We present the results of KVN Key Science Program (KSP) for evolved stars, which was launched in 2014. The first phase of KSP ended in June 2020 and the second phase started in October 2020. The goal of KSP is to study the physical characteristics of the evolved stars by observing the spatial distribution and temporal variability of the stellar masers at four frequency-bands (K, Q, W and D bands). The 22 GHz H2O maser is usually observed from the outer part of circumstellar envelopes compared to the 43, 86, 129 GHz SiO masers, thus the kinematic links between these regions can be studied by the multi-frequency simultaneous observations of KSP along the stellar pulsation cycles. This eventually enable us to study the enormous mass-loss rate of evolved stars, and the accumulated results from KSP are expected to shed light on the study of the late stage of the stellar evolution.

We present new results from a 3D modelling code for maser flares which provides the user with control over the physical conditions; maser cloud geometry and orientation; and fast runtime via parallelisation. The statistics of simulated observables suggest that achievable amplification may be dependent on viewpoints of the source and that a randomly placed observer is likely to detect an unremarkable blue- or red-shifted maser unless the line-of-sight direction is optimal for maser amplification. A preliminary model of masers towards π1 Gru based on SPH simulations also shows promising consistency with ALMA observations of high-j SiO transitions from the source.

We briefly consider the history of maser variability, and of flaring variability specifically. We consider six proposed flare generation mechanisms, and model them computationally with codes that include saturation and 3-D structure (the last mechanism is modelled in 1-D). Fits to observational light curves have been made for some sources, and we suggest that a small number of observational parameters can diagnose the flare mechanism in many cases. The strongest flares arise from mechanisms that can increase the number density of inverted molecules in addition to by geometrical effects, and in events where unsaturated quiescent masers become saturated during the flare.

Ultra-compact H ii (UC HII) regions are an important phase in the formation and early evolution of massive stars and a key component of the interstellar medium (ISM). The main objectives of this work are to study the young stellar population associated with the G45.07+0.13 and G45.12+0.13 UC HII regions, as well as the ISM in which they are embedded. We determined the distribution of the hydrogen column density (N( $\mathrm{H}_2$ )) and dust temperature ( $T_d$ ) in the molecular cloud using Modified blackbody fitting on Herschel images obtained in four bands: 160, 250, 350, and $500\,\unicode{x03BC}\mathrm{m}$ . We used near-, mid-, and far-infrared photometric data to identify and classify the young stellar objects (YSOs). Their main parameters were determined by the radiation transfer models. We also constructed a colour-magnitude diagram and K luminosity functions (KLFs) to compare the parameters of stellar objects with the results of the radiative transfer models. We found that N( $\mathrm{H}_2$ ) varies from ${\sim}3.0 \times 10^{23}$ to $5.5 \times 10^{23}\,\mathrm{cm}^{-2}$ within the G45.07+0.13 and G45.12+0.13 regions, respectively. The maximum $T_d$ value is 35 K in G45.12+0.13 and 42 K in G45.07+0.13. $T_d$ then drops significantly from the centre to the periphery, reaching about 18–20 K at distances of ${\sim}2.6$ and ${\sim}3.7\,\mathrm{pc}$ from InfraRed Astronomical Satellite (IRAS) 19110+1045 (G45.07+0.13) and IRAS 19111+1048 (G45.12+0.13), respectively. The gas plus dust mass value included in G45.12+0.13 is ${\sim}3.4 \times 10^5\,\mathrm{M}_\odot$ and ${\sim}1.7 \times 10^5\,\mathrm{M}_\odot$ in G45.07+0.13. The UC HII regions are connected through a cold ( $T_d = 19\,\mathrm{K}$ ) bridge. The radial surface density distribution of the identified 518 YSOs exhibits dense clusters in the vicinity of both IRAS sources. The parameters of YSOs in the IRAS clusters (124 objects) and 394 non-cluster objects surrounding them show some differences. About 75% of the YSOs belonging to the IRAS clusters have an evolutionary age greater than $10^6$ yr. Their slope $\alpha$ of the KLF agrees well with a Salpeter-type initial mass function (IMF) ( $\gamma = 1.35$ ) for a high mass range (O–F stars, $\beta \sim 2$ ) at 1 Myr. The non-cluster objects are uniformly distributed in the molecular cloud, 80% of which are located to the right of the 0.1 Myr isochrone. The slope $\alpha$ of the KLF of non-cluster objects is $0.55\,\pm\,0.09$ , corresponding better to a Salpeter-type IMF for low-mass objects (G–M stars, $\beta \sim 1$ ). Our results show that two dense stellar clusters are embedded in these two physically connected UC HII regions. The clusters include several high- and intermediate-mass zero-age main sequence stellar objects. Based on the small age spread of the stellar objects, we suggest that the clusters originate from a single triggering shock. The extended emission observed in both UC HII regions is likely due to the stellar clusters.

Over the last two decades there have been considerable advances in modelling the spectra of massive stars and supernovae (SNe). Despite this progress, there are still numerous uncertainties that affect the accuracy of models. For massive stars, convection, instabilities, clumping, and our inability to model stellar winds self-consistently likely introduce systematic errors into our analyses. For SNe, and particularly for core-collapse SNe, departures from spherical symmetry strongly affect observed spectra and need to be taken into account. There are also issues with clumping, and mixing processes (both in the progenitor and the SN explosion) that need to be resolved. For both massive stars and SNe, the accuracy and availability of atomic data continues to be an ongoing issue influencing analyses.

In the regime of hot stars, winds were not seen as a common thing until the era of UV astronomy. Since we have access to the UV wavelength range, it has become clear that winds are not an exotic phenomenon limited to some special objects, but actually ubiquitous among hot and massive stars. The opacities due to spectral lines are the decisive ingredient that allows hot, massive stars to launch powerful winds. While the fundamental principles of these so-called line-driven winds have been realized decades ago, their proper quantitative prediction is still a major challenge today. Established theoretical and empirical descriptions have allowed us to make major progress on all astrophysical scales. However, we are now reaching their limitations as we still lack various fundamental insights on the nature of hot star winds, thereby hampering us from drawing deeper conclusions, not least when dealing with stellar or sub-stellar companions. This has spawned a new generation of researchers searching for answers with a yet unprecedented level of detail in observational and new theoretical approaches.

In these proceedings, the fundamental principles of driving hot star winds will be briefly reviewed. Starting from the classical CAK theory and its extensions, over Monte Carlo and recent comoving-frame-based simulations, the different methods to describe and model the acceleration of hot star winds will be introduced. The review continues with briefly discussing instabilities as well as qualitative and quantitative insights for OB- and Wolf-Rayet-star winds. Moreover, the challenges of companions and their impact on radiation-driven winds are outlined.

The winds of hot, massive stars are variable from processes happening on both large and small spatial scales. A particular case of such wind variability is ‘discrete-absorption components’ (DACs) that manifest themselves as outward moving density features in UV resonance line spectra. Such DACs are believed to be caused by large-scale spiral-shaped density structures in the stellar wind. We consider novel 3-D radiation-hydrodynamic models of rotating hot star winds and study the emergence of co-rotating spiral structures due to a local (pseudo-)magnetic spot on the stellar surface. Subsequently, the hydrodynamic models are used to retrieve DAC spectral signatures in synthetic UV spectra created from a 3-D short-characteristics radiative transfer code.

Massive stars are amongst the rarest but also most intriguing stars. Their extreme, magnetised stellar winds induce, by wind-ISM interaction, famous multi-wavelengths circumstellar gas nebulae of various morphologies, spanning from large-scale wind bubbles to stellar wind bow shocks, rings and bipolar shapes. We present two- and three-dimensional magneto-hydrodynamical (MHD) simulations of the circumstellar medium of such massive stars at different phase of their evolution. Particularly, we investigate the stability properties of 3D MHD bow shock nebulae around the runaway red supergiant stars IRC-10414 and Betelgeuse. Our results show that their astrospheres are stabilised by an organised, non-parallel ambient magnetic field. These findings suggest that Betelgeuse’s bar is of interstellar origin. Last, we explore the circular aspect of the young nebula around the Wolf-Rayet stars. It is found that Wolf-Rayet nebulae are not affected by the ISM gas distribution in which the stellar objects lie, even in the case of fast stellar motion: as testifies the ring-like surroundings of the Milky Way’s fastest Wolf-Rayet star, WR124. The morphology of these nebulae is tightly related to their pre-Wolf-Rayet wind geometry and to their phase evolution transition properties, which can generate bipolar shapes. We will further discuss their diffuse projected emission by means of radiative transfer calculations and show that the projected diffuse emission can appear as bipolar structures as in NGC6888.

Evolved massive stars are major cosmic engines, providing strong mechanical and radiative feedback on their host environment. They contribute to the enrichment of their environment through a strong stellar winds, still poorly understood. Wind physics across the life cycle of these stars is the key ingredient to accomplish a complete understanding of their evolution in the near and distant Universe. Nowadays, the development of the observational instruments is so advanced that the observations became very sensitive to the details of the stellar surface making possible to quantitatively study what happens on their surfaces and above where the stellar winds become dominant. Three-dimensional radiative hydrodynamics simulations of evolved stars are essential to a proper and quantitative analysis of these observations. This work presents how these simulations have been (and will be) crucial to prepare and interpret a multitude of observations and how they are important to achieve the knowledge of the mass-loss mechanism.

To decode the information stored within a spectrum, detailed modelling of the physical state is required together with accurate radiative transfer solution schemes. In the analysis of stellar spectra, the numerical model often needs to account for high velocity outflows, multi-dimensional structures, and the effects of binary companions. Focusing now on binary systems, we present the BOSS-3D spectral synthesis code, which is capable of calculating synthetic line profiles for a variety of binary systems. Assuming the state of the circumstellar material to be known, the standard pz-geometry is extended by defining individual coordinate systems for each object. By embedding these coordinate systems within the observer’s frame, BOSS-3D automatically accounts for outflows or discs within both involved systems, and includes all Doppler shifts. Moreover, the code accounts for different length-scales, and thus could also be used to analyse transit-spectra of planetary atmospheres. As a first application of BOSS-3D, we model the phase-dependent line profiles for the enigmatic binary (or multiple) system LB-1.

We present a new algorithm to solve the equations of radiation hydrodynamics (RHD) in a frequency-integrated, two-moment formulation. Novel features of the algorithm include i) the adoption of a non-local Variable Eddington Tensor (VET) closure for the radiation moment equations, computed with a ray-tracing method, ii) support for adaptive mesh refinement (AMR), iii) use of a time-implicit Godunov method for the hyperbolic transport of radiation, and iv) a fixed-point Picard iteration scheme to accurately handle the stiff nonlinear gas-radiation energy exchange. Tests demonstrate that our scheme works correctly, yields accurate rates of energy and momentum transfer between gas and radiation, and obtains the correct radiation field distribution even in situations where more commonly used – but less accurate – closure relations like the Flux-limited Diffusion and Moment-1 approximations fail. Our scheme presents an important step towards performing RHD simulations with increasing spatial and directional accuracy, effectively improving their predictive capabilities.