arXiv subjects

Radoslaw Poleski

Publications and source records attributed to Radoslaw Poleski.

At least 37 records · Page 2Linked to original sources

arXiv2021

OGLE-2019-BLG-0960Lb: The Smallest Microlensing Planet

We report the analysis of OGLE-2019-BLG-0960, which contains the smallest mass-ratio microlensing planet found to date (q = 1.2--1.6 x 10^{-5} at 1-sigma). Although there is substantial uncertainty in the satellite parallax measured by Spitzer, the measurement of the annual parallax effect combined with the finite source effect allows us to determine the mass of the host star (M_L = 0.3--0.6 M_Sun), the mass of its planet (m_p = 1.4--3.1 M_Earth), the projected separation between the host and planet (a_perp = 1.2--2.3 au), and the distance to the lens system (D_L = 0.6--1.2 kpc). The lens is plausibly the blend, which could be checked with adaptive optics observations. As the smallest planet clearly below the break in the mass-ratio function (Suzuki et al. 2016; Jung et al. 2019), it demonstrates that current experiments are powerful enough to robustly measure the slope of the mass-ratio function below that break. We find that the cross-section for detecting small planets is maximized for planets with separations just outside of the boundary for resonant caustics and that sensitivity to such planets can be maximized by intensively monitoring events whenever they are magnified by a factor A > 5. Finally, an empirical investigation demonstrates that most planets showing a degeneracy between (s > 1) and (s < 1) solutions are not in the regime (|log s| >> 0) for which the "close"/"wide" degeneracy was derived. This investigation suggests a link between the "close"/"wide" and "inner/outer" degeneracies and also that the symmetry in the lens equation goes much deeper than symmetries uncovered for the limiting cases.

astro-ph.EP↗

arXiv2020

Microlensing optical depth and event rate in the OGLE-IV Galactic plane fields

Searches for gravitational microlensing events are traditionally concentrated on the central regions of the Galactic bulge but many microlensing events are expected to occur in the Galactic plane, far from the Galactic Center. Owing to the difficulty in conducting high-cadence observations of the Galactic plane over its vast area, which are necessary for the detection of microlensing events, their global properties were hitherto unknown. Here, we present results of the first comprehensive search for microlensing events in the Galactic plane. We searched an area of almost 3000 square degrees along the Galactic plane (|b|<7, 0<l<50, 190<l<360 deg) observed by the Optical Gravitational Lensing Experiment (OGLE) during 2013-2019 and detected 630 events. We demonstrate that the mean Einstein timescales of Galactic plane microlensing events are on average three times longer than those of Galactic bulge events, with little dependence on the Galactic longitude. We also measure the microlensing optical depth and event rate as a function of Galactic longitude and demonstrate that they exponentially decrease with the angular distance from the Galactic Center (with the characteristic angular scale length of 32 deg). The average optical depth decreases from $0.5\times 10^{-6}$ at l=10 deg to $1.5\times 10^{-8}$ in the Galactic anticenter. We also find that the optical depth in the longitude range 240<l<330 deg is asymmetric about the Galactic equator, which we interpret as a signature of the Galactic warp.

astro-ph.GA↗

arXiv2019

OGLE-2015-BLG-1771Lb: A Microlens Planet Orbiting an Ultracool Dwarf?

We report the discovery and the analysis of the short (tE < 5 days) planetary microlensing event, OGLE-2015-BLG-1771. The event was discovered by the Optical Gravitational Lensing Experiment (OGLE), and the planetary anomaly (at I ~ 19) was captured by The Korea Microlensing Telescope Network (KMTNet). The event has three surviving planetary models that explain the observed light curves, with planet-host mass ratio q \~ 5.4 * 10^{-3}, 4.5 * 10^{-3} and 4.5 * 10^{-2}, respectively. The first model is the best-fit model, while the second model is disfavored by Δχ^2 ~ 3. The last model is strongly disfavored by Δχ^2 ~ 15 but not ruled out. A Bayesian analysis using a Galactic model indicates that the first two models are probably composed of a Saturn-mass planet orbiting a late M dwarf, while the third one could consist of a super-Jovian planet and a mid-mass brown dwarf. The source-lens relative proper motion is mu_rel ~ 9 mas/yr, so the source and lens could be resolved by current adaptive-optics (AO) instruments in 2021 if the lens is luminous.

astro-ph.EP↗

arXiv2019

Spitzer Microlensing parallax reveals two isolated stars in the Galactic bulge

We report the mass and distance measurements of two single-lens events from the 2017 Spitzer microlensing campaign. The ground-based observations yield the detection of finite-source effects, and the microlens parallaxes are derived from the joint analysis of ground-based observations and Spitzer observations. We find that the lens of OGLE-2017-BLG-1254 is a $0.60 \pm 0.03 M_{\odot}$ star with $D_{\rm LS} = 0.53 \pm 0.11~\text{kpc}$, where $D_{\rm LS}$ is the distance between the lens and the source. The second event, OGLE-2017-BLG-1161, is subject to the known satellite parallax degeneracy, and thus is either a $0.51^{+0.12}_{-0.10} M_{\odot}$ star with $D_{\rm LS} = 0.40 \pm 0.12~\text{kpc}$ or a $0.38^{+0.13}_{-0.12} M_{\odot}$ star with $D_{\rm LS} = 0.53 \pm 0.19~\text{kpc}$. Both of the lenses are therefore isolated stars in the Galactic bulge. By comparing the mass and distance distributions of the eight published Spitzer finite-source events with the expectations from a Galactic model, we find that the Spitzer sample is in agreement with the probability of finite-source effects occurrence in single lens events.

astro-ph.SR↗

arXiv2019

"Auxiliary" Science with the WFIRST Microlensing Survey

The Wide Field Infrared Survey Telescope (WFIRST) will monitor $\sim 2$ deg$^2$ toward the Galactic bulge in a wide ($\sim 1-2~μ$m) W149 filter at 15-minute cadence with exposure times of $\sim$50s for 6 seasons of 72 days each, for a total $\sim$41,000 exposures taken over $\sim$432 days, spread over the 5-year prime mission. This will be one of the deepest exposures of the sky ever taken, reaching a photon-noise photometric precision of 0.01 mag per exposure and collecting a total of $\sim 10^9$ photons over the course of the survey for a W149$_{\rm AB}\sim 21$ star. Of order $4 \times 10^7$ stars will be monitored with W149$_{\rm AB}$<21, and 10$^8$ stars with W145$_{\rm AB}$<23. The WFIRST microlensing survey will detect $\sim$54,000 microlensing events, of which roughly 1% ($\sim$500) will be due to isolated black holes, and $\sim$3% ($\sim$1600) will be due to isolated neutron stars. It will be sensitive to (effectively) isolated compact objects with masses as low as the mass of Pluto, thereby enabling a measurement of the compact object mass function over 10 orders of magnitude. Assuming photon-noise limited precision, it will detect $\sim 10^5$ transiting planets with sizes as small as $\sim 2~R_\oplus$, perform asteroseismology of $\sim 10^6$ giant stars, measure the proper motions to $\sim 0.3\%$ and parallaxes to $\sim 10\%$ for the $\sim 6 \times 10^6$ disk and bulge stars in the survey area, and directly detect $\sim 5 \times 10^3$ Trans-Neptunian objects (TNOs) with diameters down to $\sim 10$ km, as well as detect $\sim 10^3$ occulations of stars by TNOs during the survey. All of this science will completely serendipitous, i.e., it will not require modifications of the WFIRST optimal microlensing survey design. Allowing for some minor deviation from the optimal design, such as monitoring the Galactic center, would enable an even broader range of transformational science.

astro-ph.SR↗

arXiv2019

Masses and Distances of Planetary Microlens Systems with High Angular Resolution Imaging

Microlensing is the only method that can detect and measure mass of wide orbit, low mass, solar system analog exoplanets. Mass measurements of such planets would yield massive science on planet formation, exoplanet demographics, free floating planets, planet frequencies towards the galaxy. High res follow-up observations of past microlens targets provide a mass measurement of microlens planets and hosts at an uncertainty of <20%. This will be primary method for mass measurement with WFIRST. We advocate for the fact that high resolution observations with AO, HST and JWST(in future) remain necessary in coming decade to develop the methods, to determine the field and filter selection, understand the systematics and to develop a robust pipeline to release high quality data products from WFIRST microlensing survey such that the astronomy community can promptly engage in the science. We also support future high res obs with US ELTs with advanced Laser AO systems in context of enhancing the science return of WFIRST microlensing survey. We endorse the 2018 Exoplanet Science Strategy report published by the National Academy. This white paper extends and complements the material presented therein. In particular, this white paper supports the recommendation of the National Academy Exoplanet Science Strategy report that: NASA should launch WFIRST to conduct its microlensing survey of distant planets and to demonstrate the technique of coronagraphic spectroscopy on exoplanet targets. This white paper also supports to the finding from that report which states "A number of activities, including precursor and concurrent observations using ground- and space-based facilities, would optimize the scientific yield of the WFIRST microlensing survey."

astro-ph.EP↗

arXiv2019

The Scientific Context of WFIRST Microlensing in the 2020s

[abridged] WFIRST is uniquely capable of finding planets with masses as small as Mars at separations comparable to Jupiter, i.e., beyond the current ice lines of their stars. These planets fall between the close-in planets found by Kepler and the wide separation gas giants seen by direct imaging and ice giants inferred from ALMA observations. Furthermore, the smallest planets WFIRST can detect are smaller than the planets probed by RV and Gaia at comparable separations. Interpreting planet populations to infer the underlying formation and evolutionary processes requires combining results from multiple detection methods to measure the full variation of planets as a function of planet size, orbital separation, and host star mass. Microlensing is the only way to find planets from 0.5 to 5M_E at 1 to 5au. The case for a microlensing survey from space has not changed in the past 20 yrs: space allows wide-field diffraction-limited observations that resolve main-sequence stars in the bulge, which allows the detection and characterization of the smallest signals including those from planets with masses at least as small as Mars. What has changed is that ground-based (GB) microlensing is reaching its limits, underscoring the scientific necessity for a space-based survey. GB microlensing has found a break in the mass-ratio distribution at about a Neptune, implying that these are the most common microlensing planet and that planets smaller than this are rare. However, GB microlensing reaches its detection limits only slightly below the observed break. WFIRST will measure the shape of the mass-ratio function below the break by finding numerous smaller planets: 500 Neptunes, 600 gas giants, 200 Earths, and planets as small as 0.1M_E. Because it will also measure host masses and distances, WFIRST will also track the behavior of the planet distribution as a function of separation and host star mass.

astro-ph.EP↗

arXiv2019

$Spitzer$ Microlensing Parallax for OGLE-2017-BLG-0896 Reveals a Counter-Rotating Low-Mass Brown Dwarf

The kinematics of isolated brown dwarfs in the Galaxy, beyond the solar neighborhood, is virtually unknown. Microlensing has the potential to probe this hidden population, as it can measure both the mass and five of the six phase-space coordinates (all except the radial velocity) even of a dark isolated lens. However, the measurements of both the microlens parallax and finite-source effects are needed in order to recover the full information. Here, we combine $Spitzer$ satellite parallax measurement with the ground-based light curve, which exhibits strong finite-source effects, of event OGLE-2017-BLG-0896. We find two degenerate solutions for the lens (due to the known satellite-parallax degeneracy), which are consistent with each other except for their proper motion. The lens is an isolated brown dwarf with a mass of either $18\pm1M_J$ or $20\pm1M_J$. This is the lowest isolated-object mass measurement to date, only $\sim$45\% more massive than the theoretical deuterium-fusion boundary at solar metallicity, which is the common definition of a free-floating planet. The brown dwarf is located at either $3.9\pm0.1$ kpc or $4.1\pm0.1$ kpc toward the Galactic bulge, but with proper motion in the opposite direction of disk stars, with one solution suggesting it is moving within the Galactic plane. While it is possibly a halo brown dwarf, it might also represent a different, unknown population.

astro-ph.SR↗

arXiv2019

Modeling microlensing events with MulensModel

We introduce MulensModel, a software package for gravitational microlensing modeling. The package provides a framework for calculating microlensing model magnification curves and goodness-of-fit statistics for microlensing events with single and binary lenses as well as a variety of higher-order effects: extended sources with limb-darkening, annual microlensing parallax, satellite microlensing parallax, and binary lens orbital motion. The software could also be used for analysis of the planned microlensing survey by the NASA flag-ship WFIRST satellite. MulensModel is available at https://github.com/rpoleski/MulensModel/.

astro-ph.IM↗

arXiv2018

Prediction on detection and characterization of Galactic disk microlensing events by LSST

Upcoming LSST survey gives an unprecedented opportunity for studying populations of intrinsically faint objects using microlensing technique. Large field of view and aperture allow effective time-series observations of many stars in Galactic disk and bulge. Here, we combine Galactic models (for |b|<10 deg) and simulations of LSST observations to study how different observing strategies affect the number and properties of microlensing events detected by LSST. We predict that LSST will mostly observe long duration microlensing events due to the source stars with the averaged magnitude around 22 in r-band, rather than high-magnification events due to fainter source stars. In Galactic bulge fields, LSST should detect on the order of 400 microlensing events per square degree as compared to 15 in disk fields. Improving the cadence increases the number of detectable microlensing events, e.g., improving the cadence from 6 to 2 days approximately doubles the number of microlensing events throughout the Galaxy. According to the current LSST strategy, it will observe some fields 900 times during a 10-year survey with the average cadence of ~4-days (I) and other fields (mostly toward the Galactic disk) around 180 times during a 1-year survey only with the average 1-day cadence (II). We anticipate that the number of events corresponding to these strategies are 7900 and 34000, respectively. Toward similar lines of sight, LSST with the first observing strategy (I) will detect more and on average longer microlensing events than those observable with the second strategy. If LSST spends enough time observing near Galactic plane, then the large number of microlensing events will allow studying Galactic distribution of planets and finding isolated black holes among wealth of other science cases.

astro-ph.IM↗

arXiv2018

The late type eclipsing binaries in the Large Magellanic Cloud: catalogue of fundamental physical parameters

We present a determination of precise fundamental physical parameters of twenty detached, double- lined, eclipsing binary stars in the Large Magellanic Cloud (LMC) containing G- or early K-type giant stars. Eleven are new systems, the remaining nine are systems already analyzed by our team for which we present updated parameters. The catalogue results from our long-term survey of eclipsing binaries in the Magellanic Clouds suitable for high-precision determination of distances (the Araucaria project). The V-band brightnesses of the systems range from 15.4 mag to 17.7 mag and their orbital periods range from 49 days to 773 days. Six systems have favorable geometry showing total eclipses. The absolute dimensions of all eclipsing binary components are calculated with a precision of better than 3% and all systems are suitable for a precise distance determination. The measured stellar masses are in the range 1.4 to 4.6 M_sun and comparison with the MESA isochrones gives ages between 0.1 and 2.1 Gyr. The systems show some weak age-metallicity relation. Two systems have components with very different masses: OGLE LMC-ECL-05430 and OGLE LMC-ECL-18365. Neither system can be fitted by single stellar evolution isochrone, explained by a past mass transfer scenario in the case of ECL-18365 and a gravitational capture or a hierarchical binary merger scenario in the case of ECL-05430. The longest period system OGLE LMC SC9 230659 shows a surprising apsidal motion which shifts the apparent position of the eclipses. In one spectrum of OGLE LMC-ECL-12669 we noted a peculiar dimming of one of the components by 65% well outside of the eclipses. We interpret this observation as arising from an extremely rare occultation event as a foreground Galactic object covers only one component of an extragalactic eclipsing binary.

astro-ph.SR↗

arXiv2018

New Self-lensing Models of the Small Magellanic Cloud: Can Gravitational Microlensing Detect Extragalactic Exoplanets?

We use three-dimensional distributions of classical Cepheids and RR~Lyrae stars in the Small Magellanic Cloud (SMC) to model the stellar density distribution of a young and old stellar population in that galaxy. We use these models to estimate the microlensing self-lensing optical depth to the SMC, which is in excellent agreement with the observations. Our models are consistent with the total stellar mass of the SMC of about 1.0 x 10^9 MSun under the assumption that all microlensing events toward this galaxy are caused by self-lensing. We also calculate the expected event rates and estimate that future large-scale surveys, like the Large Synoptic Survey Telescope (LSST), will be able to detect up to a few dozen microlensing events in the SMC annually. If the planet frequency in the SMC is similar to that in the Milky Way, a few extragalactic planets can be detected over the course of the LSST survey, provided significant changes in the SMC observing strategy are devised. A relatively small investment of LSST resources can give us a unique probe of the population of extragalactic exoplanets.

astro-ph.EP↗

arXiv2017

Reverberation Mapping of Optical Emission Lines in Five Active Galaxies

We present the first results from an optical reverberation mapping campaign executed in 2014, targeting the active galactic nuclei (AGN) MCG+08-11-011, NGC 2617, NGC 4051, 3C 382, and Mrk 374. Our targets have diverse and interesting observational properties, including a "changing look" AGN and a broad-line radio galaxy. Based on continuum-H$β$ lags, we measure black hole masses for all five targets. We also obtain H$γ$ and He{\sc ii}\,$λ4686$ lags for all objects except 3C 382. The He{\sc ii}\,$λ4686$ lags indicate radial stratification of the BLR, and the masses derived from different emission lines are in general agreement. The relative responsivities of these lines are also in qualitative agreement with photoionization models. These spectra have extremely high signal-to-noise ratios (100--300 per pixel) and there are excellent prospects for obtaining velocity-resolved reverberation signatures.

astro-ph.GA↗

arXiv2017

Science-Driven Optimization of the LSST Observing Strategy

The Large Synoptic Survey Telescope is designed to provide an unprecedented optical imaging dataset that will support investigations of our Solar System, Galaxy and Universe, across half the sky and over ten years of repeated observation. However, exactly how the LSST observations will be taken (the observing strategy or "cadence") is not yet finalized. In this dynamically-evolving community white paper, we explore how the detailed performance of the anticipated science investigations is expected to depend on small changes to the LSST observing strategy. Using realistic simulations of the LSST schedule and observation properties, we design and compute diagnostic metrics and Figures of Merit that provide quantitative evaluations of different observing strategies, analyzing their impact on a wide range of proposed science projects. This is work in progress: we are using this white paper to communicate to each other the relative merits of the observing strategy choices that could be made, in an effort to maximize the scientific value of the survey. The investigation of some science cases leads to suggestions for new strategies that could be simulated and potentially adopted. Notably, we find motivation for exploring departures from a spatially uniform annual tiling of the sky: focusing instead on different parts of the survey area in different years in a "rolling cadence" is likely to have significant benefits for a number of time domain and moving object astronomy projects. The communal assembly of a suite of quantified and homogeneously coded metrics is the vital first step towards an automated, systematic, science-based assessment of any given cadence simulation, that will enable the scheduling of the LSST to be as well-informed as possible.

astro-ph.IM↗

arXiv2017

No large population of unbound or wide-orbit Jupiter-mass planets

Gravitational microlensing is the only method capable of exploring the entire population of free-floating planets down to Mars-mass objects, because the microlensing signal does not depend on the brightness of the lensing object. A characteristic timescale of microlensing events depends on the mass of the lens: the less massive the lens, the shorter the microlensing event. A previous analysis of 474 microlensing events found an excess of very short events (1-2 days) - more than known stellar populations would suggest - indicating the existence of a large population of unbound or wide-orbit Jupiter-mass planets (reported to be almost twice as common as main-sequence stars). These results, however, do not match predictions of planet formation theories and are in conflict with surveys of young clusters. Here we report the analysis of a six times larger sample of microlensing events discovered during the years 2010-2015. Although our survey has very high sensitivity (detection efficiency) to short-timescale (1--2 days) microlensing events, we found no excess of events with timescales in this range, with a 95% upper limit on the frequency of Jupiter-mass free-floating or wide-orbit planets of 0.25 planet per main-sequence star. We detected a few possible ultrashort-timescale events (with timescales of less than 0.5 day), which may indicate the existence of Earth- and super-Earth-mass free-floating planets, as predicted by planet-formation theories. [abridged]

astro-ph.EP↗

arXiv2015

Interstellar Extinction Curve Variations Toward the Inner Milky Way: A Challenge to Observational Cosmology

We investigate interstellar extinction curve variations toward $\sim$4 deg$^{2}$ of the inner Milky Way in $VIJK_{s}$ photometry from the OGLE-III and $VVV$ surveys, with supporting evidence from diffuse interstellar bands and $F435W,F625W$ photometry. We obtain independent measurements toward $\sim$2,000 sightlines of $A_{I}$, $E(V-I)$, $E(I-J)$, and $E(J-K_{s})$, with median precision and accuracy of 2%. We find that the variations in the extinction ratios $A_{I}/E(V-I)$, $E(I-J)/E(V-I)$ and $E(J-K_{s})/E(V-I)$ are large (exceeding 20%), significant, and positively correlated, as expected. However, both the mean values and the trends in these extinction ratios are drastically shifted from the predictions of Cardelli and Fitzpatrick, regardless of how $R_{V}$ is varied. Furthermore, we demonstrate that variations in the shape of the extinction curve has at least two degrees of freedom, and not one (e.g. $R_{V}$), which we conform with a principal component analysis. We derive a median value of $ =13.44$, which is $\sim$60% higher than the "standard" value. We show that the Wesenheit magnitude $W_{I}=I-1.61(I-J)$ is relatively impervious to extinction curve variations. Given that these extinction curves are linchpins of observational cosmology, and that it is generally assumed that $R_{V}$ variations correctly capture variations in the extinction curve, we argue that systematic errors in the distance ladder from studies of type Ia supernovae and Cepheids may have been underestimated. Moreover, the reddening maps from the Planck experiment are shown to systematically overestimate dust extinction by $\sim$100%, and lack sensitivity to extinction curve variations.

astro-ph.SR↗

arXiv2015

The Araucaria Project: A study of the classical Cepheid in the eclipsing binary system OGLE LMC562.05.9009 in the Large Magellanic Cloud

We present a detailed study of the classical Cepheid in the double-lined, highly eccentric eclipsing binary system OGLE-LMC562.05.9009. The Cepheid is a fundamental mode pulsator with a period of 2.988 days. The orbital period of the system is 1550 days. Using spectroscopic data from three 4-8-m telescopes and photometry spanning 22 years, we were able to derive the dynamical masses and radii of both stars with exquisite accuracy. Both stars in the system are very similar in mass, radius and color, but the companion is a stable, non-pulsating star. The Cepheid is slightly more massive and bigger (M_1 = 3.70 +/- 0.03M_sun, R_1 = 28.6 +/- 0.2R_sun) than its companion (M_2 = 3.60 +/- 0.03M_sun, R_2 = 26.6 +/- 0.2R_sun). Within the observational uncertainties both stars have the same effective temperature of 6030 +/- 150K. Evolutionary tracks place both stars inside the classical Cepheid instability strip, but it is likely that future improved temperature estimates will move the stable giant companion just beyond the red edge of the instability strip. Within current observational and theoretical uncertainties, both stars fit on a 205 Myr isochrone arguing for their common age. From our model, we determine a value of the projection factor of p = 1.37 +/- 0.07 for the Cepheid in the OGLE-LMC562.05.9009 system. This is the second Cepheid for which we could measure its p-factor with high precision directly from the analysis of an eclipsing binary system, which represents an important contribution towards a better calibration of Baade-Wesselink methods of distance determination for Cepheids.

astro-ph.SR↗

arXiv2015

The Time Domain Spectroscopic Survey: Variable Object Selection and Anticipated Results

We present the selection algorithm and anticipated results for the Time Domain Spectroscopic Survey (TDSS). TDSS is an SDSS-IV eBOSS subproject that will provide initial identification spectra of approximately 220,000 luminosity-variable objects (variable stars and AGN) across 7,500 square degrees selected from a combination of SDSS and multi-epoch Pan-STARRS1 photometry. TDSS will be the largest spectroscopic survey to explicitly target variable objects, avoiding pre-selection on the basis of colors or detailed modeling of specific variability characteristics. Kernel Density Estimate (KDE) analysis of our target population performed on SDSS Stripe 82 data suggests our target sample will be 95% pure (meaning 95% of objects we select have genuine luminosity variability of a few magnitudes or more). Our final spectroscopic sample will contain roughly 135,000 quasars and 85,000 stellar variables, approximately 4,000 of which will be RR Lyrae stars which may be used as outer Milky Way probes. The variability-selected quasar population has a smoother redshift distribution than a color-selected sample, and variability measurements similar to those we develop here may be used to make more uniform quasar samples in large surveys. The stellar variable targets are distributed fairly uniformly across color space, indicating that TDSS will obtain spectra for a wide variety of stellar variables including pulsating variables, stars with significant chromospheric activity, cataclysmic variables and eclipsing binaries. TDSS will serve as a pathfinder mission to identify and characterize the multitude of variable objects that will be detected photometrically in even larger variability surveys such as LSST.

astro-ph.HE↗