Issue 
A&A
Volume 552, April 2013



Article Number  A70  
Number of page(s)  10  
Section  Planets and planetary systems  
DOI  https://doi.org/10.1051/00046361/201220626  
Published online  27 March 2013 
A giant planet beyond the snow line in microlensing event OGLE2011BLG0251
^{1}
European Southern Observatory, KarlSchwarzschild Straße 2, 85748
Garching bei München,
Germany
^{2}
Las Cumbres Observatory Global Telescope Network,
6740 Cortona Drive, Suite 102,
Goleta, CA
93117,
USA
^{3}
Department of Physics, Institute for Astrophysics, Chungbuk
National University, 371763
Cheongju,
Korea
^{4}
Warsaw University Observatory, Al. Ujazdowskie 4, 00478
Warszawa,
Poland
^{5}
Divisão de Astrofisica, Instituto Nacional de Pesquisas
Espeaciais, Avenida dos
Astronauntas, 1758 Sao José dos Campos, 12227010
SP,
Brazil
^{6}
School of Chemical and Physical Sciences, Victoria
University, Wellington, New Zealand
^{7}
Niels Bohr Institute, University of Copenhagen,
Juliane Maries vej 30,
2100
Copenhagen,
Denmark
^{8}
Centre for Star and Planet Formation, Geological
Museum, Øster Voldgade
5, 1350
Copenhagen,
Denmark
^{9}
Qatar Foundation, PO Box 5825, Doha, Qatar
^{10}
Dipartimento di Fisica “E.R Caianiello”, Università di
Salerno, via Ponte Don
Melillo, 84084
Fisciano,
Italy
^{11}
Istituto Nazionale di Fisica Nucleare,
Sezione di Napoli,
Italy
^{12}
SUPA School of Physics & Astronomy, University of St
Andrews, North
Haugh, St Andrews,
KY16 9SS,
UK
^{13}
Deutsches SOFIA Institut, Universität Stuttgart,
Pfaffenwaldring 31,
70569
Stuttgart,
Germany
^{14}
SOFIA Science Center, NASA Ames Research Center, Mail Stop
N2113, Moffett Field
CA
94035,
USA
^{15}
Istituto Internazionale per gli Alti Studi Scientifici
(IIASS), Vietri Sul
Mare ( SA),
Italy
^{16}
Institut für Astrophysik, GeorgAugustUniversität,
FriedrichHundPlatz 1,
37077
Göttingen,
Germany
^{17}
Korea Astronomy and Space Science Institute,
305348
Daejeon,
Korea
^{18}
National Astronomical Observatories/Yunnan Observatory, Joint
laboratory for Optical Astronomy, Chinese Academy of Sciences,
650011
Kunming, PR
China
^{19}
Department of Physics and Astronomy, Aarhus
University, Ny Munkegade
120, 8000
Århus C,
Denmark
^{20}
Armagh Observatory, College Hill, Armagh, BT61 9DG, Northern Ireland, UK
^{21}
Danmarks Tekniske Universitet, Institut for Rumforskning og
teknologi, Juliane Maries Vej
30, 2100
København,
Denmark
^{22}
Jodrell Bank Centre for Astrophysics, University of
Manchester, Oxford
Road, Manchester,
M13 9PL,
UK
^{23}
Max Planck Institute for Astronomy, Königstuhl 17, 69117
Heidelberg,
Germany
^{24}
Department of Astronomy, Ohio State University,
140 West 18th Avenue,
Columbus, OH
43210,
USA
^{25}
Department of Physics, Sharif University of
Technology, PO Box
11155–9161, Tehran,
Iran
^{26}
Perimeter Institute for Theoretical Physics,
31 Caroline St. N.,
Waterloo ON, N2L 2Y5, Canada
^{27}
Institut d’Astrophysique et de Géophysique,
Allée du 6 Août 17, Sart Tilman, Bât.
B5c, 4000
Liège,
Belgium
^{28}
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD
21218,
USA
^{29}
INFN, Gruppo Collegato di Salerno, Sezione di Napoli,
Italy
^{30}
European Southern Observatory (ESO), Alonso de Cordova 3107, Casilla 19001,
Santiago 19,
Chile
^{31}
Max Planck Institute for Solar System Research,
MaxPlanckStr. 2, 37191
KatlenburgLindau,
Germany
^{32}
Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK
^{33}
Astronomisches RechenInstitut, Zentrum für Astronomie der
Universität Heidelberg (ZAH), Mönchhofstr. 1214, 69120
Heidelberg,
Germany
^{34}
Institute of Astronomy, University of Cambridge,
Madingley Road, Cambridge
CB3 0HA,
UK
^{35}
Alsubais Establishment for Scientific Studies,
Doha,
Qatar
^{36}
Astrophysics Research Institute, Liverpool John Moores
University, Twelve Quays House,
Egerton Wharf, Birkenhead, Wirral., CH41
1LD, UK
^{37}
School of Mathematical Sciences, Queen Mary, University of
London, Mile End
Road, London
E1 4NS,
UK
^{38}
Vintage Lane Observatory, 83 Vintage Lane, RD3, Blenheim, New
Zealand
^{39}
Auckland Observatory, 670 Manukau Rd, Royal Oak 1023, Auckland, New
Zealand
^{40}
Dept. of Physics and Astronomy, Texas A&M University
College Station, TX
778434242, USA
^{41}
Possum Observatory, Patutahi, Gisbourne, New Zealand
^{42}
Farm Cove Observatory, Centre for Backyard Astrophysics,
Pakuranga, Auckland,
New Zealand
^{43}
Institute for Radiophysics and SpaceResearch, AUT
University, Auckland,
New Zealand
^{44}
Dept. of Astronomy and Space Science, Chungnam
University, Korea
^{45}
Departamento de Astronomiá y Astrofísica, Universidad de
Valencia, 46100
Burjassot, Valencia, Spain
^{46}
UPMCCNRS, UMR7095, Institut d’Astrophysique de
Paris, 98bis boulevard
Arago, 75014
Paris,
France
^{47}
University of Canterbury, Dept. of Physics and
Astronomy, Private Bag
4800, 8020
Christchurch, New
Zealand
^{48}
McDonald Observatory, 16120 St Hwy Spur 78 #2, Fort Davis, Tx
79734,
USA
^{49}
University of the Free State, Faculty of Natural and Agricultural
Sciences, Dept. of Physics, PO Box
339, 9300
Bloemfontein, South
Africa
^{50}
School of Math and Physics, University of Tasmania,
Private Bag 37, GPO Hobart,
7001
Tasmania,
Australia
^{51}
Institute of Geophysics and Planetary Physics (IGPP), L413,
Lawrence Livermore National Laboratory, PO Box 808, Livermore, CA
94551,
USA
^{52}
Université de Toulouse, UPSOMP, IRAP,
31400
Toulouse,
France
^{53}
CNRS, IRAP, 14
avenue Edouard Belin, 31400
Toulouse,
France
^{54}
Physics Department, Faculty of Arts and Sciences, University of
Rijeka, Omladinska
14, 51000
Rijeka,
Croatia
^{55}
Technical University of Vienna, Department of
Computing, Wiedner Hauptstrasse
10, Vienna,
Austria
^{56}
NASA Exoplanet Science Institute, Caltech, MS 10022, 770 S. Wilson Ave.,
Pasadena, CA
91125,
USA
^{57}
Perth Observatory, Walnut Road, Bickley,
6076
Perth,
Australia
^{58}
South African Astronomical Observatory,
PO Box 9, Observatory
7935, South
Africa
^{59}
SolarTerrestrial Environment Laboratory, Nagoya
University, 4648601
Nagoya,
Japan
^{60}
Dept. of Physics, University of Notre Dame,
Notre Dame, IN
46556,
USA
^{61}
Institute of Information and Mathematical Sciences, Massey
University, Private Bag 102904,
North Shore Mail Centre, Auckland, New Zealand
^{62}
Dept. of Physics, University of Auckland,
Private Bag 92019, Auckland, New
Zealand
^{63}
Okayama Astrophysical Observatory, National Astronomical
Observatory of Japan, Asakuchi, 7190232
Okayama,
Japan
^{64}
Mt. John Observatory, PO Box 56, 8770
Lake Tekapo, New
Zealand
^{65}
Dept. of Physics, Konan University, Nishiokamoto 891, 6588501
Kobe,
Japan
^{66}
Nagano National College of Technology,
3818550
Nagano,
Japan
^{67}
Tokyo Metropolitan College of Industrial Technology,
1168523
Tokyo,
Japan
^{68}
Dept. of Earth and Space Science, Graduate School of Science,
Osaka University, 11
Machikaneyamacho, Toyonaka, 5600043
Osaka,
Japan
^{69}
Universidad de Concepción, Departamento de
Astronomia, Casilla
160–C, Concepción,
Chile
Received:
24
October
2012
Accepted:
1
March
2013
Aims. We present the analysis of the gravitational microlensing event OGLE2011BLG0251. This anomalous event was observed by several survey and followup collaborations conducting microlensing observations towards the Galactic bulge.
Methods. Based on detailed modelling of the observed light curve, we find that the lens is composed of two masses with a mass ratio q = 1.9 × 10^{3}. Thanks to our detection of higherorder effects on the light curve due to the Earth’s orbital motion and the finite size of source, we are able to measure the mass and distance to the lens unambiguously.
Results. We find that the lens is made up of a planet of mass 0.53 ± 0.21 M_{J} orbiting an M dwarf host star with a mass of 0.26 ± 0.11 M_{⊙}. The planetary system is located at a distance of 2.57 ± 0.61 kpc towards the Galactic centre. The projected separation of the planet from its host star is d = 1.408 ± 0.019, in units of the Einstein radius, which corresponds to 2.72 ± 0.75 AU in physical units. We also identified a competitive model with similar planet and host star masses, but with a smaller orbital radius of 1.50 ± 0.50 AU. The planet is therefore located beyond the snow line of its host star, which we estimate to be around ~1−1.5 AU.
Key words: gravitational lensing: weak / planets and satellites: detection / planetary systems / Galaxy: bulge
© ESO, 2013
1. Introduction
Gravitational microlensing is one of the methods that allow us to probe the populations of extrasolar planets in the Milky Way, and has now led to the discoveries of 16 planets^{1}, several of which could not have been detected with other techniques (e.g. Beaulieu et al. 2006; Gaudi et al. 2008; Muraki et al. 2011). In particular, microlensing events can reveal cool, lowmass planets that are difficult to detect with other methods. Although this method presents several observational and technical challenges, it has recently led to several significant scientific results. Sumi et al. (2011) analysed short timescale microlensing events and concluded that these events were produced by a population of Jupitermass freefloating planets, and were able to estimate the number of such objects in the Milky Way. Cassan et al. (2012) used 6 years of observational data from the PLANET collaboration to build on the work of Gould et al. (2010) and Sumi et al. (2011), and derived a cool planet mass function, suggesting that, on average, the number of planets per star is expected to be more than 1.
Modelling gravitational microlensing events has been and remains a significant challenge, due to a complex parameter space and computationally demanding calculations. Recent developments in modelling methods (e.g. Cassan 2008; Kains et al. 2009, 2012; Bennett 2010; Ryu et al. 2010; Bozza et al. 2012), however, have allowed microlensing observing campaigns to optimise their strategies and scientific output, thanks to realtime modelling providing prompt feedback to observers as to the possible nature of ongoing events.
In this paper we present an analysis of microlensing event OGLE2011BLG0251, an anomalous event discovered during the 2011 season by the OGLE collaboration and observed intensively by followup teams. In Sect. 2, we briefly summarise the basics of relevant microlensing formalism, while we discuss our data and reduction in Sect. 3. Our modelling approach and results are outlined in Sect. 4; we translate this into physical parameters of the lens system in Sect. 5 and discuss the properties of the planetary system we infer.
2. Microlensing formalism
Microlensing can be observed when a source becomes sufficiently aligned with a lens along the line of sight that the deflection of the source light by the lens is significant. A characteristic separation at which this occurs is the Einstein ring radius. When a single point source approaches a single point lens of mass M with a projected sourcelens separation u, the source brightness is magnified following a symmetric “point sourcepoint lens” (PSPL) pattern which can be parameterised with an impact parameter u_{0} and a timescale t_{E}, both expressed in units of the angular Einstein radius (Einstein 1936), (1)where G is the gravitational constant, c is the speed of light, and D_{S} and D_{L} are the distances to the source and the lens, respectively, from the observer. The timescale is then t_{E} = θ_{E}/μ, where μ is the lenssource relative proper motion. Therefore the observable t_{E} is a degenerate function of M,D_{L} and the source’s transverse velocity v_{⊥}, assuming that D_{S} is known. However, measuring certain secondorder effects in microlensing light curves such as the parallax due to the Earth’s orbit allows us to break this degeneracy and therefore measure the properties of the lensing system directly.
When the lens is made up of two components, the magnification pattern can follow many different morphologies, because of singularities in the lens equation. These lead to source positions, along closed caustic curves, where the lensing magnification is formally infinite for point sources, although the finite size of sources means that, in practice, the magnification gradient is large rather than infinite. A pointsource binarylens (PSBL) light curve is often described by 6 parameters: the time at which the source passes closest to the centre of mass of the binary lens, t_{0}, the Einstein radius crossing time, t_{E}, the minimum impact parameter u_{0}, which are also used to describe PSPL light curves, as well as the source’s trajectory angle α with respect to the lens components, the separation between the two mass components, d, and their mass ratio q. Finite source size effects can be parameterised in a number of ways, usually by defining the angular size of the source ρ_{ ∗ } in units of θ_{E}: (2)where θ_{ ∗ } is the angular size of the source in standard units.
Data sets for OGLE2011BLG0251, with the number of data points for each telescope/filter combination.
3. Observational data
The microlensing event OGLE2011BLG0251 was discovered by the Optical Gravitational Lens Experiment (OGLE) collaboration’s Early Warning System (Udalski 2003) as part of the release of the first 431 microlensing alerts following the OGLEIV upgrade. The source of the event has equatorial coordinates α = 17^{h}38^{m}14.18^{s} and δ = −27°08′10.1′′ (J2000.0), or Galactic coordinates of (l,b) = (0.670°,2.334°). Anomalous behaviour was first detected and alerted on August 9, 2011 (HJD ~ 2 455 782.5) thanks to realtime modelling efforts by various followup teams that were observing the event, but by that time a significant part of the anomaly had already passed, with suboptimal coverage due to unfavourable weather conditions. The anomaly appears as a twoday feature spanning HJD = 2 455 779.5 to 2 455 781.5, just before the time of closest approach t_{0}. Despite difficult weather and moonlight conditions, the anomaly was securely covered by data from five followup telescopes in Brazil (μFUN Pico dos Dias), Chile (MiNDSTEp Danish 1.54 m) New Zealand (μFUN Vintage Lane, and MOA Mt. John B&C), and the Canary Islands (RoboNet Liverpool Telescope).
The descending part of the light curve also suffered from the bright Moon, with the source ~5 degrees from the Moon at ~85% of full illumination, leading to high background counts in images and more scatter in the reduced data. We opted not to include data from Mt. Canopus 1 m telescope in the modelling because of technical issues at the telescope affecting the reliability of the images, and also excluded the Iband data from CTIO because they also suffer from large scatter, probably due to the proximity of the bright full Moon to the source.
The data set amounts to 3738 images from 13 sites, from the OGLE survey team, the MiNDSTEp consortium, the RoboNet team, as well as the μFUN, PLANET and MOA collaborations in the I,V and R bands, as well as some unfiltered data; data sets are summarised in Table 1 and the light curve is shown in Fig. 1. We reduced all data using the difference imaging pipeline DanDIA (Bramich 2008; Bramich et al. 2013), except for the OGLE data, which was reduced by the OGLE team with their optimised offline pipeline.
Fig. 1 Light curve of OGLE2011BLG0251. Data points are plotted with 1σ error bars, and the upper panel shows a zoom around the perturbation region near the peak 

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For each data set, we applied an error bar rescaling factors a and b to normalise error bars with respect to our bestfit model (see Sect. 4), using the simple scaling relation where is the rescaled error bar of the ith data point and σ_{i} is the original error bar (e.g. Bachelet et al. 2012). The error bar rescaling factors for each data set is given in Table 1. We did not exclude outliers from our data sets, unless we had reasons to believe that an outlier had its origin in a bad observation, or in issues with the data reduction pipeline.
4. Modelling
We modelled the light curve of the event using a Markov chain Monte Carlo (MCMC) algorithm with adaptive step size. We first used the “standard” PSBL parameterisation in our modelling, whereby a binarylens light curve can be described by 6 parameters: those given in Sect. 2, ignoring the secondorder ρ_{ ∗ } parameter described in that section. For all models and configurations we searched the parameter space for solutions with both a positive and a negative impact parameter u_{0}.
We started without including secondorder effects of the source having a finite size or parallax due to the orbital motion of Earth around the Sun, and then added these separately in subsequent modelling runs by fitting the source size parameter ρ_{ ∗ }, as defined in Sect. 2, and the parallax parameters described below. Both effects led to a large decrease in the χ^{2} statistic of the model (>1000), which could not be explained only by the extra number of parameters.
For the finitesource effect, we additionally considered the limbdarkening variation of the source star surface brightness by modelling the surfacebrightness profile as (3)where I_{0,ψ} is the brightness at the centre of the source, and ψ is the angle between a normal to the surface and the line of sight. We adopt the limbdarkening coefficients based on the source type determined from the dereddened colour and brightness (see Sect. 5.1). The values of the adopted coefficients are c_{V} = 0.073,c_{I} = 0.624,c_{R} = 0.542, based on the catalogue of Claret (2000).
Finally, in a third round of modelling, we included both the effects of parallax and finite source size (“ESBL + parallax”). Including these effects together led to a significant improvement of the fit, with Δχ^{2} > 500 compared to the fits in which those effects were added separately. Computing the fstatistic (see e.g. Lupton 1993) for this difference tells us that the probability of this difference occurring solely due to the number of degrees of freedom decreasing by 1 or 2 is highly unlikely. Our bestfit ESBL + parallax model is shown in Fig. 1.
To model the effect of parallax, we used the geocentric formalism (Dominik 1998; An et al. 2002; Gould 2004), which has the advantage of allowing us to obtain a good estimate of t_{0},t_{E} and u_{0} from a fit that does not include parallax. This formalism adds a further 2 parallax parameters, π_{E,E} and π_{E,N}, the components of the lens parallax vector π_{E} projected on the sky along the east and north equatorial coordinates, respectively. The amplitude of π_{E} is then (4)Measuring π_{E} in addition to the source size allows us to break the degeneracy between the mass, distance and transverse velocity of the lens system that is seen in Eq. (1). This is because π_{E} also relates to the lens and source parallaxes π_{L} and π_{S} as (5)Using this in Eq. (1) allows us to solve for the mass of the lens.
As an additional secondorder effect, we also consider the orbital motion of the binary lens. Under the approximation that the change rates of the binary separation and the rotation of the binary axis are uniform during the event, the orbital effect is taken into consideration with 2 additional parameters of ḋ and , which represent the rate of change of the binary separation and the source trajectory angle with respect to the binary axis, respectively. It is found that the improvement of fits by the orbital effect is negligible and thus our bestfit model is based on a static binary lens.
Below we outline our modelling efforts that resulted in fits that were not competitive with our bestfit ESBL + parallax models, and which we therefore excluded in our light curve interpretation.
4.1. Excluded models
4.1.1. Xallarap
We attempted to model the effects of socalled xallarap, orbital motion of the source if it has companion (Griest & Hu 1992). Modelling this requires five additional parameters: the components of the xallarap vector, ξ_{E,N} and ξ_{E,E}, the orbital period P, inclination i and the phase angle ψ of the source orbital motion. By definition, the magnitude of the xallarap vector is the semimajor axis of the source’s orbital motion with respect to the centre of mass, a_{S}, normalised by the projected Einstein radius onto the source plane, , i.e. (6)The value of a_{S} is then related to the semimajor axis of the binary by (7)where M_{1} and M_{2} are the masses of the source components.
Fig. 2 Constraints from the xallarap fit as a function of the orbital period P of the source star. The top panel shows χ^{2} of the xallarap fit as a function of P, with a red circle marking the location of the best parallax model. The bottom panel shows the minimum mass of the source companion as a function of P. The shaded area in both panels indicates where models are excluded based on conservative blending constraints on the source companion’s mass. 

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Fig. 3 Residual of data, with 1σ error bars, for the various models considered. 

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In Fig. 2, we show χ^{2} of the fit plotted as a function of the orbital period of the source star. We compare this to the χ^{2} statistic of the best parallax fit. We find that xallarap models provide fits competitive with the parallax planetary models for orbital periods P > 1 year. However, the solutions in this range cannot meet the constraint provided by the source brightness. Combining Eqs. (6) and (7) with Kepler’s third law, P^{2} = a^{3}/(M_{1} + M_{2}) yields (Dong et al. 2009) (8)Rearranging this equation for M_{2}, and using the fact that M2/(M_{1} + M_{2}) < 1, we can derive an lower limit for the mass of M_{2}, (9)In the lower panel of Fig. 2, we show the minimum mass of the source companion as a function of orbital period. The blending constraint means that the source companion cannot be arbitrarily massive, and we use a conservative upper limit for its mass of 3 M_{⊙}. With this constraint, we find that xallarap models are not competitive with parallax planetary models, and we therefore exclude the xallarap interpretation of the light curve.
4.1.2. Binary source
We also attempted to model this event as a binary source  point lens (BSPL) event; indeed it has been shown that binary sources can sometimes mimic planetary signals (Gaudi 1998). For this we introduced three additional parameters: the impact parameter of the secondary source component, u_{0,2}, and its time of closest approach, t_{0,2}, as well the flux ratio between the source components. We note that parallax is also considered in our binary source modelling, for fair comparison to other models. We find that the best binarysource model provides a poorer fit, with χ^{2} = 3809, which gives Δχ^{2} ~ 180 compared to our best planetary model (including parallax, see model D in the following section). Residuals for this model, as well as all other models discussed in this section are shown in Fig. 3.
4.2. Bestfit models
We searched the parameter space using an MCMC algorithm as well as a grid of (d,q,α) to locate good starting points for the algorithm (see e.g. Kains et al. 2009), over the range −4 < log q < 0 and −1.0 < log d < 2. This encompasses both planetary and binary companions that might cause the central perturbation. In Fig. 4 we present the χ^{2} distribution in the d,q plane. We find four local solutions, all of which have a mass ratio corresponding to a planetary companion. We designate them as A, B, C and D; the degeneracy among these local solutions is rather severe, as can be seen from the residuals shown in Fig. 3.
For the identified local minima, we then further refine the lensing parameters by conducting additional modelling, considering higherorder effects of the finite source size and the Earth’s orbital motion. It is found that the higherorder effects are clearly detected with Δχ^{2} > 500. Bestfit parameter for each of the local minima are given in Table 2, while Fig. 5 shows the geometry of the source trajectories with respect to the caustics for all four minima. We note that the pairs of solutions A and D, and B and C, are degenerate under the wellknown d ↔ d^{1} degeneracy (Griest & Safizadeh 1998; Dominik 1999); this is caused by the symmetry of the lens mapping between binaries with d and d^{1}. Comparing the pairs of solutions, we find that the AD pair is favoured, with Δχ^{2} > 40 compared to the BC pair. On the other hand, the degeneracy between the A and D solutions is very severe, with only Δχ^{2} ~ 7. In Fig. 6, we also show parameterparameter correlations plots for model D, showing also the uncertainties in the measured lensing parameters.
Fig. 4 χ^{2} map in the d,q plane, showing the location of the four local minima identified by our modelling runs. Out of these, local minima A and D are competitive, with local minima B and C having Δχ^{2} ~ 50 and 70 respectively, for the same number of parameters. Minima A and D correspond to the close and wide ESBL + parallax models discussed in the text. Different colours correspond to Δχ^{2} < 25 (red), 100 (yellow), 225 (green), and 400 (blue); we note that the χ^{2} map is based on the original data, before errorbar normalisation, and therefore the Δχ^{2} levels are slightly different from those given in Table 2. The top panel shows the breadth of our parameter space exploration, encompassing planetary and nonplanteray massratio regimes, while the bottom panel shows a zoom on the region where our local minima are located. 

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Bestfit model parameters and 1σ error bars for the four identified best binarylens models including the effects of the orbital motion of the Earth (parallax).
Fig. 5 Source trajectory geometry with respect to the caustics for all four local minima identified in Fig. 4; the source size is marked as a red circle. 

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Fig. 6 Parameterparameter correlations for our 9 fitted parameters. Colours indicate the limits of the 1, 2, 3, 4 and 5σ confidence limits for each pairwise distribution. A closer view of the correlation between parallax parameters is shown on the top right inset. 

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5. Lens properties
In this section we determine the properties of the lens system, using our bestfit model parameters, i.e. our wideconfiguration ESBL + parallax model. We also calculated the lens properties for the competitive closeconfiguration model, with both sets of parameter values listed in Table 3.
5.1. Source star and Einstein radius
Fig. 7 V − I,I colour–magnitude diagram of the OGLE2011BLG0251 field obtained using OGLEIV photometry. The location of the total source + blend is indicated by a green asterisk, while the location of the deblended source is marked by a blue filled circle, and that of the blend by a red cross. The dashed lines cross at the location of the Red Clump. 

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We determined the Einstein radius by first calculating the angular size of the source. This can be done by using the magnitude and colour of the source (e.g. Yoo et al. 2004), and empirical relations between these quantities and the angular source size. We start by using the location of the red giant clump (hereafter RC) on our colour–magnitude diagram (Fig. 7) to estimate the reddening and extinction along the line of sight. We use an Iband absolute magnitude for the RC of M_{I,RC,0} = −0.12 ± 0.09 (Nataf et al. 2012), as well as a colour (V − I)_{RC,0} = 1.06 ± 0.12 (Bensby et al. 2011). We compare these values to those on our colour–magnitude diagram (CMD), which we generated using OGLE I and Vband photometry. From Fig. 7, the location of the RC on our CMD is (10)so, using a distance modulus of μ = 14.52 ± 0.09, i.e. a distance to the Galactic bulge of 8.0 ± 0.3 kpc (Yelda et al. 2011), we find A_{I} = 2.79 ± 0.10 and E(V − I) = 2.39 ± 0.13.
Using these values, the bestfit value for the magnitude of the source I_{S} = 15.97 ± 0.01, a source colour (V − I)_{S,0} = 1.15, and the empirical relations of Kervella & Fouqué (2008), we find an angular source radius θ_{ ∗ } = 10.41 ± 1.18 μas, or a source star radius of R_{ ∗ } = 10.53 ± 1.19 R_{⊙}. This, together with the bestfit value of the source size parameter ρ_{ ∗ }, allows us to calculate the size of the Einstein radius, θ_{E} = θ_{ ∗ }/ρ_{ ∗ }. Using the relevant parameter values, we find θ_{E} = 0.749 ± 0.283 mas. This in turn allows us to calculate the sourcelens relative proper motion, μ_{rel} = θ_{E}/t_{E} = 4.28 ± 1.62 mas/yr.
5.2. Masses of the lens components
Combining Eq. (1) and Eq. (5) allows us to derive an expression for the mass as a function of the parallax vector magnitude π_{E} (defined by Eq. (4)): (11)Using values found in the previous section, and our bestfit parallax parameter value π_{E} = 0.35 ± 0.05 yields a total lens mass M_{L} = 0.26 ± 0.10 M_{⊙}. Using the bestfit mass ratio parameter value of q = (1.92 ± 0.12) × 10^{3} yields component masses of 0.26 ± 0.11 M_{⊙} and 0.53 ± 0.21 M_{J}, where M_{J} is the mass of Jupiter.
5.3. Distance to the lens
We can also rearrange Eq. (1) to derive an expression for the distance to the lens D_{L}, (12)Using our parameter values as well as the lens mass derived thanks to our parallax measurement, we find a distance to the lens of D_{L} = 2.57 ± 0.61 kpc. This distance allows us to carry out a sanity check of the lens mass we derived in the previous section. By assuming that the contribution from the blended light comes from the lens, we can derive an upper limit to the Iband lens magnitude M_{I} using our bestfit blending parameter: (13)where m_{I,b} is the apparent Iband magnitude of the blend, A_{I,L} is the extinction between the observer and the lens, and D_{L} is in kpc. In practice, A_{I,L} ≤ A_{I} since the lens is in front of the source, so we use the extreme scenario where A_{I,L} = A_{I} to derive an upper brightness limit (lower limit on the magnitude) for the lens. We find this to be M_{I,L} = 2.19 ± 0.53 mag, which corresponds to a maximum mass of the lens of M_{L,max} = 1.65 ± 0.23 M_{⊙}, assuming a main sequence star massluminosity relation, and assuming that the secondary lens component (i.e. the planet) does not contribute to the blended light. This is much larger than the value we derived in Sect. 5.2 for the mass of the primary lens component, which suggests that some blending comes from stars near the source rather than from the lens, although it is difficult to quantify this without an estimate of A_{I,L}.
Finally, we can also use the distance to the lens and the size of the Einstein ring radius to calculate the projected separation r_{⊥} between the lens components in AU. Using our bestfit projected angular separation d = 1.408 ± 0.019, we find a projected (i.e. minimum) orbital radius r_{⊥} = 2.72 ± 0.75 AU.
We can compare this to an estimate of the location of the “snow line”, which is the location at which water sublimated in the midplane of the protoplanetary disk, i.e. the distance at which the midplane had a temperature of T_{mid} = 170 K (although other studies have noted that this temperature varies; see e.g. Podolak & Zucker 2004). The core accretion model of planet formation predicts that giant planets form much more easily beyond the snow line, thanks to easier condensation of icy material and therefore easier formation of large solid cores in the early stages of the circumstellar disk’s evolution. Kennedy & Kenyon (2008) modelled the evolution of the snow line’s location, taking into account heating of the disk via accretion, as well as the influence of premain sequence stellar evolution. Using a rough extrapolation of their results, we estimate that the snow line (at t = 1 Myr) for the planetary host star in OGLE2011BLG0251 is located at around ~1−1.5 AU. We therefore conclude that OGLE2011BLG0251Lb is a giant planet located beyond the snow line, with both of our competitive bestfit models yielding projected orbital radii larger than 1.5 AU.
We list all the lens properties in Table 3, both for the bestfit model parameters that we have used above, and for the closeconfiguration model, for comparison. Lens properties derived using the closeconfiguration model are very similar to those we found using the wideconfiguration model, the only major difference being in the orbital radius. For the close model, we find an orbital radius of 1.50 ± 0.50 AU, which is close to the location of the snow line.
6. Conclusions
Our coverage and analysis of OGLE2011BLG0251 has allowed us to locate and constrain a bestfit binarylens model corresponding to an M star being orbited by a giant planet. This was possible through a broad exploration of the parameters both in real time, thanks to the recent developments in microlensing modelling algorithms, and after the source had returned to its baseline magnitude. Various secondorder effects, as well as other possible, nonplanetary, interpretations for the anomaly were considered during the modelling process. Based on the bestfit solution, we were able to constrain the masses and separation of the lens components, as well as various other characteristics, thanks to a strong detection of parallax effects due to the Earth’s orbit around the Sun, in conjunction with the detection of finite source size effects. We found a planet of mass 0.53 ± 0.21 M_{J} orbiting a lens of 0.26 ± 0.11 M_{⊙} at a projected radius r_{⊥} = 2.72 ± 0.75 AU; the whole system is located at a distance of 2.57 ± 0.61 kpc. Our competitive secondbest model leads to similar properties, but a smaller projected orbital radius r_{⊥} = 1.50 ± 0.50. The two bestfit models are competitive and therefore we cannot make a strong claim about which orbital radius is favoured. However, comparing both values of the projected orbital radius to the approximate location of the snow line for a typical star of the mass of the primary lens component, we conclude that OGLE2011BLG0251Lb is a giant planet located around or beyond the snow line. This is in line with predictions from the core accretion model of planet formation, from which we expect large planets to be more numerous beyond the snow line; this is also where microlensing detection sensitivity is at its highest, enabling us to probe a region of planetary parameter space that is difficult to reach for other methods.
Acknowledgments
N.K. acknowledges an ESO Fellowship. The research leading to these results has received funding from the European Community’s Seventh Framework Programme (/FP7/20072013/) under grant agreements No 229517 and 268421. The OGLE project has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/20072013) / ERC grant agreement No. 246678 to AU. K.A., D.B., M.D., K.H., M.H., S.I., C.L., R.S., Y.T. are supported by NPRP grant NPRP09476178 from the Qatar National Research Fund (a member of Qatar Foundation). Work by C. Han was supported by Creative Research Initiative Program (20090081561) of National Research Foundation of Korea. This work is based in part on data collected by MiNDSTEp with the Danish 1.54 m telescope at the ESO La Silla Observatory. The Danish 1.54 m telescope is operated based on a grant from the Danish Natural Science Foundation (FNU). The MiNDSTEp monitoring campaign is powered by ARTEMiS (Automated Terrestrial Exoplanet Microlensing Search; Dominik et al. 2008). M.H. acknowledges support by the German Research Foundation (DFG). D.R. (boursier FRIA), O.W. (aspirant FRS – FNRS) and J. Surdej acknowledge support from the Communauté française de Belgique – Actions de recherche concertées – Académie universitaire WallonieEurope. T.C.H. gratefully acknowledges financial support from the Korea Research Council for Fundamental Science and Technology (KRCF) through the Young Research Scientist Fellowship Program. T.C.H. and C.U.L. acknowledge financial support from KASI (Korea Astronomy and Space Science Institute) grant number 2012141002. Work by J. C. Yee is supported by a National Science Foundation Graduate Research Fellowship under Grant No. 2009068160. A. Gould and B. S. Gaudi acknowledge support from NSF AST1103471. B. S. Gaudi, A. Gould, and R. W. Pogge acknowledge support from NASA grant NNX12AB99G. The MOA experiment was supported by grants JSPS22403003 and JSPS23340064. T.S. was supported by the grant JSPS23340044. Y. Muraki acknowledges support from JSPS grants JSPS23540339 and JSPS19340058.
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All Tables
Data sets for OGLE2011BLG0251, with the number of data points for each telescope/filter combination.
Bestfit model parameters and 1σ error bars for the four identified best binarylens models including the effects of the orbital motion of the Earth (parallax).
All Figures
Fig. 1 Light curve of OGLE2011BLG0251. Data points are plotted with 1σ error bars, and the upper panel shows a zoom around the perturbation region near the peak 

Open with DEXTER  
In the text 
Fig. 2 Constraints from the xallarap fit as a function of the orbital period P of the source star. The top panel shows χ^{2} of the xallarap fit as a function of P, with a red circle marking the location of the best parallax model. The bottom panel shows the minimum mass of the source companion as a function of P. The shaded area in both panels indicates where models are excluded based on conservative blending constraints on the source companion’s mass. 

Open with DEXTER  
In the text 
Fig. 3 Residual of data, with 1σ error bars, for the various models considered. 

Open with DEXTER  
In the text 
Fig. 4 χ^{2} map in the d,q plane, showing the location of the four local minima identified by our modelling runs. Out of these, local minima A and D are competitive, with local minima B and C having Δχ^{2} ~ 50 and 70 respectively, for the same number of parameters. Minima A and D correspond to the close and wide ESBL + parallax models discussed in the text. Different colours correspond to Δχ^{2} < 25 (red), 100 (yellow), 225 (green), and 400 (blue); we note that the χ^{2} map is based on the original data, before errorbar normalisation, and therefore the Δχ^{2} levels are slightly different from those given in Table 2. The top panel shows the breadth of our parameter space exploration, encompassing planetary and nonplanteray massratio regimes, while the bottom panel shows a zoom on the region where our local minima are located. 

Open with DEXTER  
In the text 
Fig. 5 Source trajectory geometry with respect to the caustics for all four local minima identified in Fig. 4; the source size is marked as a red circle. 

Open with DEXTER  
In the text 
Fig. 6 Parameterparameter correlations for our 9 fitted parameters. Colours indicate the limits of the 1, 2, 3, 4 and 5σ confidence limits for each pairwise distribution. A closer view of the correlation between parallax parameters is shown on the top right inset. 

Open with DEXTER  
In the text 
Fig. 7 V − I,I colour–magnitude diagram of the OGLE2011BLG0251 field obtained using OGLEIV photometry. The location of the total source + blend is indicated by a green asterisk, while the location of the deblended source is marked by a blue filled circle, and that of the blend by a red cross. The dashed lines cross at the location of the Red Clump. 

Open with DEXTER  
In the text 
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