Context. There is growing evidence that massive stars grow by disk accretion in a similar way to their low-mass counterparts. Early in evolution, these disks can achieve masses that are comparable to the current stellar mass, and therefore the forming disks are highly susceptible to gravitational fragmentation. Aims. We investigate the formation and early evolution of an accretion disk around a forming massive protostar, focussing on its fragmentation physics. To this end, we follow the collapse of a molecular cloud of gas and dust, the formation of a massive protostar, the formation of its circumstellar disk, and the formation and evolution of the disk fragments. Methods. We used a grid-based, self-gravity radiation hydrodynamics code including a sub-grid module for stellar evolution and dust evolution. We purposely do not use a sub-grid module for fragmentation such as sink particles to allow for all paths of fragment formation and destruction, but instead we keep the spatial grid resolution high enough to properly resolve the physical length scales of the problem, namely the pressure scale height and Jeans length of the disk. Simulations are performed on a grid in spherical coordinates with a logarithmic spacing of the grid cells in the radial direction and a cosine distribution of the grid cells in the polar direction, focusing the spatial resolution on the disk midplane. As a consequence, roughly 25% of the total number of grid cells, corresponding to ~26 million grid cells, are used to model the disk physics. These constitute the highest resolution simulations performed up to now on disk fragmentation around a forming massive star with the physics considered here. For a better understanding of the effects of spatial resolution and to compare our high-resolution results with previous lower resolution studies in the literature, we perform the same simulation at five different resolutions, each run differing in resolution from its predecessor by a factor of two. Results. The cloud collapses and a massive (proto)star is formed in its center surrounded by a fragmenting Keplerian-like accretion disk with spiral arms. The fragments have masses of ~1 M⊙, and their continuous interactions with the disk, spiral arms, and other fragments result in eccentric orbits. Fragments form hydrostatic cores surrounded by secondary disks with spiral arms that also produce new fragments. We identified several mechanisms of fragment formation, interaction, and destruction. Central temperatures of the fragments can reach the hydrogen dissociation limit, form second Larson cores, and evolve into companion stars. Based on this, we study the multiplicity predicted by the simulations and find approximately six companions at different distances from the primary: from possible spectroscopic multiples, to companions at distances between 1000 and 2000 au.

The formation of astrophysical objects of different nature and size, from black holes to gaseous giant planets, involves a disk-jet system, where the disk drives the mass accretion onto a central compact object and the jet is a fast collimated ejection along the disk rotation axis. Magnetohydrodynamic disk winds can provide the link between mass accretion and ejection, which is essential to ensure that the excess angular momentum is removed from the system and accretion onto the central object can proceed. However, up to now, we have been lacking a direct observational proof of disk winds. This work presents a direct view of the velocity field of a disk wind around a high-mass forming star. Achieving a very high spatial resolution of ≈ 0.05 au, our water maser observations trace the velocities of individual streamlines emerging from the disk orbiting the forming star. We find that, at low elevation above the disk midplane, the flow co-rotates with its launch point in the disk, in agreement with magneto-centrifugal acceleration where the gas is flung away along the magnetic field line anchored to the disk. Beyond the co-rotation point, the flow rises spiraling around the disk rotation axis along a helical magnetic field.Our results are, presently, the clearest evidence for a magnetohydrodynamic Article number, page 1 of 26 L. Moscadelli * et al.: Snapshot of a magnetohydrodynamic disk wind

Context. Similar to their lower mass siblings, massive protostars can be expected to: a) be surrounded by circumstellar disks, and b) launch magnetically driven jets and outflows. The disk formation and global evolution is thereby controlled by advection of angular momentum from large scales, the efficiency of magnetic braking and the resistivity of the medium, and the internal thermal and magnetic pressures of the disk. Aims. We determine the dominant physical mechanisms that shape the appearance of these circumstellar disks, their sizes, and aspect ratios. Methods. We performed a series of 30 simulations of a massive star forming from the gravitational collapse of a molecular cloud threaded by an initially uniform magnetic field, starting from different values for the mass of the cloud, its initial density and rotation profiles, its rotational energy content, the magnetic field strength, and the resistivity of the material. The gas and dust was modeled with the methods of resistive magnetohydrodynamics, also considering radiation transport of thermal emission and self-gravity. We checked for the impact of spatial resolution in a dedicated convergence study. Results. After the initial infall phase dominated by the gravitational collapse, an accretion disk was formed, shortly followed by the launching of magnetically driven outflows. Two layers can be distinguished in the accretion disk: a thin layer, vertically supported by thermal pressure, and a thick layer, vertically supported by magnetic pressure. Both regions exhibit Keplerian-like rotation and grow outward over time. We observed the effects of magnetic braking in the inner ∼ 50 au of the disk at late times in our fiducial case. The parameter study reveals that the size of the disk is mostly determined by the density and rotation profiles of the initial mass reservoir and not by the magnetic field strength. We find that the disk size and protostellar mass gain scale with the initial mass of the cloud. Magnetic pressure can slightly increase the size of the accretion disk, while magnetic braking is more relevant in the innermost parts of the disk as opposed to the outer disk. From the parameter study, we infer that multiple initial conditions for the onset of gravitational collapse are able to produce a given disk size and protostellar mass.

The Neutron Star Interior Composition Explorer (NICER) mission has provided a unique opportunity to constrain the equation of state of neutron stars by using the technique of pulse-profile modelling. This technique requires accurate and efficient ray tracing, that in turn requires a robust representation of the spacetime around a neutron star. Several exact and approximate metrics have been proposed, and used, to perform ray tracing around neutron stars, with both moderate and fast rotation. In this paper, we perform a comparison between several of these metrics, when used for ray tracing. We calculate the shape of the neutron star as seen by a distant observer using two different surface formulae, the thermal spectrum and pulse profiles from circular and crescent-shaped hotspots, for four configurations of pulsars with rotation rates ranging from 622 to 1000 Hz, and using both a moderate and a stiff equation of state to include realistic and extreme cases. We find small differences between the metrics for rotation frequencies starting at ∼700Hz that could theoretically be used for constraining the quadrupole moment or the spacetime models. We also determine the practicality of use of each metric in larger-scale applications such as pulse-profile modelling.