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At least 73 records · Page 4

KMT-2019-BLG-1339L: An M Dwarf with a Giant Planet or a Companion near the Planet/Brown Dwarf Boundary

We analyze KMT-2019-BLG-1339, a microlensing event with an obvious but incompletely resolved brief anomaly feature around the peak of the light curve. Although the origin of the anomaly is identified to be a companion to the lens with a low mass ratio q, the interpretation is subject to two different degeneracy types. The first type is the ambiguity in ρ, representing the angular source radius scaled to the angular radius of the Einstein ring, θ {sub E}, and the other is the s ↔ s {sup -1} degeneracy. The former type, “finite-source degeneracy,” causes ambiguities in both s and q, while the latter induces an ambiguity only in s. Here, s denotes the separation (in units of θ {sub E}) in projection between the lens components. We estimate that the lens components have masses (M{sub 1},M{sub 2})-(0.27{sub -0.15}{sup +0.36} M{sub ⊙},11{sub -7}{sup +16} M{sub J}) and -(0.48{sub -0.28}{sup +0.40} M{sub ⊙},1.3{sub -0.7}{sup +1.1} M{sub J}) according to the two solutions subject to the finite-source degeneracy, indicating that the lens comprises an M dwarf and a companion with a mass around the planet/brown dwarf boundary or a Jovian-mass planet. It is possible to lift the finite-source degeneracy by conducting future observations utilizing a high-resolution instrument because the relative lens–source proper motion predicted by the solutions is widely different.

79 ASTRONOMY AND ASTROPHYSICS↗

KMT-2019-BLG-0371 and the Limits of Bayesian Analysis

We show that the perturbation at the peak of the light curve of microlensing event KMT-2019-BLG-0371 is explained by a model with a mass ratio between the host star and planet of q ∼ 0.08. Due to the short event duration (t {sub E} ∼ 6.5 days), the secondary object in this system could potentially be a massive giant planet. A Bayesian analysis shows that the system most likely consists of a host star with a mass M{sub h}=0.09{sub −0.05}{sup +0.14}M{sub ⊙} and a massive giant planet with a mass M{sub p}=7.70{sub −3.90}{sup +11.34}M{sub Jup}. However, the interpretation of the secondary as a planet (i.e., as having M {sub p} < 13M {sub Jup}) rests entirely on the Bayesian analysis. Motivated by this event, we conduct an investigation to determine which constraints meaningfully affect Bayesian analyses for microlensing events. We find that the masses inferred from such a Bayesian analysis are determined almost entirely by the measured value of θ {sub E} and are relatively insensitive to other factors such as the direction of the event (ℓ, b), the lens–source relative proper motion μ {sub rel}, or the specific Galactic model prior.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Larger Extent for the Ophiuchus Stream

We present new kinematic data for the Ophiuchus stellar stream. Spectra have been taken of member candidates at the MMT telescope using Hectospec, Hectochelle, and Binospec, which provide more than 1800 new velocities. Combined with proper-motion measurements of stars in the field by the Gaia—DR2 catalog, we have derived stream membership probabilities, resulting in the detection of more than 200 likely members. These data show the stream extends to more than three times the length shown in the discovery data. A spur to the main stream is also detected. The high-resolution spectra allow us to resolve the stellar velocity dispersion, found to be 1.6 ± 0.3 km s{sup −1}.

79 ASTRONOMY AND ASTROPHYSICS↗

Astrometric Membership Tests for the Zinn–Newell–Gibson UV-bright Stars in Galactic Globular Clusters

In 1972, Zinn, Newell, & Gibson (ZNG) published a list of 156 candidate UV-bright stars they had found in 27 Galactic globular clusters (GCs), based on photographs in the U and V bands. UV-bright stars lie above the horizontal branch (HB) and blueward of the asymptotic giant branch (AGB) and red giant branch in the clusters’ color–magnitude diagrams. They are in rapid evolutionary phases—if they are members and not unrelated bright foreground stars. The ZNG list has inspired numerous follow-up studies, aimed at understanding late stages of stellar evolution. However, the ZNG candidates were presented only in finding charts, and celestial coordinates were not given. Using my own collection of CCD frames in u and V, I have identified all of the ZNG objects, and have assembled their coordinates, parallaxes, and proper motions from the recent Gaia Early Data Release 3 (EDR3). Based on the Gaia astrometry, I have determined which objects are probable cluster members (45% of the sample). For the members, using photometry from EDR3, I have assigned the stars to various evolutionary stages, including luminous post-AGB stars, and stars above the HB. I point out several ZNG stars of special interest that have still, to my knowledge, never been studied in detail. This study is an adjunct to a forthcoming survey of the Galactic GCs in the uBVI photometric system, designed for detection of low-gravity stars with large Balmer discontinuities.

47 OTHER INSTRUMENTATION↗

A Kinematic Perspective on the Formation Process of the Stellar Groups in the Rosette Nebula

Stellar kinematics is a powerful tool for understanding the formation process of stellar associations. Here, we present a kinematic study of the young stellar population in the Rosette nebula using recent Gaia data and high-resolution spectra. We first isolate member candidates using the published mid-infrared photometric data and the list of X-ray sources. A total of 403 stars with similar parallaxes and proper motions are finally selected as members. The spatial distribution of the members shows that this star-forming region is highly substructured. The young open cluster NGC 2244 in the center of the nebula has a pattern of radial expansion and rotation. We discuss its implication on the cluster formation, e.g., monolithic cold collapse or hierarchical assembly. On the other hand, we also investigate three groups located around the border of the H ii bubble. The western group seems to be spatially correlated with the adjacent gas structure, but their kinematics is not associated with that of the gas. The southern group does not show any systematic motion relative to NGC 2244. These two groups might be spontaneously formed in filaments of a turbulent cloud. The eastern group is spatially and kinematically associated with the gas pillar receding away from NGC 2244. This group might be formed by feedback from massive stars in NGC 2244. Our results suggest that the stellar population in the Rosette Nebula may form through three different processes: the expansion of stellar clusters, hierarchical star formation in turbulent clouds, and feedback-driven star formation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A Deep Study of an Intermediate-age Open Cluster SAI 35 (Juchert 20) Using Ground-based Imaging and Gaia EDR3 Astrometry

We present a CCD UBVI photometric study of poorly studied intermediate-age open cluster SAI 35 (Juchert 20) for the first time. To accomplish this study, we also used LAMOST DR5, Two Micron All Sky Survey, and Gaia EDR3 databases. We identified 214 most probable cluster members with membership probability higher than 50%. The mean proper motion of the cluster is found as μ{sub α}cos δ=1.10±0.01 and μ {sub δ} = −1.66 ± 0.01 mas yr{sup −1}. We find the normal interstellar extinction law using the various two-color diagrams. The age, distance, reddening, and radial velocity of the cluster are estimated to be 360 ± 40 Myr, 2.9 ± 0.15 kpc, 0.72 ± 0.05 mag, and −91.62 ± 6.39 km s{sup −1}, respectively. The overall mass function slope for main-sequence stars is found to be 1.49 ± 0.16 within the mass range 1.1–3.1 M {sub ⊙}, which is in agreement with Salpeter’s value within uncertainty. The present study demonstrates that SAI 35 is dynamically relaxed. Galactic orbital parameters are determined using Galactic potential models. We found that this object follows a circular path around the Galactic center.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Two Luminous Post-AGB Stars in the Galactic Globular Cluster M19

We report the discovery of a luminous “yellow” post–asymptotic giant branch (PAGB) star in the globular cluster (GC) M19 (NGC 6273), identified during our uBVI survey of Galactic GCs. The uBVI photometric system is optimized to detect stars with large Balmer discontinuities, indicating very low surface gravities and high luminosities. The spectral energy distribution (SED) of the star is consistent with an effective temperature of about 6250 K and a surface gravity of logg=0.5. We use Gaia data to show that the star’s proper motion and radial velocity are consistent with cluster membership. One aim of our program is to test yellow PAGB stars as candidate Population II standard candles for determining extragalactic distances. We derive a visual absolute magnitude of M {sub V} = − 3.39 ± 0.09 for the M19 star. This is in close agreement with the M {sub V} values found for yellow PAGB stars in the GCs ω Cen, NGC 5986, and M79, indicating a very narrow luminosity function. These objects are 4 mag brighter than RR Lyrae variables, and they can largely avoid the issues of interstellar extinction that are a problem for Population I distance indicators. We also identified a second luminous PAGB object in M19, this one a hotter “UV-bright” star. Its SED is consistent with an effective temperature of about 11,750 K and logg=2.0. The two objects have nearly identical bolometric luminosities, logL/L{sub ⊙}=3.24 and 3.22, respectively.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The Blue Straggler Population of the Open Clusters Trumpler 5, Trumpler 20, and NGC 2477

We present a study based on Gaia DR2 of the population of blue straggler stars in the open clusters Trumpler 5, Trumpler 20, and NGC 2477. All candidates were selected according to their position in the color–magnitude diagram, their proper motion components, and their parallax. We also looked for yellow stragglers, i.e., possible evolved blue stragglers. We found that Trumpler 5 hosts a large blue straggler star population, which allowed us to analyze their radial distribution as a probe of the cluster’s dynamical status. The blue straggler star distribution was compared with that of red giant branch stars to evaluate mass segregation. Our results indicate that blue straggler stars are not more centrally concentrated than red giant branch stars stars in any of the clusters. The radial distribution of blue straggler stars in Trumpler 5 is flat. Additionally, using a multi-epoch radial velocity survey conducted with the high-resolution spectrograph FLAMES/GIRAFFE at the Very Large Telescope, we measured the radial velocities of a sample of stragglers to compare with the mean radial velocity and velocity dispersion of the clusters. Based on the radial velocity variations for different epochs, we roughly classified these stars as possible close or long-period binaries.

47 OTHER INSTRUMENTATION↗

Shortest Microlensing Event with a Bound Planet: KMT-2016-BLG-2605

With a planet–host mass ratio q = 0.012 ± 0.001, KMT-2016-BLG-2605 has the shortest Einstein timescale, t {sub E} = 3.41 ± 0.13 days, of any planetary microlensing event to date. This prompts us to examine the full sample of seven short (t {sub E} < 7 days) planetary events with good q measurements. We find that six have clustered Einstein radii θ {sub E} = 115 ± 20 μas and lens–source relative proper motions μ {sub rel} ≃ 9.5 ± 2.5 mas yr{sup -1}. For the seventh, these two quantities could not be measured. These distributions are consistent with a Galactic bulge population of very low mass (VLM) hosts near the hydrogen-burning limit. This conjecture could be verified by imaging at first adaptive optics light on next-generation (30 m) telescopes. Based on a preliminary assessment of the sample, “planetary” companions (i.e., below the deuterium-burning limit) are divided into “genuine planets,” formed in their disks by core accretion, and VLM brown dwarfs, which form like stars. We discuss techniques for expanding the sample, which include taking account of the peculiar “anomaly-dominated” morphology of the KMT-2016-BLG-2605 light curve.

74 ATOMIC AND MOLECULAR PHYSICS↗

True Masses of the Long-period Companions to HD 92987 and HD 221420 from Hipparcos–Gaia Astrometry

The extensive time span of modern radial velocity surveys has made the discovery of long-period substellar companions more common in recent years; however, measuring the true masses of these objects remains challenging. Astrometry from the Gaia mission is expected to provide mass measurements for many of these long-period companions, but these data are not yet available. However, combining proper-motion data from Gaia DR2 and the earlier Hipparcos mission makes it possible to measure true masses of substellar companions in favorable cases. In this work, we combine radial velocities with Hipparcos–Gaia astrometry to measure the true masses of two recently discovered long-period substellar companion candidates, HD 92987 B and HD 221420 b. In both cases, we find that the true masses are significantly higher than implied by radial velocities alone. A 2087 ± 19 m s{sup −1} astrometric signal reveals that HD 92987 B is not close to its 17 M {sub J} minimum mass but is instead a 0.2562 ± 0.0045 M {sub ⊙} star viewed at a near-polar orbital inclination, whereas the 22.9 ± 2.2 M {sub J} HD 221420 b can be plausibly interpreted as a high-mass “superplanet” or a low-mass brown dwarf. With semimajor axes of ∼10 au, both companions are interesting targets for direct imaging, and HD 221420 b in particular would be a benchmark metal-rich substellar object if it proves possible to directly detect. Our results demonstrate the power of Hipparcos–Gaia astrometry for studying long-period planet and brown dwarf candidates discovered from radial velocity surveys.

36 MATERIALS SCIENCE↗

WIYN Open Cluster Study LXXIX. M48 (NGC 2548) I. Radial Velocities, Rotational Velocities, and Metallicities of Stars in the Open Cluster M48 (NGC 2548)

WIYN/Hydra spectra (R ∼ 13,500, signal-to-noise pixel{sup −1} = 50–1000) of a 400 Å region around Li 6708 Å are used to determine radial and rotational velocities for 287 photometrically selected candidate members of the open cluster M48. The sample ranges from turnoff A stars to late-K dwarfs and eight giants. We combine our V {sub RAD} measurements and power spectrum analysis with parallax and proper motion data from Gaia DR2 to evaluate membership and multiplicity. We classify 152 stars as single cluster members, 11 as binary members, 16 as members of uncertain multiplicity, 56 as single nonmembers, 28 as single “likely” nonmembers, two as single “likely” members, one as a binary “likely” member, five as binary nonmembers, 10 as “likely” members of uncertain multiplicity, three as nonmembers of uncertain multiplicity, and three as “likely” nonmembers of uncertain multiplicity. From a subsample of 95 single members, we derive V {sub RAD} = 8.512 ± 0.087 km s{sup −1} (σ {sub μ}, and σ = 0.848 km s{sup −1}). Using 16 isolated Fe I lines for a subsample of 99 single members (that have σ{sub T{sub e{sub f{sub f}}}}<75 K (from 10 colors from UBVRI), v sin i < 25 km s{sup −1}, and well-behaved Fe I lines), [Fe/H]{sub M48} = −0.063 ± 0.007 dex (σ {sub μ}). [Fe/H] is independent of T {sub eff} over an unprecedentedly large range of 2500 K. The minimum cluster binary fraction is 11%–21%. M48 exhibits a clear but modest broadening of the main-sequence turnoff, and there is no correlation between color and v sin i.

79 ASTRONOMY AND ASTROPHYSICS↗

Open Cluster IC 1369 and Its Vicinity: Multicolor Photometry and Gaia DR2 Astrometry

The open cluster IC 1369, located in Cygnus close to the galactic equator at the 89.°6 longitude, and its vicinity are investigated by applying two-dimensional photometric classification of stars down to V = 19 mag measured in the Vilnius seven-color photometric system. Employing the Gaia DR2 coordinates, parallaxes, and proper motions, 143 cluster members are found having cluster membership probabilities ≥0.75. The hottest stars of the evolved main sequence are of spectral class B9. Distances to the cluster, determined by two methods based on the Gaia parallaxes, are 3280 and 3370 pc with an uncertainty of 400–500 pc. Employing the physical HR diagram with the coordinates logL/L{sub ⊙} versus logT{sub eff} and the Padova isochrones, the cluster age is found to be between 300 and 350 Myr. Among the cluster members we identified six red giants of spectral classes G5–G8 and luminosities II–III, 17 Am stars, one Ap star, and one B5 blue straggler. The extinction shows a steep rise up to ∼2.0 mag at 300–700 pc, caused by the extensions of the dust cloud LDN 970 and the Great Cygnus Rift, and up to ∼2.5 mag at the edge of the Perseus arm at 3.0 kpc. The extinction is almost constant between 0.9 and 2.5 kpc from the Sun. The average extinction of the cluster members is 2.54 mag. A systematic error of color excesses found in the Argonaut calculator results is discussed.

79 ASTRONOMY AND ASTROPHYSICS↗

A Comprehensive Analysis of NGC 2158 in the Gaia Era: Photometric Parameters, Apex, and Orbit

We present an investigation of NGC 2158 using Gaia DR2 data. We identified 800 most likely cluster members with membership probability higher than 90%. The mean proper motions of this object are determined as (μ {sub x} = −0.203 ± 0.003, μ {sub y} = −1.99 ± 0.004) mas yr{sup −1}. The limiting radius, log(age), and distance of the cluster are obtained as 23.5 arcmin, 9.38 ± 0.04 Gyr, and 4.69 ± 0.22 kpc, respectively. The overall mass function slope (0.93 ± 0.14) is flatter than the Salpeter value (1.35) within the mass range of 1.17–1.44 M {sub ⊙}. This cluster also shows the mass-segregation effect and our study demonstrates that NGC 2158 is a dynamically relaxed open cluster. Using the apex diagram (AD), the apex coordinates of the cluster are obtained in different ways and are examined using the (μ {sub U},μ {sub T}) diagram. The best value of the apex coordinates is determined as A = 8724 ± 160, D = −3661 ± 530. We also determined the orbit of the cluster and found that NGC 2158 moves almost in the solar antapex direction. The resulting spatial velocity of NGC 2158 is 51 km s{sup −1}. A significant oscillation along the Z-coordinate up to 529 pc is detected. Various scenarios regarding the origin of this cluster are also discussed.

42 ENGINEERING↗

A Survey for New Stars and Brown Dwarfs in the Ophiuchus Star-forming Complex

We have performed a survey for new members of the Ophiuchus cloud complex using high-precision astrometry from the second data release of Gaia, proper motions measured with multi-epoch images from the Spitzer Space Telescope, and color–magnitude diagrams constructed with photometry from various sources. Through spectroscopy of candidates selected with those data, we have identified 155 new young stars. Based on available measurements of kinematics, we classify 102, 47, and 6 of those stars as members of Ophiuchus, Upper Sco, and other populations in Sco–Cen, respectively. We have also assessed the membership of all other stars in the vicinity of Ophiuchus that have spectroscopic evidence of youth from previous studies, arriving at a catalog of 373 adopted members of the cloud complex. For those adopted members, we have compiled mid-infrared photometry from Spitzer and the Wide-field Infrared Survey Explorer and have used mid-infrared colors to identify and classify circumstellar disks. We find that 210 of the members show evidence of disks, including 48 disks that are in advanced stages of evolution. Finally, we have estimated the relative median ages of the populations near the Ophiuchus clouds and the surrounding Upper Sco association using absolute K-band magnitudes (M {sub K}) based on Gaia parallaxes. If we adopt an age 10 Myr for Upper Sco, then the relative values of M {sub K} imply median ages of ∼2 Myr for L1689 and embedded stars in L1688, 3–4 Myr for low-extinction stars near L1688, and ∼6 Myr for the group containing ρ Oph.

79 ASTRONOMY AND ASTROPHYSICS↗

Searching for Dwarf Galaxies in Gaia DR2 Phase-space Data Using Wavelet Transforms

We present a wavelet-based algorithm to identify dwarf galaxies in the Milky Way in Gaia DR2 data. Our algorithm detects overdensities in 4D position–proper-motion space, making it the first search to explicitly use velocity information to search for dwarf galaxy candidates. We optimize our algorithm and quantify its performance by searching for mock dwarfs injected into Gaia DR2 data and for known Milky Way satellite galaxies. Comparing our results with previous photometric searches, we find that our search is sensitive to undiscovered systems at Galactic latitudes |b| > 20° and with half-light radii larger than the 50% detection efficiency threshold for Pan-STARRS1 (PS1) at (i) absolute magnitudes of –7 < M V < –3 and distances of 32 kpc < D < 64 kpc, and (ii) M V < –4 and 64 kpc < D < 128 kpc. Based on these results, we predict that our search is expected to discover 5 ± 2 new satellite galaxies: four in the PS1 footprint and one outside the Dark Energy Survey and PS1 footprints. We apply our algorithm to the Gaia DR2 data set and recover ~830 high-significance candidates, out of which we identify a "gold standard" list of ~200 candidates based on cross-matching with potential candidates identified in a preliminary search using Gaia EDR3 data. All of our candidate lists are publicly distributed for future follow-up studies. Here, we show that improvements in astrometric measurements provided by Gaia EDR3 increase the sensitivity of this technique; we plan to continue to refine our candidate list using future data releases.

79 ASTRONOMY AND ASTROPHYSICS↗

Searching for Active Low-mass Stars in the CMa Star-forming Region: Multi-band Photometry with T80S

An exotic environment surrounds the young stellar groups associated with the Canis Major (CMa) OB1/R1 region, which probably was formed under feedback from at least three supernova events having occurred a few million years ago. We use astrometric data from the Gaia-DR2 to confirm the membership of the stars in CMa R1, based on proper motion and parallax, which revealed 514 new members and candidates. The mean age of 5 Myr estimated from the color–magnitude diagram characterizes the sources as likely pre-main-sequence candidates. In total, a sample of 694 stars detected with the T80-South telescope was analyzed according to different color–color diagrams, which were compared with theoretical colors from evolutionary models, aiming to reveal the objects that exhibit color excess due to accretion processes. Accretion and magnetic activity were also explored on the basis of empirical flux–flux relation, such as F {sub 660} and F {sub 861} that are related to Hα and Ca ii triplet emission, respectively. A low fraction (∼3 percent) of the sample have Hα excess and other colors expected for stars exhibiting chromospheric activity. The number of Class I and Class II objects, identified by the infrared (Wide-field Infrared Survey Explorer) colors, indicates a disk fraction of ∼6 percent, which is lower than that expected for stellar clusters with a similar age. Such a large sample of objects associated with CMa R1 without evidences of circumstellar accretion can be interpreted as a lack of disk-bearing stars, unusual for young star-forming regions. However, this may be explained as the result of supernova events.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Candidate Brown-dwarf Microlensing Events with Very Short Timescales and Small Angular Einstein Radii

Short-timescale microlensing events are likely to be produced by substellar brown dwarfs (BDs), but it is difficult to securely identify BD lenses based on only event timescales t{sub E} because short-timescale events can also be produced by stellar lenses with high relative lens-source proper motions. In this paper, we report three strong candidate BD-lens events found from the search for lensing events not only with short timescales (t{sub E}≲6 days) but also with very small angular Einstein radii (θ{sub E}≲0.05 mas) among the events that have been found in the 2016–2019 observing seasons. These events include MOA-2017-BLG-147, MOA-2017-BLG-241, and MOA-2019-BLG-256, in which the first two events are produced by single lenses and the last event is produced by a binary lens. From the Monte Carlo simulations of Galactic events conducted with the combined t{sub E} and θ{sub E} constraint, it is estimated that the lens masses of the individual events are 0.051{sub −0.027}{sup +0.100} M{sub ⊙}, 0.044{sub −0.023}{sup +0.090} M{sub ⊙}, and 0.046{sub −0.023}{sup +0.067} M{sub ⊙}/0.038{sub −0.019}{sup +0.056} M{sub ⊙} and the probability of the lens mass smaller than the lower limit of stars is ∼80% for all events. We point out that routine lens mass measurements of short-timescale lensing events require survey-mode space-based observations.

79 ASTRONOMY AND ASTROPHYSICS↗

OGLE-2018-BLG-1269Lb: A Jovian Planet with a Bright I = 16 Host

We report the discovery of a planet in the microlensing event OGLE-2018-BLG-1269 with a planet–host mass ratio q ∼ 6 × 10{sup −4}, i.e., 0.6 times smaller than the Jupiter/Sun mass ratio. Combined with the Gaia parallax and proper motion, a strong one-dimensional constraint on the microlens parallax vector allows us to significantly reduce the uncertainties of lens physical parameters. A Bayesian analysis that ignores any information about light from the host yields that the planet is a cold giant (M{sub 2}=0.69{sub −0.22}{sup +0.44} M{sub J}) orbiting a Sun-like star (M{sub 1}=1.13{sub −0.35}{sup +0.72} M{sub ⊙}) at a distance of D{sub L}=2.56{sub −0.62}{sup +0.92} kpc. The projected planet–host separation is a{sub ⊥}=4.61{sub −1.17}{sup +1.70} au. Using Gaia astrometry, we show that the blended light lies ≲12 mas from the host and therefore must be either the host star or a stellar companion to the host. An isochrone analysis favors the former possibility at >99.6%. The host is therefore a subgiant. For host metallicities in the range of 0.0⩽[Fe/H]⩽+0.3, the host and planet masses are then in the range of 1.16⩽M{sub 1}/M{sub ⊙}⩽1.38 and 0.74⩽M{sub 2}/M{sub J}⩽0.89, respectively. Low host metallicities are excluded. The brightness and proximity of the lens make the event a strong candidate for spectroscopic follow-up both to test the microlensing solution and to further characterize the system.

79 ASTRONOMY AND ASTROPHYSICS↗