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We present a comprehensive analysis of the periodic flares observed in the 6.7 GHz methanol transition in G22.356+0.066, utilizing the Maxwell-Bloch equations (MBEs) as a framework to model these phenomena. By solving the one-dimensional MBEs, we describe the behavior of both the quasi-steady-state maser and transient superradiance regimes. Our findings indicate that the observed periodic flares, with varying timescales across different velocities, are consistent with the characteristics of Dicke's superradiance, triggered by a common radiative pump in regions of varying inverted column densities. This work provides new insights into the physical processes governing variability in maser-hosting regions and underscores the significance of superradiance as a powerful radiation mechanism in astrophysical environments., Comment: 5 pages, 7 figures

A Riemannian metric on a closed manifold is said to be geometrically formal if the wedge product of any two harmonic forms is harmonic; equivalently, the interior product of any two harmonic forms is harmonic. Given a Riemannian foliation on a closed manifold, we say that a bundle-like metric is transversely geometrically formal if the interior product of any two basic harmonic forms is basic harmonic. In this paper, we examine the geometric and topological consequences of this condition., Comment: 30 pages

Methanol masers at 6.7~GHz are well-known signposts of high-mass star-forming regions. [...] We aim to understand the origin of the ring-like structures outlined by methanol maser emission in a number of sources. This emission could be, a priori, spatially associated with an outflow and/or disc around a high-mass protostar. [...] Using sensitive, three-epoch observations spanning over eight years with the European VLBI Network, we have started the most direct investigations of maser rings using very accurate proper motion measurements with uncertainties below 1\,km~s$^{-1}$. We present full results for the five targets of our sample, G23.207-00.377, G23.389+00.185, G28.817+00.365, G31.047+00.356, and G31.581+00.077, where proper motions show similar characteristics; maser cloudlets do not move inwards towards the centre of the rings but rather outwards. We also include the most circular source, G23.657-00.127, in the discussion as a reference. The magnitude of maser proper motions ranges from a maximum of about 13\,km~s$^{-1}$ to 0.5~km~s$^{-1}$. In two of the five sources with a high number of maser spots (>100), namely G23.207-00.377 and G23.389+00.185, we show that the size of the best elliptical model, fitted to the distribution of persistent masers, increases in time in a manner similar to the case of G23.657-00.127. Moreover, we checked the separations between the pairs of spots from distinct regions, and we were able to assess that G28.817+00.365 and G31.047+00.356 can be interpreted as showing expanding motions. We analysed the profiles of single maser cloudlets and studied their variability. Contrary to single-dish studies, the interferometric data indicate variability of the emission of single-masing cloudlets. In five of the six targets expansion motions prevail. Only in the case of G31.581+00.077 can a scenario of disc-like rotation not be excluded. [...], Comment: 24 pages, accepted by Astronomy and Astrophysics

Aims: We report the discovery and analysis of a periodic methanol maser in the massive protostar IRAS 20216+4104. Methods: To obtain the light curve, we used the 6.7 GHz methanol maser spectra collected between 2000-2003 and 2009-2023 with the Hartebeesthoek and Torun radio telescopes, as well as spectra from the literature reported prior to 1992. Results: The velocity-integrated flux density shows sinusoidal-like variations with a period of 6.9 +/- 0.03 yr. All but one of the features show periodic changes with a relative amplitude of 2 up to >89. A slightly variable feature displays a moderate anti-correlation between the flux density and the other significantly variable features. The maser emission appears to follow the continuum emission of the red-shifted outflow cavity. A maximum emission of 3.4 and 4.6 mu m precedes the maser peak by 15 % of the period and the (infrared) IR light centroids show time-dependent displacement. The periodic behaviour of the maser and IR emission is likely due to the eclipsing effect from a wobbling inner disk., Comment: 10 figures, 2 tables, accepted by A&A

The Committee on Radio Astronomy Frequencies (CRAF) is an Expert Committee of the European Science Foundation. It aims to provide a cost-effective single voice on frequency protection issues for European radio astronomy observatories and research institutes, achieving a significantly greater impact than that achievable by individual national institutions. By working together, European observatories and institutes can profit from synergy effects, cover many more topics, and learn from each other. CRAF was founded in 1988 and has since then been engaged with the International Telecommunication Union (ITU), in particular its Radiocommunication Sector (ITU-R), and the European Conference of Postal and Telecommunications Administrations (CEPT) and its European Communications Committee (ECC). This is the self-evaluation report prepared by CRAF for its periodic review of the years 2011-2021., Comment: 75 pages

Starting with a manifold $M$ and a semi-free action of $S^3$ on it, we have the Smith-Gysin sequence: $$ \cdots \to H^{*}( M) \to H^{*-3}(M/S^3, M^{S^3}) \oplus H^{*} (M^{S^3}) \to H^{*+1}(M/S^3, M^{S^3}) \to H^{*+1}(M) \to \cdots $$ In this paper, we construct a Smith-Gysin sequence that does not require the semi-free condition. This sequence includes a new term, referred to as the "exotic term," which depends on the subset $M^{S^1}$: $$ \cdots \to H^{*}(M) \to H^{*-3} (M/S^3, \Sigma/S^3) \oplus H^{*}(M^{S^3}) \oplus \left( H^{*-2}(M^{S^1})\right)^{-\mathbb{Z}_2} \to H^{*+1}(M/S^3,M^{S^3}) \to H^{*+1}(M) \to \cdots $$ Here, $\Sigma \subset M$ is the subset of points in $M$ whose isotropy groups are infinite. The group $\mathbb{Z}_2$ acts on $M^{S^1}$ by $j \in S^3$., Comment: We have changed the abstrast, which was unreadable

The Hard Lefschetz Property (HLP) has recently been formulated in the context of isometric flows without singularities on manifolds. In this category, two versions of the HLP (transverse and not) have been proven to be equivalent, thus generalizing what happens in the important cases of both K-contact and Sasakian manifolds. In this work we define both versions of the HLP for almost-free S3 -actions, and prove that they agree for actions satisfying a cohomological condition, which includes the important category of 3-Sasakian manifolds, where those two versions of the HLP are shown to be held. We also provide a family of examples of free actions of the 3-sphere which are not 3-Sasakian manifolds, but satisfy the HLP., Comment: 8 pages

Fast radio bursts (FRBs) are extremely energetic, millisecond-duration radio flashes that reach Earth from extragalactic distances. Broadly speaking, FRBs can be classified as repeating or (apparently) non-repeating. It is still unclear, however, whether the two types share a common physical origin, differing only in their activity rate. Here we report on an unprecedented observing campaign that targeted one hyperactive repeating source, FRB 20201124A, for more than $2000~\mathrm{hr}$ using four $25-32\mathrm{-m}$ class radio telescopes. In total, we detect $46$ high-energy bursts, many more than one would expect given previous observations of lower-energy bursts using larger radio telescopes. We find a high-energy burst distribution that resembles that of the non-repeating FRB population, suggesting that apparently non-repeating FRB sources may simply be the rarest bursts from repeating sources. We also discuss how FRB 20201124A contributes strongly to the all-sky FRB rate and how similar sources would be observable even at very high redshift., Comment: 25 pages, 9 figures. Submitted, comments welcome

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. 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 HMYSO G24.33$+$0.14. 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 EVN and LBA during the flare. WISE data were used to find correlations between the 6.7 GHz maser and IR fluxes. The 6.7 GHz methanol maser cloudlets are distributed over $\sim$3500 au, and the morphology of most of them is stable although their brightness varies following the course of the total flux density on a timescale of two months. The 12.2 GHz methanol maser cloudlets cover an area an order of magnitude smaller than that of 6.7 GHz emission, and both transitions emerge from the same masing gas. The 22.2 GHz maser cloudlets lie in the central region and show a systematic increase in brightness and moderate changes in size and orientation, together with the velocity drift of the strongest cloudlet during two months of the VLBI observing period. Time lag estimates imply the propagation of changes in the physical conditions of the masing region with a subluminal speed ($\sim$0.3c). A tight correlation of IR (4.6$\mu$m) and 6.7 GHz flux densities is found, supporting the radiative pumping model. Comparison with the 230 GHz 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., Comment: Accepted by A\&A

The negative demand shock due to the COVID-19 lockdown has reduced net demand for electricity -- system demand less amount of energy produced by intermittent renewables, hydroelectric units, and net imports -- that must be served by controllable generation units. Under normal demand conditions, introducing additional renewable generation capacity reduces net demand. Consequently, the lockdown can provide insights about electricity market performance with a large share of renewables. We find that although the lockdown reduced average day-ahead prices in Italy by 45%, re-dispatch costs increased by 73%, both relative to the average of the same magnitude for the same period in previous years. We estimate a deep-learning model using data from 2017--2019 and find that predicted re-dispatch costs during the lockdown period are only 26% higher than the same period in previous years. We argue that the difference between actual and predicted lockdown period re-dispatch costs is the result of increased opportunities for suppliers with controllable units to exercise market power in the re-dispatch market in these persistently low net demand conditions. Our results imply that without grid investments and other technologies to manage low net demand conditions, an increased share of intermittent renewables is likely to increase costs of maintaining a reliable grid.

The repeating fast radio burst (FRB) source FRB 20200120E is exceptional because of its proximity and association with a globular cluster. Here we report $60$ bursts detected with the Effelsberg telescope at 1.4 GHz. We observe large variations in the burst rate, and report the first FRB 20200120E `burst storm', where the source suddenly became active and 53 bursts (fluence $\geq 0.04$ Jy ms) occurred within only 40 minutes. We find no strict periodicity in the burst arrival times, nor any evidence for periodicity in the source's activity between observations. The burst storm shows a steep energy distribution (power-law index $\alpha = 2.39\pm0.12$) and a bi-modal wait-time distribution, with log-normal means of 0.94$^{+0.07}_{-0.06}$ s and 23.61$^{+3.06}_{-2.71}$ s. We attribute these wait-time distribution peaks to a characteristic event timescale and pseudo-Poisson burst rate, respectively. The secondary wait-time peak at $\sim1$ s is $\sim50\times$ longer than the $\sim24$ ms timescale seen for both FRB 20121102A and FRB 20201124A -- potentially indicating a larger emission region, or slower burst propagation. FRB 20200120E shows order-of-magnitude lower burst durations and luminosities compared with FRB 20121102A and FRB 20201124A. Lastly, in contrast to FRB 20121102A, which has observed dispersion measure (DM) variations of $\Delta{\rm DM} >1$ pc cm$^{-3}$ on month-to-year timescales, we determine that FRB 20200120E's DM has remained stable ($\Delta{\rm DM} <0.15$ pc cm$^{-3}$) over $>10$ months. Overall, the observational characteristics of FRB 20200120E deviate quantitatively from other active repeaters, but it is unclear whether it is qualitatively a different type of source., Comment: Accepted for publication in MNRAS

Starting with a concise review of quaternionic geometry and quaternion K{\"a}hler manifolds, we define a transversely quaternion K{\"a}hler foliation. Then we formulate and prove the foliated versions of the now classical results of V.Y. Kraines and A Fujiki on the cohomology of quaternion K{\"a}hler manifolds. Finally, as any orbifold can be realized as the leaf space of a suitably defined Riemannian foliation we reformulate our results for quaternion orbifolds.

We have performed a molecular line search toward the flaring 6.7-GHz masers G24.33+0.13 and G359.62-0.24 using the Australia Telescope Compact Array. We present spectra of the 6.7-GHz class~II methanol and 22.2-GHz water masers toward these sources and provide comparison with other recent flaring events these sources have experienced. We also detect the fourth example of a 23.4-GHz class~I methanol maser, and the eleventh example of a 4.8-GHz formaldehyde maser toward G24.33+0.13. Alongside these results, we observe the previously detected ammonia (3,3) emission and report upper limits on the presence of various other cm-wavelength methanol, ammonia and OH transitions. Our results are consistent with the flaring of G24.33+0.13 being driven by a variable accretion rate in the host high-mass young stellar object., Comment: Accepted into MNRAS 2021 October 17. 10 pages, 4 figures and 3 tables

Context. Class II methanol masers at 6.7 and 12.2 GHz occur close to high-mass young stellar objects (HMYSOs). When they are observed simultaneously, such studies may contribute to refining the characterisation of local physical conditions. Aims. We aim to search for the 12.2 GHz methanol emission in 6.7 GHz methanol masers that might have gone undetected in previous surveys of northern sky HMYSOs, mainly due to their variability. Contemporaneous observations of both transitions are used to refine the flux density ratio and examine the physical parameters. Methods. We observed a sample of 153 sites of 6.7 GHz methanol maser emission in the 12.2 GHz methanol line with the Torun 32 m radio telescope, using the newly built X-band receiver. Results. The 12.2 GHz methanol maser emission was detected in 36 HMYSOs, with 4 of them detected for the first time. The 6.7 GHz to 12.2 GHz flux density ratio for spectral features of the contemporaneously observed sources has a median value of 5.1, which is in agreement with earlier reports. The ratio differs significantly among the sources and for the periodic source G107.298+5.639 specifically, the ratio is weakly recurrent from cycle to cycle, but it generally reaches a minimum around the flare peak. This is consistent with the stochastic maser process, where small variations in the physical parameters along the maser path can significantly affect the ratio. A comparison of our data with historical results (from about ten years ago) implies significant (> 50%) variability for about 47% and 14% at 12.2 GHz and 6.7 GHz, respectively. This difference can be explained via the standard model of methanol masers., Comment: 14 pages, 7 figures, accepted to A&A

The Hard Lefschetz Property (HLP) is an important property which has been studied in several categories of the symplectic world. For Sasakian manifolds, this duality is satisfied by the basic cohomology (so, it is a transverse property), but a new version of the HLP has been recently given in terms of duality of the cohomology of the manifold itself in arXiv:1306.2896. Both properties were proved to be equivalent (see arXiv:1311.1431) in the case of K-contact flows. In this paper we extend both versions of the HLP (transverse and not) to the more general category of isometric flows, and show that they are equivalent. We also give some explicit examples which illustrate the categories where the HLP could be considered., Comment: Accepted for publication in Transformation Groups. Minor changes in the exposition of the proof of Lemma 2.6

We study the properties of Ricci curvature of ${\mathfrak{g}}$-manifolds with particular attention paid to higher dimensional abelian Lie algebra case. The relations between Ricci curvature of the manifold and the Ricci curvature of the transverse manifold of the characteristic foliation are investigated. In particular, sufficient conditions are found under which the ${\mathfrak{g}}$-manifold can be a Ricci soliton or a gradient Ricci soliton. Finally, we obtain a amazing (non-existence) higher dimensional generalization of the Boyer-Galicki theorem on Einstein K-manifolds for a special class of abelian ${\mathfrak{g}}$-manifolds., Comment: 7 pages

The theory of twistors on foliated manifolds is developed and the twistor space of the normal bundle is constructed. It is demonstrated that the classical constructions of the twistor theory lead to foliated objects and permit to formulate and prove foliated versions of some well-known results on holomorphic mappings. Since any orbifold can be understood as the leaf space of a suitable defined Riemannian foliation we obtain orbifold versions of the classical results as a simple consequence of the results on foliated mappings.

The excited states of OH masers detected in the environment of high-mass young stellar objects (HMYSOs) are important for improving our understanding of the physical conditions of these objects and also provide information about their magnetic fields. We aim to search for excited-state OH 6035 MHz maser emission in HMYSOs which might have escaped detection in previous surveys or were never searched for. A sample of HMYSOs derived from untargeted surveys of the 6668 MHz methanol maser line was observed at 6035 MHz OH transition with the Torun 32 m radio telescope. The 6035 MHz detections were observed in the OH 6031 MHz line. Two-thirds of the detections were observed at least three times over a two-year period. Out of 445 targets, 37 were detected at 6035 MHz, including seven new discoveries. The 6031 MHz line was detected towards ten 6035 MHz sources, one of which was not previously reported. All the newly detected sources are faint with the peak flux density lower than 4 Jy and show significant or high variability on timescales of 4 to 20 months. Zeeman pair candidates identified in three new sources imply a magnetic field intensity of 2 to 11 mG. Comparison of our spectra with those obtained $\sim$10 yr ago indicates different degrees of variability but there is a general increase in the variability index on an $\sim$25 yr timescale, usually accompanied by significant changes in the profile shape., Comment: 8 pages, 6 figures

We determine for the first time the magnetic dipole moment of a short-lived nucleus with part-per-million (ppm) accuracy. To achieve this two orders of magnitude improvement over previous studies, we implement a number of innovations into our $\beta$-detected Nuclear Magnetic Resonance ($\beta$-NMR) setup at ISOLDE/CERN. Using liquid samples as hosts we obtain narrow, sub-kHz linewidth, resonances, while a simultaneous in-situ $^1$H NMR measurement allows us to calibrate and stabilize the magnetic field to ppm precision, thus eliminating the need for additional $\beta$-NMR reference measurements. Furthermore, we use ab initio calculations of NMR shielding constants to improve the accuracy of the reference magnetic moment, thus removing a large systematic error. We demonstrate the potential of this combined approach with the 1.1 s half-life radioactive nucleus $^{26}$Na, which is relevant for biochemical studies. Our technique can be readily extended to other isotopic chains, providing accurate magnetic moments for many short-lived nuclei. Furthermore, we discuss how our approach can open the path towards a wide range of applications of the ultra-sensitive $\beta$-NMR in physics, chemistry, and biology., Comment: re-submitted

Ring-like distributions of the 6.7 GHz methanol maser spots at milliarcsecond scales represent a family of molecular structures of unknown origin associated with high-mass young stellar objects (HMYSOs). We aim to study G23.657-00.127, which has a nearly circular ring of the 6.7 GHz methanol masers, and is the most suitable target to test hypotheses on the origin of the maser rings. The European Very Long Baseline Interferometry Network (EVN) was used at three epochs spanning 10.3 yr to derive the spatio-kinematical structure of the 6.7 GHz methanol maser emission in the target. The maser cloudlets, lying in a nearly symmetric ring, expand mainly in the radial direction with a mean velocity of 3.2 km s$^{-1}$. There is an indication that the radial component of the velocity increases with cloudlet's distance from the ring centre. The tangential component does not show any clear evidence for rotation of the cloudlets or any relationship with distance from the ring centre. The blue-shifted masers may hint at an anticlockwise rotation of cloudlets in the southern part of the ring. The nearly circular structure of the ring clearly persisted for more than 10 yr. Interferometric data demonstrated that about one quarter of cloudlets show significant variability in their brightness, although the overall spectrum was non-variable in single-dish studies. Taking into account the three-dimensional motion of the maser cloudlets and their spatial distribution along a small ring, we speculate about two possible scenarios where the methanol masers trace either a spherical outflow arising from an (almost) edge-on disc, or a wide angle wind at the base of a protostellar jet. The latter is associated with near- and mid-infrared emission detected towards the ring. High angular resolution images of complementary (thermal) tracers are needed to interpret the environment of methanol masers., Comment: accepted for publication in A\&A, 15 pages including on-line material

Periodic flares of maser emission are thought to be induced either by variations of the seed photon flux in young binary systems or the pump rate regulated by stellar and accretion luminosities. We seek to study the variability of four maser transitions of three different species in G107.298+5.639 to constrain the dominant mechanism of periodic flares. Light curves of the 6.7 GHz methanol and 22.2 GHz water vapour maser were obtained with the Torun 32m radio telescope over 39 and 34 cycles, respectively. The target was also monitored at the 1.6 GHz hydroxyl transitions with the Nan\c{c}ay radio telescope over 13 cycles. All these maser lines were imaged using VLBI arrays. The study confirms alternating flares of the methanol and water masers with a period of 34.4d and reveals the synchronised behaviour of the methanol and hydroxyl masers in this source. The observed spatial distribution of the methanol maser cloudlets and the measured time delays of the flares of individual features imply a ring-like structure of radius 240au and thickness 30au. Internal proper motions indicate that the velocity of methanol cloudlets is dominated by a disc-wind component of about 5km/s. The methanol emission detected during only one VLBI observation is located in a region about 550au from a central star, which also exhibits OH maser flares. The erratic appearance of methanol features can be related to a powering object of relatively low luminosity which, during some variability cycles, can excite molecules only in the nearest part of the disc. A careful analysis of the maser and infrared light curves reveal a strong correlation between the 6.7 GHz line and the infrared flux densities supporting a radiative pumping of the maser. The synchronised behaviour of the hydroxyl and methanol transitions indicates a common pumping mechanism for the periodic flares of G107.298+5.639., Comment: 20 pages, 15 figures