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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

The Hawaii Infrared Parallax Program. IV. A Comprehensive Parallax Survey of L0–T8 Dwarfs with UKIRT

We present parallaxes, proper motions, and J-band photometry for 348 L and T dwarfs measured using the wide-field near-infrared camera WFCAM on the United Kingdom Infrared Telescope. This is the largest single batch of infrared parallaxes for brown dwarfs to date. Our parallaxes have a median uncertainty of 3.5 mas, similar to most previous ground-based infrared parallax surveys. Our target list was designed to complete a volume-limited parallax sample of L0–T8 dwarfs out to 25 pc spanning declinations −30° to +60° (68% of the sky). We report the first parallaxes for 165 objects, and we improve on previous measurements for another 53 objects. Our targets include 104 objects (mostly early-L dwarfs) having Gaia DR2 parallax measurements with which our parallaxes are consistent. We include an extensive comparison of previous literature parallaxes for L and T dwarfs with both our results and Gaia DR2 measurements, identifying systematic offsets for some previous surveys. Our parallaxes confirm that 14 objects previously identified as wide common proper motion companions to main-sequence stars have distances consistent with companionship. We also report new J{sub MKO} photometry for our targets, including the first measurements for 193 of our targets and improvements over previously published J{sub MKO} photometry for another 60 targets. Altogether, our parallaxes will enable the first population studies using a volume-limited sample spanning spectral types L0–T8 defined entirely by parallaxes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Parallax-corrected VISST-derived pixel-level products from satellite GOES-16

The NASA Langley group led by William Smith produced GOES-16 satellite cloud retrievals over an approximate 10 by 10 degree region over the CACTI field campaign location. These retrievals are described here: https://www.arm.gov/capabilities/vaps/visst and are available for download here . They use algorithms historically called VISST that are now referred to as SatCORPS. More information can be found in Trepte et al. (2019), Minnis et al. (2021), and Yost et al. (2021). If using this dataset, please cite these references, the CACTI VISST dataset DOI found at the download link above, and this dataset’s DOI. The CACTI VISST pixel-level retrievals are on a 2 km spatial grid and available every 15 minutes (every 10 minutes late in the campaign), producing 21,765 files for the entire field campaign between October 2018 and April 2019. They are not corrected for parallax error, which is an offset in the actual geographical location of a cloud above the surface due to the satellite viewing the cloud partly from the side off nadir. This dataset applies a correction for parallax using the location relative to the satellite and the retrieved cloud top height above the surface, which allows the dataset to be geo-located with surface-based observations. The parallax correction for each location depends on the longitude, latitude and cloud top height above ground level (AGL) for that longitude and latitude in the original VISST files. The cloud top height AGL requires first computing the surface elevation at each VISST grid point. Data from the Advanced Spaceborne Thermal Emission and Reflection (ASTER) Global Digital Elevation Map Version 3 at 30-m resolution is projected onto the VISST grid using conservative coarsening (conserving surface elevation) in the xESMF Python package. The surface elevation is then subtracted from the VISST-retrieved cloud top height above mean sea level. These cloud top heights AGL are then combined with longitude and latitude to estimate the latitude and longitude corrections. Due to variability in cloud top height, the parallax shifts produce an irregular grid of values since higher cloud tops are shifted further than lower cloud tops. A ball tree-based neighbor search with Haversine distance is performed using the Python-based scikit-learn library to find the nearest VISST grid point to each parallax correction-shifted point. The data value of the shifted point is then assigned to that VISST grid point. In this manner, the irregular geographical shifts to correct for parallax are projected back to the rectilinear VISST grid. Because relatively higher clouds should obscure lower clouds, the variable values for the highest cloud top are preferentially chosen if two or more values are assigned to a grid point. The parallax correction should be viewed as an improved but still imperfect estimation of the cloud top locations, largely because the cloud top height is an imperfect retrieval. Please see the attached README document for further information. Users are encouraged to contact the authors with any additional questions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Trigonometric Parallaxes of Two T Dwarfs With Keck and ShaneAO Astrometry

We present trigonometric parallax and proper motion measurements for two T-type brown dwarfs. We derive our measurements from infrared laser guide star adaptive optics observations spanning five years from the ShaneAO/SHARCS and NIRC2/medium-cam instruments on the Shane and Keck telescopes, respectively. To improve our astrometric precision, we measure and apply a distortion correction to our fields for both instruments. We also transform the Keck and ShaneAO astrometric reference frames onto the ICRS using five-parameter parallax and proper motion solutions for background reference stars from Gaia DR2. Fitting for parallax and proper motion, we measure parallaxes of 73.5 ± 9.2 mas and 70.1 ± 6.7 mas for WISEJ19010703+47181688 (WISE1901) and WISEJ21543294+59421370 (WISE2154), respectively. We utilize Monte Carlo methods to estimate the error in our sparse field methods, taking into account overfitting and differential atmospheric refraction. Comparing to previous measurements in the literature, all of our parallax and proper motion values fall within 2σ of the published measurements, and 4 of 6 measurements are within 1σ. These data are among the first parallax measurements of these T dwarfs and serve as precise measurements for calibrating stellar formation models. These two objects are the first results of an ongoing survey of T dwarfs with Keck/NIRC2 and the Shane Adaptive Optics system at Lick Observatory.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2009

Astrometry With the Hubble Space Telescope: Trigonometric Parallaxes of Planetary Nebula Nuclei NGC 6853, NGC 7293, ABELL 31, and DeHt 5

We present absolute parallaxes and relative proper motions for the central stars of the planetary nebulae NGC 6853 (The Dumbbell), NGC 7293 (The Helix), Abell 31, and DeHt 5. This paper details our reduction and analysis using DeHt 5 as an example. We obtain these planetary nebula nuclei (PNNi) parallaxes with astrometric data from Fine Guidance Sensors FGS 1r and FGS 3, white-light interferometers on the Hubble Space Telescope. Proper motions, spectral classifications and VJHKT2M and DDO51 photometry of the stars comprising the astrometric reference frames provide spectrophotometric estimates of reference star absolute parallaxes. Introducing these into our model as observations with error, we determine absolute parallaxes for each PNN. Weighted averaging with previous independent parallax measurements yields an average parallax precision, sigma (sub pi)/ pi = 5%. Derived distances are: d(sub NGC6853) = 405(exp +28 sub -25) pc, d(sub NGC7293) = 216(exp +14 sub -12) pc, d(sub Abell31) = 621(exp +91 sub -70) pc, and d(sub DeHt5) = 345(exp +19 sub -17) pc. These PNNi distances are all smaller than previously derived from spectroscopic analyses of the central stars. To obtain absolute magnitudes from these distances requires estimates of interstellar extinction. We average extinction measurements culled from the literature, from reddening based on PNNi intrinsic colors derived from model SEDs, and an assumption that each PNN experiences the same rate of extinction as a function of distance as do the reference stars nearest (in angular separation) to each central star. We also apply Lutz-Kelker bias corrections. The absolute magnitudes and effective temperatures permit estimates of PNNi radii through both the Stefan-Boltzmann relation and Eddington fluxes. Comparing absolute magnitudes with post-AGB models provides mass estimates. Masses cluster around 0.57 solar Mass, close to the peak of the white dwarf mass distribution. Adding a few more PNNi with well-determined distances and masses, we compare all the PNNi with cooler white dwarfs of similar mass, and confirm, as expected, that PNNi have larger radii than white dwarfs that have reached their final cooling tracks.

STARS↗
NASA NTRS2004

Preliminary Parallaxes of 40 L and T Dwarfs from the US Naval Observatory Infrared Astronometry Program

We present preliminary trigonometric parallaxes and proper motions for 22 L dwarfs and 18 T dwarfs measured using the ASTROCAM infrared imager on the US naval Observatory (USNO) 1.55 m Strand Astrometric Reflector. The results presented here are based on observations obtained between 2000 September and 2002 November; about half of the objects have an observational time baseline of t 1:3 yr and half t 2:0 yr. Despite these short time baselines, the astrometric quality is sufficient to produce significant new results, especially for the nearer T dwarfs. Seven objects are in common with the USNO optical CCD parallax program for quality control and seven in common with the European Southern Observatory 3.5 m New Technology Telescope parallax program. We compare astrometric quality with both of these programs. Relative to absolute parallax corrections are made by employing Two Micron All Sky Survey and/or Sloan Digital Sky Survey photometry for reference-frame stars. We combine USNO infrared and optical parallaxes with the best available California Institute of Technology (CIT) system photometry to determine MJ , MH, and MK values for 37 L dwarfs between spectral types L0 and L8 and 19 T dwarfs between spectral types T0.5 and T8 and present selected absolute magnitude versus spectral type and color diagrams, based on these results. Luminosities and temperatures are estimated for these objects. Of special interest are the distances of several objects that are at or near the L-T dwarf boundary so that this important transition can be better understood. The previously reported early to mid T dwarf luminosity excess is clearly confirmed and found to be present at J, H, and K. The large number of objects that populate this luminosity-excess region indicate that it cannot be due entirely to selection effects. The T dwarf sequence is extended to MJ 16:9 by 2MASS J041519 0935, which, at d 5:74 pc, is found to be the lluminous LOG (L=L )pa

L DWARFS↗
DOE OSTI2020

The Gaia DR2 parallax zero-point: hierarchical modelling of red clump stars

ABSTRACT The systematic offset of Gaia parallaxes has been widely reported with Gaia’s second data release, and it is expected to persist in future Gaia data. In order to use Gaia parallaxes to infer distances to high precision, we develop a hierarchical probabilistic model to determine the Gaia parallax zero-point offset along with the calibration of an empirical model for luminosity of red clump stars by combining astrometric and photometric measurements. Using a cross-matched sample of red clump stars from the Apache Point Observatory Galactic Evolution Experiment and Gaia Data Release 2 (DR2), we report the parallax zero-point offset in DR2 to be $\varpi _0 = -48 \pm 1\,\mu \text{as}$. We infer the red clump absolute magnitude to be −1.622 ± 0.004 in Ks, 0.435 ± 0.004 in G, −1.019 ± 0.004 in J, and −1.516 ± 0.004 in H. The intrinsic scatter of the red clump is ∼0.09 mag in J, H, and Ks, or ∼ 0.12 mag in G. We tailor our models to accommodate more complex analyses such as investigating the variations of the parallax zero-point with each source’s observed magnitude, observed colour, and sky position. In particular, we find fluctuations of the zero-point across the sky to be of order or less than a few 10s of $\mu \text{as}$.

Chan, Victor C.↗
NASA NTRS1990

Spectroscopic parallaxes of MAP region stars from UBVRI, DDO, and uvbyH-beta photometry

This paper presents the results of spectral type and luminosity classification of reference stars in the Allegheny Observatory MAP parallax program, using broadband and intermediate-band photometry. In addition to the use of UBVRI and DDO photometric systems, the uvbyH-beta photometric system was included for classification of blue (B - V less than 0.6) reference stars. The stellar classifications made from the photometry are used to determine spectroscopic parallaxes. The spectroscopic parallaxes are used in turn to adjust the relative parallaxes measured with the MAP to absolute parallaxes. A new method for dereddening stars using more than one photometric system is presented. In the process of dereddening, visual extinctions, spectral types, and luminosity classes are determined, as well as a measure of the goodness of fit. The measure of goodness of fit quantifies confidence in the stellar classifications. It is found that the spectral types are reliable to within 2.5 spectral subclasses.

Persinger, Tim↗
NASA NTRS1993

Multichannel astrometric photometer parallax studies in the regions of Groombridge 1618, Zeta Bootis, and Sigma Draconis

Improved trigonometric parallaxes are reported for stars in the regions of Groombridge 1618, Zeta Bootis, and Sigma Draconis which differ from generally accepted parallaxes by two to five standard deviations. The weighted mean parallax of Groombridge 1618 becomes 0.2079 +/- 0.0013 arcsec, indicating a distance modulus of -1.59 +/- 0.014 and yielding an absolute magnitude of this K7 V star of 8.20 +/- 0.017. The parallax determined for the visual binary Zeta Bootis is 0.0202 +/- 0.0010 arcsec and implies an average absolute visual magnitude of 1.067 +/- 0.12 for the spectroscopically similar components. The weighted mean parallax of Sigma Draconis becomes 0.1747 +/- 0.0010 arcsec, indicating a distance modulus of -1.210 +/- 0.012 and yielding an absolute visual magnitude of 5.90 +/- 0.012 for this K0 V star. The absolute visual magnitudes of the high velocity star Roman 336 and of the subdwarf star AO 1187 are found to be + 4.0 +/- 0.13 and + 5.9 +/- 0.17, respectively.

Gatewood, George↗
NASA NTRS1982

Parallax studies of four selected fields

Astrometric studies have been completed for four central stars Wolf 294, 39 Com, Case 2, and Vega - and selected reference stars in each of those regions. The parallax of Wolf 294 was measured as 0.1806 + or - 0.0033 arcsec. 39 Com is a visual/astrometric binary with an estimated period of 125 yr and a parallax of 0.0297 + or - 0.0044 arcsec. C 2 was measured as a white dwarf from a Warner and Swasey Observatory spectral survey; its white dwarf status is confirmed by its parallax of 0.0186 + or - 0.0109 arcsec. Vega's parallax was measured as 0.1243 + or - 0.0049 arcsec; a small apparent nonrandom distribution in the residuals is most likely an error from the neutral density filter used for magnitude reduction of the central star.

Russell, J. L.↗
NASA NTRS1992

Map-based trigonometric parallaxes of open clusters. II - The Hyades: 51 Tauri

The trigonometric parallax, mass, and mass ratio of 51 Tauri, a binary member of the Hyades star cluster, are determined. The parallax solution, 19.4 mas with a standard error of 1.1 mas, is slightly greater than its generally accepted value and yields a cluster distance of 4.30 +/-2.0 pc or a distance modulus equivalent of 3.16 +/- 0.10 mag, in excellent agreement with recent photographic parallax results. The weighted mean of all trigonometric parallax determinations of the cluster is now 22.9 +/-0.6 mas or a modulus of 3.20 +/- 0.06 mag. The total mass of the 51 Tauri system was found to be 2.56 +/- 0.44 solar masses. Adopting a magnitude difference in line with the spectral types of the components yields individual masses of 1.61 +/- 0.28 and 0.95 +/- 0.18 solar masses. This result places the mass of both the A8 V primary and the G0 secondary stars within the errors of the measurement of the mass-luminosity relation established for solar-neighborhood main-sequence stars.

Gatewood, George↗
NASA NTRS1993

One-milliarsecond precision parallax studies in the regions of Delta Cephei and EV Lacertae

Trigonometric parallaxes for stars in the regions of the variable stars delta Cephei and EV Lacertae are derived from data collected with the Multichannel Astrometric Photometer (MAP) and the Thaw Refractor of the University of Pittsburgh's Allegheny Observatory. The weighted mean parallax of all trigonometric studies of delta Cephei is now + 0.0030 sec + or - 0.00093 sec, corresponding to a distance modulus of 7.61 + or - 0.67 mag. This indicates that this luminosity standard star is approximately one standard deviation more distance than has been generally accepted. The weighted mean trigonometric parallax of all studies of the variable star EV Lacertae (BD + 43 deg 4305) is + 0.1993 sec + or - 0.00093 sec, implying a distance modulus of - 1.498 + or - 0.0010 mag. The calculated absolute magnitude of this star is almost exactly that predicted by its (R-I)(sub Kron) magnitude and by the Gliese (R-I) main-sequence value for stars in the solar neighborhood. We also find a parallax of 0.0189 sec + or - 0.0008 sec for the FO IVn star, HR 8666 (BD + 43 sec 4300). The derived luminosity of this star is midway between that expected for luminosity class IV and V stars at the indicated temperature.

Gatewood, George↗
NASA NTRS1995

Map-based trigonometric parallaxes of open clusters: Coma

This is the fourth study in a series to determine the direct trigonometric parallaxes of four of the nearest open star clusters, the Hyades, the Pleiades, the Praesepe, and the nearby cluster in Coma (Gatewood et al. 1990; Gatewood et al. 1992); Gatewood & Kiewiet de Jonge 1994). The results for the open star cluster in Coma are compared with those of the other three clusters, and the members are found to be significantly subluminous. The trigonometric parallax of the cluster is estimated from that of three members studied with the Multichannel Astrometric Photometer (MAP) at the Thaw Refractor of the University of Pittsburgh's Allegheny Observatory. The weighted mean parallax of the cluster is +13.53 +/- 0.54 mass (0.00054 min), corresponding to a distance modulus of 4.34 +/- 0.09 mag. The U-B excess of the Coma cluster members may be used to adjust the observed absolute magnitudes and the B-V measurements as suggested by Sandage & Eggen (1959). The agreement obtained in this manner suggests that, like subdwarf stars, the stars of the Coma cluster appear subluminous because of line blanketing. One of the three members observed in this study was recognized as a member by its parallax and is the faintest known member of the cluster.

Gatewood, George↗
NASA NTRS2019

Spitzer Microlensing Parallax for OGLE-2016-BLG-1067: A Sub-Jupiter Orbiting an M Dwarf in the Disk

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 planetary microlensing anomalies toward the Galactic bulge. Most of the microlensing parameters are strongly constrained by the light-curve modeling, and in particular there is a Spitzer-based measurement of the microlens parallax, π(E). However, there are no caustic crossings, so the angular Einstein radius has only an upper limit based on the light-curve modeling alone. Additionally, the analysis leads us to identify eight degenerate configurations: the fourfold microlensing parallax degeneracy being doubled by a degeneracy in the caustic structure present at the level of the ground-based solutions. To calculate the physical parameters, and at the same time to break the parallax degeneracy, we make use of a series of arguments: the χ(exp 2) hierarchy, the Rich argument (stating that the small-parallax solution is more likely), and a prior Galactic model. The preferred configuration, favored by a likelihood ratio of at least 4000, is for a host at D(L)={3.73}(-0.67+0.66)kpc with mass M(L)=0.30(-0.12+0.15) M(☉) , orbited by a Saturn-like planet with M(planet) =0.43(-0.17+0.21) M(Jup) at projected separation a(⊥) =1.70(-0.39+0.38) au, about 2.1 times beyond the system snow line. Therefore, it adds to the growing population of sub-Jupiter planets orbiting 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.

S. Calchi Novati↗
NASA NTRS2022

Compressive Sensing Based Space Flight Instrument Constellation for Measuring Gravitational Microlensing Parallax

In this work, we provide a compressive sensing architecture for implementing on a space based observatory for detecting transient photometric parallax caused by gravitational microlensing events. Compressive sensing (CS) is a simultaneous data acquisition and compression technique, which can greatly reduce on-board resources required for space flight data storage and ground transmission. We simulate microlensing parallax observations using a space observatory constellation, based on CS detectors. Our results show that average CS error is less than 0.5% using 25% Nyquist rate samples. The error at peak magnification time is significantly lower than the error for distinguishing any two microlensing parallax curves at their peak magnification. Thus, CS is an enabling technology for detecting microlensing parallax, without causing any loss in detection accuracy.

compressive sensing↗
NASA NTRS2022

Ogle-2018-BLG-0799lb: A Q ∼ 2.7 × 10(−3) Planet With Spitzer Parallax

We report the discovery and analysis of a planet in the microlensing event OGLE-2018-BLG-0799. The planetary signal was observed by several ground-based telescopes, and the planet-host mass ratio is q = (2.65 ± 0.16) × 10(−3). The ground-based observations yield a constraint on the angular Einstein radius θE, and the microlensing parallax vector πE, is strongly constrained by the Spitzer data. However, the 2019 Spitzer baseline data reveal systematics in the Spitzer photometry, so there is ambiguity in the magnitude of the parallax. In our preferred interpretation, a full Bayesian analysis using a Galactic model indicates that the planetary system is composed of an Mplanet = 0.26+0.22 −0.11M(J) planet orbiting an Mhost = 0.093+0.082 −0.038 Mʘ , at a distance of DL = 3.71+3.24 −1.70 kpc. An alternate interpretation of the data shifts the localization of the minima along the arc-shaped microlens parallax constraints. This, in turn, yields a more massive host with median mass of 0.13 Mʘ at a distance of 6.3 kpc. This analysis demonstrates the robustness of the osculating circles formalism, but shows that further investigation is needed to assess how systematics affect the specific localization of the microlens parallax vector and, consequently, the inferred physical parameters.

gravitational lensing↗
NASA NTRS2016

Distance to the IBEX Ribbon Source Inferred From Parallax

Maps of energetic neutral atom (ENA) fluxes obtained from observations made by the Interstellar Boundary Explorer (IBEX) revealed a bright structure extending over the sky, subsequently dubbed the IBEX ribbon. The ribbon had not been expected from the existing models and theories prior to IBEX, and a number of mechanisms have since been proposed to explain the observations. In these mechanisms, the observed ENAs emerge from source plasmas located at different distances from the Sun. Since each part of the sky is observed by ibex TWICE DURING THE YEAR FROM OPPOSTIE SIDE OF THE Sun, the apparent position of the ribbon as observed in the sky is shifted due to parallax. To determine the ribbons parallax, we found the precise location of the maximum signal of the ribbon observed in each orbital arc. The apparent positions obtained were subsequently corrected for the Compton-Getting effect, gravitational deflection, and radiation pressure. Finally, we selected a part of the ribbon where its position is similar in the different IBEX ENERGY PASSBANDS. We compared the apparent positions obtained from the viewing locations on the opposite sides of the Sun, and found that they are shifted by a parallax angle of 0 41 0 15, which corresponds to a distance of AU. This finding supports models of the ribbon with the source located just outside the heliopause.

ISM: atoms↗
NASA NTRS2016

OGLE-2012-bLG-0950Lb: the First Planet Mass Measurement From Only Microlens Parallax and Lens Flux

We report the discovery of a microlensing planet OGLE-2012-BLG-0950Lb with a planet/host mass ratio Periapsis Approx. = 2 x10(exp. -4). A long term distortion detected in both MOA and OGLE light curve can be explained by themicrolens parallax due to the Earths orbital motion around the Sun. Although the finite source effect is not detected, we obtain the lens flux by the high resolution Keck AO observation. Combining the microlens parallax and the lens flux reveal the nature of the lens: a planet with mass of M(sub p) = 35(+17/-)M compared to Earth is orbiting around an M-dwarf with mass of M(sub host) = 0.56(+0.12/-0.16) M compared to the Sun with a planet-host projected separation of r1 = 2.7(+0.6/-0.7) au located at Luminosity Distance = 3.0(+0.8/-1.1) kpc from us. This is the first mass measurement from only microlens parallax and the lens flux without the finite source effect. In the coming space observation-era with Spitzer, K2, Euclid, and WFIRST, we expect many such events for which we will not be able to measure any finite source effect. This work demonstrates an ability of mass measurements in such events.

microlens parallax↗
DOE OSTI2022

Improving White Dwarfs as Chronometers with Gaia Parallaxes and Spectroscopic Metallicities

White dwarfs (WDs) offer unrealized potential in solving two problems in astrophysics: stellar age accuracy and precision. WD cooling ages can be inferred from surface temperatures and radii, which can be constrained with precision by high-quality photometry and parallaxes. Accurate and precise Gaia parallaxes along with photometric surveys provide information to derive cooling and total ages for vast numbers of WDs. Here we analyze 1372 WDs found in wide binaries with main-sequence (MS) companions and report on the cooling and total age precision attainable in these WD+MS systems. The total age of a WD can be further constrained if its original metallicity is known because the MS lifetime depends on metallicity at fixed mass, yet metallicity is unavailable via spectroscopy of the WD. We show that incorporating spectroscopic metallicity constraints from 38 wide binary MS companions substantially decreases internal uncertainties in WD total ages compared to a uniform constraint. Averaged over the 38 stars in our sample, the total (internal) age uncertainty improves from 21.04% to 16.77% when incorporating the spectroscopic constraint. Higher mass WDs yield better total age precision; for eight WDs with zero-age MS masses ≥2.0 M ⊙ , the mean uncertainty in total ages improves from 8.61% to 4.54% when incorporating spectroscopic metallicities. We find that it is often possible to achieve 5% total age precision for WDs with progenitor masses above 2.0 M ⊙ if parallaxes with ≤1% precision and Pan-STARRS g, r, and i photometry with ≤0.01 mag precision are available.

79 ASTRONOMY AND ASTROPHYSICS↗