Charles Malcolm Walmsley passed away on 1 May 2017. Over a long and highly productive career, Malcolm made numerous and fundamental contributions to the science of the interstellar medium and star formation. These have recently been summarized elsewhere (Menten & Cesaroni 2017). Here I would like to describe some of his work related to masers.

Maser theory continues to be driven by advances in observational techniques. Here, I consider the responses to VLBI with space-Earth baselines and cross-correlation spectroscopy (a re-consideration of coherence properties), routine observation in full-Stokes polarization (a re-casting of the polarization transfer equations), and long-term variability monitoring (3-D modelling of irregular domains).

The study of astrophysical maser formation provides a useful probe of the chemical composition and physical conditions of the sources they are observed in. This exploration requires continuously solving the SE equations for the populations of the energy levels in search of conditions that will produce an inversion. After evaluation of available implementations applying the Escape Probability approximation, the masers solver was developed to provide an efficient and robust matrix inversion calculation. This open source package is hosted at https://bitbucket.org/ruby_van_rooyen/masers.

As first realised in the late 1980s, methanol masers come in two varieties, termed Class I and Class II. While Class II masers had observationally been extensively studied in the past, until recently relatively little attention was paid to Class I methanol masers due to their low luminosities compared to other maser transitions. In this review, we will focus on the recent progress in our understanding of Class I methanol masers both from an observational and from a theoretical point of view.

Maser observations of both linearly and circularly polarized emission have provided unique information on the magnetic field in the densest parts of star forming regions, where non-maser magnetic field tracers are scarce. While linear polarization observations provide morphological constraints, magnetic field strengths are determined by measuring the Zeeman splitting in circularly polarized emission. Methanol is of special interest as it is one of the most abundant maser species and its different transitions probe unique areas around the protostar. However, its precise Zeeman-parameters are unknown. Experimental efforts to determine these Zeeman-parameters have failed. Here we present quantum-chemical calculations of the Zeeman-parameters of methanol, along with calculations of the hyperfine structure that are necessary to interpret the Zeeman effect in methanol. We use this model in re-analyzing methanol maser polarization observations. We discuss different mechanisms for hyperfine-state preference in the pumping of torsion-rotation transitions involved in the maser-action.

Through the observations and the analysis of maser polarization it is possible to measure the magnetic field in several astrophysical environments (e.g., star-forming regions, evolved stars). In particular from the linearly and circularly polarized emissions we can determine the orientation and the strength of the magnetic field, respectively. In these proceedings the implications, on observed data, of the new estimation of the Landé g-factors for the CH3OH maser are presented. Furthermore, some example of the most recent results achieved in observing the polarized maser emission from several maser species will also be reported.

We present a review of the properties of Class I methanol masers detected in low-mass star forming regions (LMSFRs). These masers, henceforth called LMMIs, are associated with postshock gas in the lobes of chemically active outflows in LMSFRs NGC1333, NGC2023, HH25, and L1157. LMMIs share the main properties with powerful masers in regions of massive star formation and are a low-luminosity edge of the total Class I maser population. However, the exploration of just these objects may push forward the exploration of Class I masers, since many LMSFRs are located only 200–300 pc from the Sun, making it possible to study associated objects in detail. EVLA observations with a 0.2″ spatial resolution show that the maser images consist of unresolved or barely resolved spots with brightness temperatures up to 5 × 105 K. The results are “marginally” consistent with the turbulent model of maser emission.

Methanol and water masers indicate young stellar objects. They often exhibit flares, and a fraction shows periodic activity. Several mechanisms might explain this behavior but the lack of concurrent infrared (IR) data complicates the identification of its cause. Recently, 6.7 GHz methanol maser flares were observed, triggered by accretion bursts of high-mass YSOs which confirmed the IR-pumping of these masers. This suggests that regular IR changes might lead to maser periodicity. Hence, we scrutinized space-based IR imaging of YSOs associated with periodic methanol masers. We succeeded to extract the IR light curve from NEOWISE data for the intermediate mass YSO G107.298+5.639. Thus, for the first time a relationship between the maser and IR variability could be established. While the IR light curve shows the same period of ~34.6 days as the masers, its shape is distinct from that of the maser flares. Possible reasons for the IR periodicity are discussed.

High-mass young stellar objects (HMYSO) displaying methanol maser flux variability probably trace a variety of phenomena such as accretion events, magnetospheric activity, stellar flares and stellar wind interactions in binary systems. A long-term monitoring of the 6.7 GHz methanol line in a large sample of HMYSOs has been undertaken to characterize the variability patterns and examine their origins. The majority of the masers show significant variability on time-scales between a week and a few years. High amplitude short flares of individual features occurred in several HMYSOs. The maser features with low luminosity tend to be more variable than those with high luminosity. The variability of the maser features increases when the bolometric luminosity the powering star decreases. Statistical analysis of basic properties of exciting objects and the variability measures supports an idea that burst activity of methanol masers is driven mainly by changes in the infrared pumping rate.

We initiated a long-term and highly frequent monitoring project toward 442 methanol masers at 6.7 GHz (Dec >−30 deg) using the Hitachi 32-m radio telescope in December 2012. The observations have been carried out daily, monitoring a spectrum of each source with intervals of 9–10 days. In September 2015, the number of the target sources and intervals were redesigned into 143 and 4–5 days, respectively. This monitoring provides us complete information on how many sources show periodic flux variations in high-mass star-forming regions, which have been detected in 20 sources with periods of 29.5–668 days so far (e.g., Goedhart et al. 2004). We have already obtained new detections of periodic flux variations in 31 methanol sources with periods of 22–409 days. These periodic flux variations must be a unique tool to investigate high-mass protostars themselves and their circumstellar structure on a very tiny spatial scale of 0.1–1 au.

The Bulge Asymmetries and Dynamical Evolution (BAaDE) project aims to map the positions and velocities of up to ~20,000 late-type stars with SiO maser emission along the full Galactic plane, with a large concentration in the Galactic Bulge and inner Galaxy. Both J = 1 → 0 and J = 2 → 1 transitions using the Very Large Array (VLA) and the Atacama Large Millimeter Array (ALMA) are being observed. In the VLA observing setup, in addition to the 28SiO, v = 1 and v = 2J = 1 → 0 maser transitions, the bandwidth was wide enough to include the J = 1 → 0 transitions of the rare isotopologues of the SiO molecule in both the ground and vibrationally excited states: 29SiO, v = 0, 30SiO, v = 0, 29SiO, v = 1, and 29SiO, v = 2. Approximately 10% of the initial ~3500 targets of the project show maser emission from at least one of these lines. Some of these stars (with isotopic maser emission) show high radial velocities which implies that they are indeed in the Galactic Bulge or inner Galaxy (i.e. not foreground objects). We present line profiles, refined detection statistics, and the implications of the detection of the isotopic maser emission on pumping schemes that have been previously presented.

The full theory of polarized SiO maser emission from the near-circumstellar environment of Asymptotic Giant Branch stars has been the subject of debate, with theories ranging from classical Zeeman origins to predominantly non-Zeeman anisotropic excitation or propagation effects. Features with an internal electric vector position angle (EVPA) rotation of ∼π/2 offer unique constraints on theoretical models. In this work, results are presented for one such feature that persisted across five epochs of SiO ν = 1, J = 1 − 0 VLBA observations of TX Cam. We examine the fit to the predicted dependence of linear polarization and EVPA on angle (θ) between the line of sight and the magnetic field against theoretical models. We also present results on the dependence of mc on θ and their theoretical implications. Finally, we discuss potential causes of the observed differences, and continuing work.

In the current paper we describe results of an extensive and refined analysis which shows that the beaming leads to considerable changes in the model line ratios and brightness estimates. For example, beaming shifts the locus of the brightest masers to the lower values of the gas densities. Recent theoretical paper by Leurini et al. (2016) presented extensive consideration of the Class I methanol maser (MMI) pumping. Their study allowed to distinguish only 3 of 4 MMI pumping regimes found in Sobolev et al. (2005) and Sobolev et al. (2007) on the basis of analysis of observational data combined with theoretical considerations. The regime when the line from the J−2 − (J − 1)−1E series is the brightest was missing in Leurini et al. (2016) results. This may be explained by considering the fact that the authors did not take into account considerable beaming effects.

The statistical rate equations are used to model the OH masers to see if they will always have a one-to-one correspondence with the variation of dust temperature. It is concluded that one has to be careful to argue that the masers will always follow the dust temperature variation profile, and it is possible that different maser transitions from the same molecule respond differently to the same dust temperature variations.

We report another 6.7 GHz methanol maser burst in the high mass star region G33.641-0.228. The flare is in its second component at vLSR = 59.6 km s−1 and was observed in August-September 2016 by VIRAC radio telescope RT-32 in Irbene, Latvia. Several bursts of the second spatial component of G33.641-0.228 have been reported previously by Fujisawa et al. The maximum peak flux density of the source was measured to reach 343 Jy that is 13 times increase from its ground level. Significant oscillations were discovered during the decay phase indicating a more complex burst mechanism that cannot be explained by a simple heating of the region.

The interferometric and single-dish observations of the Extended Green Objects sample have been carried out in order to check the possible common pumping mechanism of class I methanol maser (cIMM) and OH(1720 MHz) maser and their identification with a front of bipolar outflow as a source of interstellar shock stimulating collisional pumping of the molecules. High spatial and spectral resolution observations of OH masers allow us to investigate structure, kinematics, and magnetic field configuration of the inner region of the source, i.e., the outflow ejection region. Analysis of magnetic field strength in a disk area is crucial to understanding of the outflow origin.

Since the IAU (maser-)Symposium 287 in Stellenbosch/South Africa (Jan. 2012), great progress has been achieved in studying extragalactic maser sources. Sensitivity has reached a level allowing for dedicated maser surveys of extragalactic objects. These included, during the last years, water vapor (H2O), methanol (CH3OH), and formaldehyde (H2CO), while surveys related to hydroxyl (OH), cyanoacetylene (HC3N) and ammonia (NH3) may soon become (again) relevant. Overall, with the upgraded Very Large Array (VLA), the Atacama Large Millimeter/submillimeter Array (ALMA), FAST (Five hundred meter Aperture Synthesis Telescope) and the low frequency arrays APERTIF (APERture Tile in Focus), ASKAP (Australian Square Kilometer Array Pathfinder) and MeerKAT (Meer Karoo Array Telescope), extragalactic maser studies are expected to flourish during the upcoming years. The following article provides a brief sketch of past achievements, ongoing projects and future perspectives.

The Hubble constant is a key cosmological parameter that sets the present-day expansion rate as well as the age, size, and critical density of the Universe. Intriguingly, there is currently a tension in the measurements of its value in the standard flat ΛCDM model – observations of the Cosmic Microwave Background with the Planck satellite lead to a value of the Hubble constant that is lower than the measurements from the local Cepheids-supernovae distance ladder and strong gravitational lensing. Precise and accurate Hubble constant measurements from independent probes, including water masers, are necessary to assess the significance of this tension and the possible need of new physics beyond the current standard cosmological model. We present the progress toward an accurate Hubble constant determination.

The Megamaser Cosmology Project (MCP) measures the Hubble Constant by determining geometric distances to circumnuclear 22 GHz H2O megamasers in galaxies at low redshift (z < 0.05) but well into the Hubble flow. In combination with the recent, exquisite observations of the Cosmic Microwave Background by WMAP and Planck, these measurements provide a direct test of the standard cosmological model and constrain the equation of state of dark energy. The MCP is a multi-year project that has recently completed observations and is currently working on final analysis. Based on distance measurements to the first four published megamasers in the sample, the MCP currently determines H0 = 69.3 ± 4.2 km s−1 Mpc−1. The project is finalizing analysis for five additional galaxies. When complete, we expect to achieve a ~4% measurement. Given the tension between the Planck prediction of H0 in the context of the standard cosmological model and astrophysical measurements based on standard candles, the MCP provides a critical and independent geometric measurement that does not rely on external calibrations or a distance ladder.

Analyzing archival data from different telescopes, H2O megamaser Seyfert 2s appeared to exhibit higher nuclear radio luminosities than non-masing Seyfert 2s (Zhang et al. 2012). This has been confirmed by our follow-up study on multi-band (11, 6, 3.6, 2, 1.3 cm) radio properties of maser host Seyfert 2s, through systematic Effelsberg observations (Liu et al. 2017). The nuclear radio luminosity was supposed to be a suitable indicator to guide future AGN maser searches. Thus we performed a pilot survey with the Effelsberg telescope on H2O maser emission toward a small sample of radio-bright Seyfert 2 galaxies with relatively higher redshift (>0.04). Our pilot survey led to one new megamaser source and one additional possible detection, which reflects our success in selecting H2O megamaser candidates compared to previous observations (higher detection rate, larger distance). Our successful selection technique choosing Seyfert 2s with radio-bright nuclei may provide good guiding for future H2O megamaser surveys. Therefore we are conducting a large systematic survey toward a big Seyfert 2 sample with such radio-bright nuclei. Detections of luminous H2O masers at large distance (z>0.04) may hold the great potential to increase our knowledge on the central highly obscured but still very enigmatic regions of active Seyfert galaxies (Zhang et al. 2017).