Theory Of Star Formation Research Articles

The VLT-FLAMES Tarantula Survey

The 30 Doradus (30 Dor) nebula in the Large Magellanic Cloud (LMC) is the brightest HII region in the Local Group and a prototype starburst similar to those found in high redshift galaxies. It is thus a stepping stone to understand the complex formation processes of stars in starburst regions across the Universe. Here, we have studied the formation history of massive stars in 30 Dor using masses and ages derived for 452 mainly OB stars from the spectroscopic VLT-FLAMES Tarantula Survey (VFTS). We find that stars of all ages and masses are scattered throughout 30 Dor. This is remarkable because it implies that massive stars either moved large distances or formed independently over the whole field of view in relative isolation. We find that both channels contribute to the 30 Dor massive star population. Massive star formation rapidly accelerated about 8 Myr ago, first forming stars in the field before giving birth to the stellar populations in NGC 2060 and NGC 2070. The R136 star cluster in NGC 2070 formed last and, since then, about 1 Myr ago, star formation seems to be diminished with some continuing in the surroundings of R136. Massive stars within a projected distance of 8 pc of R136 are not coeval but show an age range of up to 6 Myr. Our mass distributions are well populated up to 200 M⊙. The inferred IMF is shallower than a Salpeter-like IMF and appears to be the same across 30 Dor. By comparing our sample of stars to stellar models in the Hertzsprung–Russell diagram, we find evidence for missing physics in the models above log L/L⊙ = 6 that is likely connected to enhanced wind mass loss for stars approaching the Eddington limit. Our work highlights the key information about the formation, evolution and final fates of massive stars encapsulated in the stellar content of 30 Dor, and sets a new benchmark for theories of massive star formation in giant molecular clouds.

EPIC 203868608: A Low-mass Quadruple Star System in the Upper Scorpius OB Association

Abstract Young multiple star systems provide excellent testing grounds for theories of star formation and evolution. EPIC 203868608 was previously studied as a triple star system in the Upper Scorpius OB association, but the followup Keck NIRC2/HIRES/NIRSPAO observations reported here reveal its quadruple nature. We find that the system consists of a double-lined spectroscopic binary (SB2) Aab (M5+M5) and an eclipsing binary (EB) Bab with a total mass that is lower than that of the SB2. Furthermore, we measure the obliquity of the EB using the Doppler tomography technique during the primary eclipse. EPIC 203868608 Bab is likely on an inclined orbit with a projected obliquity of degrees. The inclined orbit is used to constrain the tidal quality factor for low-mass stars and the evolution of the quadruple system. The analytic framework to infer obliquity that has been developed in this paper can be applied to other EB systems as well as transiting planets.

Geometry, Kinematics, and Magnetization of Simulated Prestellar Cores

Abstract We utilize the more than 100 gravitationally bound dense cores formed in our three-dimensional, turbulent MHD simulations reported in Chen & Ostriker to analyze structural, kinematic, and magnetic properties of prestellar cores. Our statistical results disagree with the classical theory of star formation in which cores evolve to be oblate with magnetic fields parallel to the minor axes. Instead, we find that cores are generally triaxial, although the core-scale magnetic field is still preferentially most parallel to the core’s minor axis and most perpendicular to the major axis. The internal and external magnetic field directions are correlated, but the direction of integrated core angular momentum is misaligned with the core’s magnetic field, which is consistent with recent observations. The ratio of rotational/total kinetic and rotational/gravitational energies are independent of core size and consistent in magnitude with observations. The specific angular momentum also follows the observed relationship L/M ∝ R 3/2, indicating that rotation is acquired from ambient turbulence. With typical , rotation is not the dominant motion when cores collapse.

Correction to: Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics

When we published this article, the biographies of Gregor J Gassner and Stefanie Walch have been mixed up during the type-setting process. Sadly, this mistake remained unnoticed. The correct biographies are: Gregor Gassner is a professor in numerical analysis/scientific computing at the Mathematical Institute at the University of Cologne. Gregor obtained a diploma degree in aerospace engineering (2004) and a diploma degree in mathematics (2005) from the University of Stuttgart. In 2009 he received his doctoral degree at the Institute of Aerodynamics and Gasdynamics, Stuttgart. He got an offer for a Junior professorship at TU Braunschweig in computational fluid dynamics, an offer for scientific computing at the TU Hamburg-Harburg and an offer from University of Cologne, where he joined in 2013. In 2016 he received an ERC starting grant on the topic of adaptive, robust and highly efficient numerical methods for the simulation of non-linear conservation laws. Stefanie Walch is a full professor for theoretical astrophysics at the University of Cologne since 2013. After the diploma in physics in 2004, Stefanie received her doctoral degree in theoretical physics from the Ludwig-Maximilians-Universitat Munchen in 2008. Afterwards she has spent 3 years at Cardiff University in Wales, and approximately 2 years at the Max-Planck-Institute for Astrophysics in Garching as a postdoctoral researcher before being appointed at the University of Cologne. She specialises in the physics of the interstellar medium including star formation and stellar feedback in the form of ionizing radiation, stellar winds, and supernovae. The evolution of gas in galaxies is studied using massively parallel, three-dimensional magneto-hydrodynamics simulations with additional (self-)gravity, radiative transfer, and chemical networks to follow the formation and dissociation of molecules and to bridge the gap to observations in different tracers. Synthetic observations ranging from X-ray emission to CO and dust polarization maps are now used to put modern theories of star formation and feedback to the test. In 2015, she received an ERC Starting Grant on the topic of “The radiative interstellar medium”. The original article has been corrected. The publisher apologises for this mistake.

Complete ejection of OB stars from very young star clusters and the formation of multiple populations

Recently, three stellar sequences separated in age by about 1 Myr were discovered in the Orion Nebula Cluster (ONC; Beccari et al. 2017). Kroupa et al. (2018) suggest that such small dense subpopulations eject all their OB stars via the decay of unstable few-body systems such that the gas can recombine and form new stars. This explains the multisequence phenomenon without introducing an extra mechanism into star formation theory. In this work, we apply the recently updated primordial binary distribution model (Belloni et al. 2017; implemented here in a new version of MCLUSTER) and perform a large set of direct N-body simulations to investigate the feasibility of this dynamical scenario. Our results suggest that if 3-4 OB stars in the ONC formed primordially mass-segregated in the cluster centre with a maximum separation of about 0.003 pc, all OB stars have a high chance (50-70 per cent) to escape from the centre and do not come back within 1 Myr and the dynamical ejection scenario is a viable channel to form short-age-interval multipopulation sequences as observed in the ONC. This is also consistent with self-regulated star formation.

Role of magnetic field in star formation

AbstractMagnetic fields are a key component in star formation theories. Nevertheless, their exact role in the formation of stars is still a matter of debate. The process of angular momentum transportation by the disturbance caused during magnetic field reconnection still needs theoretical formulation in terms of the collapsing cloud’s parameters. The purposes of this study are: to model the critical mass of a magnetized, gravitating and turbulent star forming molecular cloud (MC) and to formulate the momentum carried out by a magnetic field through magnetic field reconnection in terms of the MC’s parameters. By applying theoretical modeling, we show how angular momentum transported via an Alfvén wave can be described in terms of mass, radius and dispersion velocity of a collapsing cloud core and a model equation of the critical mass for a gravitating, turbulent, and magnetized molecular cloud core. The outflow of angular momentum by magnetic fields facilitates the inflow of mass. On the other side, magnetic pressure prevents collapse. Therefore, magnetic fields have a dual purpose in the process of star formation. This momentum outflow triggers the inflow of mass to conserve angular momentum. The results show that Alfvén waves are like a machine that extracts angular momentum from a magnetized collapsing cloud core. Thus the total angular momentum transported by magnetic field at a distance R from the core’s center depends on the size, mass and turbulent velocity dispersion of the collapsing cloud core.

Isothermal Fragmentation: Is there a low-mass cut-off?

The evolution of self-gravitating clouds of isothermal gas forms the basis of many star formation theories. Therefore it is important to know under what conditions such a cloud will undergo homologous collapse into a single, massive object, or will fragment into a spectrum of smaller ones. And if it fragments, do initial conditions (e.g. Jeans mass, sonic mass) influence the mass function of the fragments, as predicted by many theories of star formation? In this paper we show that the relevant parameter separating homologous collapse from fragmentation is not the Mach number of the initial turbulence (as suspected by many), but the infall Mach number $\mathcal{M}_{\rm infall}\sim\sqrt{G M/(R c_s^2)}$, equivalent to the number of Jeans masses in the initial cloud $N_J$. We also show that fragmenting clouds produce a power-law mass function with slopes close to the expected -2 (i.e. equal mass in all logarithmic mass intervals). However, the low-mass cut-off of this mass function is entirely numerical; the initial properties of the cloud have no effect on it. In other words, if $\mathcal{M}_{\rm infall}\gg 1$, fragmentation proceeds without limit to masses much smaller than the initial Jeans mass.

Lucky Spectroscopy, an equivalent technique to Lucky Imaging

Context. Many massive stars have nearby companions whose presence hamper their characterization through spectroscopy. Aims. We want to obtain spatially resolved spectroscopy of close massive visual binaries to derive their spectral types. Methods. We obtained a large number of short long-slit spectroscopic exposures of five close binaries under good seeing conditions. We selected those with the best characteristics, extracted the spectra using multiple-profile fitting, and combined the results to derive spatially separated spectra. Results. We demonstrate the usefulness of Lucky Spectroscopy by presenting the spatially resolved spectra of the components of each system, in two cases with separations of only ~0.′′3. Those are δ Ori Aa+Ab (resolved in the optical for the first time) and σ Ori AaAb+B (first time ever resolved). We also spatially resolve 15 Mon AaAb+B, ζ Ori AaAb+B (both previously resolved with GOSSS, the Galactic O-Star Spectroscopic Survey), and η Ori AaAb+B, a system with two spectroscopic B+B binaries and a fifth visual component. The systems have in common that they are composed of an inner pair of slow rotators orbited by one or more fast rotators, a characteristic that could have consequences for the theories of massive star formation.

A cosmological solution to the Impossibly Early Galaxy Problem

To understand the formation and evolution of galaxies at redshifts z < 10, one must invariably introduce specific models (e.g., for the star formation) in order to fully interpret the data. Unfortunately, this tends to render the analysis compliant to the theory and its assumptions, so consensus is still somewhat elusive. Nonetheless, the surprisingly early appearance of massive galaxies challenges the standard model, and the halo mass function estimated from galaxy surveys at z > 4 appears to be inconsistent with the predictions of LCDM, giving rise to what has been termed "The Impossibly Early Galaxy Problem" by some workers in the field. A simple resolution to this question may not be forthcoming. The situation with the halos themselves, however, is more straightforward and, in this paper, we use linear perturbation theory to derive the halo mass function over the redshift range z < 10 for the R_h=ct universe. We use this predicted halo distribution to demonstrate that both its dependence on mass and its very weak dependence on redshift are compatible with the data. The difficulties with LCDM may eventually be overcome with refinements to the underlying theory of star formation and galaxy evolution within the halos. For now, however, we demonstrate that the unexpected early formation of structure may also simply be due to an incorrect choice of the cosmology, rather than to yet unknown astrophysical issues associated with the condensation of mass fluctuations and subsequent galaxy formation.

Confusing Binaries: The Role of Stellar Binaries in Biasing Disk Properties in the Galactic Center

Abstract The population of young stars near the supermassive black hole (SMBH) in the Galactic Center (GC) has presented an unexpected challenge to theories of star formation. Kinematic measurements of these stars have revealed a stellar disk structure (with an apparent 20% disk membership) that has provided important clues regarding the origin of these mysterious young stars. However, many of the apparent disk properties are difficult to explain, including the low disk membership fraction and the high eccentricities given the youth of this population. Thus far, all efforts to derive the properties of this disk have made the simplifying assumption that stars at the GC are single stars. Nevertheless, stellar binaries are prevalent in our Galaxy, and recent investigations suggested that they may also be abundant in the Galactic Center. Here, we show that binaries in the disk can largely alter the apparent orbital properties of the disk. The motion of binary members around each other adds a velocity component, which can be comparable to the magnitude of the velocity around the SMBH in the GC. Thus, neglecting the contribution of binaries can significantly vary the inferred stars’ orbital properties. While the disk orientation is unaffected, the apparent disk’s 2D width will be increased to about 11.°2, similar to the observed width. For a population of stars orbiting the SMBH with zero eccentricity, unaccounted for binaries will create a wide apparent eccentricity distribution with an average of 0.23. This is consistent with the observed average eccentricity of the stars’ in the disk. We suggest that this high eccentricity value, which poses a theoretical challenge, may be an artifact of binary stars. Finally, our results suggest that the actual disk membership might be significantly higher than the one inferred by observations that ignore the contribution of binaries, alleviating another theoretical challenge.

Radiation Transfer of Models of Massive Star Formation. IV. The Model Grid and Spectral Energy Distribution Fitting

Abstract We present a continuum radiative transfer model grid for fitting observed spectral energy distributions (SEDs) of massive protostars. The model grid is based on the paradigm of core accretion theory for massive star formation with pre-assembled gravitationally bound cores as initial conditions. In particular, following the turbulent core model, initial core properties are set primarily by their mass and the pressure of their ambient clump. We then model the evolution of the protostar and its surround structures in a self-consistent way. The model grid contains about 9000 SEDs with four free parameters: initial core mass, the mean surface density of the environment, the protostellar mass, and the inclination. The model grid is used to fit observed SEDs via minimization, with the foreground extinction additionally estimated. We demonstrate the fitting process and results using the example of massive protostar G35.20-0.74. Compared with other SED model grids currently used for massive star formation studies, the properties of the protostar and its surrounding structures are more physically connected in our model grid, which reduces the dimensionality of the parameter spaces and the total number of models. This excludes possible fitting of models that are physically unrealistic or are not internally self-consistent in the context of the turbulent core model. Thus, this model grid serves not only as a fitting tool to estimate properties of massive protostars, but also as a test of core accretion theory. The SED model grid is publicly released with this paper.

Stellar kinematics in the IC 348 cluster

In 30 - 40s of the last century Viktor Ambartsumian has published several studies on the kinematics and dynamics of stellar systems. The scientific issues of these papers not only remain relevant up to nowadays, but also are of key importance for the construction of the generalized theory of star formation. The launch of the Gaia spacecraft on December 19, 2013, opens up new horizons in the study of young stellar systems origin and evolution. The accuracy of astrometric measurements (the typical uncertainty is about 0.04 - 0.7 mas for the positions and parallaxes, and about 0.05 - 1.2 mas yr-1 for the proper motions), undoubtedly, will allow lifting the possibilities of study the kinematics and dynamics of star-forming regions to a new level. We focus our present research on the young (∼ 2 - 3Myr) stellar cluster IC 348. It has a complex structure, which includes the older compact core and the younger subgroup in the vicinity of HH 211 outflow. Based on the Gaia DR2 data, we considered the kinematic properties of both the cluster as a whole and its subgroups. We found that special velocity dispersion significantly exceeds the virial velocity dispersion and, therefore, the IC 348 stellar cluster is a supervirial or gravitationally unbound system.

Observations in the UV Band and Problems of Star Formation Studies

In this contribution, I consider those aspects of the modern star formation theory, which can be substantiated with observations in the UV band, paying special attention to early stages of molecular cloud formation and initial conditions for the chemical evolution of starless cores. I describe the main results of available diffuse cloud observations in the UV band, as well as prospective directions for future studies with the instrumentation of the World Space Observatory project.

Medium-resolution near-infrared spectroscopy of massive young stellar objects

We present medium-resolution (R~7000) near-infrared echelle spectroscopic data for 36 MYSOs drawn from the Red MSX Source (RMS) survey. This is the largest sample observed at this resolution at these wavelengths of MYSOs to date. The spectra are characterized mostly by emission from hydrogen recombination lines and accretion diagnostic lines. One MYSO shows photospheric HI absorption, a comparison with spectral standards indicates that the star is an A type star with a low surface gravity, implying that the MYSOs are probably swollen, as also suggested by evolutionary calculations. An investigation of the Br$\gamma$ line profiles shows that most are in pure emission, while 13$\pm$5 % display P Cygni profiles, indicative of outflow, while less than 8$\pm$4 % have inverse P Cygni profiles, indicative of infall. These values are comparable with investigations into the optically bright Herbig Be stars, but not with those of Herbig Ae and T Tauri stars, consistent with the notion that the more massive stars undergo accretion in a different fashion than lower mass objects which are undergoing magnetospheric accretion. Accretion luminosities and rates as derived from the Br$\gamma$ line luminosities agree with results for lower mass sources, providing tentative evidence for massive star formation theories based on scaling of low-mass scenarios. We present Br$\gamma$/Br12 line profile ratios exploiting the fact that optical depth effects can be traced as a function of Doppler shift across the lines. These show that the winds of MYSOs in this sample are nearly equally split between constant, accelerating, and decelerating velocity structures. There are no trends between the types of features we see and bolometric luminosities or near-infrared colours.

Implications of Galaxy Buildup for Putative IMF Variations in Massive Galaxies

Abstract Recent observational evidence for initial mass function (IMF) variations in massive quiescent galaxies at z = 0 challenges the long-established paradigm of a universal IMF. While a few theoretical models relate the IMF to birth cloud conditions, the physical driver underlying these putative IMF variations is still largely unclear. Here we use post-processing analysis of the Illustris cosmological hydrodynamical simulation to investigate possible physical origins of IMF variability with galactic properties. We do so by tagging stellar particles in the simulation (each representing a stellar population of ) with individual IMFs that depend on various physical conditions, such as velocity dispersion, metallicity, or star formation rate, at the time and place in which the stars are formed. We then follow the assembly of these populations throughout cosmic time and reconstruct the overall IMF of each z = 0 galaxy from the many distinct IMFs it is composed of. Our main result is that applying the observed relations between IMF and galactic properties to the conditions at the star formation sites does not result in strong enough IMF variations between z = 0 galaxies. Steeper physical IMF relations are required for reproducing the observed IMF trends, and some stellar populations must form with more extreme IMFs than those observed. The origin of this result is the hierarchical nature of massive galaxy assembly, and it has implications for the reliability of the strong observed trends, for the ability of cosmological simulations to capture certain physical conditions in galaxies, and for theories of star formation aiming to explain the physical origin of a variable IMF.

IN-SYNC. V. Stellar Kinematics and Dynamics in the Orion A Molecular Cloud

Abstract The kinematics and dynamics of young stellar populations enable us to test theories of star formation. With this aim, we continue our analysis of the SDSS-III/APOGEE IN-SYNC survey, a high-resolution near-infrared spectroscopic survey of young clusters. We focus on the Orion A star-forming region, for which IN-SYNC obtained spectra of ∼2700 stars. In Paper IV we used these data to study the young stellar population. Here we study the kinematic properties through radial velocities (v r ). The young stellar population remains kinematically associated with the molecular gas, following a gradient along the filament. However, near the center of the region, the v r distribution is slightly blueshifted and asymmetric; we suggest that this population, which is older, is slightly in the foreground. We find evidence for kinematic subclustering, detecting statistically significant groupings of colocated stars with coherent motions. These are mostly in the lower-density regions of the cloud, while the ONC radial velocities are smoothly distributed, consistent with it being an older, more dynamically evolved cluster. The velocity dispersion varies along the filament. The ONC appears virialized, or just slightly supervirial, consistent with an old dynamical age. Here there is also some evidence for ongoing expansion, from a v r -extinction correlation. In the southern filament, is ∼2–3 times larger than virial in the L1641N region, where we infer a superposition along the line of sight of stellar subpopulations, detached from the gas. In contrast, decreases toward L1641S, where the population is again in agreement with a virial state.

The SOFIA Massive (SOMA) Star Formation Survey. I. Overview and First Results

Abstract We present an overview and first results of the Stratospheric Observatory For Infrared Astronomy Massive (SOMA) Star Formation Survey, which is using the FORCAST instrument to image massive protostars from ∼10 to 40 μm. These wavelengths trace thermal emission from warm dust, which in Core Accretion models mainly emerges from the inner regions of protostellar outflow cavities. Dust in dense core envelopes also imprints characteristic extinction patterns at these wavelengths, causing intensity peaks to shift along the outflow axis and profiles to become more symmetric at longer wavelengths. We present observational results for the first eight protostars in the survey, i.e., multiwavelength images, including some ancillary ground-based mid-infrared (MIR) observations and archival Spitzer and Herschel data. These images generally show extended MIR/FIR emission along directions consistent with those of known outflows and with shorter wavelength peak flux positions displaced from the protostar along the blueshifted, near-facing sides, thus confirming qualitative predictions of Core Accretion models. We then compile spectral energy distributions and use these to derive protostellar properties by fitting theoretical radiative transfer models. Zhang and Tan models, based on the Turbulent Core Model of McKee and Tan, imply the sources have protostellar masses m * ∼ 10–50 M ⊙ accreting at ∼10−4–10−3 M ⊙ yr−1 inside cores of initial masses M c ∼ 30–500 M ⊙ embedded in clumps with mass surface densities Σcl ∼ 0.1–3 g cm−2. Fitting the Robitaille et al. models typically leads to slightly higher protostellar masses, but with disk accretion rates ∼100× smaller. We discuss reasons for these differences and overall implications of these first survey results for massive star formation theories.

Disk-driven rotating bipolar outflow in Orion Source I

One of the outstanding problems in star-formation theory concerns the transfer of angular momentum such that mass can accrete onto a newly born young stellar object (YSO). From a theoretical standpoint, outflows and jets are predicted to play an essential role in angular momentum transfer and their rotation motions have been reported for both low- and high-mass YSOs. However, little quantitative discussion on outflow launching mechanisms have been presented for high-mass YSOs due to a lack of observational data. Here we present a clear signature of rotation in the bipolar outflow driven by Orion Source I, a high-mass YSO candidate, using the Atacama Large Millimeter/Submillimeter Array (ALMA). A rotational transition of silicon monoxide (Si18O) reveals a velocity gradient perpendicular to the outflow axis which is consistent with that of the circumstellar disk traced by a high-excitation water (H2O) line. The launching radii and outward velocity of the outflow are estimated to be >10 au and 10 km s-1, respectively. These parameters rule out a possibility that the observed outflow is produced by entrainment of a high-velocity jet, and that contribution from stellar-wind or X-wind which have smaller launching radii are significant in the case of Source I. Thus, present results provide a convincing evidence of a rotating outflow directly driven by the magneto-centrifugal disk wind launched by a high-mass YSO candidate.

A Massive Prestellar Clump Hosting No High-mass Cores

Abstract The infrared dark cloud (IRDC) G028.23-00.19 hosts a massive (1500 M ⊙), cold (12 K), and 3.6–70 μm IR dark clump (MM1) that has the potential to form high-mass stars. We observed this prestellar clump candidate with the Submillimeter Array (∼3.″5 resolution) and Jansky Very Large Array (∼2.″1 resolution) in order to characterize the early stages of high-mass star formation and to constrain theoretical models. Dust emission at 1.3 mm wavelength reveals five cores with masses ≤15 M ⊙. None of the cores currently have the mass reservoir to form a high-mass star in the prestellar phase. If the MM1 clump will ultimately form high-mass stars, its embedded cores must gather a significant amount of additional mass over time. No molecular outflows are detected in the CO (2-1) and SiO (5-4) transitions, suggesting that the SMA cores are starless. By using the NH3 (1, 1) line, the velocity dispersion of the gas is determined to be transonic or mildly supersonic (ΔV nt/ΔV th ∼ 1.1–1.8). The cores are not highly supersonic as some theories of high-mass star formation predict. The embedded cores are four to seven times more massive than the clump thermal Jeans mass and the most massive core (SMA1) is nine times less massive than the clump turbulent Jeans mass. These values indicate that neither thermal pressure nor turbulent pressure dominates the fragmentation of MM1. The low virial parameters of the cores (0.1–0.5) suggest that they are not in virial equilibrium, unless strong magnetic fields of ∼1–2 mG are present. We discuss high-mass star formation scenarios in a context based on IRDC G028.23-00.19, a study case believed to represent the initial fragmentation of molecular clouds that will form high-mass stars.

No preferential spatial distribution for massive stars expected from their formation

We analyse N-body and Smoothed Particle Hydrodynamic (SPH) simulations of young star-forming regions to search for differences in the spatial distributions of massive stars compared to lower-mass stars. The competitive accretion theory of massive star formation posits that the most massive stars should sit in deeper potential wells than lower-mass stars. This may be observable in the relative surface density or spatial concentration of the most massive stars compared to other, lower-mass stars. Massive stars in cool--collapse N-body models do end up in significantly deeper potentials, and are mass segregated. However, in models of warm (expanding) star-forming regions, whilst the massive stars do come to be in deeper potentials than average stars, they are not mass segregated. In the purely hydrodynamical SPH simulations, the massive stars do come to reside in deeper potentials, which is due to their runaway growth. However, when photoionisation and stellar winds are implemented in the simulations, these feedback mechanisms regulate the mass of the stars and disrupt the inflow of gas into the clouds' potential wells. This generally makes the potential wells shallower than in the control runs, and prevents the massive stars from occupying deeper potentials. This in turn results in the most massive stars having a very similar spatial concentration and surface density distribution to lower-mass stars. Whilst massive stars do form via competitive accretion in our simulations, this rarely translates to a different spatial distribution and so any lack of primordial mass segregation in an observed star-forming region does not preclude competitive accretion as a viable formation mechanism for massive stars.