Planetary Orbital Motion Research Articles

Keck and Hubble Observations Show that MOA-2008-BLG-379Lb is a Super-Jupiter Orbiting an M Dwarf

We present high angular resolution imaging that detects the MOA-2008-BLG-379L exoplanet host star using Keck adaptive optics and the Hubble Space Telescope. These observations reveal host star and planet masses of M host = 0.434 ± 0.065 M ⊙ and m p = 2.44 ± 0.49 M Jupiter. They are located at a distance of D L = 3.44 ± 0.53 kpc, with a projected separation of 2.70 ± 0.42 au. These results contribute to our determination of exoplanet host star masses for the Suzuki et al. statistical sample, which will determine the dependence of the planet occurrence rate on the mass and distance of the host stars. We also present a detailed discussion of the image-constrained modeling version of the eesunhong light-curve modeling code that applies high angular resolution image constraints to the light-curve modeling process. This code increases modeling efficiency by a large factor by excluding models that are inconsistent with the high angular resolution images. The analysis of this and other events from the Suzuki et al. statistical sample reveals the importance of including higher-order effects, such as microlensing parallax and planetary orbital motion, even when these features are not required to fit the light-curve data. The inclusion of these effects may be needed to obtain accurate estimates of the uncertainty of other microlensing parameters that affect the inferred properties of exoplanet microlens systems. This will be important for the exoplanet microlensing survey of the Roman Space Telescope, which will use both light-curve photometry and high angular resolution imaging to characterize planetary microlens systems.

Constraining stellar tidal quality factors from planet‐induced stellar spin‐up

AbstractThe dynamical evolution of tight star‐planet systems is influenced by tidal interactions between the star and the planet, as was shown recently. The rate at which spins and orbits in such a system evolve depends on the stellar and planetary tidal dissipation efficiency. Here, we present a method to constrain the modified tidal quality factor of a planet‐hosting star whose rotational evolution has been altered by its planet through angular momentum transfer from the planetary orbital motion to the rotation of the stellar convective zone. The altered rotation is estimated from an observed discrepancy of magnetic activity of the planet‐hosting star and a coeval companion star, that is, this method is applicable to star‐planet systems with wide stellar companions. We give an example of the planet‐hosting wide binary system HD189733 and find that the planet host's modified tidal quality factor is constrained to be .

Связи изменений ледовой обстановки на Северном морском пути с движением планет Солнечной системы

The paper considers the progress in the hydrographic support for navigation in various parts of the Northern Sea Route in terms of improving the methods for developing tentative forecasts of interannual changes of ice conditions. Among the approaches to solve the task the authors take into account factors that do not depend on the uncertainty of regional climate changes in the future. One of such factors is the main mechanical process in the Solar System — the orbital planetary motion. The paper goal is to confirm the existence of water areas in the seas under study, changes in the ice coverage of which in the summer-autumn period can be significantly associated with planetary orbital motion factor. The authors apply statistical methods to achieve the study goal. As factual material on changes in the ice coverage of the sections of the Northern Sea Route, they use information of GLORYS12v1 and ICDC global reanalysis databases for the period 1993—2019 and 1979—2020 respectively. As a result the authors have revealed locations of the water areas, for which the reliability of the conclusion about the significance of the relationship under consideration in certain months is at least 90%. They have stated that the reliability of such inference is the highest for some water areas of the East Siberian Sea in October and the Chukchi Sea in November. To confirm the suitability of the identified links for the development of tentative forecasts of trends in interannual changes in the ice conditions on the Northern Sea Route, the authors insist on additional testing to check the resistance to updating the actual material.

External Forcing of the Solar Dynamo

In this paper I examine whether external forcing of the solar dynamo on long timescales can produce detectable signal in the form of long term modulation of the magnetic cycle. This task is motivated in part by some recent proposals (Abreu et al., 2012; Astron. Ap., 548, A88; Stefani et al., 2021; Solar Phys., 296, 88), whereby modulation of the solar activity cycle on centennial and millennial timescales, as recovered from the cosmogenic radioisotope record, is attributed to perturbation of the tachocline driven by planetary orbital motions. Working with a two-dimensional mean-field-like kinematic dynamo model of the Babcock-Leighton variety, I show that such an external forcing signal may be detectable in principle but is likely to be obliterated by other internal sources of fluctuations, in particular stochastic perturbations of the dynamo associated with convective turbulence, unless a very efficient amplification mechanism is at play. I also examine the ability of external tidal forcing to synchronize an otherwise autonomous, internal dynamo operating at a nearby frequency. Synchronization is readily achieved, and turns out to be very robust to the introduction of stochastic noise, but requires very high forcing amplitudes, again highlighting the critical need for a powerful amplification mechanism.

Detecting Atmospheric Molecules of Nontransiting Temperate Terrestrial Exoplanets Using High-resolution Spectroscopy in the Mid-infrared Domain

Abstract Motivated by the development of high-dispersion spectrographs in the mid-infrared (MIR) range, we study their application to the atmospheric characterization of nearby nontransiting temperate terrestrial planets around M-type stars. We examine the detectability of CO2, H2O, N2O, and O3 features in high-resolution planetary thermal emission spectra at 12–18 μm assuming an Earth-like profile and a simplified thermal structure. The molecular line width of such planets can be comparable to or broader than the Doppler shift due to the planetary orbital motion. Given the likely difficulty in knowing the high-resolution MIR spectrum of the host star with sufficient accuracy, we propose observing the target system at two quadrature phases and extracting the differential spectra as the planetary signal. In this case, the signals can be substantially suppressed compared with the case where the host star spectrum is perfectly known, as some parts of the spectral features do not remain in the differential spectra. Despite this self-subtraction, the CO2 and H2O features of nearby (≲5 pc) systems with mid-/late-M host stars would be feasible with a 6.5 m class cryogenic space telescope, and orbital inclination could also be constrained for some of them. For CO2 and N2O in a 1 bar Earth-like atmosphere, this method would be sensitive when the mixing ratio is 1–103 ppm. The detectability of molecules except O3 is not significantly improved when the spectral resolution is higher than , although the constraint on the orbital inclination is improved. This study provides some benchmark cases useful for assessing the value of MIR high-resolution spectroscopy in terms of characterization of potentially habitable planets.

Detection of Na in WASP-21b’s lower and upper atmosphere

Optical transmission spectroscopy provides crucial constraints on the reference pressure levels and scattering properties for the atmospheres of hot Jupiters. For certain planets, where alkali atoms are detected in the atmosphere, their line profiles could serve as a good probe to link upper and lower atmospheric layers. The planet WASP-21b is a Saturn-mass hot Jupiter orbiting a thick-disk star, with a low density and an equilibrium temperature of 1333 K, which makes it a good target for transmission spectroscopy. Here, we present a low-resolution transmission spectrum for WASP-21b based on one transit observed by the OSIRIS spectrograph at the 10.4 m Gran Telescopio Canarias (GTC), and a high-resolution transmission spectrum based on three transits observed by HARPS-N at Telescopio Nazinale Galileo (TNG) and HARPS at the ESO 3.6 m telescope. We performed spectral retrieval analysis on GTC’s low-resolution transmission spectrum and report the detection of Na at a confidence level of >3.5-σ. The Na line exhibits a broad line profile that can be attributed to pressure broadening, indicating a mostly clear planetary atmosphere. The spectrum shows a tentative excess absorption at the K D1 line. Using HARPS-N and HARPS, we spectrally resolved the Na doublet transmission spectrum. An excess absorption at the Na doublet is detected during the transit, and shows a radial velocity shift consistent with the planet orbital motion. We proposed a metric to quantitatively distinguish hot Jupiters with relatively clear atmospheres from others, and WASP-21b has the largest metric value among all the characterized hot Jupiters. The detection of Na both in the lower and upper atmospheres of WASP-21b reveals that it is an ideal target for future follow-up observations, providing the opportunity to understand the nature of its atmosphere across a wide range of pressure levels.

Modelling atmospheric escape and Mg ii near-ultraviolet absorption of the highly irradiated hot Jupiter WASP-12b

We present two-dimensional multi-fluid numerical modelling of the upper atmosphere of the hot Jupiter WASP-12b. The model includes hydrogen chemistry, and self-consistently describes the expansion of the planetary upper atmosphere and mass loss due to intensive stellar irradiation, assuming a weakly magnetized planet. We simulate the planetary upper atmosphere and its interaction with the stellar wind (SW) with and without the inclusion of tidal force and consider different XUV irradiation conditions and SW parameters. With the inclusion of tidal force, even for a fast SW, the escaping planetary material forms two streams, propagating towards and away from the star. The atmospheric escape and related mass loss rate reaching the value of 10^12 gs^-1 appear to be mostly controlled by the stellar gravitational pull. We computed the column density and dynamics of MgII ions considering three different sets of SW parameters and XUV fluxes. The simulations enable to compute the absorption at the position of the Mg h line and to reproduce the times of ingress and egress. In case of a slow SW and without accounting for tidal force, the high orbital velocity leads to the formation of a shock approximately in the direction of the planetary orbital motion. In this case, mass loss is proportional to the stellar XUV flux. At the same time, ignoring of tidal effects for WASP-12b is a strong simplification, so the scenario with a shock, altogether is an unrealistic one.

An extended hydrogen envelope of the extremely hot giant exoplanet KELT-9b

Giant exoplanets orbiting close to their host stars have high temperatures because of the immense stellar irradiation which they receive. The extreme energy input leads to the expansion of the atmosphere and the escape of neutral hydrogen. A particularly intriguing case among the hot giant planets is KELT-9b -- an exoplanet orbiting very close to an early A-type star with the highest temperature (~4600 K at day-side) among all the exoplanets known so far. The atmospheric composition and dynamic of such a unique planet have been unknown. Here we report the first detection of an extended hot hydrogen atmosphere around KELT-9b. The detection was achieved by measuring the atomic hydrogen absorption during transit with the Balmer H{\alpha} line, which is unusually strong mainly due to the high level of extreme-ultraviolet radiation from the star. We detected a significant wavelength shift of the H{\alpha} absorption which is mostly attributed to the planetary orbital motion. The obtained transmission spectrum has a significant line contrast (1.15% extra absorption at the H{\alpha} line centre). The observation implies that the effective radius at the H{\alpha} line centre is ~1.64 times the size of the planetary radius, indicating the planet has a largely extended hydrogen envelope close to the size of the Roche lobe (1.91 Rplanet) and is probably undergoing dramatic atmosphere escape.

Effective Induction Heating around Strongly Magnetized Stars

Abstract Planets that are embedded in the changing magnetic fields of their host stars can experience significant induction heating in their interiors caused by the planet’s orbital motion. For induction heating to be substantial, the planetary orbit has to be inclined with respect to the stellar rotation and dipole axes. Using WX UMa, for which the rotation and magnetic axes are aligned, as an example, we show that for close-in planets on inclined orbits, induction heating can be stronger than the tidal heating occurring inside Jupiter’s satellite Io; namely, it can generate a surface heat flux exceeding 2 W m−2. An internal heating source of such magnitude can lead to extreme volcanic activity on the planet’s surface, possibly also to internal local magma oceans, and to the formation of a plasma torus around the star aligned with the planetary orbit. A strongly volcanically active planet would eject into space mostly SO2, which would then dissociate into oxygen and sulphur atoms. Young planets would also eject CO2. Oxygen would therefore be the major component of the torus. If the O i column density of the torus exceeds ≈1012 cm−2, the torus could be revealed by detecting absorption signatures at the position of the strong far-ultraviolet O i triplet at about 1304 Å. We estimate that this condition is satisfied if the O i atoms in the torus escape the system at a velocity smaller than 1–10 km s−1. These estimates are valid also for a tidally heated planet.

Magma oceans and enhanced volcanism on TRAPPIST-1 planets due to induction heating

Low-mass M stars are plentiful in the Universe and often host small, rocky planets detectable with the current instrumentation. Recently, seven small planets have been discovered orbiting the ultracool dwarf TRAPPIST-1\cite{Gillon16,Gillon17}. We examine the role of electromagnetic induction heating of these planets, caused by the star's rotation and the planet's orbital motion. If the stellar rotation and magnetic dipole axes are inclined with respect to each other, induction heating can melt the upper mantle and enormously increase volcanic activity, sometimes producing a magma ocean below the planetary surface. We show that induction heating leads the three innermost planets, one of which is in the habitable zone, to either evolve towards a molten mantle planet, or to experience increased outgassing and volcanic activity, while the four outermost planets remain mostly unaffected.

EXOPLANETARY DETECTION BY MULTIFRACTAL SPECTRAL ANALYSIS

ABSTRACT Owing to technological advances, the number of exoplanets discovered has risen dramatically in the last few years. However, when trying to observe Earth analogs, it is often difficult to test the veracity of detection. We have developed a new approach to the analysis of exoplanetary spectral observations based on temporal multifractality, which identifies timescales that characterize planetary orbital motion around the host star and those that arise from stellar features such as spots. Without fitting stellar models to spectral data, we show how the planetary signal can be robustly detected from noisy data using noise amplitude as a source of information. For observation of transiting planets, combining this method with simple geometry allows us to relate the timescales obtained to primary and secondary eclipse of the exoplanets. Making use of data obtained with ground-based and space-based observations we have tested our approach on HD 189733b. Moreover, we have investigated the use of this technique in measuring planetary orbital motion via Doppler shift detection. Finally, we have analyzed synthetic spectra obtained using the SOAP 2.0 tool, which simulates a stellar spectrum and the influence of the presence of a planet or a spot on that spectrum over one orbital period. We have demonstrated that, so long as the signal-to-noise-ratio ≥ 75, our approach reconstructs the planetary orbital period, as well as the rotation period of a spot on the stellar surface.

CAUSTIC STRUCTURES AND DETECTABILITY OF CIRCUMBINARY PLANETS IN MICROLENSING

Recent discoveries of circumbinary planets in Kepler data show that there is a viable channel of planet formation around binary main sequence stars. Motivated by these discoveries, we have investigated the caustic structures and detectability of circumbinary planets in microlensing events. We have produced a suite of animations of caustics as a function of the projected separation and angle of the binary host to efficiently explore caustic structures over the entire circumbinary parameter space. Aided by these animations, we have derived a semi-empirical analytic expression for the location of planetary caustics, which are displaced in circumbinary lenses relative to those of planets with a single host. We have used this expression to show that the dominant source of caustic motion will be due to the planet's orbital motion and not that of the binary star. Finally, we estimate the fraction of circumbinary microlensing events that are recognizable as such to be significant (5-50 percent) for binary projected separations in the range 0.1-0.5 in units of Einstein radii.

Seasonal changes on Jupiter: 1. Factor of activity of the hemispheres

To identify temporal variations of the characteristics of Jupiter’s cloud layer, we take into account the geometric modulation caused by the rotation of the planet and planetary orbital motion. Inclination of the rotation axis to the orbital plane of Jupiter is 3.13°, and the angle between the magnetic axis and the rotation axis is β ≈ 10°. Therefore, over a Jovian year, the jovicentric magnetic declination of the Earth φm varies from–13.13° to +13.13°, and the subsolar point on Jupiter’s magnetosphere is shifted by 26.26° per orbital period. In this connection, variations of the Earth’s jovimagnetic latitude on Jupiter will have a prevailing influence in the solar-driven changes of reflective properties of the cloud cover and overcloud haze on Jupiter. Because of the orbit eccentricity (e = 0.048450), the northern hemisphere receives 21% greater solar energy inflow to the atmosphere, because Jupiter is at perihelion near the time of the summer solstice. The results of our studies have shown that the brightness ratio Aj of northern to southern tropical and temperate regions is an evident factor of photometric activity of Jupiter’s atmospheric processes. The analysis of observational data for the period from 1962 to 2015 reveals the existence of cyclic variations of the activity factor Aj of the planetary hemispheres with a period of 11.86 years, which allows us to talk about the seasonal rearrangement of Jupiter’s atmosphere.

Spectrally resolved detection of sodium in the atmosphere of HD 189733b with the HARPS spectrograph

Atmospheric properties of exoplanets can be constrained with transit spectroscopy. The signature of atomic sodium NaI, known to be present above the clouds, is a powerful probe of the upper atmosphere, where it can be best detected and characterized at high spectral resolution. Our goal is to obtain a high-resolution transit spectrum of HD189733b in the region around the resonance doublet of NaI at 589 nm, to characterize the absorption signature previously detected from space at low resolution. We analyze archival transit data of HD189733b obtained with the HARPS spectrograph. We retrieve the transit spectrum and light curve of the planet, implementing corrections for telluric contamination and planetary orbital motion. We spectrally resolve the NaI D doublet and measure line contrasts of $0.64\pm0.07\%$ (D2) and $0.40\pm0.07\%$ (D1) and FWHMs of $0.52\pm0.08~\AA$. This corresponds to a detection at the 10-$\sigma$ level of excess of absorption of $0.32\pm0.03\%$ in a passband of $2\times0.75\ \AA$ centered on each line. We derive temperatures of $2\,600\pm600$ K and $3270\pm330$ K at altitudes of $9\,800\pm2\,800$ km and $12\,700\pm2\,600$ km in the NaI D1 and D2 line cores, respectively. We measure a temperature gradient of $\sim0.2$ K km$^{-1}$ from comparison with theoretical models. We also detect a blueshift of $0.16\pm0.04\ \AA$ (4 $\sigma$) in the line positions. This blueshift may be due to winds blowing at $8\pm2$ km s$^{-1}$ in the upper layers of the atmosphere. We demonstrate the relevance of studying exoplanet atmospheres with high-resolution spectrographs mounted on 4-meter-class telescopes. Our results pave the way towards in-depth characterization of physical conditions in the atmospheres of many exoplanetary systems with future spectrographs such as ESPRESSO on the VLT or HiReS and METIS on the E-ELT.

Stellar diameters and temperatures – VI. High angular resolution measurements of the transiting exoplanet host stars HD 189733 and HD 209458 and implications for models of cool dwarfs

We present direct radii measurements of the well-known transiting exoplanet host stars HD 189733 and HD 209458 using the CHARA Array interferometer. We find the limb-darkened angular diameters to be θLD = 0.3848 ± 0.0055 and 0.2254 ± 0.0072 mas for HD 189733 and HD 209458, respectively. HD 189733 and HD 209458 are currently the only two transiting exoplanet systems where detection of the respective planetary companion's orbital motion from high-resolution spectroscopy has revealed absolute masses for both star and planet. We use our new measurements together with the orbital information from radial velocity and photometric time series data, Hipparcos distances, and newly measured bolometric fluxes to determine the stellar effective temperatures (Teff = 4875 ± 43, 6092 ± 103 K), stellar linear radii (R* = 0.805 ± 0.016, 1.203 ± 0.061 R⊙), mean stellar densities (ρ* = 1.62 ± 0.11, 0.58 ± 0.14 ρ⊙), planetary radii (Rp = 1.216 ± 0.024, 1.451 ± 0.074 RJup), and mean planetary densities (ρp = 0.605 ± 0.029, 0.196 ± 0.033 ρJup) for HD 189733b and HD 209458b, respectively. The stellar parameters for HD 209458, an F9 dwarf, are consistent with indirect estimates derived from spectroscopic and evolutionary modelling. However, we find that models are unable to reproduce the observational results for the K2 dwarf, HD 189733. We show that, for stellar evolutionary models to match the observed stellar properties of HD 189733, adjustments lowering the solar-calibrated mixing-length parameter to αMLT =1.34 need to be employed.

F (T) gravity: effects on astronomical observations and Solar system experiments and upper bounds

The effects of the f (T) gravity have previously been investigated and constrained by using perihelion advances. As an extension of previous work and as an attempt to find more stringent constraints on its parameters, we investigate here its effects on astronomical observations and on experiments conducted in the Solar system. The expression for f (T) contains a quadratic correction of α*T2 (where α is a model parameter) and the cosmological constant Λ. Using a spherical solution describing the Sun's gravitational field, the resulting secular evolution of planetary orbital motions, in addition to the light deflection, gravitational time delay and frequency shift are calculated up to the leading contribution. From these results, we find qualitatively that the light deflection provides a unique bound on α, without dependence on Λ, and that the time delay experiments during inferior conjunction impose a clean constraint on Λ, regardless of α. Based on observations and experiments, especially the supplementary advances in the perihelia provided by the INPOP10a ephemeris, we obtain the upper bounds quantitatively: |α| ≤ 1.2 × 102 m2 and |Λ| ≤ 1.8 × 10−43 m−2, which are at least 10 times tighter than the previous results.

THREE-DIMENSIONAL GAS DYNAMIC SIMULATION OF THE INTERACTION BETWEEN THE EXOPLANET WASP-12b AND ITS HOST STAR

HST transit observations in the near-UV performed in 2009 made WASP-12b one of the most "mysterious" exoplanets; the system presents an early-ingress, which can be explained by the presence of optically thick matter located ahead of the planet at a distance of 4-5 planet radii. This work follows previous attempts to explain this asymmetry with an exospheric outflow or a bow shock, induced by a planetary magnetic field, and provides a numerical solution of the early-ingress, though we did not perform any radiative transfer calculation. We performed pure 3D gas dynamic simulations of the plasma interaction between WASP-12b and its host star, and describe the flow pattern in the system. In particular, we show that the overfilling of the planet's Roche lobe leads to a noticeable outflow from the upper atmosphere in the direction of the L1 and L2 points. Due to the conservation of the angular momentum, the flow to the L1 point is deflected in the direction of the planet's orbital motion, while the flow towards L2 is deflected in the opposite direction, resulting in a non-axisymmetric envelope, surrounding the planet. The supersonic motion of the planet inside the stellar wind leads to the formation of a bow shock with a complex shape. The existence of the bow shock slows down the outflow through the L1 and L2 points, allowing us to consider a long-living flow structure which is in the steady-state.

Local cosmological effects of the order of H in the orbital motion of a binary system

A two-body system hypothetically affected by an additional radial acceleration H v_r, where v_r is the radial velocity of the binary's proper orbital motion, would experience long-term temporal changes of both its semimajor axis a and the eccentricity e qualitatively different from any other standard competing effect for them. Contrary to what one might reasonably expect, the analytical expressions of such rates do not vanish in the limit M--> 0, where M is the mass of the primary, being independent of it. This is a general requirement that any potentially viable physical mechanism able to provide such a putative acceleration should meet. Nonetheless, if H had the same value H_0 of the Hubble parameter at present epoch, such rates of change would have magnitude close to the present-day level of accuracy in determining planetary orbital motions in our Solar System. A tension with recent observations may even be present for Mercury and Mars. However, general relativity, applied to a localized gravitationally bound binary system immersed in an expanding Friedmann-Lemaitre-Robertson-Walker, does not predict the existence of such a putative radial acceleration at Newtonian level. Instead, it was recently shown in literature that an acceleration of order H and directed along the velocity v of the test particle occurs at post-Newtonian level. We worked out its orbital effects finding well-behaved secular rates of change for both a and e proportional to the Schwarzschild radius r_s of the primary. Their magnitude is quite small: the rate of change of a amounts to just 20 microns per century in our Solar System. Finally, we discussed certain basic criteria of viability that modified models of gravity should generally meet when their observable effects are calculated.

Constraining the Angular Momentum of the Sun with Planetary Orbital Motions and General Relativity

The angular momentum of a star is an important astrophysical quantity related to its internal structure, formation and evolution. On average, helioseismology yields S = 1.92 10^41 kg m^2 s^-1 for the angular momentum of the Sun. We show how it should be possible to measure or, at least, constrain it in a near future by using the gravitomagnetic Lense-Thirring effect predicted by general relativity for the orbit of a test particle moving around a central rotating body. We also discuss the present-day situation in view of the latest determinations of the supplementary perihelion precession of Mercury.

MOA 2010-BLG-477Lb: CONSTRAINING THE MASS OF A MICROLENSING PLANET FROM MICROLENSING PARALLAX, ORBITAL MOTION, AND DETECTION OF BLENDED LIGHT

Microlensing detections of cool planets are important for the construction of an unbiased sample to estimate the frequency of planets beyond the snow line, which is where giant planets are thought to form according to the core accretion theory of planet formation. In this paper, we report the discovery of a giant planet detected from the analysis of the light curve of a high-magnification microlensing event MOA-2010-BLG-477. The measured planet-star mass ratio is $q=(2.181\pm0.004)\times 10^{-3}$ and the projected separation is $s=1.1228\pm0.0006$ in units of the Einstein radius. The angular Einstein radius is unusually large $\theta_{\rm E}=1.38\pm 0.11$ mas. Combining this measurement with constraints on the "microlens parallax" and the lens flux, we can only limit the host mass to the range $0.13<M/M_\odot<1.0$. In this particular case, the strong degeneracy between microlensing parallax and planet orbital motion prevents us from measuring more accurate host and planet masses. However, we find that adding Bayesian priors from two effects (Galactic model and Keplerian orbit) each independently favors the upper end of this mass range, yielding star and planet masses of $M_*=0.67^{+0.33}_{-0.13}\ M_\odot$ and $m_p=1.5^{+0.8}_{-0.3}\ M_{\rm JUP}$ at a distance of $D=2.3\pm0.6$ kpc, and with a semi-major axis of $a=2^{+3}_{-1}$ AU. Finally, we show that the lens mass can be determined from future high-resolution near-IR adaptive optics observations independently from two effects, photometric and astrometric.