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Interferometric observations of gravitational microlensing events offer an opportunity for precise, efficient, and direct mass and distance measurements of lensing objects, especially those of isolated neutron stars and black holes. However, such observations were previously possible for only a handful of extremely bright events. The recent development of a dual-field interferometer, GRAVITY Wide, has made it possible to reach out to significantly fainter objects, and increase the pool of microlensing events amenable to interferometric observations by two orders of magnitude. Here, we present the first successful observation of a microlensing event with GRAVITY Wide and the resolution of microlensed images in the event OGLE-2023-BLG-0061/KMT-2023-BLG-0496. We measure the angular Einstein radius of the lens with a sub-percent precision, $\theta_{\rm E} = 1.280 \pm 0.009$ mas. Combined with the microlensing parallax detected from the event light curve, the mass and distance to the lens are found to be $0.472 \pm 0.012 M_{\odot}$ and $1.81 \pm 0.05$ kpc, respectively. We present the procedure for the selection of targets for interferometric observations, and discuss possible systematic effects affecting GRAVITY Wide data. This detection demonstrates the capabilities of the new instrument and it opens up completely new possibilities for the follow-up of microlensing events, and future routine discoveries of isolated neutron stars and black holes., Comment: submitted to AAS Journals

We report the analysis of planetary microlensing event OGLE-2018-BLG-1185, which was observed by a large number of ground-based telescopes and by the $Spitzer$ Space Telescope. The ground-based light curve indicates a low planet-host star mass ratio of $q = (6.9 \pm 0.2) \times 10^{-5}$, which is near the peak of the wide-orbit exoplanet mass-ratio distribution. We estimate the host star and planet masses with a Bayesian analysis using the measured angular Einstein radius under the assumption that stars of all masses have an equal probability to host this planet. The flux variation observed by $Spitzer$ was marginal, but still places a constraint on the microlens parallax. Imposing a conservative constraint that this flux variation should be $\Delta f_{\rm Spz} < 4$ instrumental flux units indicates a host mass of $M_{\rm host} = 0.37^{+0.35}_{-0.21}\ M_\odot$ and a planet mass of $m_{\rm p} = 8.4^{+7.9}_{-4.7}\ M_\oplus$. A Bayesian analysis including the full parallax constraint from $Spitzer$ suggests smaller host star and planet masses of $M_{\rm host} = 0.091^{+0.064}_{-0.018}\ M_\odot$ and $m_{\rm p} = 2.1^{+1.5}_{-0.4}\ M_\oplus$, respectively. Future high-resolution imaging observations with $HST$ or ELTs could distinguish between these two scenarios and help to reveal the planetary system properties in more detail., Comment: 30 pages, 11 figures, 5 tables, Accepted for publication in Astronomical Journal (AJ)

Some low-mass planets are expected to be ejected from their parent planetary systems during early stages of planetary system formation. According to planet-formation theories, such as the core accretion theory, typical masses of ejected planets should be between 0.3 and 1.0 $M_{\oplus}$. Although in practice such objects do not emit any light, they may be detected using gravitational microlensing via their light-bending gravity. Microlensing events due to terrestrial-mass rogue planets are expected to have extremely small angular Einstein radii (< 1 uas) and extremely short timescales (< 0.1 day). Here, we present the discovery of the shortest-timescale microlensing event, OGLE-2016-BLG-1928, identified to date ($t_{\rm E} \approx 0.0288\ \mathrm{day} = 41.5 \mathrm{min}$). Thanks to the detection of finite-source effects in the light curve of the event, we were able to measure the angular Einstein radius of the lens $\theta_{\rm E} = 0.842 \pm 0.064$ uas, making the event the most extreme short-timescale microlens discovered to date. Depending on its unknown distance, the lens may be a Mars- to Earth-mass object, with the former possibility favored by the Gaia proper motion measurement of the source. The planet may be orbiting a star but we rule out the presence of stellar companions up to the projected distance of 8.0 au from the planet. Our discovery demonstrates that terrestrial-mass free-floating planets can be detected and characterized using microlensing., Comment: accepted for publication in ApJ Letters, minor changes

We report the analysis of the microlensing event OGLE-2018-BLG-0677. A small feature in the light curve of the event leads to the discovery that the lens is a star-planet system. Although there are two degenerate solutions that could not be distinguished for this event, both lead to a similar planet-host mass ratio. We perform a Bayesian analysis based on a Galactic model to obtain the properties of the system and find that the planet corresponds to a super-Earth/sub-Neptune with a mass $M_{\mathrm{planet}} = {3.96}^{+5.88}_{-2.66}\mathrm{M_\oplus}$. The host star has a mass $ M_{\mathrm{host}} = {0.12}^{+0.14}_{-0.08}\mathrm{M_\odot}$. The projected separation for the inner and outer solutions are ${0.63}^{+0.20}_{-0.17}$~AU and ${0.72}^{+0.23}_{-0.19}$~AU respectively. At $\Delta\chi^2=\chi^2({\rm 1L1S})-\chi^2({\rm 2L1S})=46$, this is by far the lowest $\Delta\chi^2$ for any securely-detected microlensing planet to date, a feature that is closely connected to the fact that it is detected primarily via a "dip" rather than a "bump"., Comment: 15 page, 12 figures, Published in AJ

We report two microlensing planet candidates discovered by the KMTNet survey in $2017$. However, both events have the 2L1S/1L2S degeneracy, which is an obstacle to claiming the discovery of the planets with certainty unless the degeneracy can be resolved. For KMT-2017-BLG-0962, the degeneracy cannot be resolved. If the 2L1S solution is correct, KMT-2017-BLG-0962 might be produced by a super Jupiter-mass planet orbiting a mid-M dwarf host star. For KMT-2017-BLG-1119, the light curve modeling favors the 2L1S solution but higher-resolution observations of the baseline object tend to support the 1L2S interpretation rather than the planetary interpretation. This degeneracy might be resolved by a future measurement of the lens-source relative proper motion. This study shows the problem of resolving 2L1S/1L2S degeneracy exists over a much wider range of conditions than those considered by the theoretical study of Gaudi (1998)., Comment: 15 pages, 12 figures, 4 tables, accepted in AJ

We report two microlensing events, KMT-2017-BLG-1038 and KMT-2017-BLG-1146 that are caused by planetary systems. These events were discovered by KMTNet survey observations from the $2017$ bulge season. The discovered systems consist of a planet and host star with mass ratios, $5.3_{-0.4}^{+0.2} \times 10^{-3}$ and $2.0_{-0.1}^{+0.6} \times 10^{-3}$, respectively. Based on a Bayesian analysis assuming a Galactic model without stellar remnant hosts, we find that the planet, KMT-2017-BLG-1038Lb, is a super Jupiter-mass planet ($M_{\rm p}= 2.04_{-1.15}^{+2.02}\,M_{\rm J}$) orbiting a mid-M dwarf host ($M_{\rm h}= 0.37_{-0.20}^{+0.36}\, M_{\odot}$) that is located at $6.01_{-1.72}^{+1.27}$ kpc toward the Galactic bulge. The other planet, KMT-2017-BLG-1146Lb, is a sub Jupiter-mass planet ($M_{\rm p}= 0.71_{-0.42}^{+0.80}\,M_{\rm J}$) orbiting a mid-M dwarf host ($M_{\rm h}= 0.33_{-0.20}^{+0.36}\,M_{\odot}$) at a distance toward the Galactic bulge of $6.50_{-2.00}^{+1.38}$ kpc. Both are potentially gaseous planets that are beyond their hosts' snow lines. These typical microlensing planets will be routinely discovered by second-generation microlensing surveys, rapidly increasing the number of detections., Comment: 8 pages, 10 figures, 2 tables, accepted for publication in AJ

Planet formation theories predict the existence of free-floating planets that have been ejected from their parent systems. Although they emit little or no light, they can be detected during gravitational microlensing events. Microlensing events caused by rogue planets are characterized by very short timescales $t_{\rm E}$ (typically below two days) and small angular Einstein radii $\theta_{\rm E}$ (up to several uas). Here we present the discovery and characterization of two ultra-short microlensing events identified in data from the Optical Gravitational Lensing Experiment (OGLE) survey, which may have been caused by free-floating or wide-orbit planets. OGLE-2012-BLG-1323 is one of the shortest events discovered thus far ($t_{\rm E}$=0.155 +/- 0.005 d, $\theta_{\rm E}$=2.37 +/- 0.10 uas) and was caused by an Earth-mass object in the Galactic disk or a Neptune-mass planet in the Galactic bulge. OGLE-2017-BLG-0560 ($t_{\rm E}$=0.905 +/- 0.005 d, $\theta_{\rm E}$=38.7 +/- 1.6 uas) was caused by a Jupiter-mass planet in the Galactic disk or a brown dwarf in the bulge. We rule out stellar companions up to a distance of 6.0 and 3.9 au, respectively. We suggest that the lensing objects, whether located on very wide orbits or free-floating, may originate from the same physical mechanism. Although the sample of ultrashort microlensing events is small, these detections are consistent with low-mass wide-orbit or unbound planets being more common than stars in the Milky Way., Comment: accepted for publication in A&A, minor changes

We present the analysis of the caustic-crossing binary microlensing event OGLE-2017-BLG-0039. Thanks to the very long duration of the event, with an event time scale $t_{\rm E}\sim 130$ days, the microlens parallax is precisely measured despite its small value of $\pie\sim 0.06$. The analysis of the well-resolved caustic crossings during both the source star's entrance and exit of the caustic yields the angular Einstein radius $\thetae\sim 0.6$~mas. The measured $\pie$ and $\thetae$ indicate that the lens is a binary composed of two stars with masses $\sim 1.0~M_\odot$ and $\sim 0.15~M_\odot$, and it is located at a distance of $\sim 6$ kpc. From the color and brightness of the lens estimated from the determined lens mass and distance, it is expected that $\sim 2/3$ of the $I$-band blended flux comes from the lens. Therefore, the event is a rare case of a bright lens event for which high-resolution follow-up observations can confirm the nature of the lens., Comment: 8 pages, 6 figures, 5 tables

We present the analysis of the binary-lens microlensing event OGLE-2017-BLG-0537. The light curve of the event exhibits two strong caustic-crossing spikes among which the second caustic crossing was resolved by high-cadence surveys. It is found that the lens components with a mass ratio $\sim 0.5$ are separated in projection by $\sim 1.3\thetae$, where $\thetae$ is the angular Einstein radius. Analysis of the caustic-crossing part yields $\thetae=1.77\pm 0.16$~mas and a lens-source relative proper motion of $\mu =12.4\pm 1.1~{\rm mas}~{\rm yr}^{-1}$. The measured $\mu$ is the third highest value among the events with measured proper motions and $\sim 3$ times higher than the value of typical Galactic bulge events, making the event a strong candidate for follow-up observations to directly image the lens by separating it from the source. From the angular Einstein radius combined with the microlens parallax, it is estimated that the lens is composed of two main-sequence stars with masses $M_1\sim 0.4~M_\odot$ and $M_2\sim 0.2~M_\odot$ located at a distance of $D_{\rm L}\sim 1.2$~kpc. However, the physical lens parameters are not very secure due to the weak microlens-parallax signal, and thus we cross check the parameters by conducting a Bayesian analysis based on the measured Einstein radius and event timescale combined with the blending constraint. From this, we find that the physical parameters estimated from the Bayesian analysis are consistent with those based on the measured microlens parallax. Resolving the lens from the source can be done in about 5 years from high-resolution follow-up observations and this will provide a rare opportunity to test and refine the microlensing model., Comment: 9 pages, 6 figure, 2 tables

We present Korea Microlensing Telescope Network (KMTNet) light curves for microlensing-event candidates for the 2016 season, which covers an area of 97 sq.deg observed at cadences ranging from Gamma=0.2/hr to Gamma=8/hr from three southern sites in Chile, South Africa, and Australia. These 2163 light curves are comprised of 1856 "clear microlensing" and 307 "possible microlensing" events (including 265 previously released from the K2 C9 field). The data policy is very similar to the one governing the 2015 release. The changes relative to 2015 in the algorithms to find and vet microlensing events are comprehensively described., Comment: 14 pages, 2 Figures, submitted to AAS Journals

We report the discovery and the analysis of the short timescale binary-lens microlensing event, MOA-2015-BLG-337. The lens system could be a planetary system with a very low mass host, around the brown dwarf/planetary mass boundary, or a brown dwarf binary. We found two competing models that explain the observed light curves with companion/host mass ratios of q~0.01 and ~0.17, respectively. From the measurement of finite source effects in the best-fit planetary model, we find a relatively small angular Einstein radius of theta_E ~ 0.03 mas which favors a low mass lens. We conduct a Bayesian analysis to obtain the probability distribution of the lens properties. The results for the planetary models strongly depend on the minimum mass, M_min, in the assumed mass function. In summary, there are two solutions of the lens system: (1) a brown dwarf/planetary mass boundary object orbited by a super-Neptune (the planetary model with M_min=0.001 M_sun) and (2) a brown dwarf binary (the binary model). If the planetary models is correct, this system can be one of a new class of planetary system, having a low host mass and also a planetary mass ratio (q <0.03) between the host and its companion. The discovery of the event is important for the study of planetary formation in very low mass objects. In addition, it is important to consider all viable solutions in these kinds of ambiguous events in order for the future comprehensive statistical analyses of planetary/binary microlensing events., Comment: 17 pages, 7 figures, Accepted for publication in AJ

We report the discovery of a planetary system in which a super-earth orbits a late M-dwarf host. The planetary system was found from the analysis of the microlensing event OGLE-2017-BLG-0482, wherein the planet signal appears as a short-term anomaly to the smooth lensing light curve produced by the host. Despite its weak signal and short duration, the planetary signal was firmly detected from the dense and continuous coverage by three microlensing surveys. We find a planet/host mass ratio of $q\sim 1.4\times 10^{-4}$. We measure the microlens parallax $\pi_{\rm E}$ from the long-term deviation in the observed lensing light curve, but the angular Einstein radius $\theta_{\rm E}$ cannot be measured because the source trajectory did not cross the planet-induced caustic. Using the measured event timescale and the microlens parallax, we find that the masses of the planet and the host are $M_{\rm p}=9.0_{-4.5}^{+9.0}\ M_\oplus$ and $M_{\rm host}=0.20_{-0.10}^{+0.20}\ M_\odot$, respectively, and the projected separation between them is $a_\perp=1.8_{-0.7}^{+0.6}$ au. The estimated distance to the lens is $D_{\rm L}=5.8_{-2.1}^{+1.8}$ kpc. The discovery of the planetary system demonstrates that microlensing provides an important method to detect low-mass planets orbiting low-mass stars., Comment: 10 pages, 10 figures, 2 tables

We report the discovery of a giant planet in the OGLE-2017-BLG-1522 microlensing event. The planetary perturbations were clearly identified by high-cadence survey experiments despite the relatively short event timescale of $t_{\rm E} \sim 7.5$ days. The Einstein radius is unusually small, $\theta_{\rm E} = 0.065\,$mas, implying that the lens system either has very low mass or lies much closer to the microlensed source than the Sun, or both. A Bayesian analysis yields component masses $(M_{\rm host}, M_{\rm planet})=(46_{-25}^{+79}, 0.75_{-0.40}^{+1.26})~M_{\rm J}$ and source-lens distance $D_{\rm LS} = 0.99_{-0.54}^{+0.91}~{\rm kpc}$, implying that this is a brown-dwarf/Jupiter system that probably lies in the Galactic bulge, a location that is also consistent with the relatively low lens-source relative proper motion $\mu = 3.2 \pm 0.5~{\rm mas}~{\rm yr^{-1}}$. The projected companion-host separation is $0.59_{-0.11}^{+0.12}~{\rm AU}$, indicating that the planet is placed beyond the snow line of the host, i.e., $a_{sl} \sim 0.12~{\rm AU}$. Planet formation scenarios combined with the small companion-host mass ratio $q \sim 0.016$ and separation suggest that the companion could be the first discovery of a giant planet that formed in a protoplanetary disk around a brown dwarf host., Comment: 20 pages, 6 figures

We analyze the combined Spitzer and ground-based data for OGLE-2017-BLG-1140 and show that the event was generated by a Jupiter-class $(m_p\simeq 1.6\,M_{\rm jup})$ planet orbiting a mid-late M dwarf $(M\simeq 0.2\,M_\odot)$ that lies $D_{LS}\simeq 1.0\,\mathrm{kpc}$ in the foreground of the microlensed, Galactic-bar, source star. The planet-host projected separation is $a_\perp \simeq 1.0\,\mathrm{au}$, i.e., well-beyond the snow line. By measuring the source proper motion ${\mathbf{\mu}}_s$ from ongoing, long-term OGLE imaging, and combining this with the lens-source relative proper motion ${\mathbf{\mu}}_\mathrm{rel}$ derived from the microlensing solution, we show that the lens proper motion ${\mathbf{\mu}}_l={\mathbf{\mu}}_\mathrm{rel} + {\mathbf{\mu}}_s$ is consistent with the lens lying in the Galactic disk, although a bulge lens is not ruled out. We show that while the Spitzer and ground-based data are comparably well fitted by planetary (i.e., binary-lens, 2L1S) models and by binary-source (1L2S) models, the combination of Spitzer and ground-based data decisively favor the planetary model. This is a new channel to resolve the 2L1S/1L2S degeneracy, which can be difficult to break in some cases., Comment: Revised version accepted for publication in The Astronomical Journal

We present the analysis of KMT-2016-BLG-0212, a low flux-variation $(I_{\rm flux-var}\sim 20$) microlensing event, which is well-covered by high-cadence data from the three Korea Microlensing Telescope Network (KMTNet) telescopes. The event shows a short anomaly that is incompletely covered due to the brief visibility intervals that characterize the early microlensing season when the anomaly occurred. We show that the data are consistent with two classes of solutions, characterized respectively by low-mass brown-dwarf $(q=0.037)$ and sub-Neptune $(q<10^{-4})$ companions, respectively. Future high-resolution imaging should easily distinguish between these solutions., Comment: 9 pages, 8 figures

We report the discovery of microlensing planet OGLE-2017-BLG-0373Lb. We show that while the planet-host system has an unambiguous microlens topology, there are two geometries within this topology that fit the data equally well, which leads to a factor 2.5 difference in planet-host mass ratio, i.e., $q=1.5\times 10^{-3}$ vs. $q=0.6\times 10^{-3}$. We show that this is an "accidental degeneracy" in the sense that it is due to a gap in the data. We dub it "the caustic-chirality degeneracy". We trace the mathematical origins of this degeneracy, which should enable similar degenerate solutions to be easily located in the future. A Bayesian estimate, based on a Galactic model, yields a host mass $M=0.25^{+0.30}_{-0.15} M_\odot$ at a distance $D_L=5.9^{+1.3}_{-1.95}$ kpc. The lens-source relative proper motion is relatively fast, $\mu=9$ mas/yr, which implies that the host mass and distance can be determined by high-resolution imaging after about 10 years. The same observations could in principle resolve the discrete degeneracy in $q$, but this will be more challenging., Comment: 24 pages, 7 figures, 3 tables. Accepted for publication in Acta Astronomica. Light curves and callibration data are available on arXiv as Ancillary files and http://www.astrouw.edu.pl/~jskowron/ogle/ob170373/

Mass measurements of gravitational microlenses require one to determine the microlens parallax $\pie$, but precise $\pie$ measurement, in many cases, is hampered due to the subtlety of the microlens-parallax signal combined with the difficulty of distinguishing the signal from those induced by other higher-order effects. In this work, we present the analysis of the binary-lens event OGLE-2017-BLG-0329, for which $\pie$ is measured with a dramatically improved precision using additional data from space-based $Spitzer$ observations. We find that while the parallax model based on the ground-based data cannot be distinguished from a zero-$\pie$ model at 2$\sigma$ level, the addition of the $Spitzer$ data enables us to identify 2 classes of solutions, each composed of a pair of solutions according to the well-known ecliptic degeneracy. It is found that the space-based data reduce the measurement uncertainties of the north and east components of the microlens-parallax vector $\pivec_{\rm E}$ by factors $\sim 18$ and $\sim 4$, respectively. With the measured microlens parallax combined with the angular Einstein radius measured from the resolved caustic crossings, we find that the lens is composed of a binary with components masses of either $(M_1,M_2)\sim (1.1,0.8)\ M_\odot$ or $\sim (0.4,0.3)\ M_\odot$ according to the two solution classes. The first solution is significantly favored but the second cannot be securely ruled out based on the microlensing data alone. However, the degeneracy can be resolved from adaptive optics observations taken $\sim 10$ years after the event., Comment: 9 pages, 4 tables, 6 figures

We report the discovery, via the microlensing method, of a new very-low-mass binary system. By combining measurements from Earth and from the Spitzer telescope in Earth-trailing orbit, we are able to measure the microlensing parallax of the event, and find that the lens likely consists of an $(12.0 \pm 0.6) M_{\rm J}$ + $(15.7 \pm 1.5) M_{\rm J}$ super-Jupiter / brown-dwarf pair. The binary is located at a distance of $(3.08 \pm 0.18)$ kpc in the Galactic Plane, and the components have a projected separation of $(0.43 \pm 0.03)$ AU. Two alternative solutions with much lower likelihoods are also discussed, an 8- and 6-$M_{\rm J}$ model and a 90- and 70-$M_{\rm J}$ model. Although disfavored at the 3-$\sigma$ and 5-$\sigma$ levels, these alternatives cannot be rejected entirely. We show how the more-massive of these models could be tested with future direct imaging., Comment: 23 pages, 7 figures, submitted to AAS Journals

We analyze the binary gravitational microlensing event OGLE-2017-BLG-1130 (mass ratio q~0.45), the first published case in which the binary anomaly was only detected by the Spitzer Space Telescope. This event provides strong evidence that some binary signals can be missed by observations from the ground alone but detected by Spitzer. We therefore invert the normal procedure, first finding the lens parameters by fitting the space-based data and then measuring the microlensing parallax using ground-based observations. We also show that the normal four-fold space-based degeneracy in the single-lens case can become a weak eight-fold degeneracy in binary-lens events. Although this degeneracy is resolved in event OGLE-2017-BLG-1130, it might persist in other events., Comment: 14 pages, 5 figures

We report the discovery of a cold Super-Earth planet (m_p=4.4 +/- 0.5 M_Earth) orbiting a low-mass (M=0.23 +/- 0.03 M_Sun) M dwarf at projected separation a_perp = 1.18 +/- 0.10 AU, i.e., about 1.9 times the snow line. The system is quite nearby for a microlensing planet, D_Lens = 0.86 +/- 0.09 kpc. Indeed, it was the large lens-source relative parallax pi_rel=1.0 mas (combined with the low mass M) that gave rise to the large, and thus well-measured, "microlens parallax" that enabled these precise measurements. OGLE-2017-BLG-1434Lb is the eighth microlensing planet with planet-host mass ratio q < 1 * 10^-4. We apply a new planet-detection sensitivity method, which is a variant of "V/V_max", to seven of these eight planets to derive the mass-ratio function in this regime. We find dN/d(ln q) ~ q^p, with p = 1.05 (+0.78,-0.68), which confirms the "turnover" in the mass function found by Suzuki et al. relative to the power law of opposite sign n = -0.93 +/- 0.13 at higher mass ratios q >~ 2 * 10^-4. We combine our result with that of Suzuki et al. to obtain p = 0.73 (+0.42,-0.34)., Comment: 53 pages, 16 figures

We present Korea Microlensing Telescope Network (KMTNet) light curves for microlensing-event candidates in the Kepler K2 C9 field having peaks within 3 effective timescales of the Kepler observations. These include 181 "clear microlensing" and 84 "possible microlensing" events found by the KMTNet event finder, plus 56 other events found by OGLE and/or MOA that were not found by KMTNet. All data for the first two classes are immediately available for public use without restriction., Comment: Submitted AAS Journals, 10 pages, 1 Figure. Lightcurves are available at http://kmtnet.kasi.re.kr/ulens/

We report the discovery of a sub-Jupiter mass planet orbiting beyond the snow line of an M-dwarf most likely in the Galactic disk as part of the joint Spitzer and ground-based monitoring of microlensing planetary anomalies toward the Galactic bulge. The microlensing parameters are strongly constrained by the light curve modeling and in particular by the Spitzer-based measurement of the microlens parallax, $\pi_\mathrm{E}$. However, in contrast to many planetary microlensing events, there are no caustic crossings, so the angular Einstein radius, $\theta_\mathrm{E}$ has only an upper limit based on the light curve modeling alone. Additionally, the analysis leads us to identify 8 degenerate configurations: the four-fold microlensing parallax degeneracy being doubled by a degeneracy in the caustic structure present at the level of the ground-based solutions. To pinpoint the physical parameters, and at the same time to break the parallax degeneracy, we make use of a series of arguments: the $\chi^2$ hierarchy, the Rich argument, and a prior Galactic model. The preferred configuration is for a host at $D_L=3.73_{-0.67}^{+0.66}~\mathrm{kpc}$ with mass $M_\mathrm{L}=0.30_{-0.12}^{+0.15}~\mathrm{M_\odot}$, orbited by a Saturn-like planet with $M_\mathrm{planet}=0.43_{-0.17}^{+0.21}~\mathrm{M_\mathrm{Jup}}$ at projected separation $a_\perp = 1.70_{-0.39}^{+0.38}~\mathrm{au}$, about 2.1 times beyond the system snow line. Therefore, it adds to the growing population of sub-Jupiter planets orbiting near or beyond the snow line of M-dwarfs discovered by microlensing. Based on the rules of the real-time protocol for the selection of events to be followed up with Spitzer, this planet will not enter the sample for measuring the Galactic distribution of planets., Comment: Submitted to AAS Journals

Microlensing is a powerful and unique technique to probe isolated objects in the Galaxy. To study the characteristics of these interesting objects based on the microlensing method, measurement of the microlens parallax is required to determine the properties of the lens. Of the various methods to measure microlens parallax, the most robust way is to make simultaneous ground- and space-based observations, i.e., by measuring the space-based microlens parallax. However, space-based campaigns usually require "expensive" resources. Gould & Yee (2012) proposed an idea called the "cheap space-based microlens parallax" that can measure the lens-parallax using only $2$ or $3$ space-based observations of high-magnification events. This cost-effective observation strategy to measure microlens parallaxes could be used by space-borne telescopes to build a complete sample for studying isolated objects. This would enable a direct measurement of the mass function including both extremely low-mass objects and high-mass stellar remnants. However, to adopt this idea requires a test to check how it would work in actual situations. Thus, we present the first practical test of the idea using the high-magnification microlensing event OGLE-2016-BLG-1045, for which a subset of Spitzer observations fortuitously duplicate the prescription of Gould & Yee (2012). From the test, we confirm that the measurement of the lens-parallax adopting this idea has sufficient accuracy to determine the physical properties of the isolated lens., Comment: 7 Figures and 2 Tables, Accepted for publication in the ApJ

Current microlensing surveys are sensitive to free-floating planets down to Earth-mass objects. All published microlensing events attributed to unbound planets were identified based on their short timescale (below two days), but lacked an angular Einstein radius measurement (and hence lacked a significant constraint on the lens mass). Here, we present the discovery of a Neptune-mass free-floating planet candidate in the ultrashort ($t_{\rm E}=0.320\pm0.003$ days) microlensing event OGLE-2016-BLG-1540. The event exhibited strong finite-source effects, which allowed us to measure its angular Einstein radius of $\theta_{\rm E}=9.2\pm0.5\,\mu$as. There remains, however, a degeneracy between the lens mass and distance. The combination of the source proper motion and source-lens relative proper motion measurements favors a Neptune-mass lens located in the Galactic disk. However, we cannot rule out that the lens is a Saturn-mass object belonging to the bulge population. We exclude stellar companions up to 15 au., Comment: accepted to AJ

We show that dense OGLE and KMTNet $I$-band survey data require four bodies (sources plus lenses) to explain the microlensing light curve of OGLE-2015-BLG-1459. However, these can equally well consist of three lenses and one source (3L1S), two lenses and two sources (2L2S) or one lens and three sources (1L3S). In the 3L1S and 2L2S interpretations, the host is a brown dwarf and the dominant companion is a Neptune-class planet, with the third body (in the 3L1S case) being a Mars-class object that could have been a moon of the planet. In the 1L3S solution, the light curve anomalies are explained by a tight (five stellar radii) low-luminosity binary source that is offset from the principal source of the event by $\sim 0.17\,\au$. These degeneracies are resolved in favor of the 1L3S solution by color effects derived from comparison to MOA data, which are taken in a slightly different ($R/I$) passband. To enable current and future ($WFIRST$) surveys to routinely characterize exomoons and distinguish among such exotic systems requires an observing strategy that includes both a cadence faster than 9 min$^{-1}$ and observations in a second band on a similar timescale., Comment: 29 pages, 8 figures, accepted for publication in AJ

We report the discovery of OGLE-2016-BLG-1190Lb, which is likely to be the first Spitzer microlensing planet in the Galactic bulge/bar, an assignation that can be confirmed by two epochs of high-resolution imaging of the combined source-lens baseline object. The planet's mass M_p= 13.4+-0.9 M_J places it right at the deuterium burning limit, i.e., the conventional boundary between "planets" and "brown dwarfs". Its existence raises the question of whether such objects are really "planets" (formed within the disks of their hosts) or "failed stars" (low mass objects formed by gas fragmentation). This question may ultimately be addressed by comparing disk and bulge/bar planets, which is a goal of the Spitzer microlens program. The host is a G dwarf M_host = 0.89+-0.07 M_sun and the planet has a semi-major axis a~2.0 AU. We use Kepler K2 Campaign 9 microlensing data to break the lens-mass degeneracy that generically impacts parallax solutions from Earth-Spitzer observations alone, which is the first successful application of this approach. The microlensing data, derived primarily from near-continuous, ultra-dense survey observations from OGLE, MOA, and three KMTNet telescopes, contain more orbital information than for any previous microlensing planet, but not quite enough to accurately specify the full orbit. However, these data do permit the first rigorous test of microlensing orbital-motion measurements, which are typically derived from data taken over <1% of an orbital period., Comment: 63 pages, 13 figures, 7 tables, AJ, in press

We present microlensing planet OGLE-2017-BLG-0173Lb, with planet-host mass ratio either $q\simeq 2.5\times 10^{-5}$ or $q\simeq 6.5\times 10^{-5}$, the lowest or among the lowest ever detected. The planetary perturbation is strongly detected, $\Delta\chi^2\sim 10,000$, because it arises from a bright (therefore, large) source passing over and enveloping the planetary caustic: a so-called "Hollywood" event. The factor $\sim 2.5$ offset in $q$ arises because of a previously unrecognized discrete degeneracy between Hollywood events in which the caustic is fully enveloped and those in which only one flank is enveloped, which we dub "Cannae" and "von Schlieffen", respectively. This degeneracy is "accidental" in that it arises from gaps in the data. Nevertheless, the fact that it appears in a $\Delta\chi^2=10,000$ planetary anomaly is striking. We present a simple formalism to estimate the sensitivity of other Hollywood events to planets and show that they can lead to detections close to, but perhaps not quite reaching, the Earth/Sun mass ratio of $3\times 10^{-6}$. This formalism also enables an analytic understanding of the factor $\sim 2.5$ offset in $q$ between the Cannae and von Schlieffen solutions. The Bayesian estimates for the host-mass, system distance, and planet-host projected separation are $M=0.39^{+0.40}_{-0.24}\,M_\odot$, $D_L=4.8^{+1.5}_{-1.8}\,\kpc$, and $a_\perp=3.8\pm 1.6\,\au$. The two estimates of the planet mass are $m_p=3.3^{+3.8}_{-2.1}\,M_\oplus$ and $m_p=8^{+11}_{-6}\,M_\oplus$. The measured lens-source relative proper motion $\mu=6\,\masyr$ will permit imaging of the lens in about 15 years or at first light on adaptive-optics imagers on next-generation telescopes. These will allow to measure the host mass but probably cannot resolve the planet-host mass-ratio degeneracy., Comment: 30 pages, 9 figures, AJ in press

Algol ($\beta$ Persei) is the prototypical semi-detached eclipsing binary and a hierarchical triple system. From 2006 to 2010 we obtained 121 high-resolution and high-S/N \'{e}chelle spectra of this object. Spectral disentangling yields the individual spectra of all three stars, and greatly improved elements both the inner and outer orbits. We find masses of $M_{\rm A} = 3.39\pm0.06$ M$_\odot$, $M_{\rm B} = 0.770\pm0.009$ M$_\odot$ and $M_{\rm C} = 1.58\pm0.09$ M$_\odot$. The disentangled spectra also give the light ratios between the components in the $B$ and $V$ bands. Atmospheric parameters for the three stars are determined, including detailed elemental abundances for Algol A and Algol C. We find the following effective temperatures: $T_{\rm A} = 12\,550\pm120$ K, $T_{\rm B} = 4900\pm300$ K and $T_{\rm C} = 7550\pm250$ K. The projected rotational velocities are $v_{\rm A} \sin i_{\rm A} = 50.8\pm0.8$ km/s, $v_{\rm B} \sin i_{\rm B} = 62\pm2$ km/s and $v_{\rm C} \sin i_{\rm C} = 12.4\pm0.6$ km/s. This is the first measurement of the rotational velocity for Algol B, and confirms that it is synchronous with the orbital motion. The abundance patterns of components A and C are identical to within the measurement errors, and are basically solar. They can be summarised as mean metal abundances: [M/H]$_{\rm A} = -0.03\pm0.08$ and [M/H]$_{\rm C} = 0.04\pm0.09$. A carbon deficiency is confirmed for Algol A, with tentative indications for a slight overabundance of nitrogen. The ratio of their abundances is (C/N)$_{\rm A} = 2.0\pm0.4$, half of the solar value of (C/N)$_{\odot} = 4.0\pm0.7$. The new results derived in this study, including detailed abundances and metallicities, will enable tight constraints on theoretical evolutionary models for this complex system., Comment: Accepted for publication in MNRAS

We consider mechanically generated molecular braids composed of two molecules where long range interactions between them can be considered to be very weak. We describe a model that takes account of the thermal fluctuations of the braid, steric interactions between the molecules, and external mechanical forces. In this model, both sets of ends, of the two molecules, are considered to be separated by a fixed distance apart much larger than the radius of the braid. One set of ends are rotated to generate a braid of a certain number of pitches (or turns), while the other set remains fixed. This model may describe the situation in which the ends of each molecule are attached to a substrate and a magnetic bead; to the latter a pulling force and rotational torque can be applied. We discuss various aspects of our model. Most importantly, an expression for the free energy is given, from which equations, determining the various geometric parameters of the braid, can be obtained. By numerically solving these equations, we give predictions from the model for the external torque needed to produce a braid with a certain number of turns per bending persistence length, as well as the end to end extension of the two molecules for a given pulling force. Other geometric parameters, as well as the lateral force required to keep the ends of the two molecules apart, are also calculated., Comment: 25 pages, 9 figures. To be submitted to Journal of Physics Condensed Matter

This is an archival document; the work contains theoretical development to be used in new publications and to stimulate further development. Here, we develop a statistical mechanical treatment of a braid formed of two molecules subject to an external pulling force and an applied moment at one of the braid ends. The braids, considered here, are those whose axis is straight when thermal fluctuations are absent. Firstly, the geometry and topology of the fluctuating braid are characterized and an energy functional is built, including a generalized interaction potential between the two molecules. To obtain expressions for the free energy, we use variational approximations for two cases. In one case, the interaction potential is considered weak and steric interactions between the two molecules determine the mean squared amplitude of fluctuations in the braid radius. In the second case, where the interactions are strong, the mean squared amplitude is self consistently calculated and the effects of the intermolecular interaction on the twisting of the two molecules in the braid are considered. In the last case, two specific examples are considered. The first of these is two uniformly charged rods with a repulsive mean field electrostatic interaction, as well as a shorter ranged attractive component. This second component may model correlation forces. The second example includes possible helix specific forces in a braid formed of two DNA molecules., Comment: 81 pages. Some typos corrected

This paper extends on a recent work where it was shown that forces dependent on the helical structure may cause two DNA molecules to spontaneously braid [R. Cortini et Al, Biophys. J. 101, 875 (2011)]. Here, bending fluctuations of DNA centre lines about the braid axis are incorporated into the braiding theory. The free energy of the pair of molecules is recalculated and compared to its value without incorporating undulations. We find that the loss of configurational entropy due to confinement of the molecules in the braid is rather high. This contribution to the Free Energy pushes up the amount of attraction needed for spontaneous braiding due to helix dependant forces. The theory will be further developed for plectonemes and braids under mechanical forces, in later work., Comment: Main Text+Supplemental material. 5 figures

This is a technical document that outlines a calculation of an electrostatic interaction energy between two rods, with charge helices on them, forming a braid. We deal here with screened electrostatics. A general braid geometry is considered, though to obtain local expressions for the energy the curvature of the rods is considered to be small. Further approximations are made for small tilt angle. This is a generalization of the calculations given in the supplemental material of [R. Cortini et Al, Biophys. J. 101 875 (2011)] for a straight symmetric braid structure, using a different method of calculation where the braid geometry does not need to be supposed a priori., Comment: This document may be updated with any corrections or extensions. Feedback welecome

In columnar assemblies of helical bio-molecules the azimuthal degrees of freedom, i.e. rotations about the long axes of molecules, may be important in determining the structure of the assemblies especially when the interaction energy between neighbouring molecules explicitly depends on their relative azimuthal orientations. For DNA this leads to a rich variety of mesophases for columnar assemblies, each categorized by a specific azimuthal ordering. In a preceding paper [A. Wynveen, D. J. Lee, and A. A. Kornyshev, Eur. Phys. J. E, 16, 303 (2005)] a statistical mechanical theory was developed for the assemblies of torsionally rigid molecues in order to determine how thermal fluctuations influence the structure of these mesophases. Here we extend this theory by including torsional fluctuations of the molecules, where a DNA molecule may twist about its long axis at the cost of torsional elastic energy. Comparing this with the previous study, we find that inclusion of torsional fluctuations further increases the density at which the transition between the hexagonal structure and the predicted rhombic phase occurs and reduces the level of distortion in the rhombic phase. As X-ray diffraction may probe the 2-D lattice structure of such assemblies and provide information concerning the underlying interaction between molecules, we have also calculated correlation functions for the azimuthal ordering which are manifest in an x-ray scattering intensity profiles., Comment: 33 pages, 8 figures

Many physical systems can be mapped onto solved or "solvable" models of magnetism. In this work, we have mapped the statistical mechanics of columnar phases of ideally helical rigid DNA -- subject to the earlier found unusual, frustrated pair potential [A. A. Kornyshev and S. Leikin, J. Chem. Phys. 107, 3656 (1997)] -- onto an exotic, unknown variant of the XY model on a fixed or restructurable lattice. Here the role of the 'spin' is played by the azimuthal orientation of the molecules. We have solved this model using a Hartree-Fock approximation, ground state calculations, and finite temperature Monte Carlo simulations. We have found peculiar spin order transitions, which may also be accompanied by positional restructuring, from hexagonal to rhombohedric lattices. Some of these have been experimentally observed in dense columnar aggregates. Note that DNA columnar phases are of great interest in biophysical research, not only because they are a useful in vitro tool for the study of DNA condensation, but also since these structures have been detected in living matter. Within the approximations made, our study provides insight into the statistical mechanics of these systems., Comment: 19 pages, 18 figures

A serious problem with the Schwinger-Dyson approach to dynamical mass generation in QED3 at finite temperature is that the contribution from the transverse part of the photon propagator, in the Landau gauge, leads to infrared divergences in both the mass function and the wavefunction renormalisation. We show how, by using a simple choice of vertex anatz and a choice of non-local gauge (the `D-gauge') both quantities can be made finite. We formulate an equation for the physical mass M. and show that it reduces to the coresponding equation obtained in the constant physical mass approximation M=M(0,pi T) (which is finite). There for at finite temperature, we are able to justify a `constant' mass approximation for M, and show that the value of r (the ratio of twice the physical mass at zero temperature to the critical temperature) remains close to the value obtained in previous calculations with retardation., Comment: 19 pages including 3 diagrams

The effect of retardation on dynamical mass generation in is studied, in the imaginary time formalism. The photon porarization tensor is evaluated to leading order in 1/N (N is the number of flavours), and simple closed form expressions are found for the fully retarded longitudinal and transverse propagators, which have the correct limit when T goes to zero. The resulting S-D equation for the fermion mass (at order 1/N) has an infrared divergence associated with the contribution of the transverse photon propagator; only the longitudinal contribution is retained, as in earlier treatments. For solutions of constant mass, it is found that the retardation reduces the value of the parameter r (the ratio of twice the mass to the critical temperature) from about 10 to about 6. The gap equation is then solved allowing for the mass to depend on frequency. It was found that the r value remained close to 6. Possibilities for including the transverse propagator are discussed., Comment: 26 pages 8 figures