The stellar initial mass function (IMF) is commonly assumed to be an invariant probability density distribution function of initial stellar masses. These initial stellar masses are generally represented by the canonical IMF, which is defined as the result of one star formation event in an embedded cluster. As a consequence, the galaxy-wide IMF (gwIMF) should also be invariant and of the same form as the canonical IMF; gwIMF is defined as the sum of the IMFs of all star-forming regions in which embedded clusters form and spawn the galactic field population of the galaxy. Recent observational and theoretical results challenge the hypothesis that the gwIMF is invariant. In order to study the possible reasons for this variation, it is useful to relate the observed IMF to the gwIMF. Starting with the IMF determined in resolved star clusters, we apply the IGIMF-theory to calculate a comprehensive grid of gwIMF models for metallicities, [Fe/H] ∈ (−3, 1), and galaxy-wide star formation rates (SFRs), SFR ∈ (10−5, 105) M⊙ yr−1. For a galaxy with metallicity [Fe/H] < 0 and SFR > 1 M⊙ yr−1, which is a common condition in the early Universe, we find that the gwIMF is both bottom light (relatively fewer low-mass stars) and top heavy (more massive stars), when compared to the canonical IMF. For a SFR < 1 M⊙ yr−1 the gwIMF becomes top light regardless of the metallicity. For metallicities [Fe/H] > 0 the gwIMF can become bottom heavy regardless of the SFR. The IGIMF models predict that massive elliptical galaxies should have formed with a gwIMF that is top heavy within the first few hundred Myr of the life of the galaxy and that it evolves into a bottom heavy gwIMF in the metal-enriched galactic centre. Using the gwIMF grids, we study the SFR−Hα relation and its dependency on metallicity and the SFR. We also study the correction factors to the Kennicutt SFRK − Hα relation and provide new fitting functions. Late-type dwarf galaxies show significantly higher SFRs with respect to Kennicutt SFRs, while star-forming massive galaxies have significantly lower SFRs than hitherto thought. This has implications for gas-consumption timescales and for the main sequence of galaxies. We explicitly discuss Leo P and ultra-faint dwarf galaxies.

Here we present a full description of the integrated galaxy-wide initial mass function (IGIMF) theory in terms of the optimal sampling and compare it with available observations. Optimal sampling is the method we use to discretize the IMF deterministically into stellar masses. Evidence indicates that nature may be closer to deterministic sampling as observations suggest a smaller scatter of various relevant observables than random sampling would give, which may result from a high level of self-regulation during the star formation process. We document the variation of IGIMFs under various assumptions. The results of the IGIMF theory are consistent with the empirical relation between the total mass of a star cluster and the mass of its most massive star, and the empirical relation between the star formation rate (SFR) of a galaxy and the mass of its most massive cluster. Particularly, we note a natural agreement with the empirical relation between the IMF power-law index and the SFR of a galaxy. The IGIMF also results in a relation between the SFR of a galaxy and the mass of its most massive star such that, if there were no binaries, galaxies with SFR < 10 −4 M /yr should host no Type II supernova events. In addition, a specific list of initial stellar masses can be useful in numerical simulations of stellar systems. For the first time, we show optimally sampled galaxy-wide IMFs (OSGIMF) that mimic the IGIMF with an additional serrated feature. Finally, a Python module, GalIMF, is provided allowing the calculation of the IGIMF and OSGIMF dependent on the galaxy-wide SFR and metallicity.

The so-called ultra-diffuse galaxy NGC 1052-DF2 was announced to be a galaxy lacking dark matter based on a spectroscopic study of its constituent globular clusters. Here we present the first spectroscopic analysis of the stellar body of this galaxy using the MUSE integral-field spectrograph at the (ESO) Very Large Telescope. The MUSE datacube simultaneously provides DF2's stellar velocity field and systemic velocities for seven globular clusters (GCs). We further discovered three planetary nebulae (PNe) that are likely part of this galaxy. While five of the clusters had velocities measured in the literature, we were able to confirm the membership of two more candidates through precise radial velocity measurements, which increases the measured specific frequency of GCs in DF2. The mean velocity of the diffuse stellar body, 1792.9 −1.8 +1.4 km s −1 , is consistent with the mean globular cluster velocity. We detect a weak but significant velocity gradient within the stellar body, with a kinematic axis close to the photometric major axis, making it a prolate-like rotator. We estimate a velocity dispersion from the clusters and PNe of σ int = 10.6 +3.9 −2.3 km s −1 . The velocity dispersion σ DF2 (R e ) for the stellar body within one effective radius is 10.8 −4.0 +3.2 km s −1 . Considering various sources of systemic uncertainties, this central value varies between 5 and 13 km s −1 , and we conservatively report a 95% confidence upper limit to the dispersion within one R e of 21 km s −1 . We provide updated mass estimates based on these dispersions corresponding to the different distances to NGC 1052-DF2 that have been reported in the recent literature.

The tidal tails of stellar clusters provide an important tool for studying the birth conditions of the clusters and their evolution, coupling, and interaction with the Galactic potential. The Gaia satellite, with its high-quality astrometric data, opened this field of study, allowing us to observe large-scale tidal tails. Theoretical models of tidal-tail formation and evolution are available. However, the exact appearance of tidal features as seen in the Gaia catalogue has not yet been studied. Here we present the N-body evolution of a Hyades-like stellar cluster with backward-integrated initial conditions on a realistic 3D orbit in the Milky Way galaxy computed within the AMUSE framework. For the first time, we explore the effect of the initial cluster rotation and the presence of lumps in the Galactic potential on the formation and evolution of tidal tails. For all of our simulations we present Gaia observables and derived parameters in the convergent point (CP) diagram. We show that the tidal tails are not naturally clustered in any coordinate system and that they can span up to 40 km s−1 relative to the cluster centre in proper motions for a cluster age of 600–700 Myr. Models with initial rotation result in significant differences in the cluster mass loss and follow different angular momentum time evolution. Thus the orientation of the tidal tails relative to the motion vector of the cluster and the current cluster angular momentum constrain the initial rotation of the cluster. We highlight the use of the standard CP method in searches for co-moving groups and introduce a new compact CP (CCP) method that accounts for internal kinematics based on an assumed model. Using the CCP method, we are able to recover candidate members of the Hyades tidal tails in the Gaia Data Release 2 and early Data Release 3 (eDR3) reaching a total extent of almost 1 kpc. We confirm the previously noted asymmetry in the detected tidal tails. In the eDR3 data we recovered spatial overdensities in the leading and trailing tails that are kinematically consistent with being epicyclic overdensities and thus would present candidates for the first such detection in an open star cluster. We show that the epicyclic overdensities are able to provide constraints not only on the cluster properties, but also on the Galactic potential. Finally, based on N-body simulations, a close encounter with a massive Galactic lump can explain the observed asymmetry in the tidal tails of the Hyades.

NGC 1052-DF2, an ultra-diffuse galaxy (UDG), has been the subject of intense debate. Its alleged absence of dark matter, and the brightness and number excess of its globular clusters (GCs) at an initially assumed distance of 20 Mpc suggest a new formation channel for UDGs. We present the first systematic spectroscopic analysis of the stellar body and the GCs in this galaxy (six previously known and one newly confirmed member) using MUSE at the VLT. Even though NGC 1052-DF2 does not show any spatially extended emission lines, we report the discovery of three planetary nebulae (PNe). We conduct full spectral fitting on the UDG and the stacked spectra of all the GCs. The UDG’s stellar population is old, 8.9 ± 1.5 Gyr; metal poor, [M/H] = −1.07 ± 0.12; and with little or no α-enrichment. The stacked spectrum of all GCs indicates a similar age of 8.9 ± 1.8 Gyr, but a lower metallicity of [M/H] = −1.63 ± 0.09 and a similarly low α-enrichment. There is no evidence for a variation in age and metallicity in the GC population with the available spectra. The significantly more metal-rich stellar body with respect to its associated GCs, the age of the population, its metallicity, and its α-enrichment are all in line with other dwarf galaxies. NGC 1052-DF2 thus falls on the same empirical mass–metallicity relation as other dwarfs for the full distance range assumed in the literature. We find that both debated distance estimates (13 and 20 Mpc) are similarly likely, given the three discovered PNe.

We present FORS2 (attached to ESO's Very Large Telescope) observations of the exoplanet WASP-17b during its primary transit, for the purpose of differential spectrophotometry analysis. We use the instrument in its Mask eXchange Unit (MXU) mode to simultaneously obtain low resolution spectra of the planet hosting star, as well as several reference stars in the field of view. The integration of these spectra within broadband and smaller 100Å bins provides us with 'white' and spectrophotometric light curves, from 5700 to 8000Å. Through modelling the white light curve, we obtain refined bulk and transit parameters of the planet, as well as wavelength-dependent variations of the planetary radius from smaller spectral bins through which the transmission spectrum is obtained. The inference of transit parameters, as well as the noise statistics, is performed using a Gaussian Process model. We achieve a typical precision in the transit depth of a few hundred parts per million from various transit light curves. From the transmission spectra we rule out a flat spectrum at >3σ and detect marginal presence of the pressure-broadened sodium wings. Furthermore, we detect the wing of the potassium absorption line in the upper atmosphere of the planet with 3-σ confidence, both facts pointing to a relatively shallow temperature gradient of the atmosphere. These conclusions are mostly consistent with previous studies of this exo-atmosphere, although previous potassium measurements have been inconclusive.

A scenario for the formation of multiple co-eval populations separated in age by about 1 Myr in very young clusters (VYCs, ages less than 10 Myr) and with masses in the range 600 − 20000 M is outlined. It rests upon a converging inflow of molecular gas building up a first population of pre-main sequence stars. The associated just-formed O stars ionise the inflow and suppress star formation in the embedded cluster. However, they typically eject each other out of the embedded cluster within 10 6 yr, that is before the molecular cloud filament can be ionised entirely. The inflow of molecular gas can then resume forming a second population. This sequence of events can be repeated maximally over the life-time of the molecular cloud (about 10 Myr), but is not likely to be possible in VYCs with mass < 300 M , because such populations are not likely to contain an O star. Stellar populations heavier than about 2000 M are likely to have too many O stars for all of these to eject each other from the embedded cluster before they disperse their natal cloud. VYCs with masses in the range 600 − 2000 M are likely to have such multi-age populations, while VYCs with masses in the range 2000 − 20000 M can also be composed solely of co-eval, mono-age populations. More massive VYCs are not likely to host sub-populations with age differences of about 1 Myr. This model is applied to the Orion Nebula Cluster (ONC), in which three well-separated pre-main sequences in the color-magnitude diagram of the cluster have recently been discovered. The mass-inflow history is constrained using this model and the number of OB stars ejected from each population are estimated for verification using Gaia data. As a further consequence of the proposed model, the three runaway O star systems, AE Aur, µ Col and ι Ori, are considered as significant observational evidence for stellar-dynamical ejections of massive stars from the oldest population in the ONC. Evidence for stellar-dynamical ejections of massive stars in the currently forming population is also discussed.

The observation of quasars at very high redshift such as Pōniuā’ena is a challenge for models of super-massive black hole (SMBH) formation. This work presents a study of SMBH formation via known physical processes in star-burst clusters formed at the onset of the formation of their hosting galaxy. While at the early stages hyper-massive star-burst clusters reach the luminosities of quasars, once their massive stars die, the ensuing gas accretion from the still forming host galaxy compresses its stellar black hole (BH) component to a compact state overcoming heating from the BH–BH binaries such that the cluster collapses, forming a massive SMBH-seed within about a hundred Myr. Within this scenario the SMBH–spheroid correlation emerges near-to-exactly. The highest-redshift quasars may thus be hyper-massive star-burst clusters or young ultra-compact dwarf galaxies (UCDs), being the precursors of the SMBHs that form therein within about 200 Myr of the first stars. For spheroid masses ≲ 109.6 M⊙ a SMBH cannot form and instead only the accumulated nuclear cluster remains. The number evolution of the quasar phases with redshift is calculated and the possible problem of missing quasars at very high redshift is raised. SMBH-bearing UCDs and the formation of spheroids are discussed critically in view of the high redshift observations. A possible tension is found between the high star-formation rates (SFRs) implied by downsizing and the observed SFRs, which may be alleviated within the IGIMF theory and if the downsizing times are somewhat longer.