W. L. Sweatman

A Low-Mass Planet with a Possible Sub-Stellar-Mass Host in Microlensing Event MOA-2007-BLG-192

We report the detection of an extrasolar planet of mass ratio q~2×10-4 in microlensing event MOA-2007-BLG-192. The best-fit microlensing model shows both the microlensing parallax and finite source effects, and these can be combined to obtain the lens masses of M=0.060+0.028-0.021 Msolar for the primary and m=3.3+4.9-1.6 M? for the planet. However, the observational coverage of the planetary deviation is sparse and incomplete, and the radius of the source was estimated without the benefit of a source star color measurement. As a result, the 2 ? limits on the mass ratio and finite source measurements are weak. Nevertheless, the microlensing parallax signal clearly favors a substellar mass planetary host, and the measurement of finite source effects in the light curve supports this conclusion. Adaptive optics images taken with the Very Large Telescope (VLT) NACO instrument are consistent with a lens star that is either a brown dwarf or a star at the bottom of the main sequence. Follow-up VLT and/or Hubble Space Telescope (HST) observations will either confirm that the primary is a brown dwarf or detect the low-mass lens star and enable a precise determination of its mass. In either case, the lens star, MOA-2007-BLG-192L, is the lowest mass primary known to have a companion with a planetary mass ratio, and the planet, MOA-2007-BLG-192Lb, is probably the lowest mass exoplanet found to date, aside from the lowest mass pulsar planet.

Masses and Orbital Constraints for the OGLE-2006-BLG-109Lb,c Jupiter/Saturn Analog Planetary System

We present a new analysis of the Jupiter+Saturn analog system, OGLE-2006-BLG-109Lb,c, which was the first double planet system discovered with the gravitational microlensing method. This is the only multi-planet system discovered by any method with measured masses for the star and both planets. In addition to the signatures of two planets, this event also exhibits a microlensing parallax signature and finite source effects that provide a direct measure of the masses of the star and planets, and the expected brightness of the host star is confirmed by Keck AO imaging, yielding masses of , Mb = 231 ± 19 M ⊕, and Mc = 86 ± 7 M ⊕. The Saturn-analog planet in this system had a planetary light-curve deviation that lasted for 11 days, and as a result, the effects of the orbital motion are visible in the microlensing light curve. We find that four of the six orbital parameters are tightly constrained and that a fifth parameter, the orbital acceleration, is weakly constrained. No orbital information is available for the Jupiter-analog planet, but its presence helps to constrain the orbital motion of the Saturn-analog planet. Assuming co-planar orbits, we find an orbital eccentricity of and an orbital inclination of . The 95% confidence level lower limit on the inclination of i > 49° implies that this planetary system can be detected and studied via radial velocity measurements using a telescope of 30 m aperture.

MOA-2011-BLG-293Lb: A TEST OF PURE SURVEY MICROLENSING PLANET DETECTIONS

Mathematical and Physical Sciences: 1st Place (The Ohio State University Edward F. Hayes Graduate Research Forum)

The Extreme Microlensing Event OGLE-2007-BLG-224: Terrestrial Parallax Observation of a Thick-Disk Brown Dwarf

Parallax is the most fundamental technique for measuring distances to astronomical objects. Although terrestrial parallax was pioneered over 2000 years ago by Hipparchus (ca. 140 B.C.E.) to measure the distance to the Moon, the baseline of the Earth is so small that terrestrial parallax can generally only be applied to objects in the Solar System. However, there exists a class of extreme gravitational microlensing events in which the effects of terrestrial parallax can be readily detected and so permit the measurement of the distance, mass, and transverse velocity of the lens. Here we report observations of the first such extreme microlensing event OGLE-2007-BLG-224, from which we infer that the lens is a brown dwarf of mass M = 0.056 ± 0.004 M ☉, with a distance of 525 ± 40 pc and a transverse velocity of 113 ± 21 km s–1. The velocity places the lens in the thick disk, making this the lowest-mass thick-disk brown dwarf detected so far. Follow-up observations may allow one to observe the light from the brown dwarf itself, thus serving as an important constraint for evolutionary models of these objects and potentially opening a new window on substellar objects. The low a priori probability of detecting a thick-disk brown dwarf in this event, when combined with additional evidence from other observations, suggests that old substellar objects may be more common than previously assumed.

EXTREME MAGNIFICATION MICROLENSING EVENT OGLE-2008-BLG-279: STRONG LIMITS ON PLANETARY COMPANIONS TO THE LENS STAR

We analyze the extreme high-magnification microlensing event OGLE-2008-BLG-279, which peaked at a maximum magnification of A ~ 1600 on 2008 May 30. The peak of this event exhibits both finite-source effects and terrestrial parallax, from which we determine the mass of the lens, Ml = 0.64 ? 0.10 M ?, and its distance, Dl = 4.0 ? 0.6 kpc. We rule out Jupiter-mass planetary companions to the lens star for projected separations in the range 0.5-20 AU. More generally, we find that this event was sensitive to planets with masses as small as with projected separations near the Einstein ring (~3 AU).

A mathematical model for pollution in a river and its remediation by aeration

Abstract We present a simple mathematical model for river pollution and investigate the effect of aeration on the degradation of pollutant. The model consists of a pair of coupled reaction–diffusion–advection equations for the pollutant and dissolved oxygen concentrations, respectively. The coupling of these equations occurs because of reactions between oxygen and pollutant to produce harmless compounds. Here we consider the steady-state case in one spatial dimension. For simplified cases the model is solved analytically. We also present a numerical approach to the solution in the general case. The extension to the transient spatial model is relatively straightforward. The study is motivated by the crucial problem of water pollution in many countries and specifically within the Tha Chin River in Thailand. For such real situations, simple models can provide decision support for planning restrictions to be imposed on farming and urban practices.

Mass measurement of a single unseen star and planetary detection efficiency for OGLE 2007-BLG-050

We analyze OGLE-2007-BLG-050, a high magnification microlensing event (A ~ 432) whose peak occurred on 2 May, 2007, with pronounced finite-source and parallax effects. We compute planet detection efficiencies for this event in order to determine its sensitivity to the presence of planets around the lens star. Both finite-source and parallax effects permit a measurement of the angular Einstein radius \theta_E = 0.48 +/- 0.01 mas and the parallax \pi_E = 0.12 +/- 0.03, leading to an estimate of the lens mass M = 0.50 +/- 0.14 M_Sun and its distance to the observer D_L = 5.5 +/- 0.4 kpc. This is only the second determination of a reasonably precise (<30%) mass estimate for an isolated unseen object, using any method. This allows us to calculate the planetary detection efficiency in physical units (r_\perp, m_p), where r_\perp is the projected planet-star separation and m_p is the planet mass. When computing planet detection efficiency, we did not find any planetary signature and our detection efficiency results reveal significant sensitivity to Neptune-mass planets, and to a lesser extent Earth-mass planets in some configurations. Indeed, Jupiter and Neptune-mass planets are excluded with a high confidence for a large projected separation range between the planet and the lens star, respectively [0.6 - 10] and [1.4 - 4] AU, and Earth-mass planets are excluded with a 10% confidence in the lensing zone, i.e. [1.8 - 3.1] AU.

MOA-2007-BLG-197 : exploring the brown dwarf desert

We present the analysis of MOA-2007-BLG-197Lb, the first brown dwarf companion to a Sun-like star detected through gravitational microlensing. The event was alerted and followed-up photometrically by a network of telescopes from the PLANET, MOA, and uFUN collaborations, and observed at high angular resolution using the NaCo instrument at the VLT. From the modelling of the microlensing light curve, we derived the binary lens separation in Einstein radius units (s~1.13) and a mass ratio of (4.732+/-0.020)x10^{-2}. Annual parallax, lens orbital motion and finite source effects were included in the models. To recover the lens systems physical parameters, we combined the resulting light curve best-fit parameters with (J,H,Ks) magnitudes obtained with VLT NaCo and calibrated using IRSF and 2MASS data. We derived a lens total mass of 0.86+/-0.04 Msun and a lens distance of 4.2+/-0.3 kpc. We find that the companion of MOA-2007-BLG-197L is a brown dwarf of 41+/-2 Mjup observed at a projected separation of 4.3+/-0.1 AU, and orbits a 0.82+/-0.04 Msun G-K dwarf star. We study the statistical properties of this population of brown dwarfs detected by microlensing, transit, radial velocity, and direct imaging (most of these objects orbit solar-type stars), and we performed a two-dimensional, non-parametric probability density distribution fit to the data, which draws a structured brown dwarf landscape. We confirm the existence of a region that is strongly depleted in objects at short periods and intermediate masses (P 500 d) and high masses (M>50 Mjup). While these data provide important clues on mechanisms of brown dwarfs formation, more data are needed to establish their relative importance, in particular as a function of host star mass.

A model for spray droplet adhesion, bounce or shatter at a crop leaf surface

Improvements in crop spray methods can result in great environmental and cost benefits. By developing a greater understanding of the physical processes involved, it should be possible to tailor spray formulations to maximise retention by plant foliage. This would enable the reduction of the chemical active required to achieve agrochemical efficacy. In the present paper one important aspect of the retention process is considered: a droplet-leaf impaction model is presented allowing for bounce, shatter or adhesion of the droplets by the leaf surface.

Candidate gravitational microlensing events for future direct lens imaging

The mass of the lenses giving rise to Galactic microlensing events can be constrained by measuring the relative lenssource proper motion and lens flux. The flux of the lens can be separated from that of the source, companions to the source, and unrelated nearby stars with high-resolution images taken when the lens and source are spatially resolved.