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At least 577 records · Page 32

SOFT X-RAY SPECTROSCOPY OF THE CYGNUS LOOP SUPERNOVA REMNANT

We present the results of a suborbital rocket flight whose scientific target was the Cygnus Loop Supernova Remnant. The payload consists of wire grid collimators, off-plane grating arrays, and gaseous electron multiplier (GEM) detectors. The system is designed for spectral measurements in the 17-107 A bandpass with a resolution up to {approx}60 ({lambda}/{Delta}{lambda}). The Extended X-ray Off-plane Spectrometer (EXOS) was launched on a Terrier-Black Brant rocket on 2009 November 13 from White Sands Missile Range and obtained 340 s of useable scientific data. The X-ray emission is dominated by O VII and O VIII, including the He-like O VII triplet at {approx}22 A. Another emission feature at {approx}45 A is composed primarily of Si XI and Si XII. The best-fit model to this spectrum is an equilibrium plasma model at a temperature of log(T) = 6.4 (0.23 keV).

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

TWO BEYOND-PRIMITIVE EXTRASOLAR PLANETESIMALS

Using the Cosmic Origins Spectrograph on board the Hubble Space Telescope, we have obtained high-resolution ultraviolet observations of GD 362 and PG 1225-079, two helium-dominated, externally polluted white dwarfs. We determined or placed useful upper limits on the abundances of two key volatile elements, carbon and sulfur, in both stars; we also constrained the zinc abundance in PG 1225-079. In combination with previous optical data, we find strong evidence that each of these two white dwarfs has accreted a parent body that has evolved beyond primitive nebular condensation. The planetesimal that accreted onto GD 362 had a bulk composition roughly similar to that of a mesosiderite meteorite based on a reduced chi-squared comparison with solar system objects; however, additional material is required to fully reproduce the observed mid-infrared spectrum for GD 362. No single meteorite can reproduce the unique abundance pattern observed in PG 1225-079; the best fit model requires a blend of ureilite and mesosiderite material. From a compiled sample of nine well-studied polluted white dwarfs, we find evidence for both primitive planetesimals, which are a direct product from nebular condensation, as well as beyond-primitive planetesimals, whose final compositions were mainly determined by post-nebular processing.

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A GAS GIANT CIRCUMBINARY PLANET TRANSITING THE F STAR PRIMARY OF THE ECLIPSING BINARY STAR KIC 4862625 AND THE INDEPENDENT DISCOVERY AND CHARACTERIZATION OF THE TWO TRANSITING PLANETS IN THE KEPLER-47 SYSTEM

We report the discovery of a transiting, gas giant circumbinary planet orbiting the eclipsing binary KIC 4862625 and describe our independent discovery of the two transiting planets orbiting Kepler-47. We describe a simple and semi-automated procedure for identifying individual transits in light curves and present our follow-up measurements of the two circumbinary systems. For the KIC 4862625 system, the 0.52 {+-} 0.018 R{sub Jupiter} radius planet revolves every {approx}138 days and occults the 1.47 {+-} 0.08 M{sub Sun }, 1.7 {+-} 0.06 R{sub Sun} F8 IV primary star producing aperiodic transits of variable durations commensurate with the configuration of the eclipsing binary star. Our best-fit model indicates the orbit has a semi-major axis of 0.64 AU and is slightly eccentric, e = 0.1. For the Kepler-47 system, we confirm the results of Orosz et al. Modulations in the radial velocity of KIC 4862625A are measured both spectroscopically and photometrically, i.e., via Doppler boosting, and produce similar results.

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MARVELS-1: A FACE-ON DOUBLE-LINED BINARY STAR MASQUERADING AS A RESONANT PLANETARY SYSTEM AND CONSIDERATION OF RARE FALSE POSITIVES IN RADIAL VELOCITY PLANET SEARCHES

We have analyzed new and previously published radial velocity (RV) observations of MARVELS-1, known to have an ostensibly substellar companion in a {approx}6 day orbit. We find significant ({approx}100 m s{sup -1}) residuals to the best-fit model for the companion, and these residuals are naievely consistent with an interior giant planet with a P = 1.965 days in a nearly perfect 3:1 period commensurability (|P{sub b} /P{sub c} - 3| < 10{sup -4}). We have performed several tests for the reality of such a companion, including a dynamical analysis, a search for photometric variability, and a hunt for contaminating stellar spectra. We find many reasons to be critical of a planetary interpretation, including the fact that most of the three-body dynamical solutions are unstable. We find no evidence for transits, and no evidence of stellar photometric variability. We have discovered two apparent companions to MARVELS-1 with adaptive optics imaging at Keck; both are M dwarfs, one is likely bound, and the other is likely a foreground object. We explore false-alarm scenarios inspired by various curiosities in the data. Ultimately, a line profile and bisector analysis lead us to conclude that the {approx}100 m s{sup -1} residuals are an artifact of spectral contamination from a stellar companion contributing {approx}15%-30% of the optical light in the system. We conclude that origin of this contamination is the previously detected RV companion to MARVELS-1, which is not, as previously reported, a brown dwarf, but in fact a G dwarf in a face-on orbit.

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SEARCH FOR RAYLEIGH SCATTERING IN THE ATMOSPHERE OF GJ1214b

We investigate the atmosphere of GJ1214b, a transiting super-Earth planet with a low mean density, by measuring its transit depth as a function of wavelength in the blue optical portion of the spectrum. It is thought that this planet is either a mini-Neptune, consisting of a rocky core with a thick, hydrogen-rich atmosphere, or a planet with a composition dominated by water. Most observations favor a water-dominated atmosphere with a small scale-height, however, some observations indicate that GJ1214b could have an extended atmosphere with a cloud layer muting the molecular features. In an atmosphere with a large scale-height, Rayleigh scattering at blue wavelengths is likely to cause a measurable increase in the apparent size of the planet toward the blue. We observed the transit of GJ1214b in the B band with the FOcal Reducing Spectrograph at the Very Large Telescope and in the g band with both ACAM on the William Herschel Telescope (WHT) and the Wide Field Camera at the Isaac Newton Telescope (INT). We find a planet-to-star radius ratio in the B band of 0.1162 {+-} 0.0017, and in the g band 0.1180 {+-} 0.0009 and 0.1174 {+-} 0.0017 for the WHT and INT observations, respectively. These optical data do not show significant deviations from previous measurements at longer wavelengths. In fact, a flat transmission spectrum across all wavelengths best describes the combined observations. When atmospheric models are considered, a small scale-height water-dominated model fits the data best.

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MULTIWAVELENGTH PHOTOMETRY AND HUBBLE SPACE TELESCOPE SPECTROSCOPY OF THE OLD NOVA V842 CENTAURUS

We present ground-based optical and near infrared photometric observations and Hubble Space Telescope (HST) COS spectroscopic observations of the old nova V842 Cen (Nova Cen 1986). Analysis of the optical light curves reveals a peak at 56.5 {+-} 0.3 s with an amplitude of 8.9 {+-} 4.2 mma, which is consistent with the rotation of a magnetic white dwarf primary in V842 Cen that was detected earlier by Woudt et al., and led to its classification as an intermediate polar. However, our UV lightcurve created from the COS time-tag spectra does not show this periodicity. Our synthetic spectral analysis of an HST COS spectrum rules out a hot white dwarf photosphere as the source of the FUV flux. The best-fitting model to the COS spectrum is a full optically thick accretion disk with no magnetic truncation, a low disk inclination angle, low accretion rate and a distance less than half the published distance that was determined on the basis of interstellar sodium D line strengths. Truncated accretion disks with truncation radii of 3 R{sub wd} and 5 R{sub wd} yielded unsatisfactory agreement with the COS data. The accretion rate is unexpectedly low for a classical nova only 24 yr after the explosion when the accretion rate is expected to be high and the white dwarf should still be very hot, especially if irradiation of the donor star took place. Our low accretion rate is consistent with those derived from X-ray and ground-based optical data.

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THE TRENDS HIGH-CONTRAST IMAGING SURVEY. III. A FAINT WHITE DWARF COMPANION ORBITING HD 114174

The nearby Sun-like star HD 114174 exhibits a strong and persistent Doppler acceleration indicating the presence of an unseen distant companion. We have acquired high-contrast imaging observations of this star using NIRC2 at Keck and report the direct detection of the body responsible for causing the ''trend''. HD 114174 B has a projected separation of 692 {+-} 9 mas (18.1 AU) and is 10.75 {+-} 0.12 mag (contrast of 5 Multiplication-Sign 10{sup -5}) fainter than its host in the K-band, requiring aggressive point-spread function subtraction to identify. Our astrometric time baseline of 1.4 yr demonstrates physical association through common proper motion. We find that the companion has absolute magnitude, M{sub J} = 13.97 {+-} 0.11, and colors, J - K = 0.12 {+-} 0.16 mag. These characteristics are consistent with an Almost-Equal-To T3 dwarf, initially leading us to believe that HD 114174 B was a substellar object. However, a dynamical analysis that combines radial velocity measurements with available imaging data indicates a minimum mass of 0.260 {+-} 0.010 M{sub Sun }. We conclude that HD 114174 B must be a white dwarf. Assuming a hydrogen-rich composition, atmospheric and evolutionary model fits yield an effective temperature T{sub eff} = 8200 {+-} 4000 K, surface gravity log g = 8.90 {+-} 0.02, and cooling age of t{sub c} Almost-Equal-To 3.4 Gyr, which is consistent with the 4.7{sup +2.3}{sub -2.6} Gyr host star isochronal age estimate. HD 114174 B is a benchmark object located only 26.14 {+-} 0.37 pc from the Sun. It may be studied at a level of detail comparable to Sirius and Procyon, and used to understand the link between the mass of white dwarf remnants with that of their progenitors.

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[Fe II] 1.64 μm FEATURES OF JETS AND OUTFLOWS FROM YOUNG STELLAR OBJECTS IN THE CARINA NEBULA

We present [Fe II] 1.64 μm imaging observations for jets and outflows from young stellar objects (YSOs) over the northern part (∼24' × 45') of the Carina Nebula, a massive star-forming region. The observations were performed with IRIS2 of the Anglo-Australian Telescope and the seeing was ∼1.''5 ± 0.''5. Eleven jet and outflow features are detected at eight different regions and are termed ionized Fe objects (IFOs). One Herbig-Haro candidate that was missed in Hubble Space Telescope Hα observations is newly identified as HHc-16, referring to our [Fe II] images. IFOs have knotty or longish shapes, and the detection rate of IFOs against previously identified YSOs is 1.4%, which should be treated as a lower limit. Four IFOs show anti-correlated peak intensities in [Fe II] and Hα, where the ratio I([Fe II])/I(Hα) is higher for longish IFOs than for knotty IFOs. We estimate the outflow mass loss rate from the [Fe II] flux using two different methods. The jet-driving objects are identified for three IFOs (IFO-2, -4, and -7) for which we study the relations between the outflow mass loss rate and the YSO physical parameters from the radiative transfer model fitting. The ratios of the outflow mass loss rate over the disk accretion rate for IFO-4 and -7 are consistent with the previously reported values (10{sup –2}-10{sup +1}), while the ratio is higher for IFO-2. This excess may result from underestimating the disk accretion rate. The jet-driving objects are likely to be low- or intermediate-mass stars. Other YSO physical parameters, such as luminosity and age, show reasonable relations or trends.

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Metal distributions out to 0.5 r {sub 180} in the intracluster medium of four galaxy groups observed with Suzaku

We studied the distributions of metal abundances and metal-mass-to-light ratios in the intracluster medium (ICM) of four galaxy groups, MKW 4, HCG 62, the NGC 1550 group, and the NGC 5044 group, out to ∼0.5 r {sub 180} observed with Suzaku. The iron abundance decreases with radius and is about 0.2-0.4 solar beyond 0.1 r {sub 180}. At a given radius in units of r {sub 180}, the iron abundance in the ICM of the four galaxy groups was consistent with or smaller than those of clusters of galaxies. The Mg/Fe and Si/Fe ratios in the ICM are nearly constant at the solar ratio out to 0.5 r {sub 180}. We also studied systematic uncertainties in the derived metal abundances, comparing the results from two versions of atomic data for astrophysicists (ATOMDB) and single- and two-temperature model fits. Since the metals have been synthesized in galaxies, we collected K-band luminosities of galaxies from the Two Micron All Sky Survey catalog and calculated the integrated iron-mass-to-light-ratios (IMLR), or the ratios of the iron mass in the ICM to light from stars in galaxies. The groups with smaller gas-mass-to-light ratios have smaller IMLR values and the IMLR is inversely correlated with the entropy excess. Based on these abundance features, we discussed the past history of metal enrichment processes in groups of galaxies.

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Spitzer observations of the thermal emission from WASP-43b

WASP-43b is one of the closest-orbiting hot Jupiters, with a semimajor axis of a = 0.01526 ± 0.00018 AU and a period of only 0.81 days. However, it orbits one of the coolest stars with a hot Jupiter (T {sub *} = 4520 ± 120 K), giving the planet a modest equilibrium temperature of T {sub eq} = 1440 ± 40 K, assuming zero Bond albedo and uniform planetary energy redistribution. The eclipse depths and brightness temperatures from our jointly fit model are 0.347% ± 0.013% and 1670 ± 23 K at 3.6 μm and 0.382% ± 0.015% and 1514 ± 25 K at 4.5 μm. The eclipse timings improved the estimate of the orbital period, P, by a factor of three (P = 0.81347436 ± 1.4 × 10{sup –7} days) and put an upper limit on the eccentricity (e=0.010{sub −0.007}{sup +0.010}). We use our Spitzer eclipse depths along with four previously reported ground-based photometric observations in the near-infrared to constrain the atmospheric properties of WASP-43b. The data rule out a strong thermal inversion in the dayside atmosphere of WASP-43b. Model atmospheres with no thermal inversions and fiducial oxygen-rich compositions are able to explain all the available data. However, a wide range of metallicities and C/O ratios can explain the data. The data suggest low day-night energy redistribution in the planet, consistent with previous studies, with a nominal upper limit of about 35% for the fraction of energy incident on the dayside that is redistributed to the nightside.

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On the mid-infrared variability of candidate eruptive variables (exors): A comparison between Spitzer and WISE data

Aiming to statistically study the variability in the mid-IR of young stellar objects, we have compared the 3.6, 4.5, and 24 μm Spitzer fluxes of 1478 sources belonging to the C2D (Cores to Disks) legacy program with the WISE fluxes at 3.4, 4.6, and 22 μm. From this comparison, we have selected a robust sample of 34 variable sources. Their variations were classified per spectral Class (according to the widely accepted scheme of Class I/flat/II/III protostars), and per star forming region. On average, the number of variable sources decreases with increasing Class and is definitely higher in Perseus and Ophiuchus than in Chamaeleon and Lupus. According to the paradigm Class ≡ Evolution, the photometric variability can be considered to be a feature more pronounced in less evolved protostars, and, as such, related to accretion processes. Moreover, our statistical findings agree with the current knowledge of star formation activity in different regions. The 34 selected variables were further investigated for similarities with known young eruptive variables, namely the EXors. In particular, we analyzed (1) the shape of the spectral energy distribution, (2) the IR excess over the stellar photosphere, (3) magnitude versus color variations, and (4) output parameters of model fitting. This first systematic search for EXors ends up with 11 bona fide candidates that can be considered as suitable targets for monitoring or future investigations.

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Abundance patterns in the interstellar medium of early-type galaxies observed with Suzaku

We have analyzed 17 early-type galaxies, 13 ellipticals and 4 S0 galaxies, observed with Suzaku, and investigated metal abundances (O, Mg, Si, and Fe) and abundance ratios (O/Fe, Mg/Fe, and Si/Fe) in the interstellar medium (ISM). The emission from each on-source region, which is four times the effective radius, r {sub e}, is reproduced with one-temperature (1T) or two-temperature (2T) thermal plasma models as well as a multi-temperature model, using APEC plasma code version 2.0.1. The multi-temperature model gave almost the same abundances and abundance ratios with the 1T or 2T models. The weighted averages of the O, Mg, Si, and Fe abundances of all the sample galaxies derived from the multi-temperature model fits are 0.83 ± 0.04, 0.93 ± 0.03, 0.80 ± 0.02, and 0.80 ± 0.02 solar, respectively, in solar units according to the solar abundance table by Lodders in 2003. These abundances show no significant dependence on the morphology and environment. The systematic differences in the derived metal abundances between versions 2.0.1 and 1.3.1 of the APEC plasma codes were investigated. The derived O and Mg abundances in the ISM agree with the stellar metallicity within an aperture with a radius of one r {sub e} derived from optical spectroscopy. From these results, we discuss the past and present Type Ia supernova rates and star formation histories in early-type galaxies.

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High-resolution submillimeter and near-infrared studies of the transition disk around Sz 91

To reveal the structures of a transition disk around a young stellar object in Lupus, Sz 91 , we have performed aperture synthesis 345 GHz continuum and CO(3-2) observations with the Submillimeter Array (∼1''-3'' resolution) and high-resolution imaging of polarized intensity at the K{sub s} -band using the HiCIAO instrument on the Subaru Telescope (0.''25 resolution). Our observations successfully resolved the inner and outer radii of the dust disk to be 65 and 170 AU, respectively, which indicates that Sz 91 is a transition disk source with one of the largest known inner holes. The model fitting analysis of the spectral energy distribution reveals an H{sub 2} mass of 2.4 × 10{sup –3} M {sub ☉} in the cold (T < 30 K) outer part at 65 AU 3 × 10{sup –9} M {sub ☉}) of hot (T ∼ 180 K) dust possibly remains inside the inner hole of the disk. The structure of the hot component could be interpreted as either an unresolved self-luminous companion body (not directly detected in our observations) or a narrow ring inside the inner hole. Significant CO(3-2) emission with a velocity gradient along the major axis of the dust disk is concentrated on the Sz 91 position, suggesting a rotating gas disk with a radius of 420 AU. The Sz 91 disk is possibly a rare disk in an evolutionary stage immediately after the formation of protoplanets because of the large inner hole and the lower disk mass than other transition disks studied thus far.

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A two-parameter model for the infrared/submillimeter/radio spectral energy distributions of galaxies and active galactic nuclei

A two-parameter semi-empirical model is presented for the spectral energy distributions of galaxies with contributions to their infrared-submillimeter-radio emission from both star formation and accretion disk-powered activity. This model builds upon a previous one-parameter family of models for star-forming galaxies, and includes an update to the mid-infrared emission using an average template obtained from Spitzer Space Telescope observations of normal galaxies. Star-forming/active galactic nucleus (AGN) diagnostics based on polycyclic aromatic hydrocarbon equivalent widths and broadband infrared colors are presented, and example mid-infrared AGN fractional contributions are estimated from model fits to the Great Observatories All-Sky LIRG Survey sample of nearby U/LIRGS and the Five mJy Unbiased Spitzer Extragalactic Survey sample of 24 μm selected sources at redshifts 0 ≲ z ≲ 4.

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Measuring quasar variability with Pan-STARRS1 and SDSS

We measure quasar variability using the Panoramic Survey Telescope and Rapid Response System 1 Survey (Pan-STARRS1 or PS1) and the Sloan Digital Sky Survey (SDSS) and establish a method of selecting quasars via their variability in 10{sup 4} deg{sup 2} surveys. We use 10{sup 5} spectroscopically confirmed quasars that have been well measured in both PS1 and SDSS and take advantage of the decadal timescales that separate SDSS measurements and PS1 measurements. A power law model fits the data well over the entire time range tested, 0.01-10 yr. Variability in the current PS1-SDSS data set can efficiently distinguish between quasars and nonvarying objects. It improves the purity of a griz quasar color cut from 4.1% to 48% while maintaining 67% completeness. Variability will be very effective at finding quasars in data sets with no u band and in redshift ranges where exclusively photometric selection is not efficient. We show that quasars' rest-frame ensemble variability, measured as a root mean squared in Δ magnitudes, is consistent with V(z, L, t) = A {sub 0}(1 + z){sup 0.37}(L/L {sub 0}){sup –0.16}(t/1 yr){sup 0.246}, where L {sub 0} = 10{sup 46} erg s{sup –1} and A {sub 0} = 0.190, 0.162, 0.147, or 0.141 in the g {sub P1}, r {sub P1}, i {sub P1}, or z {sub P1}filter, respectively. We also fit across all four filters and obtain median variability as a function of z, L, and λ as V(z, L, λ, t) = 0.079(1 + z){sup 0.15}(L/L {sub 0}){sup –0.2}(λ/1000 nm){sup –0.44}(t/1 yr){sup 0.246}.

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The origin of the plateau and late rebrightening in the afterglow of GRB 120326A

GRB 120326A is an unusual gamma-ray burst (GRB) that has a long plateau and a very late rebrightening in both X-ray and optical bands. The similar behavior of the optical and X-ray light curves suggests that they may share a common origin. The long plateau starts at several hundred seconds and ends at tens of thousands of seconds, and the peak time of the late rebrightening is about 30,000 s. We analyze the energy injection model by means of numerical and analytical solutions, considering both the wind environment and the interstellar medium environment for GRB afterglows. We particularly study the influence of the injection starting time, ending time, stellar wind density (or density of the circumburst environment), and injection luminosity on the shape of the afterglow light curves, respectively. In the wind model, we find that the light curve is largely affected by the parameters and that there is a 'bump' in the late stage. In the wind environment, we found that the longer the energy is injected, the more obvious the rebrightening will be. We also find that the peak time of the bump is determined by the stellar wind density. We use the late continuous injection model to interpret the unusual afterglow of GRB 120326A. The model fits the observational data well; however, we find that the timescale of the injection must be higher than 10,000 s, which implies that the timescale of the central engine activity must also be more than 10,000 s. This information can give useful constraints on the central engines of GRBs—we consider a newborn millisecond pulsar with a strong magnetic field to be the central engine. On the other hand, our results suggest that the circumburst environment of GRB 120326A is very likely a stellar wind.

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A multi-wavelength view of the central kiloparsec region in the luminous infrared galaxy NGC 1614

The Luminous Infrared Galaxy NGC 1614 hosts a prominent circumnuclear ring of star formation. However, the nature of the dominant emitting mechanism in its central ∼100 pc is still under debate. We present sub-arcsecond angular resolution radio, mid-infrared, Paα, optical, and X-ray observations of NGC 1614, aimed at studying in detail both the circumnuclear ring and the nuclear region. The 8.4 GHz continuum emission traced by the Very Large Array and the Gemini/T-ReCS 8.7 μm emission, as well as the Paα line emission, show remarkable morphological similarities within the star-forming ring, suggesting that the underlying emission mechanisms are tightly related. We used a Hubble Space Telescope/NICMOS Paα map of similar resolution to our radio maps to disentangle the thermal free-free and non-thermal synchrotron radio emission, from which we obtained the intrinsic synchrotron power law for each individual region within the central kiloparsec of NGC 1614. The radio ring surrounds a relatively faint, steep-spectrum source at the very center of the galaxy, suggesting that the central source is not powered by an active galactic nucleus (AGN), but rather by a compact (r ≲ 90 pc) starburst (SB). Chandra X-ray data also show that the central kiloparsec region is dominated by SB activity, without requiring the existence of an AGN. We also used publicly available infrared data to model-fit the spectral energy distribution of both the SB ring and a putative AGN in NGC 1614. In summary, we conclude that there is no need to invoke an AGN to explain the observed bolometric properties of the galaxy.

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Distance and proper motion measurement of water masers in sharpless 269 IRS 2w

We present astrometric analysis of archival data of water masers in the star-forming region Sharpless 269 (S269) IRS 2w, observed with the VLBI Exploration of Radio Astrometry. An annual parallax of one of the bright maser features in this region was previously reported to be 0.189 ± 0.008 milliarcsecond (mas) using part of the same archival data as we used. However, we found that this maser feature is not the best to represent the annual parallax to S269 IRS 2w because the morphology is remarkably elongated in the east-west direction. For this study we have selected another maser feature showing simpler morphology. This makes the new annual parallax estimate more credible. Our newly obtained annual parallax is 0.247 ± 0.034 mas, corresponding to 4.05{sub −0.49}{sup +0.65} kpc. This value is well consistent with the 3.7-3.8 kpc obtained using the kinematic distance estimates and photometric distance modulus. We considered two hypotheses for the water-maser spatial distribution, a bipolar outflow and an expanding ring, in a kinematic model fitting analysis with a radially expanding flow. At this stage, any conclusions about the systemic proper motion could not be drawn from the kinematic analysis. Alternatively, we evaluated the mean proper motion to be (0.39 ± 0.92, –1.27 ± 0.90) mas yr{sup –1} eastward and northward, respectively, from the obtained proper motions of the detected water-maser features. The newly obtained annual parallax and mean proper motion give the peculiar motion of S269 IRS 2w to be (U {sub s}, V {sub s}, W {sub s}) of (8 ± 6, –21 ± 17, 1 ± 18) km s{sup –1}.

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