Search

We present an analysis of adaptive optics (AO) images from the Keck-I telescope of the microlensing event MOA-2011-BLG-262. The original discovery paper by Bennett et al. 2014 reports two distinct possibilities for the lens system; a nearby gas giant lens with an exomoon companion or a very low mass star with a planetary companion in the galactic bulge. The $\sim$10 year baseline between the microlensing event and the Keck follow-up observations allows us to detect the faint candidate lens host (star) at $K = 22.3$ mag and confirm the distant lens system interpretation. The combination of the host star brightness and light curve parameters yields host star and planet masses of $M_{\rm host} = 0.19 \pm 0.03M_{\odot}$ and $m_p = 28.92 \pm 4.75M_{\oplus}$ at a distance of $D_L = 7.49 \pm 0.91\,$kpc. We perform a multi-epoch cross reference to \textit{Gaia} DR3 and measure a transverse velocity for the candidate lens system of $v_L = 541.31 \pm 65.75$ km s$^{-1}$. We conclude this event consists of the highest velocity exoplanet system detected to date, and also the lowest mass microlensing host star with a confirmed mass measurement. The high-velocity nature of the lens system can be definitively confirmed with an additional epoch of high-resolution imaging at any time now. The methods outlined in this work demonstrate that the \textit{Roman} Galactic Exoplanet Survey (RGES) will be able to securely measure low-mass host stars in the bulge., Comment: 21 pages, 6 figures, 4 tables, submitted to AJ

When compressed, certain lattices undergo phase transitions that may allow nuclei to gain significant kinetic energy. To explore the dynamics of this phenomenon, we develop a framework to study Coulomb coupled N-body systems constrained to a parametric surface, focusing specifically on the case of a sphere, as in the Thomson problem. We initialize $N$ total Boron nuclei as point particles on the surface of a sphere, allowing the particles to equilibrate via Coulomb scattering with a viscous damping term. To simulate a phase transition, we remove $N_{rm}$ particles, forcing the system to rearrange into a new equilibrium. We develop a scaling relation for the average peak kinetic energy attained by a single particle as a function of $N$ and $N_{rm}$. For certain values of $N$, we find an order of magnitude energy gain when increasing $N_{rm}$ from 1 to 6, indicating that it may be possible to engineer a lattice that maximizes the energy output., Comment: 8 pages, 11 figures, submitted to Physical Review B

Magnetic reconnection is a ubiquitous fundamental process in space and astrophysical plasmas that rapidly converts magnetic energy into some combination of flow energy, thermal energy, and non-thermal energetic particles. Over the past decade, a new experimental platform has been developed to study magnetic reconnection using strong coil currents powered by high power lasers at low plasma beta, typical conditions under which reconnection is energetically important in astrophysics. KJ-class lasers were used to drive parallel currents to reconnect MG-level magnetic fields in a quasi-axisymmetric geometry, similar to the Magnetic Reconnection Experiment or MRX, and thus this platform is named micro-MRX. This presentation summarizes two major findings from micro-MRX: direct measurement of accelerated electrons and observation of ion acoustic waves during anti-parallel reconnection. The angular dependence of the measured electron energy spectrum and the resulting accelerated energies, supported by particle-in-cell simulations, indicate that direct acceleration by the out-of-plane reconnection electric field is at work. Furthermore, a sudden onset of ion acoustic bursts has been measured by collective Thomson scattering in the exhaust of magnetic reconnection, followed by electron acoustic bursts with electron heating and bulk acceleration. These results demonstrate that the micro-MRX platform offers a novel and unique approach to study magnetic reconnection in the laboratory in addition to the capabilities provided by traditional magnetized plasma experiments such as MRX and the upcoming FLARE (Facility for Laboratory Reconnection experiments). Future approaches to study other particle acceleration mechanisms and ion acoustic waves from magnetic reconnection are also discussed., Comment: 16 pages, 13 figures, 89 references, accepted for publication in Physics of Plasmas

As mass-losing asymptotic giant branch (AGB) stars evolve to planetary nebulae (PNe), the mass outflow geometries transform from nearly spherical to extreme aspherical. The physical mechanisms governing this transformation are widely believed to be linked to binarity and the associated production of disks and fast jets during transitional (post-AGB) evolutionary stages. We are carrying out a systematic ALMA survey ($P$re-planet$A$ry $N$ebulae high-angular-res$O$lution su$R$vey with $A$L$MA$ or PANORAMA) of a representative sample of bipolar and multipolar post-AGB objects. We have obtained high angular-resolution (0".1-0".4) observations of the CO(3--2) and/or 6--5 emission in order to probe the spatio-kinematic structure of the collimated outflows and the central disk/torii. The results are remarkable, generally showing the presence of bipolar or multipolar high-velocity outflows, dense toroidal waists, and in one case, a geometrically-thin circular ring around the central bipolar nebula. A high degree of point-symmetry characterizes the morphology of the mass ejecta. In this contribution, we present these and other highlights from our survey. We aim to use 2D/3D radiative transfer modeling in order to derive accurate outflow momenta, masses and mass-loss rates for our sample, and build hydrodynamical models that can explain the observed spatio-kinematic structures. These results will then be used to distinguish between different classes of PN-shaping binary interaction models.

Earth's geodynamo has operated for over 3.5 billion years. The magnetic field is currently powered by thermocompositional convection in the outer core, which involves the release of light elements and latent heat as the inner core solidifies. However, since the inner core nucleated no more than 1.5 billion years ago, the early dynamo could not rely on these buoyancy sources. Given recent estimates of the thermal conductivity of the outer core, an alternative mechanism may be required to sustain the geodynamo prior to nucleation of the inner core. One possibility is a silicate dynamo operating in a long-lived basal magma ocean. Here, we investigate the structural, thermal, buoyancy, and magnetic evolution of an Earth-like terrestrial planet. Using modern equations of state and melting curves, we include a time-dependent parameterization of the compositional evolution of an iron-rich basal magma ocean. We combine an internal structure integration of the planet with energy budgets in a coupled core, basal magma ocean, and mantle system. We determine the thermocompositional convective stability of the core and the basal magma ocean, and assess their respective dynamo activity using entropy budgets and magnetic Reynolds numbers. Our conservative nominal model predicts a transient basal magma ocean dynamo followed by a core dynamo after 1 billion years. The model is sensitive to several parameters, including the initial temperature of the core-mantle boundary, the parameterization of mantle convection, the composition of the basal magma ocean, the radiogenic content of the planet, as well as convective velocity and magnetic scaling laws. We use the nominal model to constrain the range of basal magma ocean electrical conductivity and core thermal conductivity that sustain a dynamo.

RISTRETTO is a visible high-resolution spectrograph fed by an extreme adaptive optics (AO) system, to be proposed as a visitor instrument on ESO VLT. The main science goal of RISTRETTO is to pioneer the detection and atmospheric characterisation of exoplanets in reflected light, in particular the temperate rocky planet Proxima b. RISTRETTO will be able to measure albedos and detect atmospheric features in a number of exoplanets orbiting nearby stars for the first time. It will do so by combining a high-contrast AO system working at the diffraction limit of the telescope to a high-resolution spectrograph, via a 7-spaxel integral-field unit (IFU) feeding single-mode fibers. Further science cases for RISTRETTO include the study of accreting protoplanets such as PDS70b/c through spectrally-resolved H-alpha emission, and spatially-resolved studies of Solar System objects such as icy moons and the ice giants Uranus and Neptune. The project is in the manufacturing phase for the spectrograph sub-system, and the preliminary design phase for the AO front-end. Specific developments for RISTRETTO include a novel coronagraphic IFU combining a phase-induced amplitude apodizer (PIAA) to a 3D-printed microlens array feeding a bundle of single-mode fibers. It also features an XAO system with a dual wavefront sensor aiming at high robustness and sensitivity, including to pupil fragmentation. RISTRETTO is a pathfinder instrument in view of similar developments at the ELT, in particular the SCAO-IFU mode of ELT-ANDES and the future ELT-PCS instrument., Comment: 6 pages, 1 figure, SPIE Astronomical Telescopes + Instrumentation, 2024, Yokohama, Japan

Backward stimulated Raman scattering is a three-wave coupling instability requiring the matching of an incoming pump light wave to a scattered light wave and electron plasma wave. It can be harmful to laser-driven inertial confinement fusion because of the reflection of a part of incident laser flux and the generation of suprathermal electrons that preheat the fuel. It is believed that by increasing the laser bandwidth one can suppress the excitation of Raman scattering and mitigate its detrimental effects. It is demonstrated in this paper that using a broad bandwidth laser has little effect on stimulated Raman scattering in the kinetic inflation regime where Landau damping dominates, as the additional bandwidth allows the electron plasma wave to match a wider range of laser frequencies. As a result, plasma wave saturation and Raman backscattering levels remain high even when the laser bandwidth is much larger than the effective instability growth rate., Comment: 12 pages, 13 figures. To be submitted to Physical Review E

We propose that certain white dwarf (WD) planets, such as WD 1856+534 b, may form out of material from a stellar companion that tidally disrupts from common envelope (CE) evolution with the WD progenitor star. The disrupted companion shreds into an accretion disc, out of which a gas giant protoplanet forms due to gravitational instability. To explore this scenario, we make use of detailed stellar evolution models consistent with WD 1856+534. The minimum mass companion that produces a gravitationally-unstable disk after tidal disruption is $\sim$$0.15\,\mathrm{M}_\odot$. Planet formation from tidal disruption is a new channel for producing second-generation planets around WDs., Comment: 9 pages, 2 figures, 1 table. Submitted to PASA. Comments welcome

In this paper, we propose an algorithm for non-myopic sensor management for Bernoulli filtering, i.e., when there may be at most one target present in the scene. The algorithm is based on selecting the action that solves a Bellman-type minimisation problem, whose cost function is the mean square generalised optimal sub-pattern assignment (GOSPA) error, over a future time window. We also propose an implementation of the sensor management algorithm based on an upper bound of the mean square GOSPA error and a Gaussian single-target posterior. Finally, we develop a Monte Carlo tree search algorithm to find an approximate optimal action within a given computational budget. The benefits of the proposed approach are demonstrated via simulations., Comment: Paper accepted to IEEE Transactions on Aerospace and Electronic Systems, 25th June 2024

We present a detailed characterization of the structure and evolution of differentially rotating plasmas driven on the MAGPIE pulsed-power generator (1.4 MA peak current, 240 ns rise-time). The experiments were designed to simulate physics relevant to accretion discs and jets on laboratory scales. A cylindrical aluminium wire array Z pinch enclosed by return posts with an overall azimuthal off-set angle was driven to produce ablation plasma flows that propagate inwards in a slightly off-radial trajectory, injecting mass, angular momentum, and confining ram pressure to a rotating plasma column on the axis. However, the plasma is free to expand axially, forming a collimated, differentially rotating axial jet that propagates at $\approx 100$ km/s. The density profile of the jet corresponds to a dense shell surrounding a low-density core, which is consistent with the centrifugal barrier effect being sustained along the jet's propagation. We show analytically that, as the rotating plasma accretes mass, conservation of mass and momentum implies plasma radial growth scaling as $r \propto t^{1/3}$. As the characteristic moment of inertia increases, the rotation velocity is predicted to decrease and settle on a characteristic value $\approx 20$ km/s. We find that both predictions are in agreement with Thomson scattering and optical self-emission imaging measurements., Comment: Final Production Files accepted by the Journal of Plasma Physics on 18th May 2024. 9 figures

We present an analysis of high angular resolution images of the microlensing target MOA-2007-BLG-192 using Keck adaptive optics and the Hubble Space Telescope. The planetary host star is robustly detected as it separates from the background source star in nearly all of the Keck and Hubble data. The amplitude and direction of the lens-source separation allows us to break a degeneracy related to the microlensing parallax and source radius crossing time. Thus, we are able to reduce the number of possible solutions by a factor of ${\sim}2$, demonstrating the power of high angular resolution follow-up imaging for events with sparse light curve coverage. Following Bennett et al. 2023, we apply constraints from the high resolution imaging on the light curve modeling to find host star and planet masses of $M_{\textrm{host}} = 0.28 \pm 0.04M_{\odot}$ and $m_p = 12.49^{+65.47}_{-8.03}M_{\oplus}$ at a distance from Earth of $D_L = 2.16 \pm 0.30\,$kpc. This work illustrates the necessity for the Nancy Grace Roman Galactic Exoplanet Survey (RGES) to use its own high resolution imaging to inform light curve modeling for microlensing planets that the mission discovers., Comment: 25 pages, 12 figures, accepted in AJ

We revisit the planetary microlensing event OGLE-2013-BLG-0132/MOA-2013-BLG-148 using Keck adaptive optics imaging in 2013 with NIRC2 and in 2020, 7.4 years after the event, with OSIRIS. The 2020 observations yield a source and lens separation of $ 56.91 \pm 0.29$ mas, which provides us with a precise measurement of the heliocentric proper motion of the event $\mu_{rel,hel} = 7.695 \pm 0.039$ mas $yr^{-1}$. We measured the magnitude of the lens in K-band as $K_{lens} = 18.69 \pm 0.04 $. Using these constraints, we refit the microlensing light curve and undertake a full reanalysis of the event parameters including the microlensing parallax $\pi_{E}$ and the distance to the source D$_S$. We confirm the results obtained in the initial study by \cite{Mroz_2017} and improve significantly upon the accuracy of the physical parameters. The system is an M dwarf of $0.495 \pm 0.054$ $M_\odot$ orbited by a cold, Saturn-mass planet of $0.26 \pm 0.028$ $M_{Jup}$ at projected separation $r_{\perp}$ = 3.14 $\pm$ 0.28 AU. This work confirms that the planetary system is at a distance of 3.48 $\pm$ 0.36 kpc, which places it in the Galactic disk and not the Galactic bulge., Comment: 16 pages, 7 figures. Resubmitted to AJ after minor revisions

We report superluminal jet motion with an apparent speed of $\beta_\mathrm{app}=1.65\pm0.57$ in the radio-quiet (RQ) low ionisation nuclear emission line region (LINER) galaxy, KISSR872. This result comes from two epoch phase-referenced very long baseline interferometry (VLBI) observations at 5 GHz. The detection of bulk relativistic motion in the jet of this extremely radio faint AGN, with a total 1.4 GHz flux density of 5 mJy in the 5.4 arcsec resolution Very Large Array (VLA) FIRST survey image and 1.5 mJy in the $\sim5$ milli-arcsec resolution Very Long Baseline Array (VLBA) image, is the first of its kind in a RQ LINER galaxy. The presence of relativistic jets in lower accretion rate objects like KISSR872, with an Eddington ratio of 0.04, reveals that even RQ AGN can harbor relativistic jets, and evidentiates their universality over a wide range of accretion powers., Comment: 9 pages, 4 figures, accepted for publication in ApJ

Recent pulsed-power experiments have demonstrated the formation of astrophysically-relevant, differentially rotating plasmas [1]. Key features of the plasma flows are the discovery of a quasi-Keplerian rotation curve, the launching of highly-collimated angular-momentum-transporting axial jets, and a hollow density structure sustained by the centrifugal barrier effect. In this communication we discuss several features of the plasma structure in these experiments through order-of-magnitude models. First, we show that the observed rotation velocity would produce a centrifugal force strong enough to support the hollow density profile. Second, we show that the axial jet should diverge much faster than what was observed, were it not for a magnetized halo with 3T which surrounds the jet and exerts pressure on the interface.Finally, we discuss the temperature structure in the axial jet and plasma halo.We show that a 3T magnetic field would also suppress electron heat conduction,leading to the flat profile observed experimentally. We also find that the axial jet is efficiently radiatively cooled,whereas the halo is not, which would explain the thermal decoupling between the two regions., Comment: Second version with clarifications on text and figures, and explicit calculations regarding the omega-effect. Manuscript re-submitted to IEEE Transactions On Plasma Science. 4 Figures

We report on the results of a simulation based study of colliding magnetized plasma flows. Our set-up mimics pulsed power laboratory astrophysical experiments but, with an appropriate frame change, are relevant to astrophysical jets with internal velocity variations. We track the evolution of the interaction region where the two flows collide. Cooling via radiative loses are included in the calculation. We systematically vary plasma beta ($\beta_m$) in the flows, the strength of the cooling ($\Lambda_0$) and the exponent ($\alpha$) of temperature-dependence of the cooling function. We find that for strong magnetic fields a counter-propagating jet called a "spine" is driven by pressure from shocked toroidal fields. The spines eventually become unstable and break apart. We demonstrate how formation and evolution of the spines depends on initial flow parameters and provide a simple analytic model that captures the basic features of the flow., Comment: 14 pages, 16 figures. Submitted to MNRAS

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 $M_{\rm host}=0.434\pm0.065 M_\odot$, and $m_p=2.44 \pm 0.49 M_{\rm Jupiter}$. They are located at a distance of $D_L=3.44\pm0.53\,$kpc, with a projected separation of $2.70\pm 0.42\,$AU. These results contribute to our determination of exoplanet host star masses for the Suzuki et al. (2016) 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. (2016) 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., Comment: 42 pages, with 4 figures, accepted for publication in the Astronomical Journal

This is the executive summary for the report, "Survey of Evidence in Education for Schools (SEE-S) Descriptive Report." In the United States, increased pressure through accountability policy and through the production and dissemination of scientifically based research are intended to create conditions for improving research use. Concurrently, researchers, education agencies, and funders have mounted efforts to strengthen relationships between research and educational practice to improve decisions about and outcomes for children. Accompanying these efforts is a need to understand, at scale, educational decision-making, and the role of research in it. To date, studies of research use in the United States have tended to focus on various stakeholders' research use (e.g., Biddle & Saha, 2002; Dagenais et al., 2012), case studies of schools or districts (e.g., Asen et al., 2013; Finnigan et al., 2013), or case studies of specific education policies or practices (e.g., Hopkins et al., 2019; Scott et al., 2017). The purpose of the report is to broadly portray research use in U.S. schools at scale to better understand where we are as an educational system in the more than forty-year journey to improve the role of research in education policy and practice. [For the full report, see ED628007. For the technical report, see ED628010.]

In this technical report, the Center for Research Use in Education (CRUE) presents the methodological design of a large-scale quantitative investigation of research use by school-based practitioners through the "Survey of Evidence in Education for Schools (SEE-S)." It documents the major technical aspects of the development of SEE-S, including item development, sample selection, and reliability and validity assessment. Descriptive statistics for data collected during the survey field trial are also detailed in this report. Through the development and validation of multiple survey measures, this study aims to deepen the fields' understanding of the actions and activities that educators are involved in concerning the use of evidence in decision-making. [For the descriptive report, see ED628007. For the executive summary, see ED628009.]

In this paper, we investigate the base-$p$ expansions of putative counterexamples to the $p$-adic Littlewood conjecture of de Mathan and Teuli\'e. We show that if a counterexample exists, then so does a counterexample whose base-$p$ expansion is uniformly recurrent. Furthermore, we show that if the base-$p$ expansion of $x$ is a morphic word $\tau(\phi^\omega(a))$ where $\phi^\omega(a)$ contains a subword of the form $uXuXu$ with $\lim_{n\to\infty}|\phi^n(u)|=\infty$, then $x$ satisfies the $p$-adic Littlewood conjecture. In the special case when $p=2$, we show that the conjecture holds for all pure morphic words., Comment: 14 pages, no figures

We perform 3D hydrodynamical simulations to study recombination and ionization during the common envelope (CE) phase of binary evolution, and develop techniques to track the ionic transitions in time and space. We simulate the interaction of a $2\,M_\odot$ red giant branch primary and a $1\,M_\odot$ companion modeled as a particle. We compare a run employing a tabulated equation of state (EOS) that accounts for ionization and recombination, with a run employing an ideal gas EOS. During the first half of the simulations, $\sim15$ per cent more mass is unbound in the tabulated EOS run due to the release of recombination energy, but by simulation end the difference has become negligible. We explain this as being a consequence of (i) the tabulated EOS run experiences a shallower inspiral and hence smaller orbital energy release at late times because recombination energy release expands the envelope and reduces drag, and (ii) collision and mixing between expanding envelope gas, ejecta and circumstellar ambient gas assists in unbinding the envelope, but does so less efficiently in the tabulated EOS run where some of the energy transferred to bound envelope gas is used for ionization. The rate of mass unbinding is approximately constant in the last half of the simulations and the orbital separation steadily decreases at late times. A simple linear extrapolation predicts a CE phase duration of $\sim2\,\mathrm{yr}$, after which the envelope would be unbound., Comment: 20 pages, 18 figures, 2 tables. Accepted for publication in MNRAS

NGC 6302 (The ''Butterfly Nebula'') is an extremely energetic bipolar nebula whose central star is among the most massive, hottest, and presumably rapidly evolving of all central stars of planetary nebulae. Our proper-motion study of NGC 6302, based on excellent HST WFC3 images spanning 11 yr, has uncovered at least four different pairs of expanding internal lobes that were ejected at various times over the past two millennia at speeds ranging from 10 to 600 km s^-1. In addition, we find a pair of off-axis flows in constant motion at 760 +/- 100 km s^-1 within which bright [Fe II] feathers are conspicuous. Combining our results with those previously published, we find that the ensemble of flows has an ionized mass > 0.1 M_sun. The kinetic energy of the ensemble, 10^46 - 10^48 ergs, lies at the upper end of gravity-powered processes such as stellar mergers or mass accretion and is too large to be explained by stellar radiation pressure or convective ejections. The structure and dynamics of the Butterfly Nebula suggests that its central engine has had a remarkable history, and the highly unusual patterns of growth within its wings challenge our current understanding of late stellar mass ejection., Comment: 17 pages, 3 figures, 1 table

We measured precise masses of the host and planet in OGLE-2003-BLG-235 system, when the lens and source were resolving, with 2018 Keck high resolution images. This measurement is in agreement with the observation taken in 2005 with the Hubble Space Telescope (HST). In 2005 data, the lens and sources were not resolved and the measurement was made using color-dependent centroid shift only. Nancy Grace Roman Space Telescope will measure masses using data typically taken within 3-4 years of the peak of the event which is much shorter baseline compared to most of the mass measurements to date. Hence, color dependent centroid shift will be one of the primary method of mass measurements for Roman. Yet, mass measurements of only two events (OGLE-2003-BLG-235 and OGLE-2005-BLG-071) are done using the color dependent centroid shift method so far. The accuracy of the measurements using this method are neither completely known nor well studied. The agreement of Keck and HST results, shown in this paper, is very important since this agreement confirms the accuracy of the mass measurements determined at a small lens-source separation using the color dependent centroid shift method. This also shows that with >100 high resolution images, Roman telescope will be able to use color dependent centroid shift at 3-4 years time baseline and produce mass measurements. We find that OGLE-2003-BLG-235 is a planetary system consists of a 2.34 +- 0.43M_Jup planet orbiting a 0.56 +- 0.06M_Sun K-dwarf host star at a distance of 5.26 +- 0.71 kpc from the Sun., Comment: Submitted to AJ, under review. arXiv admin note: substantial text overlap with arXiv:2009.02329

Understanding large-scale magnetic field growth in astrophysical objects is a persistent challenge. We tackle the long-standing question of how much helical large-scale dynamo growth occurs independent of the magnetic Reynolds number (Rm) in a closed volume. From modest-Rm numerical simulations, we identify a pre-saturation regime when the large-scale field grows independently of Rm, but to an Rm-dependent magnitude. For plausible magnetic spectra however, the analysis predicts the magnitude to be Rm-independent and substantial as Rm$\to\infty$. This gives renewed optimism for the relevance of closed dynamos and pinpoints how modest Rm and hyper-diffusive simulations can cause misapprehension of the Rm$\to\infty$ behavior., Comment: manuscript shortened to 6 pages, 1 figure; added Supplemental Material

This paper is dedicated to providing an introduction into multidimensional integer trigonometry. We start with an exposition of integer trigonometry in two dimensions, which was introduced in 2008, and use this to generalise these integer trigonometric functions to arbitrary dimension. We then move on to study the basic properties of integer trigonometric functions. We find integer trigonometric relations for transpose and adjacent simplicial cones, and for the cones which generate the same simplices. Additionally, we discuss the relationship between integer trigonometry, the Euclidean algorithm, and continued fractions. Finally, we use adjacent and transpose cones to introduce a notion of best approximations of simplicial cones. In two dimensions, this notion of best approximation coincides with the classical notion of the best approximations of real numbers., Comment: 24 pages, 12 illustrations

We present the analysis of high resolution follow-up observations of OGLE-2016-BLG-1195 using Laser Guide Star Adaptive Optics with Keck, seven years after the event's peak. We resolve the lens, measuring its flux and the relative source-lens proper motion, thus finding the system to be a $M_{\rm p} = 10.08\pm 1.18\ M_{\rm \oplus}$ planet orbiting an M-dwarf, $M_{\rm L} = 0.62\pm 0.05\ M_{\odot}$, beyond the snow line, with a projected separation of $r_\perp=2.24\pm 0.21$ AU at $D_{\rm L} = 7.45\pm 0.55$ kpc. Our results are consistent with the discovery paper, which reports values with 1-sigma uncertainties based on a single mass-distance constraint from finite source effects. However, both the discovery paper and our follow-up results disagree with the analysis of a different group that also present the planetary signal detection. The latter utilizes \textit{Spitzer} photometry to measure a parallax signal claiming the system is an Earth-mass planet orbiting an ultracool dwarf. Their parallax signal though is improbable since it suggests a lens star in the disk moving perpendicular to Galactic rotation. Moreover, microlensing parallaxes can be impacted by systematic errors in the photometry. Therefore, we reanalyze the \textit{Spitzer} photometry using a Pixel Level Decorrelation (PLD) model to detrend detector systematics. We find that we can not confidently recover the same detrended light curve that is likely dominated by systematic errors in the photometric data. The results of this paper act as a cautionary tale that a careful understanding of detector systematics and how they influence astrophysical constraints is crucial., Comment: Submitted to AJ