Discovery and Mass Measurements of a Cold, 10-Earth Mass Planet and Its Host Star

Full text

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Discovery and Mass Measurements of a Cold, 10-Earth Mass Planet and Its
Host Star
Y. Muraki1,67, C. Han2,68,∗, D.P. Bennett3,67,70,∗, D. Suzuki4,67, L.A.G. Monard5,68,
R. Street6,69, U.G. Jorgensen7,71, P. Kundurthy8, J. Skowron9,68, A.C. Becker8,
M.D. Albrow10,70, P. Fouqu´ e11,70, D. Heyrovsk´ y12, R.K. Barry13, J.-P. Beaulieu14,70,
D.D. Wellnitz15, I.A. Bond16,67, T. Sumi4,17,67, S. Dong18,68, B.S. Gaudi9,68,
D.M. Bramich19,69, M. Dominik20,21,69,71,
and
F. Abe4, C.S. Botzler22, M. Freeman22, A. Fukui4, K. Furusawa4, F. Hayashi4,
J.B. Hearnshaw10, S. Hosaka4, Y. Itow4, K. Kamiya4, A.V. Korpela23, P.M. Kilmartin24,
W. Lin16, C.H. Ling16, S. Makita4, K. Masuda4, Y. Matsubara4, N. Miyake4, K. Nishimoto4,
K. Ohnishi25, Y.C. Perrott22, N.J. Rattenbury26, To. Saito27, L. Skuljan16,
D.J. Sullivan23, W.L. Sweatman16, P.J. Tristram24, K. Wada1, P.C.M. Yock22,
(The MOA Collaboration)
G.W. Christie28, D.L. DePoy29, E. Gorbikov30, A. Gould9, S. Kaspi30, C.-U. Lee31,
F. Mallia32, D. Maoz30, J. McCormick33, D. Moorhouse34, T. Natusch28, B.-G. Park31,
R.W. Pogge9, D. Polishook35, A. Shporer30, G. Thornley34, J.C. Yee9,
(The µFUN Collaboration)
A. Allan36, P. Browne20,71, K. Horne20, N. Kains19,
C. Snodgrass37,38,71, I. Steele39, Y. Tsapras6,40,
(The RoboNet Collaboration)
V. Batista14, C.S. Bennett41, S. Brillant37, J.A.R. Caldwell42, A. Cassan14, A. Cole43,
R. Corrales14, Ch. Coutures14, S. Dieters43, D. Dominis Prester44, J. Donatowicz45,
J. Greenhill43, D. Kubas14,37, J.-B. Marquette14, R. Martin46, J Menzies47,
K.C. Sahu48, I. Waldman49, A. Williams46M. Zub50,
(The PLANET Collaboration)
H. Bourhrous51, Y. Matsuoka52, T. Nagayama52, N. Oi53, Z. Randriamanakoto47,
(IRSF Observers)
V. Bozza54,55, M.J. Burgdorf56,57, S. Calchi Novati54, S. Dreizler58, F. Finet59, M. Glitrup6,
K. Harpsøe7, T.C. Hinse7,31, M. Hundertmark58, C. Liebig20, G. Maier50,
L. Mancini54,61, M. Mathiasen7, S. Rahvar62, D. Ricci59, G. Scarpetta54,55, J. Skottfelt7,
J. Surdej59, J. Southworth63, J. Wambsganss50, F. Zimmer50,
(The MiNDSTEp Consortium)
A. Udalski64, R. Poleski64, ? L. Wyrzykowski64,65, K. Ulaczyk64, M.K. Szyma´ nski64,
M. Kubiak64, G. Pietrzy´ nski64,66, I. Soszy´ nski64
(The OGLE Collaboration)
arXiv:1106.2160v1 [astro-ph.EP] 10 Jun 2011

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1Department of Physics, Konan University, Nishiokamoto 8-9-1, Kobe 658-8501, Japan
∗To whom correspondence should be addressed; E-mail: bennett@nd.edu, cheongho@chungbuk.ac.kr
2Department of Physics, Chungbuk National University, 410 Seongbong-Rho, Hungduk-Gu, Chongju 371-763,
Korea
3Department of Physics, 225 Nieuwland Science Hall, University of Notre Dame, Notre Dame, IN 46556, USA
4Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya, 464-8601, Japan
5Bronberg Observatory, Centre for Backyard Astrophysics, Pretoria, South Africa
6Las Cumbres Observatory Global Telescope Network, 6740 Cortona Dr., Suite 102, Goleta, CA 93117, USA
7Niels Bohr Institute and Centre for Stars and Planet Formation, Juliane Mariesvej 30, 2100 Copenhagen, Denmark
8Astronomy Department, University of Washington, Seattle, WA 98195
9Department of Astronomy, Ohio State University, 140 West 18th Avenue, Columbus, OH 43210, USA
10University of Canterbury, Department of Physics and Astronomy, Private Bag 4800, Christchurch 8020, New
Zealand
11IRAP, CNRS, Universit´ e de Toulouse, 14 avenue Edouard Belin, 31400 Toulouse, France
12Institute of Theoretical Physics, Charles University, V Holeˇ soviˇ ck´ ach 2, 18000 Prague, Czech Republic
13Goddard Space Flight Center, Greenbelt, MD 20771, USA
14Institut d’Astrophysique de Paris, F-75014, Paris, France
15University of Maryland, College Park, MD 20742, USA
16Institute for Information and Mathematical Sciences, Massey University, Private Bag 102-904, Auckland 1330,
New Zealand
17Department of Earth and Space Science, Osaka University, 1-1 Machikaneyama-cho, Toyonaka, Osaka 560-0043,
Japan
18Sagan Fellow; Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA
19European Southern Observatory, Karl-Schwarzschild-Straße 2, 85748 Garching bei M¨ unchen, Germany
20SUPA, University of St Andrews, School of Physics & Astronomy,North Haugh, St Andrews, KY16 9SS, UK
21Royal Society University Research Fellow
22Department of Physics, University of Auckland, Private Bag 92-019, Auckland 1001, New Zealand
23School of Chemical and Physical Sciences, Victoria University, Wellington, New Zealand
24Mt. John University Observatory, P.O. Box 56, Lake Tekapo 8770, New Zealand
25Nagano National College of Technology, Nagano 381-8550, Japan
26Jodrell Bank Observatory, The University of Manchester, Macclesfield, Cheshire SK11 9DL, UK
27Tokyo Metropolitan College of Aeronautics, Tokyo 116-8523, Japan
28Auckland Observatory, P.O. Box 24-180, Auckland, New Zealand
29Department of Physics, Texas A&M University, 4242 TAMU, College Station, TX 77843-4242, USA

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30School of Physics and Astronomy, Raymond and Beverley Sackler Faculty of Exact Sciences, Tel-Aviv University,
Tel Aviv 69978, Israel
31Korea Astronomy and Space Science Institute, 776 Daedukdae-ro, Yuseong-gu 305-348 Daejeon, Korea
32Campo Catino Austral Observatory, San Pedro de Atacama, Chile
33Farm Cove Observatory, 2/24 Rapallo Place, Pakuranga, Auckland 1706, New Zealand
34Kumeu Observatory, Kumeu, New Zealand
35Benoziyo Center for Astrophysics, Weizmann Institute of Science
36School of Physics, University of Exeter, Stocker Road, Exeter, EX4 4QL, UK
37European Southern Observatory, Casilla 19001, Vitacura 19, Santiago, Chile
38Max-Planck-Institut fr Sonnensystemforschung, Katlenburg-Lindau, Germany
39Astrophysics Research Institute, Liverpool John Moores University, Twelve Quays House, Egerton Wharf, Birken-
head CH41 1LD, UK
40Astronomy Unit, School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS
41Department of Physics, Massachusetts Institute of Technology, 77 Mass. Ave., Cambridge, MA 02139
42McDonald Observatory, 16120 St Hwy Spur 78 #2, Fort Davis, TX 79734
43University of Tasmania, School of Mathematics and Physics, Private Bag 37, Hobart, TAS 7001, Australia
44Department of Physics, University of Rijeka, Omladinska 14, 51000 Rijeka, Croatia
45Technische Universitaet Wien, Wieder Hauptst. 8-10, A-1040 Wienna, Austria
46Perth Observatory, Walnut Road, Bickley, Perth 6076, WA, Australia
47South African Astronomical Observatory, P.O. Box 9 Observatory 7925, South Africa
48Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
49University College London, Dept. of Physics and Astronomy, Gower Street, London WC1E 6BT, UK
50Astronomisches Rechen-Institut, Zentrum f¨ ur Astronomie der Universit¨ at Heidelberg, M¨ onchhofstrasse 12-14,
69120 Heidelberg, Germany
51Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, Cape Town,
South Africa
52Graduate School of Science, Nagoya University, Furo- cho, Chikusa-ku, Nagoya 464-8602, Japan
53Department of Astronomical Science, The Graduate University for Advanced Studies (Sokendai), Mitaka, Tokyo
181-8588, Japan
54Department of Physics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano (SA), Italy
55Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Italy
56SOFIA Science Center, NASA Ames Research Center, Mail Stop N211-3, Moffett Field CA 94035, USA
57Deutsches SOFIA Institut, Universitaet Stuttgart, Pfaffenwaldring 31, 70569 Stuttgart, Germany
58Institut fur Astrophysik, Georg-August-Universitat, Friedrich-Hund-Platz 1, 37077 Gottingen, Germany
59Institut dAstrophysique et de Geophysique, Allee du 6 Aout 17, Sart Tilman, Bat. B5c, 4000 Liege, Belgium

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ABSTRACT
We present the discovery and mass measurement of the cold, low-mass planet MOA-
2009-BLG-266Lb, made with the gravitational microlensing method. This planet has
a mass of mp = 10.4 ± 1.7M⊕ and orbits a star of mass M? = 0.56 ± 0.09M? at a
semi-major axis of a = 3.2+1.9
and host star mass measurements are enabled by the measurement of the microlensing
parallax effect, which is seen primarily in the light curve distortion due to the orbital
motion of the Earth. But, the analysis also demonstrates the capability to measure
microlensing parallax with the Deep Impact (or EPOXI) spacecraft in a Heliocentric
orbit. The planet mass and orbital distance are similar to predictions for the critical core
mass needed to accrete a substantial gaseous envelope, and thus may indicate that this
planet is a “failed” gas giant. This and future microlensing detections will test planet
formation theory predictions regarding the prevalence and masses of such planets.
−0.5AU and an orbital period of P = 7.6+7.7
−1.5yrs. The planet
Subject headings: gravitational lensing: micro, planetary systems
1.Introduction
In the leading core accretion planet formation model (Lissauer 1993), a key role is played by
the “snow line”, where the proto-planetary disk becomes cold enough for ices to condense. The
timescale for agglomeration of small bodies into protoplanets is shortest just beyond the snow line,
because this is where the surface density of solid material is highest. The largest protoplanets in
60Department of Physics & Astronomy, Aarhus University, Ny Munkegade 120, 8000 Arhus C, Denmark
61Max Planck Institute for Astronomy, K¨ onigstuhl 17, 69117 Heidelberg, Germany
62Department of Physics, Sharif University of Technology, and School of Astronomy, IPM, 19395-5531, Tehran,
Iran
63Astrophysics Group, Keele University, Staffordshire, ST5 5BG, United Kingdom
64Warsaw University Observatory, Al. Ujazdowskie 4, 00-478 Warszawa, Poland
65Institute of Astronomy, Univ. of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
66Universidad de Concepci´ on, Departamento de Astronomia, Casilla 160–C, Concepci´ on, Chile
67Microlensing Observations in Astrophysics (MOA) Collaboration
68Microlensing Follow Up Network (µFUN) Collaboration
69RoboNet Collaboration
70Probing Lensing Anomalies Network (PLANET) Collaboration
71Microlensing Network for the Detection of Small Terrestrial Exoplanets (MiNDSTEp) Collaboration

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these regions are expected to quickly reach a mass of ∼ 10M⊕by accumulating the majority of
the solid material in their vicinity. They then slowly accrete a gaseous envelope of hydrogen and
helium. The envelope can no longer maintain hydrostatic equilibrium when it reaches the mass of
the core, so it collapses, starting a rapid gas accretion phase that leads to a massive giant planet.
The hydrostatic accretion phase is predicted to have a much longer duration than the other two
phases of solid accretion and rapid gas accretion (Pollack et al. 1996). This has several possible
implications, including a higher frequency of low-mass, rocky/icy planets than gas giants, a feature
in the final mass function of planets near the critical core mass of ∼ 10 M⊕, a relative paucity of
planets with masses of 10 − 100 M⊕(Ida & Lin 2004), and the formation of very few gas giants
orbiting low-mass hosts (Laughlin et al. 2004), where the gas disks are expected to dissipate before
the critical core mass is reached.
These predictions follow from general physical considerations, but they also rely upon a number
of simplifying assumptions that make the calculations tractable. So, they could be incorrect. For
example, recent work suggests that uncertainties in the initial surface density of solids in the
protoplanetary disk, grain opacities in protoplanetary atmospheres, and the size distribution of
accreting planetesimals can radically alter the timescales of these various phases and thus the
resulting distribution of final planet masses (Rafikov 2011; Hubickyj et al. 2005; Movshovitz &
Podolak 2008). Therefore, the measurement of the mass function of planets down to below the
predicted critical core mass will provide important constraints on the physics of planet formation.
Attempts to test core accretion theory predictions with the mass distribution of the ∼ 500
detected exoplanets and the ∼ 1200 candidate exoplanets found by the Kepler mission (Borucki
et al. 2011) have met with varied success. Radial velocity detections confirm the prediction that
massive gas giants should be rare around low-mass stars (Johnson et al. 2010), but the prediction
that 10−100 M⊕planets should be rare in short period orbits is contradicted by the data (Howard
et al. 2010). Kepler finds a large population of planets at ∼ 2.5R⊕in short period orbits, which
is consistent with a result from the radial velocity planet detection method (Howard et al. 2010).
This might be considered a confirmation of the core accretion theory prediction that ∼ 10M⊕
“failed gas giant core” planets should be common, but in fact all of the low-mass planets found by
radial velocity and transit methods have been well interior to the snow line, where these “failed
core” planets are thought to form. It is possible that the exoplanet mass (or radius) function is
quite different outside the snow line due to such processes as sorting by mass through migration
(Ward 1997) and photo-evaporation of gaseous envelopes (Baraffe et al. 2005). Thus, a study of the
exoplanet mass function beyond the snow line should provide a sharper test of the core accretion
theory.
The gravitational microlensing method (Mao & Paczy´ nski 1991; Bennett 2008; Gaudi 2010)
has demonstrated sensitivity extending down to planets of mass < 10M⊕ in orbits beyond the
snow line (Bennett & Rhie 1996; Beaulieu et al. 2006; Bennett et al. 2008). Thus it can provide a
complementary probe of the physics of planet formation for planets that have migrated little from
their putative birth sites. A statistical analysis of some of the first microlensing discoveries (Gould

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et al. 2010) indicates that cold, Saturn-mass planets beyond the snow line are more common than
gas giants found in closer orbits with the Doppler radial velocity method (Cumming et al. 2008).
Another microlensing study (Sumi et al. 2010) of the mass function slope showed that planets
of ∼ 10M⊕are even more common than these cold Saturns, in general agreement with the core
accretion theory prediction for “failed gas giant cores” (Kennedy & Kenyon 2008; Thommes et al.
2008).
A well sampled planetary microlensing light curve provides a direct determination of the
planet:star mass ratio, but not the individual masses of planet and host star. Furthermore, planets
found by microlensing typically have distant, low-mass host stars, so their faintness makes them
difficult to characterize. While finite source effects in the light curve do constrain a combination
of the mass and distance, it has often been necessary to estimate the planet and host masses and
distance with a Bayesian analysis (Beaulieu et al. 2006) based on a Galactic model and prior as-
sumptions about the exoplanet distribution. When the masses of planetary microlenses and their
host stars can be measured, they will provide tighter constraints on planet formation theory.
Here, we present the first example of a mass measurement for a cold, low-mass planet discovered
by microlensing, which has a mass very similar to the expected critical mass for gas accretion.
The light curve of microlensing event MOA-2009-BLG-266 exhibits a planetary signal due to a
companion with a mass ratio of ∼ 6×10−5(see Figure 1). The light curve also reveals a microlensing
parallax signal due to the orbital motion of the Earth (Gould 1992; Alcock et al. 1995). When
combined with the information from the finite size of the source during the planetary perturbation,
this allows one to work out the complete geometry of the microlensing event (Gould 1992), yielding a
measurement of the host and planet masses. This has been done previously at this level of precision
only for the giant planets in the system OGLE-2006-BLG-109L (Gaudi et al. 2008; Bennett et al.
2010). In addition, observations from the EPOXI spacecraft in a heliocentric orbit corroborate the
mass measurement for MOA-2009-BLG-266Lb, and demonstrate the potential of obtaining masses
for planetary events that are too brief for a parallax measurement due to the Earth’s orbit.
Our observations are described in Section 2, and Section 3 details our data reduction proce-
dures. Section 4 presents a detailed discussion of the source star properties, and we discuss the
determination of the properties of the planetary system in Section 5. Finally, we discuss some of
the implications of this discovery in Section 6.
2. Observations
The microlensing event MOA-2009-BLG-266 [(RA,DEC) = (17h48m05.95s,−35◦00?19.48??)
and (l,b) = (−4.9◦,−3.6◦)] was discovered on 1 June 2009 by the Microlensing Observations in
Astrophysics (MOA) collaboration MOA-II 1.8m survey telescope at Mt. John University Ob-
servatory in New Zealand. The Probing Lensing Anomalies NETwork (PLANET), Microlensing
Follow-Up Network (µFUN) and Microlensing Network for the Detection of Small Terrestrial Ex-

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oplanets (MiNDSTEp) teams followed some of the early part of the light curve. The wide field of
view (2.2deg2) of the MOA-II survey telescope allows MOA to monitor the Galactic bulge with
a high enough cadence to discover planetary signals in any of the 500-600 microlensing events
they discover every year, and this has resulted in the discovery of several exoplanets (Sumi et al.
2010; Bennett et al. 2008). On 11 September 2009, the MOA survey detected such an anomaly
in the MOA-2009-BLG-266 light curve and announced it as a probable planetary anomaly. In re-
sponse to the alert, the event was intensively observed using the combined telescopes of the µFUN,
PLANET, RoboNet, and MINDSTEp teams, resulting in nearly complete light curve coverage for
the last ∼ 75% of the anomaly. Within four hours, modeling by MOA confirmed that this was
almost certainly a planetary event, which led to observations by the IRSF infrared telescope at the
South African Astronomical Observatory (SAAO). This and further modeling by MOA and µFUN,
as well as rapid reduction of µFUN data prevented observing resources from being diverted to other
interesting events that were found the same day.
Our data set consists of observations from 13 different telescopes, with several telescopes
contributing data in different passbands. We treat each telescope-passband combination as an
independent data set with independent flux parameters in the microlensing light curve fits, and
this combined data set includes 18 telescope-passband combinations. The planetary signal was
first seen in data from the MOA-II 1.8m survey telescope (Sako et al. 2008) at Mt. John University
Observatory in New Zealand. This analysis includes 1996 MOA-II observations taken from 2007-
2009.
In response to the MOA-II microlensing event alert on 1 June 2009 and the microlensing
anomaly alert on 11 September 2009, data were obtained from a number of follow-up groups.
The PLANET collaboration (Beaulieu et al. 2006) added this event to its target list for the 1.0m
telescope at Mt. Canopus Observatory near Hobart, Australia, and the 1.0m telescope at the
South African Astronomical Observatory (SAAO) on 16 July 2009 as a regular planet search target
following the alert plus follow-up planet detection strategy (Gould & Loeb 1992). Unfortunately,
the PLANET observing time allocation at SAAO ended on 18 August 2009, which was nearly a
month prior to the planetary signal. Additional observations prior to the detection of the planetary
anomaly were also obtained from µFUN-CTIO, MiNDSTEp-Danish, and Robonet-Faulkes South.
These observations help to constrain the microlensing parallax signal, but the parallax signal is
primarily detected in the MOA data.
Canopus had 35 observations spanning 49 days prior to the planetary signal, including four
observations on the night prior to the beginning of the planetary signal. MOA had no observations
on the two days prior to the beginning of the planetary anomaly, so the Canopus data were the only
observations taken on the night before the planetary anomaly began. These observations indicated
no deviation from a single lens light curve, and this indicated that the anomaly had a very short
duration, as is typical for light curve deviations due to low-mass planets. Thus, the Canopus data
contributed to the identification of the planetary nature of the anomaly identified in the MOA
data. This was important because another anomalous event and a high magnification event were

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also identified by MOA on the same day. The final data set contains 205 I band observations from
Canopus and 33 I band observations from SAAO.
The first data in response to MOA’s 11 September 2009 alert on the planetary anomaly came
from the Microlensing Follow-up Network (µFUN) with observations from the 0.4 m telescope
Bronberg Observatory in Pretoria, South Africa and the 1.0 m telescope of Wise Observatory in
Israel, which were able to begin observations ∼ 4hours after the anomaly alert (which coincided
with the last MOA observation on the night of the alert). About two hours later (after the MOA
planetary light curve model had been circulated), a series of observations were begun with the 1.4m
InfraRed Survey Telescope (IRSF), which is located at SAAO and features simultaneous imaging
in the J, H,and K bands. The final data set includes 597 unfiltered observations from Bronberg,
36 and 30 observations in I and R (respectively) from Wise, and 19, 20, and 18 observations in the
J, H, and K bands from IRSF. The raw Bronberg data consist primarily of very densely sampled
observations during the two nights of the planetary deviation, and the 1705 observations from
Bronberg were binned to a 7.2 minute cadence to yield the 597 measurements that were used for all
the light curve modeling. The IRSF observations are much sparser, but they do include coverage of
the first caustic crossing endpoint, as well as observations from March 2010, when the microlensing
magnification was < 1.01.
The µFUN group also obtained a large number of observations in the H, I, and V bands from
the ANDICAM instrument on the 1.3 m SMARTS telescope at CTIO in Chile. This instrument
observes simultaneously in the optical and infrared, so the final data set includes 861 H band
observations, which mostly overlap in time with the 317 I band and 56 V band observations
that are included in the final data set. The CTIO data also include regular sampling of the
stellar microlensing light curve after the planetary anomaly and a few images from 2010, so they
contribute significantly to the microlensing parallax constraints. The Microlensing Network for the
Detection of Small Terrestrial Exoplanets (MiNDSTEp) also obtained dense light curve coverage of
the planetary deviation using the 1.54 m Danish Telescope at the European Southern Observatory
in La Silla, Chile, and their data set consists of 611 I band observations. Another µFUN telescope
in the Americas was the 1.0 m telescope at Mt. Lemmon Observatory in Arizona which contributed
73 I band observations to the final data set.
The rise of the light curve from the planetary magnification “trough” was covered largely by
the 2.0m Faulkes telescopes operated by the Las Cumbres Global Telescope Network (LCOGTN).
The Faulkes North telescope (FTN) located in Haleakala, Hawaii contributed 148 SDSS-I band
observations to the final data set, while the Faulkes South Telescope (FTS) located in Siding
Springs, Australia, contributed 128 SDSS-I band observations to the final data set. The Canopus
and MOA telescopes also covered the last part of the rise from the light curve “trough. ”
The Robonet group also obtained a substantial amount of FTS data in the SDSS-g, r and
Pan Starrs-z and y with 52, 51, 49, and 115 images in each passband. This multi-color data was
obtained because it was thought that it might be helpful to help calibrate the unfiltered EPOXI

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data.
Our complete light curve data set also includes 929 OGLE-III I-band observations that ended
on 3 May 2009 with the termination of the OGLE-III survey, when the magnification was A ≈ 1.06.
(OGLE-III was terminated to enable an upgrade to a more sensitive camera with a larger field of
view for the OGLE-IV survey.)
Finally, we obtained high angular resolution AO images from the NACO instrument on the
European Southern Observatory’s Very Large Telescope (VLT) facility in 2010 after the event was
over.
3. Data Reduction
Most of the photometry was done using the Difference Image Analysis (DIA) method (Tomaney
& Crotts 1996). The MOA images were reduced with the MOA DIA pipeline (Bond et al. 2001),
while the PLANET, RoboNet-II, MINDSTEp and most of the µFUN data were reduced with a DIA
routine following the same basic strategy as ISIS (Alard & Lupton 1998), but using a numerical
kernel (Bramich 2008). The implementation of this numerical kernel DIA routine that was used
for most of the data was pySIS (v3.0) (Albrow et al. 2009) but the Robonet pipeline was used for
the FTS data (Bramich 2008). The OGLE data were reduced with the OGLE pipeline (Udalski
2003). The Mt. Lemmon data were reduced with DoPHOT (Schechter, Mateo, & Saha 1993), and
the IRSF data were reduced with SoDoPHOT, which was derived from DoPHOT (Bennett et al.
1993). SoDoPHOT was also used to reduce the CTIO I and V band data, but this SoDoPHOT
reduction was only used to help calibrate the EPOXI photometry. The multicolor FTS data and
the CTIO data were also reduced with ALLFRAME (Stetson 1994) to aid the EPOXI photometry
calibration, but only the SoDoPHOT reductions of the CTIO I and V band data were used in
the final EPOXI calibrations. The pySIS reductions of the CTIO data were used for light curve
modeling.
One difficulty that is sometimes encountered with DIA photometry is that excess photometric
scatter can result for images where the target star is much brighter or much fainter than it is in
the reference frame. This effect was noticed in the pySIS reductions of the Canopus data. So, the
final Canopus photometry was a combination of two reductions based on reference frames in which
the brightness of the target was very different. The relative normalization of these two reductions
was determined by a linear fit with the 3-σ outliers removed from each data set. Then, the final
Canopus photometry was determined by a weighted sum of these two data sets with the weighting
determined by the difference between the target brightness in the image being reduced and the two
reference frames.
An additional correction is necessary for the unfiltered Bronberg data. The color dependence of
atmospheric extinction can give rise to systematic photometry errors because the color of the source
star is typically slightly different from the color of the stars used to normalize the photometry. This

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gives rise to a photometry error that scales as the airmass for monochromatic light and a static
atmosphere. For a very wide passband, like that of Bronberg, the effective passband depends on
the amount of atmospheric extinction, so the photometric error does not follow the scaling with
airmass very precisely (Stubbs et al. 2007). Furthermore, the amount of dust in the atmosphere
can change with time. So, we correct the Bronberg photometry by normalizing the photometry of
the target star to a set of stars with a similar color (Bennett et al. 2010).
The VLT/NACO data were reduced following the procedures used for the analysis of MOA-
2007-BLG-192 (Kubas et al. 2011).
3.1. Reduction of EPOXI Data
For a period of just under three days on 10-12 October 2009, we were able to obtain observations
using the High Resolution Instrument (HRI) visible imager on the EPOXI (Christiansen et al.
2011) spacecraft when it was located ∼ 0.1AU from Earth. Observations with the EPOXI HRI
were requested in an attempt to constrain the microlensing parallax effect and obtain precise
mass measurements of the MOA-2009-BLG-266Lb planet and its host star. We could obtain these
observations because our target field was able to provide a better test of newly installed pointing
control software than a less dense stellar field.
The EPOXI data consist of 4127 50 sec exposures with the “clear-6” filter. To minimize data
transfer requirements, the data were taken as 128 × 128 and 256 × 256 pixel sub-frames. The first
3375 exposures used 128 × 128 sub-frames, and the last 752 images were 256 × 256 sub-frames.
However, the pointing stability was such that the target occasionally drifted out of the 128 × 128
sub-frames, and it was only possible to do photometry on 2900 of these 3375 128×128 pixel images.
An example of one of these 128 × 128 pixel images is shown on the right side of Figure 2.
The instrumental point-spread function (PSF) of the High Resolution Instrument (HRI) on
the Deep Impact probe is strongly dependent on the color of the target star. In addition, the
instrument is permanently defocussed, yielding a toroidal–shaped PSF. This is clearly not optimal
for crowded field photometry, which typically requires a spatially varying empirical PSF model for
deblending. Since we performed photometry using the Daophot/Allstar/Allframe software suite
(Stetson 1994), we first required a model of the instrumental PSF that is usable by Daophot.
Instrumental PSFs have been generated by Barry (2010) for the HRI using the Drizzle algo-
rithm (Fruchter & Hook 2002). In this process several hundred images of a standard star were
added together to create a ten–times oversampled PSF model appropriate for that object. To ap-
proximate the PSF of MOA-2009-BLG-266, with V −I = 1.82, we coadded the instrumental PSFs
of GJ436 with V − I = 2.44; and XO-2 with V − I = 0.75 with weightings of 0.795 and 0.205,
respectively. This composite PSF was added to an otherwise empty image in a 3 by 3 grid, with
each realization downsampled to standard resolution using a center pixel shifted by ± 5 pixels in
x and/or y. Daophot was then run on this image, using all 9 images to build its own internal,

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double–resolution PSF model using an empirical function plus “lookup table”.
Approximately 1% of pixels in our 50s observations contain signatures of cosmic rays. We
filtered these pixels using an algorithm that identifies features sharper than expected from the
PSF, through pairwise comparison of neighboring pixels. These pixels were masked and objects
underneath these pixels ignored when generating lightcurves. We used Daophot to detect stars in
each image, and then Allstar to perform joint PSF photometry on all stars in a given image. We
generated a master starlist by matching the results of the Allstar analysis using Daomatch and
Daomaster. This starlist was then sent to Allframe, which simultaneously photometered all images
in a self–consistent manner with regards to centroiding and deblending.
To assemble the final light curves, we first aggregated the Allframe measurements of a given
star across all images. Due to the difficulty of obtaining precise flat field images in space, we cannot
calibrate these images using the same methods as would be used for ground-based images. As a
result, the light curves of all the stars observed by EPOXI/HRI show variations at the ∼ 1% level
on a time scale of a few hours, which is the time that it takes for the pointing to drift a distance
of order the PSF FWHM. Because this is the dominant term in the EPOXI/HRI photometry
errors, we bin the data at an interval of 2.4 hours, which seems to remove most, but not all, of
the correlations. This gives the light curve shown in the inset in the upper right hand corner of
Figure 1.
We had also hoped to get EPOXI/HRI observations after the MOA-2009-BLG-266 microlensing
event had returned to its baseline brightness in March or April, 2010. Unfortunately, the EPOXI
operations team was busy with preparations for the November, 2010 encounter with comet Hartley
2, so no baseline observations were possible. Therefore, we have determined the baseline brightness
in the EPOXI by comparing the EPOXI images to V and I band CTIO images taken in June 2010,
when the microlensing event had returned to baseline. The I band CTIO image is compared to one
of the EPOXI frames in Figure 2. Because of the relatively large EPOXI/HRI PSF, we consider
only stars in the EPOXI images that have only one counterpart star within a radius of 3??of the
position of the EPOXI star. We also limit our consideration to stars within 0.9 mag of the V − I
color of the microlensed target star. There are 4 stars that satisfy this condition and appear in
more than half of the images in which the target star appears. These are the 4 stars indicated
by the green circles in Figure 2. We fit the mean “clear”-filter EPOXI magnitude, CEPOXI to
the instrumental CTIO magnitudes from the SoDoPHOT reductions, and this yields the following
linear relationship between the average EPOXI magnitudes and CTIO magnitudes,
CEPOXI= 0.520ICTIO+ 0.480VCTIO. (1)
The fit to the magnitude of these 4 comparison stars gives χ2= 0.22 for 2 degrees of freedom if the
uncertainty in the EPOXI magnitudes is assumed to be 0.004 mag. We use this formula to determine
the baseline CEPOXI magnitude, and we add this to the light curve as a final measurement with
an assumed uncertainty of 0.01 mag.
We note that this calibration procedure for the EPOXI data is probably more reasonably

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considered to be a procedure to calibrate the source star flux instead of the baseline brightness,
which includes the brightness of any unresolved stars blended with the source. But we chose to treat
the unmagnified flux estimate as an estimate of the baseline brightness as this is more conservative.
4. Source Star Properties and Einstein Radius
Planetary microlensing events typically have caustic crossing or cusp approach features that
resolve the finite angular size of the source star, and MOA-2009-BLG-266 is no exception as it has
clear caustic crossing features. The modeling of such features constrains the source radius crossing
time, t?, and this can be quite useful because t?can be used to determine the angular Einstein
radius, θE= θ?tE/t?, as long as the source star angular radius, θ?can be determined. In events
such as MOA-2009-BLG-266, with a strong microlensing parallax signal, θEcan be combined with
the parallax measurement to yield the lens system mass. Therefore, it is important to make an
accurate determination of the angular radius of the source star, θ?.
4.1. Source Star Colors and Extinction
The angular radius of the source star can be determined from its brightness and color, once
the effect of interstellar extinction has been removed. We start from the CTIO V and I band
magnitudes and the IRSF H band magnitude that have been determined from the best fit model.
The V and I band magnitudes have been calibrated to the OGLE-III system (Udalski et al. 2008)
and IRSF H band has been calibrated to 2MASS (Carpenter 2001)1. The comparison between the
2MASS and the IRSF H-band data is subject to complications due to variability and blending,
because the 2MASS images, with their 2” pixels, have significantly worse angular resolution than
IRSF. This means that many of the apparent 2MASS “stars” cannot be used for the calibrations
because they are actually blended images of two or more stars that are resolved in the IRSF
images. This makes calibration of the CTIO H band images difficult, because of the relatively
small 5.5arc min2CTIO H field of view (FOV). Fortunately, the IRSF FOV is ∼ 60arc min2, and
it is possible to use over 400 unblended 2MASS stars for the H band calibration. These calibrations
combined with the best fit light curve models yield source magnitudes of
Hs= 13.780 ± 0.030
15.856 ± 0.030
17.677 ± 0.030 ,
(2)
Is=(3)
Vs=(4)
where the uncertainties are almost entirely due to the calibrations (including the uncertainty in the
OGLE-III calibration. These magnitudes are indicated by the green dots in the color magnitude
1Improved calibrations are available at
http://www.ipac.caltech.edu/2mass/releases/allsky/doc/sec6 4b.html

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diagrams shown in Figures 3 and 4. The fit uncertainties are ≤ 0.005mag in all three passbands,
and the u0> 0 model predicts a source that is 0.005mag brighter than the best fit u0< 0 model.
4.2.Source Star Radius
We can use the magnitudes from equations 2-4 to determine the source star angular radius,
but first we must estimate the foreground extinction. We determine the source radius using the
method of Bennett et al. (Bennett et al. 2010), which is a generalization to three colors of an earlier
two-color method (Albrow et al. 2000). Following this procedure, we find the V IH magnitudes of
the center of the red clump giant distribution to be
Hrc= 13.59 ± 0.10
15.73 ± 0.10
17.64 ± 0.10 ,
(5)
Irc= (6)
Vrc= (7)
for stars within 2?of the source star. These are indicated by the red spots in Figures 3 and
4. Assuming a distance to the source of 8.8kpc (Rattenbury 2007), we can use these red clump
magnitudes to estimate the extinction, which we find to be AH= 0.36, AI= 1.22, and AV = 2.14,
following a RV = 2.77 Cardelli et al. (Cardelli et al. 1989) extinction law. These then yield de-
reddened magnitudes of Hs0= 13.42, Is0= 14.64, and Vs0= 15.54. Unlike the case for dwarf stars,
the accuracy of the V − I, V − H, and I − H surface brightness-color relations (Kervella et al.
2004) is similar, but the I −H relation yields an angular radius estimate that is almost completely
independent of the reddening law, if it follows the Cardelli et al. extinction law (Cardelli et al.
1989), but this may be due to the fact that the AI/AHratio doesn’t vary much with this extinction
law. In any case, all three of these relations imply that the angular radius of the source star is
θ?= 5.2 ± 0.2 µas.(8)
This and the source radius crossing time of t?= 0.326±0.007days imply that the relative lens-source
proper motion and Einstein radius are
µrel= θ?/t?= 5.86 ± 0.26 mas yr−1, (9)
and
θE= µreltE= 0.98 ± 0.04 mas,(10)
respectively.
4.3. Limb Darkening
During caustic crossings the lens effectively scans the source star with high angular resolution.
As a result, the shape of the light curve reflects the underlying limb darkening of the star (Witt

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1995; Bennett & Rhie 1996). Hence, in order to analyze caustic-crossing events such as MOA-2009-
BLG-266, one needs to account for the limb darkening appropriately. For the previous planetary
microlensing events (Bond et al. 2004; Udalski et al. 2005; Beaulieu et al. 2006; Gould et al. 2006;
Gaudi et al. 2008; Bennett et al. 2008; Dong et al. 2009b; Sumi et al. 2010; Janczak et al. 2010;
Miyake et al. 2011; Batista et al. 2011), limb darkening has generally been treated within the linear
limb-darkening approximation. In some cases, the two-parameter square-root limb-darkening law
was used (Dong et al. 2009b; Janczak et al. 2010), even though there has been no indication that
the details of the limb-darkening treatment had any noticeable effect on the other model parameters
for a planetary microlensing event.
In the case of MOA-2009-BLG-266, there was reason to suspect that the treatment of limb
darkening could be important. This is because, as we discuss below in Section 5.1, there are
two approximately degenerate microlensing parallax models that have slightly different binary lens
parameters. The source crosses the caustics at a slightly different angle for the two models. This
suggests that the detailed treatment of limb darkening might have some influence on the difference
in χ2between these two degenerate models. As shown by Heyrovsky (2007), using linear limb
darkening may introduce photometric errors at the level of 0.01 due to the approximation itself and
the choice of method used for computing the linear model coefficients. In order to avoid introducing
any such inaccuracies in the analysis of the event, we directly use the limb-darkening profile from
a theoretical model atmosphere of the source star, instead of its analytical approximations.
Based on the location of the source star on the color magnitude diagram, we assume a tem-
perature of Teff ≈ 4750K, surface gravity of logg = 2.5, and solar metallicity. We use a model
atmosphere from Kurucz’s ATLAS9 grid (Kurucz 1996, 1993a,b)2corresponding to these param-
eters. The raw model data provide values of the specific intensity as a function of wavelength for
17 different positions on the stellar disk. In order to obtain the light-curve-specific limb-darkening
profile, we integrate the specific intensity over the relevant filter passband, weighted by the filter
transmission, the quantum efficiency of the CCD, and interstellar extinction (see Section 4.1). In
order to compute the limb darkening at an arbitrary position on the stellar disk, we interpolate
the obtained points using cubic splines with natural boundary conditions (Heyrovsky 2003, 2007).
The light curve modeling code uses pre-computed tabulated intensity values for a sufficiently dense
spacing of radial positions on the stellar disk.
This approach avoids a potential source of low-level systematic error without any degrees of
freedom to the model. In Table 1 we compare the results of our analysis with those obtained
by the usual approach, using linear limb-darkening coefficients from Claret (Claret 2000). For
the parameters of the source star Claret (Claret 2000) provides coefficient values uλ = 0.7844,
0.7035, 0.6087, 0.4868, 0.4181, and 0.358 for the V , R, I, J, H, and Kspassbands, respectively.
Ttabulated intensity values give a χ2improvement over the linear approximation of ∆χ2= 7.27
for the best-fit static models without orbital motion. So, the tabulated limb darkening tables fit
2Updated online at http://kurucz.harvard.edu

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the data somewhat better, at least for the static lens case, but the implied planetary parameters
do not change significantly.
5. Planet Characterization and Modeling
5.1.Modeling
The basic parameters for planetary events like MOA-2009-BLG-266 are straightforward to
determine, as a reasonable estimate can be made from the single lens parameters (found from a
fit with the planetary deviation excluded) and inspection of the light curve (Gould & Loeb 1992).
The main feature of the deviation is the half-magnitude decrease in magnification centered at
HJD?= 5086.5. This indicates that a planet is perturbing the minor (saddle) image created by the
stellar lens and that the star-planet separation is less than the Einstein radius. Such a light curve
cannot be mimicked by non-planetary perturbations (Gaudi & Gould 1997). The basic planetary
parameters can then be estimated following the arguments given in Sumi et al. (2010). In practice,
this is not how the parameters were determined, however.
We model the data using standard methods (Bennett 2010; Dong et al. 2006) to extract the
precise parameters and uncertainties of the light curve fit. It is convenient to describe microlensing
events in terms of the Einstein ring radius, RE =
of ring image seen when the source and (single) lens are in perfect alignment. Here ML is the
lens system mass, x = DL/DS, and DLand DS are the lens and source distances. Microlensing
by a single lens, such as an isolated star, is described by three parameters: the Einstein radius
crossing time, tE, and the time, t0, and distance (with respect to RE), u0, of closest alignment
between the source and lens center of mass. Planetary microlensing events require three additional
parameters: the planet:star mass ratio, q, the star-planet separation, s, in units of RE, and angle
of the source trajectory with respect to the star-planet axis, θ. The source radius crossing time,
t?, is also required because, like most planetary events, MOA-2009-BLG-266 has sharp light curve
features that resolve the angular size of the source star.
?(4GML/c2)DSx(1 − x), which is the radius
The MOA and Canopus data for the event were modeled immediately upon the detection of the
planetary perturbation using the method of Bennett (2010), supplemented with the addition of the
hexadecapole approximation (Pejcha & Heyrovsky 2009; Gould 2008). This found the basic solution
that we present here, plus a disfavored alternative s > 1 solution, which was excluded within hours
when the planetary deviation data from South Africa, Israel, and Chile became available. The
s < 1 solution was refined as more data came in, and the two degenerate solutions that we present
here emerged when microlensing parallax was added to the modeling.
We also conducted a blind search of parameter space using the approach of Dong et al. (2006),
where the binary parameters s, q, and θ are fixed at a grid of values, while the remaining parameters
are allowed to vary so that the model light curve results in minimum χ2at each grid point. A