Methanol Masers Research Articles

Inverse MultiView. II. Microarcsecond Trigonometric Parallaxes for Southern Hemisphere 6.7 GHz Methanol Masers G232.62+00.99 and G323.74–00.26

We present the first results from the Southern Hemisphere Parallax Interferometric Radio Astrometry Legacy Survey: 10 μas accurate parallaxes and proper motions for two Southern Hemisphere 6.7 GHz methanol masers obtained using the inverse MultiView calibration method. Using an array of radio telescopes in Australia and New Zealand, we measured trigonometric parallaxes and proper motions for the masers associated with the star formation region G232.62+00.99 of π = 0.610 ± 0.011 mas, μ x = −2.266 ± 0.021 mas yr−1, and μ y = 2.249 ± 0.049 mas yr−1, which implies its distance to be d = 1.637 ± 0.029 kpc. These measurements represent an improvement in accuracy by more than a factor of 3 over the previous measurements obtained through Very Long Baseline Array observations of the 12 GHz methanol masers associated with this region. We also measure the trigonometric parallax and proper motion for G323.74–00.26 as π = 0.364 ± 0.009 mas, μ x = −3.239 ± 0.025 mas yr−1, and μ y = − 3.976 ± 0.039 mas yr−1, which implies a distance of d = 2.747 ± 0.068 kpc. These are the most accurate measurements of trigonometric parallax obtained for 6.7 GHz class II methanol masers to date. We confirm that G232.62+00.99 is in the Local Arm and find that G323.74–00.26 is in the Scutum–Centaurus arm. We also investigate the structure and internal dynamics of both masers.

SCOTCH − search for clandestine optically thick compact H iis

ABSTRACT This study uses archival high-frequency continuum data to expand the search for Hypercompact H ii regions and determine the conditions at which they appear, as this stage high mass star formation is short-lived and rare. We use 23 GHz continuum data taken towards methanol masers, which are an excellent signpost for very young embedded high-mass protostars. We have searched for high-frequency, optically thick radio sources to identify HC H ii region candidates. The data cover 128 fields that include 141 methanol masers identified by the Methanol Multibeam (MMB) survey. We have detected 68 high-frequency radio sources and conducted a multiwavelength analysis to determine their nature. This has identified 49 H ii regions, 47 of which are embedded in dense clumps fourteen of which do not have a 5 GHz radio counterpart. We have identified 13 methanol maser sites that are coincident with radio sources that have a steep positive spectral index. The majority of these are not detected in the mid-infrared and have been classified as protostellar or young stellar objects in the literature and we therefore consider to be good HC H ii region candidates, however, further work and higher resolution data are needed to confirm these candidates.

ATLASGAL: 3 mm class I methanol masers in high-mass star formation regions

Context. Class I methanol masers are known to be associated with shocked outflow regions around massive protostars, indicating a possible link between the maser properties and those of their host clumps. Aims. The main goals of this study are (1) to search for new class I methanol masers, (2) to statistically study the relationship between class I masers and shock tracers, (3) to compare the properties between class I masers and their host clumps, also as a function of their evolutionary stage, and (4) to constrain the physical conditions that excite multiple class I masers simultaneously. Methods. We analysed the 3 mm wavelength spectral line survey of 408 clumps identified by the APEX Telescope Large Area Survey of the Galaxy (ATLASGAL), which were observed with the IRAM 30-meter telescope, focusing on the class I methanol masers with frequencies near 84, 95, and 104.3 GHz. Results. We detect narrow maser-like features towards 54, 100, and 4 sources in the maser lines near 84, 95, and 104.3 GHz, respectively. Among them, 50 masers at 84 GHz, 29 masers at 95 GHz, and 4 rare masers at 104.3 GHz are new discoveries. The new detections increase the number of known 104.3 GHz masers from five to nine. The 95 GHz class I methanol maser is generally stronger than the 84 GHz maser counterpart. We find nine sources showing class I methanol masers, but no SiO emission, indicating that class I methanol masers might be the only signpost of protostellar outflow activity in extremely embedded objects at the earliest evolutionary stage. Class I methanol masers that are associated with sources that show SiO line wings are more numerous and stronger than those without such wings. The total integrated intensity of class I methanol masers is well correlated with the integrated intensity and velocity coverage of the SiO (2−1) emission. The properties of class I methanol masers are positively correlated with the bolometric luminosity, clump mass, and peak H2 column density of their associated clumps, but are uncorrelated with the luminosity-to-mass ratio, dust temperature, and mean H2 volume density. Conclusions. We suggest that the properties of class I masers are related to shocks traced by SiO. Based on our observations, we conclude that class I methanol masers at 84 and 95 GHz can trace a similar evolutionary stage to the H2O maser, and appear prior to 6.7 and 12.2 GHz methanol and OH masers. Despite their small number, the 104.3 GHz class I masers appear to trace a shorter and more evolved stage compared to the other class I masers.

Milliarcsecond structure and variability of methanol maser emission in three high-mass protostars

ABSTRACT The variability study of 6.7 GHz methanol masers has become a useful way to improve our understanding of the physical conditions in high-mass star-forming regions. Based on the single-dish monitoring using the Irbene telescopes, we selected three sources with close sky positions. We imaged them using the European very long baseline interferometry (VLBI) Network and searched available data on VLBI archives to follow detailed changes in their structures and single maser spot variability. All three targets show a few groups of maser cloudlets of a typical size of 3.5 mas and the majority of them show linear or arched structures with velocity gradients of order 0.22 km s−1 mas−1. The cloudlets and overall source morphologies are remarkably stable on time-scales of 7–15 yr, supporting a scenario of variability due to changes in the maser pumping rate.

AFGL 5180 and AFGL 6366S: sites of hub–filament systems at the opposite edges of a filamentary cloud

ABSTRACT We present a multiscale and multiwavelength study to unveil massive star formation (MSF) processes around sites AFGL 5180 and AFGL 6366S, both hosting a Class ii 6.7 GHz methanol maser emission. The radio continuum map at 8.46 GHz reveals a small cluster of radio sources towards AFGL 5180. Signatures of the early stages of MSF in our target sites are spatially seen at the opposite edges of a filamentary cloud (length ∼5 pc), which is observed in the submillimetre dust continuum maps. Using the near-infrared photometric data, the spatial distribution of young stellar objects is found towards the entire filament, primarily clustered at its edges. The getsf utility on the Herschel far-infrared images reveals a hub–filament system (HFS) towards each target site. The analysis of the molecular line data, which benefits from large area coverage (∼1° × 1°), detects two cloud components with a connection in both position and velocity space. This supports the scenario of a cloud–cloud collision (CCC) that occurred ∼1 Myr ago. The filamentary cloud, connecting AFGL 5180 and AFGL 6366S, seems spatially close to an H ii region Sh 2−247 excited by a massive O9.5 star. Based on the knowledge of various pressures exerted by the massive star on its surroundings, the impact of its energetic feedback on the filamentary cloud is found to be insignificant. Overall, our observational outcomes favour the possibility of the CCC scenario driving MSF and the formation of HFSs towards the target sites.

The Effelsberg survey of FU Orionis and EX Lupi objects

Context. FU Orionis (FUor) and EX Lupi (EXor) type objects are two groups of peculiar and rare pre-main sequence low-mass stars that are undergoing powerful accretion outbursts during their early stellar evolution. Although water masers are widespread in star-forming regions and serve as powerful probes of mass accretion and ejection on small scales, little is known about the prevalence of water masers toward FUors and EXors. Aims. We aim to perform the first systematic search for the 22.2 GHz water maser line in FUors and EXors in order to determine its overall incidence in these eruptive variables and to facilitate high angular-resolution follow-up observations. Methods. We used the Effelsberg 100-m radio telescope to observe the H2O (616 – 523) transition at 22.2GHz toward a sample of 51 eruptive young stellar objects. Results. We detected a total of five water masers in our survey; three are associated with eruptive stars, equivalent to a detection rate of ~6% for our sample of eruptive sources. These detections include one EXor, V512 Per (also known as SVS 13 or SVS 13A), and two FUors, Z CMa, and HH 354 IRS. This is the first reported detection of water maser emission towards HH 354 IRS. We also detected water maser emission in our pointing towards the FUor binary RNO 1B/1C, which most likely originates from the nearby deeply embedded source IRAS 00338+6312 (~4″ from RNO 1B/1C). Emission was also detected from H2O(B), (also known as SVS 13C), a Class 0 source ~30″ from the EXor V512 Per. The peak flux density of H2O(B) in our observations, 498.7 Jy, is the highest observed to date, indicating that we have serendipitously detected a water maser flare in this source. In addition to the two non-eruptive Class 0 sources (IRAS 00338+6312 and H2O(B)/SVS 13C), we detected maser emission towards one Class 0/I (HH 354 IRS) and two Class I (V512 Per/SVS 13A and Z CMa) eruptive stars. Conclusions. Despite the low detection rate, we demonstrate the presence of 22.2 GHz water maser emission in both FUor and EXor systems, paving the way to radio interferometric observations to study the environments of these eruptive stars on small scales. Comparisons of our data with historical observations spanning several decades suggest that multiple water maser flares have occurred in both V512 Per and H2O(B).

Nature of continuum emission in the source of the water maser super-flare G25.65+1.04

Context. The G25.65+1.04 source is one of the few known ‘super-flare’ water masers in the Milky Way, but in contrast to other super-flare sources, it remains the least studied. In fact, even the nature of the source driving the water maser is still unclear. Aims. With this project, we aim to clarify the composition and properties of the G25.65+1.04 region by means of examining the parameters of the continuum sources and establishing their association with masers of different types. Methods. Our previous VLA (Karl G. Jansky Very Large Array) observation detected four continuum peaks (VLA 1-4), three of which (VLA 1-3) were closely spaced and presented a linear orientation. However, the observation, which used the VLA B configuration, lacked the spatial resolution to resolve individual sources. A higher-resolution (A configuration) VLA observation of the continuum and spectral lines was conducted in 2019 using the L, S, C, and Ku bands. Results. For the first time, the continuum source VLA 1 – associated with the flaring water maser – is resolved into two components: VLA 1A and 1B. The component VLA 1A and the water maser are found to spatially coincide and are thought to be powered by the same source, a protostar at an early stage of evolution showing active ejection. We argue that VLA 2 pinpoints an actively ejecting high-mass protostar, as it is associated with a 6.7 GHz methanol maser and a magnetised jet traced by a 22 GHz H2O maser. Highly polarised OH maser emission is detected in the vicinity of VLA 1-2, with the brightest OH maser found in VLA 2. The magnetic field, identified from the OH maser emission, ranges from ∼ + 0.4 mG in VLA 1A to ∼ − 8 mG in VLA 2. Conclusions. The G25.65+1.04 region is found to consist of at least two young stellar objects: VLA 1A and VLA 2. Both sources are found to be at an active accretion and ejection stage of evolution.

The Parallax and 3D Kinematics of Water Masers in the Massive Star-forming Region G034.43+0.24

We report a measurement of the trigonometric parallax of 22 GHz water masers in the massive star-forming region G034.43+0.24 as part of the Bar and Spiral Structure Legacy Survey using the Very Long Baseline Array. The parallax is 0.330 ± 0.018 mas, corresponding to a distance of kpc. This locates G034.43+0.24 near the inner edge of the Sagittarius spiral arm and at one end of a linear distribution of massive young stars that cross nearly the full width of the arm. The measured three-dimensional motion of G034.43+0.24 indicates a near-circular Galactic orbit. The water masers display arc-like distributions, possibly bow shocks, associated with winds from one or more massive young stars.

Ammonia masers towards G 358.931−0.030

ABSTRACT We report the detection of ammonia masers in the non-metastable (6, 3), (7, 5), and (6, 5) transitions; the latter being the first unambiguous maser detection of that transition ever made. Our observations include the first very long baseline interferometry detection of ammonia maser emission, which allowed effective constraining of the (6, 5) maser brightness temperature. The masers were detected towards G 358.931−0.030, a site of 6.7-GHz class II methanol maser emission that was recently reported to be undergoing a period of flaring activity. These ammonia masers appear to be flaring contemporaneously with the class II methanol masers during the accretion burst event of G 358.931−0.030. This newly detected site of ammonia maser emission is only the 12th such site discovered in the Milky Way. We also report the results of an investigation into the maser pumping conditions, for all three detected masing transitions, through radiative transfer calculations constrained by our observational data. These calculations support the hypothesis that the ammonia (6, 5) maser transition is excited through high colour temperature infrared emission, with the (6, 5) and (7, 5) transition line ratio implying dust temperatures >400 K. Additionally, we detect significant linearly polarized emission from the ammonia (6, 3) maser line. Alongside our observational and radiative transfer calculation results, we also report newly derived rest frequencies for the ammonia (6, 3) and (6, 5) transitions.

The distance to the Serpens South cluster from H2O masers

In this Letter we report Very Long Baseline Array observations of 22 GHz water masers toward the protostar CARMA–6, located at the center of the Serpens South young cluster. From the astrometric fits to maser spots, we derive a distance of 440.7±3.5 pc for the protostar (1% error). This represents the best direct distance determination obtained so far for an object this young and deeply embedded in this highly obscured region. Taking depth effects into account, we obtain a distance to the cluster of 440.7 ± 4.6 pc. Stars visible in the optical that have astrometric solutions in the Gaia Data Release 3 are, on the other hand, all located at the periphery of the cluster. Their mean distance of 437−41+51 pc is consistent within 1σ with the value derived from maser astrometry. As the maser source is at the center of Serpens South, we finally solve the ambiguity of the distance to this region that has prevailed over the years.

Physical Environments of the Luminosity Outburst Source NGC 6334I Traced by Thermal and Maser Lines of Multiple Molecules

We have conducted a systematic line survey, primarily focused on transitions of the methanol and ammonia molecules, and monitoring observations of masers toward the high-mass star-forming region NGC 6334I. These observations were undertaken between 2019 and 2022 in the C, K, Ka, and Q bands with the Tianma Radio Telescope. In total, 63 CH3OH (including 11 class I and nine class II maser or maser candidate), 18 13CH3OH, and 34 NH3 (including seven maser or maser candidate) transitions were detected. The emission is likely associated with the luminosity outburst source MM1. Rotation diagram analysis of multiple ammonia transitions shows that the gas temperature in the molecular core was a factor of 2 higher than that measured in previous observations in the pre-burst stage. This suggests that the molecular core has likely been heated by radiation originating from the luminosity outburst. Maser variability in the methanol and excited-state OH masers shows a general trend that the maser components associated with the luminosity outburst have decreased in their intensity since 2020. The decay in the maser luminosity indicates that the outburst is possibly declining, and as a result, the duration of the MM1 luminosity outburst may be shorter than the predicted 40 yr duration. Compared to the masers detected toward another luminosity outburst source, G358.93-0.03, abundant class I methanol masers and strong water maser flares were also detected toward NGC 633I, but masers from rare class II methanol transitions and new molecules were absent toward NGC 6334I. The large number of detections of maser transitions toward the two burst sources provided a database for further maser modeling to explore the physical environments associated with accretion burst events.

An unusually powerful and long-lasting water maser flare phenomenon in IRAS 16293-2422

Aims. Our goal is to obtain new detailed observational data on the water maser flare phenomenon, unprecedented in power and duration, that occurred in IRAS 16293-2422 and determine the physical characteristics of the individual flares. Methods. We used the ground-based 22 m radio telescope to conduct long-term observations of the water maser features near – 1.5 km s−1 in IRAS 16293-2422. The movement of the radio telescope, collection of observational data, and processing were performed automatically. We used spectral-temporal data analysis to identify water maser flares in a complex flare phenomenon and determine their physical parameters. Results. The detected maser emission came from the largest structure of maser spots, the high density of which resulted in their partial overlap in time. There were a total of ten individual powerful flares in the phenomenon. The existence of such a complex configuration of emitting maser spots with very similar radial velocities has been confirmed for the first time. We were able to determine that masers of the powerful flares were in an unsaturated state due to a cascade pumping of radiation from several masers located in the observer’s line of sight. We obtained new important physical parameters of maser flares: the detailed shape of flares, the state of the water maser during flares, the H2O kinetic temperature, the density of the medium, the degree of ionization, and the velocities of the maser spots responsible for the flares.

A multiwavelength study of the IRAS 23139+5939 (G111.256−0.770) star-forming site and its relation to Sh2-157

ABSTRACTThe far-infrared source IRAS 23139+5939 (G111.25−0.77) is a well-studied massive star-forming region at the centre of a dense molecular clump. It is associated with a low-luminosity and variable methanol maser, a number of water maser clusters, and several compact H ii regions. We present new sub-arcsec-resolution broad- and narrow-band near- and mid-infrared calibrated images. These were analysed together with Wide-field Infrared Survey Explorer images and longer wavelength published data. We establish that IRAS 23139+5939 is a multiple massive young stellar object (YSO) with a spectral energy distribution characteristic of a Class I object. Its deeply embedded (AV = 21) central YSOs have a total luminosity of 3 × 104 L⊙ and a mass of 16 M⊙. We find several small knots of H2 emission in its vicinity, bordering a large CO outflow driven by the protostar. Their distribution suggests the presence of several YSOs with jets. A young embedded stellar cluster of size ∼40 arcsec (0.65 pc) is found around the massive protostar, with evidence of protoplanetary discs in more than 50 per cent of the likely members. We also report a large arc of H2 emission surrounding a nearby H α-emission star displaying a large infrared excess, with a total luminosity of 1.5 × 103 L⊙. Gaia Data Release 3 and very long baseline interferometry parallaxes indicate a common distance of 3.34 kpc to these two YSOs, a distance similar to that to Sh2-157, a nearby massive star-forming region, which appears connected to IRAS 23139+5939 by a warm dust filament.

Extremely powerful flare phenomenon of H2O maser in W49N near −40 km s−1

ABSTRACT As a result of detailed observations of the water vapour maser at the 22-m Simeiz radio telescope from 2017 June to 2019 December, two powerful flares were recorded in the Galactic source W49N, which occurred near the high-velocity feature −40 km s−1. The extremely powerful flare had an ultrashort duration of about 2 d and reached a flux density of 110 kJy. An ultrashort flare occurred at the top of a less powerful, but ten times longer one. To our knowledge, a flare of a water maser with such extreme characteristics has never been reported before. A correlation between the exponential increase and decrease in the flare flux density and decrease in line widths with increasing flux density, which is characteristic of an unsaturated maser, is found. The maser of the third flare was in a saturated state and provided a large input flux density 9.5 kJy for the occurrence of two powerful flares, the masers of which were in an unsaturated state. New data have been obtained concerning the physical characteristics of the water maser phenomenon during powerful flares.

Multi-frequency VLBI observations of maser lines during the 6.7 GHz maser flare in the high-mass young stellar object G24.33+0.14

Context. Recent studies have shown that 6.7 GHz methanol maser flares can be a powerful tool for verifying the mechanisms of maser production and even the specific signatures of accretion rate changes in the early stages of high-mass star formation. Aims. We characterize the spatial structure and evolution of methanol and water masers during a flare of methanol maser emission at 6.7 GHz in the high-mass young stellar object (HMYSO) G24.33+0.14. Methods. Very Long Baseline Array (VLBA) was used to image the 6.7 and 12.2 GHz methanol and 22.2 GHz water vapor masers at three epochs guided by monitoring the methanol line with the Torun 32m telescope. The 6.7 GHz maser maps were also obtained with the European VLBI Network (EVN) and Long Baseline Array (LBA) during the flare. The Wide-field Infrared Survey Explorer (WISE) data were used to find correlations between the 6.7 GHz maser and infrared (IR) fluxes. Results. The 6.7 GHz methanol maser cloudlets are distributed over ~3500 au, and the morphology of most of them is stable although their brightness varies following the course of the total flux density on a timescale of two months. The 12.2 GHz methanol maser cloudlets cover an area an order of magnitude smaller than that of 6.7 GHz emission, and both transitions emerge from the same masing gas. The 22.2 GHz maser cloudlets lie in the central region and show a systematic increase in brightness and moderate changes in size and orientation, together with the velocity drift of the strongest cloudlet during two months of the Very Long Baseline Interferometry (VLBI) observing period. Time lag estimates imply the propagation of changes in the physical conditions of the masing region with a subluminal speed (~0.3c). A tight correlation of IR (4.6 μm) and 6.7 GHz flux densities is found, supporting the radiative pumping model. Proper motion analysis does not reveal any signs of expansion or inflow of the methanol cloudlets within ~6 mas over ~10 yr. Comparison with the 230 GHz Atacama Large Millimeter Array (ALMA) data indicates that the methanol masers are distributed in the inner part of the rotating disk, whereas the 22.2 GHz emission traces the compact inner component of the bipolar outflow or a jet structure. Conclusions. The maser morphology in the target is remarkably stable over the course of the flare and is similar to the quiescent state, possibly due to less energetic accretion events that can repeat on a timescale of ~8 yr.

Sample and Statistical Analysis of the Near-Earth Object Wide-field Infrared Survey Explorer Variability of the 6.7 GHz Methanol Maser Sources

We present a statistical study of infrared variability using the Near-Earth Object Wide-field Infrared Survey Explorer (NEOWISE) database for a sample consisting of 1085 high-mass young stellar objects (YSOs) related to 6.7 GHz methanol masers. A total of 383 maser sources were identified as NEOWISE variables and classified in two variability behavior classifications: 204 secular (linear, curved, and periodic) and 179 stochastic (burst, drop, and irregular) variables. Statistical analysis of the properties of these variables (e.g., the dust temperature, bolometric luminosity, hydrogen column density, W4 luminosity, and W1−W2 color) has revealed a potential evolutionary sequence among different light-curve types of variables. There is a possible general evolutionary (from less to more evolved) trend between the three variable types from secular to stochastic to nonvariable. For the specific classifications, the evolutionary trend for secular variables is linear to sin to sin+linear, and for stochastic variables it is burst to irregular to drop. These sequences may reflect the evolution of the envelope or accretion disk of high-mass YSOs, from large to small radii due to gravitational collapse. Although no significant variability correlation was established between the 6.7 GHz methanol maser and the W2-band emission based on the data collected so far, a number of candidates were found for further investigating the accretion burst events via future variability monitoring programs of both mid-infrared emission and masers.

ALMA detection of 321 GHz water maser emission in the radio galaxy NGC 1052

Abstract The Atacama Large Millimeter/submillimeter Array (ALMA) serendipitously detected H2O $J_{K_{\rm a}, K_{\rm c}} = 10_{2,9}$–93, 6 emission at 321 GHz in NGC 1052. This is the first submillimeter maser detection in a radio galaxy and the most luminous 321 GHz H2O maser known to-date with the isotropic luminosity of $1090\, L_{\odot }$. The line profile consists of a broad velocity component with FWHM = 208 ± 12 km s−1 straddling the systemic velocity and a narrow component with FWHM = 44 ± 3 km s−1 blueshifted by 160 km s−1. The profile is significantly different from the known 22 GHz 61, 6–52, 3 maser which shows a broad profile redshifted by 193 km s−1. The submillimeter maser is spatially unresolved with a synthesized beam of ${0{^{\prime \prime}_{.}}68} \times {0{^{\prime \prime}_{.}}56}$ and coincides with the continuum core position within 12 pc. These results indicate amplification of the continuum emission through high-temperature (>1000 K) and dense [n(H2O) > 104 cm−3] molecular gas in front of the core.

Ammonia mapping observations of the Galactic infrared bubble N49: Three NH3 clumps along the molecular filament

Abstract We have carried out the NH3(J, K) = (1, 1), (2, 2), and (3, 3) mapping observations toward the Galactic infrared bubble N49 (G28.83−0.25) using the Nobeyama 45 m telescope. Three NH3 clumps (A, B, and C) were discovered along the molecular filament with the radial velocities of ∼96, 87, and 89 km s−1, respectively. The kinetic temperature derived from the NH3(2, 2)/NH3(1, 1) shows Tkin = 27.0 ± 0.6 K enhanced at Clump B in the eastern edge of the bubble, where position coincides with massive young stellar objects (MYSOs) associated with the 6.7 GHz class II methanol maser source. This result shows the dense clump is locally heated by stellar feedback from the embedded MYSOs. The NH3 Clump B also exists at the 88 km s−1 and 95 km s−1 molecular filament intersection. We therefore suggest that the NH3 dense gas formation in Clump B can be explained by a filament–filament interaction scenario. On the other hand, NH3 Clumps A and C at the northern and southern sides of the molecular filament might be the sites of spontaneous star formation because these clumps are located ∼ 5–10 pc away from the edge of the bubble.

Polarized Maser Emission with In-source Faraday Rotation

We discuss studies of polarization in astrophysical masers with particular emphasis on the case where the Zeeman splitting is small compared to the Doppler profile, resulting in a blend of the transitions between magnetic substates. A semiclassical theory of the molecular response is derived, and coupled to radiative transfer solutions for 1 and 2-beam linear masers, resulting in a set of nonlinear, algebraic equations for elements of the molecular density matrix. The new code, PRISM, implements numerical methods to compute these solutions. Using PRISM, we demonstrate a smooth transfer between this case and that of wider splitting. For a J = 1–0 system, with parameters based on the v = 1, J = 1–0 transition of SiO, we investigate the behavior of linear and circular polarization as a function of the angle between the propagation axis and the magnetic field, and with the optical depth, or saturation state, of the model. We demonstrate how solutions are modified by the presence of Faraday rotation, generated by various abundances of free electrons, and that strong Faraday rotation leads to additional angles where the Stokes Q changes sign. We compare our results to a number of previous models, from the analytical limits derived by Goldreich, Keeley, and Kwan in 1973, through computational results by W. Watson and coauthors, to the recent work by Lankhaar and Vlemmings in 2019. We find that our results are generally consistent with those of other authors given the differences in the approach and the approximations made.

Proper Motions of Water Masers in W49 N Measured by KaVA

We report the proper motions of 22 GHz water masers toward W49 N that were observed by the KVN and VERA Array (KaVA) during 2017 February–May. We found 263, 268, and 310 features in three successive epochs; they were distributed in a region of size 4 × 4 arcsec2. The strongest flux density was in the third epoch, and its averaged value was 18,090 Jy at V LSR +0.47 km s−1. For 102 H2O maser features, proper motion was detected across all three epochs. The average proper motions in R.A. and decl. offset were −0.352 and +0.890 mas yr−1, respectively. The morphology of the distribution of the H2O maser features was found to be a bipolar outflow structure with an inclination angle of 37° ± 13° to the line of sight, and the features were expanding from a well-defined outflow center. A model of the source combining expansion and rotation yielded a distance to W49 of 11.12 ± 0.96 kpc that is consistent with the results from trigonometric parallax. A redshifted lobe was situated in the northeast direction and a blueshifted lobe in the southwest direction. We also discussed the location of the powerful flaring H2O maser feature at V LSR = + 6 km s−1 and its possible mechanisms on the basis of spatial structures for the maser feature in VLBI maps observed with the KaVA, timed just before and during the rebrightening phase.