Stellar clusters form by gravitational collapse of turbulent molecular clouds, with up to several thousand stars per cluster 1 . They are thought to be the birthplace of most stars and therefore play an important role in our understanding of star formation, a fundamental problem in astrophysics 2, 3 . The initial conditions of the molecular cloud establish its dynamical history until the stellar cluster is born. However, the evolution of the cloud's angular momentum during cluster formation is not well understood 4 . Current observations have suggested that turbulence scrambles the angular momentum of the cluster-forming cloud, preventing spin alignment amongst stars within a cluster 5 . Here we use asteroseismology [6][7][8] to measure the inclination angles of spin axes in 48 stars from the two old open clusters NGC 6791 and NGC 6819. The stars within each cluster show strong alignment. Threedimensional hydrodynamical simulations of proto-cluster formation show that at least 50% of the initial proto-cluster kinetic energy has to be rotational in order to obtain strong stellarspin alignment within a cluster. Our result indicates that the global angular momentum of the cluster-forming clouds was efficiently transferred to each star and that its imprint has survived after several gigayears since the clusters formed. About half of the overall star formation in the Milky Way is occurring in the 24 most massive giant molecular clouds 1 . The star forming regions are obscured by dust, hence direct observations are limited to the infrared and radio bands 2,3 . However, open clusters can be studied in a broad range of wavelengths because they contain small amounts of interstellar gas and dust. The great advantage of studying stars in a cluster -as opposed to field stars that often originate from dissolved small stellar systems -is that they can preserve the signature of the initial conditions of the progenitor molecular cloud.It is believed that molecular clouds satisfying the Jeans instability undergo gravitational fragmentation in which the internal motions are strongly influenced by turbulence 4,9 . This suggests that the angular momentum from the progenitor cloud cannot leave any significant imprint of its action on the stars born in the cluster. However, if the stars inherit the physical properties of the molecular cloud, they should to some extent reflect its average angular momentum. To investigate the angular momentum imprint, requires measurements of the space orientation of the stellar-spin axis. Previous analyses conducted on young open clusters did not find evidence of stellar-spin alignment 5 . Asteroseismology, the study of stellar oscillations, has proven to be a powerful tool to obtain model-independent information on the inclination angle of the stellar angular momentum vector, especially for red giant stars 7,8,10,11 . Red giants are typically low-and intermediate-mass stars that have evolved off the main sequence of the stellar evolution. Most red giants oscillate and their oscillations can be analyz...

Context High-mass stars and star clusters commonly form within hub-filament systems. Monoceros R2 (hereafter Mon R2), at a distance of 830 pc, harbors one of the closest such systems, making it an excellent target for case studies. Aims We investigate the morphology, stability and dynamical properties of the Mon R2 hub-filament system. Methods We employ observations of the 13CO and C18O 1→0 and 2→1 lines obtained with the IRAM-30m telescope. We also use H2 column density maps derived from Herschel dust emission observations. Results We identified the filamentary network in Mon R2 with the DisPerSE algorithm and characterized the individual filaments as either main (converging into the hub) or secondary (converging to a main filament) filaments. The main filaments have line masses of 30–100 M⊙ pc−1 and show signs of fragmentation, while the secondary filaments have line masses of 12–60 M⊙ pc−1 and show fragmentation only sporadically. In the context of Ostriker’s hydrostatic filament model, the main filaments are thermally supercritical. If non-thermal motions are included, most of them are trans-critical. Most of the secondary filaments are roughly transcritical regardless of whether non-thermal motions are included or not. From the morphology and kinematics of the main filaments, we estimate a mass accretion rate of 10−4–10−3 M⊙ yr−1 into the central hub. The secondary filaments accrete into the main filaments with a rate of 0.1–0.4×10−4 M⊙ yr−1. The main filaments extend into the central hub. Their velocity gradients increase towards the hub, suggesting acceleration of the gas.We estimate that with the observed infall velocity, the mass-doubling time of the hub is ~ 2:5 Myr, ten times larger than the free-fall time, suggesting a dynamically old region. These timescales are comparable with the chemical age of the Hii region. Inside the hub, the main filaments show a ring- or a spiral-like morphology that exhibits rotation and infall motions. One possible explanation for the morphology is that gas is falling into the central cluster following a spiral-like pattern.

Context. Planets form in protoplanetary discs. Their masses, distribution, and orbits sensitively depend on the structure of the protoplanetary discs. However, what sets the initial structure of the discs in terms of mass, radius and accretion rate is still unknown. Aims. It is therefore of great importance to understand exactly how protoplanetary discs form and what determine their physical properties. We aim at quantifying the role of the initial dense core magnetisation, rotation, turbulence and misalignment between rotation and magnetic field axis as well as the role of the accretion scheme onto the central object.Methods. We perform non-ideal MHD numerical simulations using the adaptive mesh refinement code Ramses, of a collapsing, one solar mass, molecular core to study the disc formation and early, up to 100 kyr, evolution, paying great attention to the impact of numerical resolution and accretion scheme.Results. We found that while the mass of the central object is almost independent of the numerical parameters such as the resolution and the accretion scheme onto the sink particle, the disc mass, and to a lower extent its size, heavily depend on the accretion scheme, which we found, is itself resolution dependent. This implies that the accretion onto the star and through the disc are largely decoupled. For a relatively large domain of initial conditions (except at low magnetisation), we found that the properties of the disc do not change too significantly. In particular both the level of initial rotation and turbulence do not influence the disc properties provide the core is sufficiently magnetized. After a short relaxation phase, the disc settles in a stationary state. It then slowly grows in size but not in mass. The disc itself is weakly magnetized but its immediate surrounding is on the contrary highly magnetized. Conclusions. Our results show that the disc properties directly depend on the inner boundary condition, i.e. the accretion scheme onto the central object, suggesting that the disc mass is eventually controlled by the small scale accretion process, possibly the stardisc interaction. Because of ambipolar diffusion and its significant resistivity, the disc diversity remains limited and except for low magnetisation, their properties are weakly sensitive to initial conditions such as rotation and turbulence.

Context. Stars are often observed to form in clusters and it is therefore important to understand how such a region of concentrated mass is assembled out of the diffuse medium. The properties of such a region eventually prescribe the important physical mechanisms and determine the characteristics of the stellar cluster. Aims. We study the formation of a gaseous protocluster inside a molecular cloud and associate its internal properties with those of the parent cloud by varying the level of the initial turbulence of the cloud with a view to better characterize the subsequent stellar cluster formation. Methods. We performed high resolution magnetohydrodynamic (MHD) simulations of gaseous protoclusters forming in molecular clouds collapsing under self-gravity. We determined ellipsoidal cluster regions via gas kinematics and sink particle distribution, permitting us to determine the mass, size, and aspect ratio of the cluster. We studied the cluster properties, such as kinetic and gravitational energy, and made links to the parent cloud. Results. The gaseous protocluster is formed out of global collapse of a molecular cloud and has non-negligible rotation owing to angular momentum conservation during the collapse of the object. Most of the star formation occurs in this region, which occupies only a small volume fraction of the whole cloud. This dense entity is a result of the interplay between turbulence and gravity. We identify such regions in simulations and compare the gas and sink particles to observed star-forming clumps and embedded clusters, respectively. The gaseous protocluster inferred from simulation results presents a mass-size relation that is compatible with observations. We stress that the stellar cluster radius, although clearly correlated with the gas cluster radius, depends sensitively on its definition. Energy analysis is performed to confirm that the gaseous protocluster is a product of gravoturbulent reprocessing and that the support of turbulent and rotational energy against self-gravity yields a state of global virial equilibrium, although collapse is occurring at a smaller scale and the cluster is actively forming stars. This object then serves as the antecedent of the stellar cluster, to which the energy properties are passed on. Conclusions. The gaseous protocluster properties are determined by the parent cloud out of which it forms, while the gas is indeed reprocessed and constitutes a star-forming environment that is different from that of the parent cloud.

Recent observations have suggested that circumstellar disks may commonly form around young stellar objects. Although the formation of circumstellar disks can be a natural result of the conservation of angular momentum in the parent cloud, theoretical studies instead show disk formation to be difficult from

Context. Stars constitute the building blocks of our Universe, and their formation is an astrophysical problem of great importance. Aims. We aim to understand the fragmentation of massive molecular star-forming clumps and the effect of initial conditions, namely the density and the level of turbulence, on the resulting distribution of stars. For this purpose, we conduct numerical experiments in which we systematically vary the initial density over four orders of magnitude and the turbulent velocity over a factor ten. In a companion paper, we investigate the dependence of this distribution on the gas thermodynamics. Methods. We performed a series of hydrodynamical numerical simulations using adaptive mesh refinement, with special attention to numerical convergence. We also adapted an existing analytical model to the case of collapsing clouds by employing a density probability distribution function (PDF) ∝ ρ −1.5 instead of a lognormal distribution.Results. Simulations and analytical model both show two support regimes, a thermally dominated regime and a turbulence-dominated regime. For the first regime, we infer that dN/d log M ∝ M 0 , while for the second regime, we obtain dN/d log M ∝ M −3/4 . This is valid up to about ten times the mass of the first Larson core, as explained in the companion paper, leading to a peak of the mass spectrum at ∼ 0.2 M . From this point, the mass spectrum decreases with decreasing mass except for the most diffuse clouds, where disk fragmentation leads to the formation of objects down to the mass of the first Larson core, that is, to a few 10 −2 M . Conclusions. Although the mass spectra we obtain for the most compact clouds qualitatively resemble the observed initial mass function, the distribution exponent is shallower than the expected Salpeter exponent of −1.35. Nonetheless, we observe a possible transition toward a slightly steeper value that is broadly compatible with the Salpeter exponent for masses above a few solar masses. This change in behavior is associated with the change in density PDF, which switches from a power-law to a lognormal distribution. Our results suggest that while gravitationally induced fragmentation could play an important role for low masses, it is likely the turbulently induced fragmentation that leads to the Salpeter exponent.

Context. Understanding the origin of the initial mass function (IMF) of stars is a major problem for the star formation process and beyond. Aim. We investigate the dependence of the peak of the IMF on the physics of the so-called first Larson core, which corresponds to the point where the dust becomes opaque to its own radiation. Methods. We performed numerical simulations of collapsing clouds of 1000 M⊙ for various gas equations of state (eos), paying great attention to the numerical resolution and convergence. The initial conditions of these numerical experiments are varied in the companion paper. We also develop analytical models that we compare to our numerical results. Results. When an isothermal eos is used, we show that the peak of the IMF shifts to lower masses with improved numerical resolution. When an adiabatic eos is employed, numerical convergence is obtained. The peak position varies with the eos, and using an analytical model to infer the mass of the first Larson core, we find that the peak position is about ten times its value. By analyzing the stability of nonlinear density fluctuations in the vicinity of a point mass and then summing over a reasonable density distribution, we find that tidal forces exert a strong stabilizing effect and likely lead to a preferential mass several times higher than that of the first Larson core. Conclusions. We propose that in a sufficiently massive and cold cloud, the peak of the IMF is determined by the thermodynamics of the high-density adiabatic gas as well as the stabilizing influence of tidal forces. The resulting characteristic mass is about ten times the mass of the first Larson core, which altogether leads to a few tenths of solar masses. Since these processes are not related to the large-scale physical conditions and to the environment, our results suggest a possible explanation for the apparent universality of the peak of the IMF.