.71±0.13 8.51±0.61 -8.47±0.61 8.28±0.62 8.22±0.66 -8.67±0.63 7.52±0.63 -8.56±0.62

µhel,E(mas yr−1) -8.59±0.59 -2.96±0.19 -3.42±0.20 -2.53±0.14 -2.47±0.14 -3.17±0.18 -2.16±0.03 -2.53±0.06

Dl(kpc) 3.74+0.68

−0.55 3.70+0.49

−0.55 1.93+0.38

−0.19 2.00+0.20

−0.26 1.95+0.16

−0.16 1.81+0.38

−0.08 0.86+0.10

−0.04 0.87+0.07

−0.08

Mh(M⊙) 0.201+0.053

−0.045 0.210+0.033

−0.050 0.074+0.022

−0.010 0.077+0.009

−0.016 0.074+0.007

−0.009 0.070+0.023

−0.005 0.026+0.005

−0.000 0.026+0.003

−0.004

Mp(M⊕) 23.54+6.29

−5.07 21.96+3.84

−4.88 8.45+2.26

−1.04 8.66+1.07

−1.46 8.35+0.75

−0.71 7.67+2.40

−0.28 3.27+0.43

−0.20 3.39+0.29

−0.35

a⊥(AU) 4.31+0.72

−0.65 4.33+0.54

−0.66 2.22+0.44

−0.22 2.31+0.19

−0.34 2.25+0.14

−0.17 2.08+0.47

−0.08 0.97+0.08

−0.02 0.97+0.04

−0.08

a⊥/asnow 7.95+1.41

−0.99 7.64+1.47

−0.62 11.17+0.82

−0.96 11.08+1.25

−0.40 11.22+0.93

−0.54 11.09+0.71

−1.00 13.73+0.25

−1.26 13.99+1.00

−0.51

aexp (AU) 5.28+0.88

−0.79 5.31+0.67

−0.81 2.72+0.54

−0.28 2.83+0.23

−0.41 2.75+0.17

−0.21 2.55+0.58

−0.10 1.19+0.10

−0.02 1.18+0.05

−0.10

aexp/asnow 9.73+1.72

−1.21 9.36+1.80

−0.76 13.68+1.01

−1.18 13.57+1.53

−0.48 13.74+1.14

−0.66 13.58+0.87

−1.22 16.81+0.31

−1.54 17.13+1.23

−0.62

akep (AU) 4.57+3.03

−0.76 4.78+3.10

−1.75 2.46+2.15

−0.13 2.31+0.38

−0.27 2.25+0.70

−0.27 2.40+2.86

−0.45 0.97+0.64

−0.00 0.98+0.29

−0.06

akep/asnow 8.42+5.38

−1.28 8.43+6.10

−2.52 12.37+9.35

−1.19 11.09+2.92

−0.46 11.26+3.72

−0.92 12.76+12.25

−3.20 13.74+7.07

−0.42 14.16+4.96

−0.21

P(yr) 21.8+22.4

−3.622.8+25.3

−10.414.2+20.0

−1.212.7+2.9

−1.212.4+6.1

−1.714.1+28.5

−4.05.9+6.1

−0.06.0+2.9

−0.3

e0.00+0.37

−0.00 0.00+0.83

−0.00 0.00+0.40

−0.00 0.00+0.16

−0.00 0.00+0.31

−0.00 0.00+0.69

−0.00 0.00+0.48

−0.00 0.00+0.19

−0.00

i20.8+15.0

−6.386.7+3.0

−1.2151.2+4.8

−25.112.6+11.4

−7.1126.0+8.0

−15.263.1+4.2

−29.43.1+28.3

−0.0164.3+3.5

−17.2

˜vt,l(km s−1) -83.2±37.0 210.0±51.7 -99.4±15.3 88.7±13.8 86.0±5.8 -91.0±11.1 37.8±1.7 -29.2±2.5

˜vt,b(km s−1) 290.9±60.9 234.5±33.2 -8.3±10.0 88.6±8.4 84.9±3.5 -10.7±7.0 33.5±1.0 -2.8±1.5

Teﬀ,kep (K) 27+6

−11 28+8

−10 14+2

−715+3

−214+2

−313+1

−98+0

−37+1

−1

KE/PE⊥0.464 0.081 0.430 0.477 0.175 0.196 0.499 0.470

KE/PE 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500

Note. — Notation is the same as for Table 9.

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Some dynamical aspects of the accretion of Uranus and Neptune: The exchange of orbital angular momentum with planetesimals

Article

Apr 1984

The final stage of the accretion of Uranus and Neptune is numerically investigated. The four Jovian planets are considered with Jupiter and Saturn assumed to have reached their present sizes, whereas Uranus and Neptune are taken with initial masses 0.2 of their present ones. Allowance is made for the orbital variation of the Jovian planets due to the exchange of angular momentum with interacting bodies (“planetesimals”). Two possible effects that may have contributed to the accretion of Uranus and Neptune are incorporated in our model: (1) an enlarged cross section for accretion of incoming planetesimals due to the presence of extended gaseous envelopes and/or circumplanetary swarms of bodies; and (2) intermediate protoplanets in mid-range orbits between the Jovian planets. Significant radial displacements are found for Uranus and Neptune during their accretion and scattering of planetesimals. The orbital angular momentum budgets of Neptune, Uranus, and Saturn turn out to be positive; i.e., they on average gain orbital angular momentum in their interactions with planetesimals and hence they are displaced outwardly. Instead, Jupiter as the main ejector of bodies loses orbital angular momentum so it moves sunward. The gravitational stirring of planetesimals caused by the introduction of intermediate protoplanets has the effect that additional solid matter is injected into the accretion zones of Uranus and Neptune. For moderate enlargements of the radius of the accretion cross section (2–4 times), the accretion time scale of Uranus and Neptune are found to be a few 108 years and the initial amount of solid material required to form them of a few times their present masses. Given the crucial role played by the size of the accretion cross section, questions as to when Uranus and Neptune acquired their gaseous envelopes, when the envelopes collapsed onto the solid cores, and how massive they were are essential in defining the efficiency and time scale of accretion of the two outer Jovian planets.

A Jupiter-Mass Companion to a Solar-Type Star

Article

Nov 1995

The presence of a Jupiter-mass companion to the star 51 Pegasi is inferred from observations of periodic variations in the star's radial velocity. The companion lies only about eight million kilometres from the star, which would be well inside the orbit of Mercury in our Solar System. This object might be a gas-giant planet that has migrated to this location through orbital evolution, or from the radiative stripping of a brown dwarf.

Jan 2013
775-91

T Bensby
J C Yee
S Feltzing

Bensby, T., Yee, J. C., Feltzing, S., et al. 2013, A&A, 549, A147 Berta, Z. K. ; Irwin, J., Charbonneau, D., 2013, ApJ, 775, 91

Jan 2012
NATURE
167

A Cassan
D Kubas
J.-P Beaulieu

Cassan, A., Kubas, D., Beaulieu, J.-P., et al. 2012, Nature, 481, 167

Jan 2015
74

A Fukui

Fukui, A. et al. 2015, ApJ, 809, 74

Jan 2013
91

K Furusawa

Furusawa, K. et al. 2013, ApJ, 779, 91

Jan 2008
927

B S Gaudi
D P Bennett
A Udalski

Gaudi, B. S., Bennett, D. P., Udalski, A., et al. 2008, Science, 319, 927

Jan 1992
442

A Gould

Gould, A. 1992, ApJ, 392, 442

Jan 1993
819

G Laughlin
P Bodenheimer
F C Adams

Laughlin, G., Bodenheimer, P., & Adams, F.C. 2004, ApJ, 612, L73 Malhotra, R., 1993, Nature, 365, 819

Jan 2003
195

L Verde

Verde L., et al, 2003 ApJS, 148,195

The First Cold Neptune Analog Exoplanet: MOA-2013-BLG-605Lb

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