Competitive Accretion Models Research Articles

The outer orbit of the high-mass stellar triple system Herschel 36 determined with the VLTI

ABSTRACT Multiplicity is a ubiquitous characteristic of massive stars. Multiple systems offer us a unique observational constraint on the formation of high-mass systems. Herschel 36 A is a massive triple system composed of a close binary (Ab1-Ab2) and an outer component (Aa). We measured the orbital motion of the outer component of Herschel 36 A using infrared interferometry with the AMBER and PIONIER instruments of ESO’s Very Large Telescope Interferometer. Our immediate aims are to constrain the masses of all components of this system and to determine if the outer orbit is co-planar with the inner one. Reported spectroscopic data for all two components of this system and our interferometric data allow us to derive full orbital solutions for the outer orbit Aa-Ab and the inner orbit Ab1-Ab2. For the first time, we derive the absolute masses of mAa = 22.3 ± 1.7, mAb1 = 20.5 ± 1.5, and mAb2 = 12.5 ± 0.9 M⊙. Despite not being able to resolve the close binary components, we infer the inclination of their orbit by imposing the same parallax as the outer orbit. Inclinations derived from the inner and outer orbits imply a modest difference of about 22° between the orbital planes. We discuss this result and the formation of Herschel 36 A in the context of Core Accretion and Competitive Accretion models, which make different predictions regarding the statistic of the relative orbital inclinations.

Completing the protostellar luminosity function in Cygnus-X with SOFIA/FORCAST imaging

ABSTRACT We present a new SOFIA/FORCAST mid-infrared survey of luminous protostars and crowded star-forming environments in Cygnus X, the nearest million-solar mass molecular cloud complex. We derive bolometric luminosities for over 1000 sources in the region with these new data in combination with extant Spitzer and UKIDSS photometry, with 63 new luminous protostar candidates identified by way of the high-quality SOFIA/FORCAST data. By including FORCAST data, we construct protostellar luminosity functions (PLFs) with improved completeness at the high luminosity end. The PLFs are well described by a power-law function with an index of ∼−0.5. Based on the Herschel temperature and column density measurements, we find no obvious dependence of the PLFs on the local gas temperature, but PLFs in regions of high stellar density or gas column density exhibit some excess at higher luminosities. Through the comparison between our observed PLFs and existing accretion models, both the turbulent core and the competitive accretion models are consistent with our results, while the isothermal sphere model is disfavoured. The implications of these results on the star formation process are discussed.

Lack of high-mass pre-stellar cores in the starless MDCs of NGC 6334

Context. The formation of high-mass stars remains unknown in many aspects. There are two competing families of models to explain the formation of high-mass stars. On the one hand, quasi-static models predict the existence of high-mass pre-stellar cores sustained by a high degree of turbulence. On the other hand, competitive accretion models predict that high-mass proto-stellar cores evolve from low or intermediate mass proto-stellar cores in dynamic environments. Aims. The aim of the present work is to bring observational constraints at the scale of high-mass cores (~0.03 pc). Methods. We targeted with ALMA and MOPRA a sample of nine starless massive dense cores (MDCs) discovered in a recent Herschel/HOBYS study. Their mass and size (~110 M⊙ and r = 0.1 pc, respectively) are similar to the initial conditions used in the quasi-static family of models explaining for the formation of high-mass stars. We present ALMA 1.4 mm continuum observations that resolve the Jeans length (λJeans ~ 0.03 pc) and that are sensitive to the Jeans mass (MJeans ~ 0.65 M⊙) in the nine starless MDCs, together with ALMA-12CO(2–1) emission line observations. We also present HCO+(1–0), H13CO+(1–0) and N2H+(1–0) molecular lines from the MOPRA telescope for eight of the nine MDCs. Results. The nine starless MDCs have the mass reservoir to form high-mass stars according to the criteria by Baldeschi et al. (2017). Three of the starless MDCs are subvirialized with αvir ~ 0.35, and four MDCs show sign of collapse from their molecular emission lines. ALMA observations show very little fragmentation within the MDCs. Only two of the starless MDCs host compact continuum sources, whose fluxes correspond to <3 M⊙ fragments. Therefore, the mass reservoir of the MDCs has not yet been accreted onto compact objects, and most of the emission is filtered out by the interferometer. Conclusions. These observations do not support the quasi-static models for high-mass star formation since no high-mass pre-stellar core is found in NGC 6334. The competitive accretion models, on the other hand, predict a level of fragmentation much higher than what we observe.

The Role of Gravity in Producing Power-law Mass Functions

Abstract Numerical simulations of star formation have found that a power-law mass function can develop at high masses. In a previous paper, we employed isothermal simulations that created large numbers of sinks over a large range in masses to show that the power-law exponent of the mass function, , asymptotically and accurately approaches Γ = −1. Simple analytic models show that such a power law can develop if the mass accretion rate , as in Bondi–Hoyle accretion; however, the sink mass accretion rates in the simulations show significant departures from this relation. In this paper, we show that the expected accretion rate dependence is more closely realized provided the gravitating mass is taken to be the sum of the sink mass and the mass in the near environment. This reconciles the observed mass functions with the accretion rate dependencies, and demonstrates that power-law upper mass functions are essentially the result of gravitational focusing, a mechanism present in, for example, the competitive accretion model.

THE NH3HYPERFINE INTENSITY ANOMALY IN HIGH-MASS STAR-FORMING REGIONS

Anomalous ammonia (NH3) spectra, exhibiting asymmetric hyperfine satellite intensity profiles in the () = (1, 1) inversion transition, have been observed in star-forming regions for over 35 years. We present a systematic study of this “hyperfine intensity anomaly” (HIA) toward a sample of 334 high-mass star forming regions: 310 high-mass (≳100 ) clumps and 24 infrared dark clouds. The HIA is ubiquitous in high-mass star forming regions. Although LTE excitation predicts that the intensity ratios of the outer satellites and inner satellites are exactly unity, for this sample the ensemble average ratios are 0.812 ± 0.004 and 1.125 ± 0.005, respectively. We have quantified the HIA and find no significant relationships between the HIA and temperature, line width, optical depth, and the stage of stellar evolution. The fact that HIAs are common in high-mass star-forming regions suggests that the conditions that lead to HIAs are ubiquitous in these regions. A possible link between HIAs and the predictions of the competitive accretion model of high-mass star formation is suggested; however, the expected trends of HIA strength with clump evolutionary stage, rotational temperature, and line width for evolving cores in competitive accretion models are not found. Thus, the exact gas structures that produce HIAs remain unknown. Turbulent gas structures are a possible explanation, but the details need to be explored.

BONDI-HOYLE ACCRETION IN AN ISOTHERMAL MAGNETIZED PLASMA

In regions of star formation, protostars and newborn stars accrete mass from their natal clouds. These clouds are threaded by magnetic fields with a strength characterized by the plasma beta---the ratio of thermal and magnetic pressures. Observations show molecular clouds have beta <= 1, so magnetic fields can play a significant role in the accretion process. We have carried out a numerical study of the effect of large-scale magnetic fields on the rate of accretion onto a uniformly moving point particle from a uniform, non-self-gravitating, isothermal gas. We consider gas moving with sonic Mach numbers of up M ~ 45, magnetic fields that are either parallel, perpendicular, or oriented 45 degrees to the flow, and beta as low as 0.01. Our simulations utilize AMR to obtain high spatial resolution where needed; this also allows the simulation boundaries to be far from the accreting object. Additionally, we show our results are independent of our exact prescription for accreting mass in the sink particle. We give simple expressions for the steady-state accretion rate as a function of beta, M, and field orientation. Using typical molecular clouds values of M ~ 5 and beta ~ 0.04 from the literature, our fits suggest a 0.4 M_Sun star accretes ~ 4*10^{-9} M_Sun/year, almost a factor of two less than accretion rates predicted by hydrodynamic models. This disparity grows to orders of magnitude for stronger fields and lower Mach numbers. We discuss the applicability of these accretion rates versus accretion rates expected from gravitational collapse, and when a steady state is possible. This reduction in Mdot increases the time required to form stars in competitive accretion models, making such models less efficient. In numerical codes, our results should enable accurate subgrid models of sink particles accreting from magnetized media.

A DENSITY DEPENDENCE FOR PROTOSTELLAR LUMINOSITY IN CLASS I SOURCES: COLLABORATIVE ACCRETION

Class I protostars in three high-mass star-forming regions are found to have correlations among the local projected density of other Class I protostars, the summed flux from these other protostars, and the protostellar luminosity in the WISE 22 micron band. Brighter Class I sources form in higher-density and higher-flux regions, while low luminosity sources form anywhere. These correlations depend slightly on the number of neighbors considered (from 2 to 20) and could include a size-of-sample effect from the initial mass function (i.e., larger numbers include rarer and more massive stars). Luminosities seem to vary by neighborhood with nearby protostars having values proportional to each other and higher density regions having higher values. If Class I luminosity is partially related to the accretion rate, then this luminosity correlation is consistent with the competitive accretion model, although it is more collaborative than competitive. The correlation is also consistent with primordial mass segregation, and could explain why the stellar initial mass function resembles the dense core mass function even when cores form multiple stars.

THE DYNAMICS OF MASSIVE STARLESS CORES WITH ALMA

How do stars that are more massive than the Sun form, and thus how is the stellar initial mass function (IMF) established? Such intermediate- and high-mass stars may be born from relatively massive pre-stellar gas cores, which are more massive than the thermal Jeans mass. The Turbulent Core Accretion model invokes such cores as being in approximate virial equilibrium and in approximate pressure equilibrium with their surrounding clump medium. Their internal pressure is provided by a combination of turbulence and magnetic fields. Alternatively, the Competitive Accretion model requires strongly sub-virial initial conditions that then lead to extensive fragmentation to the thermal Jeans scale, with intermediate- and high-mass stars later forming by competitive Bondi-Hoyle accretion. To test these models, we have identified four prime examples of massive (~100Msun) clumps from mid-infrared extinction mapping of infrared dark clouds (IRDCs). Fontani et al. found high deuteration fractions of N2H+ in these objects, which are consistent with them being starless. Here we present ALMA observations of these four clumps that probe the N2D+(3-2) line at 2.3" resolution. We find six N2D+ cores and determine their dynamical state. Their observed velocity dispersions and sizes are broadly consistent with the predictions of the Turbulent Core model of self-gravitating, magnetized (with Alfven Mach number m_A~1) and virialized cores that are bounded by the high pressures of their surrounding clumps. However, in the most massive cores, with masses up to ~60Msun, our results suggest that moderately enhanced magnetic fields (so that m_A~0.3) may be needed for the structures to be in virial and pressure equilibrium. Magnetically regulated core formation may thus be important in controlling the formation of massive cores, inhibiting their fragmentation, and thus helping to establish the stellar IMF.

Dense molecular cocoons in the massive protocluster W3 IRS5: a test case for models of massive star formation

[Context] Two competing models describe the formation of massive stars in objects like the Orion Trapezium. In the turbulent core accretion model, the resulting stellar masses are directly related to the mass distribution of the cloud condensations. In the competitive accretion model, the gravitational potential of the protocluster captures gas from the surrounding cloud for which the individual cluster members compete. [Aims] With high resolution submillimeter observations of the structure, kinematics, and chemistry of the proto-Trapezium cluster W3 IRS5, we aim to determine which mode of star formation dominates. [Methods] We present 354 GHz Submillimeter Array observations at resolutions of 1"-3" (1800-5400 AU) of W3 IRS5. ...... [Results] The observations show five emission peaks (SMM1-5). SMM1 and SMM2 contain massive embedded stars (~20 Msun); SMM3-5 are starless or contain low-mass stars (<8 Msun). The inferred densities are high, >= 10^7 cm^-3, but the core masses are small, 0.2-0.6 Msun. The detected molecular emission reveals four different chemical zones. ...... [Conclusions] The proto-Trapezium cluster W3 IRS5 is an ideal test case to discriminate between models of massive star formation. Either the massive stars accrete locally from their local cores; in this case the small core masses imply that W3 IRS5 is at the very end stages (1000 yr) of infall and accretion, or the stars are accreting from the global collapse of a massive, cluster forming core. We find that the observed masses, densities and line widths observed toward W3 IRS 5 and the surrounding cluster forming core are consistent with the competitive accretion of gas at rates of Macc~10^-4 Msun yr^-1 by the massive young forming stars. ......

THE PROTOSTELLAR LUMINOSITY FUNCTION

The protostellar luminosity function (PLF) is the present-day luminosity function of the protostars in a region of star formation. It is determined using the protostellar mass function (PMF) in combination with a stellar evolutionary model that provides the luminosity as a function of instantaneous and final stellar mass. As in McKee & Offner (2010), we consider three main accretion models: the Isothermal Sphere model, the Turbulent Core model, and an approximation of the Competitive Accretion model. We also consider the effect of an accretion rate that tapers off linearly in time and an accelerating star formation rate. For each model, we characterize the luminosity distribution using the mean, median, maximum, ratio of the median to the mean, standard deviation of the logarithm of the luminosity, and the fraction of very low luminosity objects. We compare the models with bolometric luminosities observed in local star forming regions and find that models with an approximately constant accretion time, such as the Turbulent Core and Competitive Accretion models, appear to agree better with observation than those with a constant accretion rate, such as the Isothermal Sphere model. We show that observations of the mean protostellar luminosity in these nearby regions of low-mass star formation suggest a mean star formation time of 0.3$\pm$0.1 Myr. Such a timescale, together with some accretion that occurs non-radiatively and some that occurs in high-accretion, episodic bursts, resolves the classical "luminosity problem" in low-mass star formation, in which observed protostellar luminosities are significantly less than predicted. An accelerating star formation rate is one possible way of reconciling the observed star formation time and mean luminosity.

The Red MSX Source survey: critical tests of accretion models for the formation of massive stars

There is currently no accepted theoretical framework for the formation of the most massive stars, and the manner in which protostars continue to accrete and grow in mass beyond \sim10Msun is still a controversial topic. In this study we use several prescriptions of stellar accretion and a description of the Galactic gas distribution to simulate the luminosities and spatial distribution of massive protostellar population of the Galaxy. We then compare the observables of each simulation to the results of the Red MSX Source (RMS) survey, a recently compiled database of massive young stellar objects. We find that the observations are best matched by accretion rates which increase as the protostar grows in mass, such as those predicted by the turbulent core and competitive accretion (i.e. Bondi-Hoyle) models. These 'accelerating accretion' models provide very good qualitative and quantitative fits to the data, though we are unable to distinguish between these two models on our simulations alone. We rule out models with accretion rates which are constant with time, and those which are initially very high and which fall away with time, as these produce results which are quantitatively and/or qualitatively incompatible with the observations. To simultaneously match the low- and high-luminosity YSO distribution we require the inclusion of a 'swollen-star' pre-main-sequence phase, the length of which is well-described by the Kelvin-Helmholz timescale. Our results suggest that the lifetime of the YSO phase is \sim 10^5yrs, whereas the compact Hii-region phase lasts between \sim 2 - 4 \times 10^5yrs depending on the final mass of the star. Finally, the absolute numbers of YSOs are best matched by a globally averaged star-formation rate for the Galaxy of 1.5-2Msun/yr.

THE SPARSEST CLUSTERS WITH O STARS

There is much debate on how high-mass star formation varies with environment, and whether the sparsest star-forming environments are capable of forming massive stars. To address this issue, we have observed eight apparently isolated OB stars in the SMC using HST's Advanced Camera for Surveys. Five of these objects appear as isolated stars, two of which are confirmed to be runaways. The remaining three objects are found to exist in sparse clusters, with <10 companion stars revealed, having masses of 1-4 solar mass. Stochastic effects dominate in these sparse clusters, so we perform Monte Carlo simulations to explore how our observations fit within the framework of empirical, galactic cluster properties. We generate clusters using a simplistic -2 power-law distribution for either the number of stars per cluster (N_*) or cluster mass (M_cl). These clusters are then populated with stars randomly chosen from a Kroupa IMF. We find that simulations with cluster lower-mass limits of M_cl,lo >20 solar mass and N_*,lo >40 match best with observations of SMC and Galactic OB star populations. We examine the mass ratio of the second-most massive and most massive stars (m_max,2/m_max), finding that our observations all exist below the 20th percentile of our simulated clusters. However, all of our observed clusters lie within the parameter space spanned by the simulated clusters, although some are in the lowest 5th percentile frequency. These results suggest that clusters are built stochastically by randomly sampling stars from a universal IMF with a fixed stellar upper-mass limit. In particular, we see no evidence to suggest a m_max - M_cl relation. Our results may be more consistent with core accretion models of star formation than with competitive accretion models, and they are inconsistent with the proposed steepening of the integrated galaxy IMF (IGIMF).

THE PROTOSTELLAR MASS FUNCTION

The protostellar mass function (PMF) is the Present-Day Mass Function of the protostars in a region of star formation. It is determined by the initial mass function weighted by the accretion time. The PMF thus depends on the accretion history of protostars and in principle provides a powerful tool for observationally distinguishing different protostellar accretion models. We consider three basic models here: the Isothermal Sphere model (Shu 1977), the Turbulent Core model (McKee & Tan 2003), and an approximate representation of the Competitive Accretion model (Bonnell et al. 1997, 2001a). We also consider modified versions of these accretion models, in which the accretion rate tapers off linearly in time. Finally, we allow for an overall acceleration in the rate of star formation. At present, it is not possible to directly determine the PMF since protostellar masses are not currently measurable. We carry out an approximate comparison of predicted PMFs with observation by using the theory to infer the conditions in the ambient medium in several star-forming regions. Tapered and accelerating models generally agree better with observed star-formation times than models without tapering or acceleration, but uncertainties in the accretion models and in the observations do not allow one to rule out any of the proposed models at present. The PMF is essential for the calculation of the Protostellar Luminosity Function, however, and this enables stronger conclusions to be drawn (Offner & McKee 2010).

Driven and Decaying Turbulence Simulations of Low‐Mass Star Formation: From Clumps to Cores to Protostars

Molecular clouds are observed to be turbulent, but the origin of this turbulence is not well understood. As a result, there are two different approaches to simulating molecular clouds, one in which the turbulence is allowed to decay after it is initialized, and one in which it is driven. We use the adaptive mesh refinement (AMR) code, Orion, to perform high-resolution simulations of molecular cloud cores and protostars in environments with both driven and decaying turbulence. We include self-gravity, use a barotropic equation of state, and represent regions exceeding the maximum grid resolution with sink particles. We analyze the properties of bound cores such as size, shape, linewidth, and rotational energy, and we find reasonable agreement with observation. At high resolution, the different rates of core accretion in the two cases have a significant effect on protostellar system development. Clumps forming in a decaying turbulence environment produce high-multiplicity protostellar systems with Toomre-Q unstable disks that exhibit characteristics of the competitive accretion model for star formation. In contrast, cores forming in the context of continuously driven turbulence and virial equilibrium form smaller protostellar systems with fewer low-mass members. Our simulations of driven and decaying turbulence show some statistically significant differences, particularly in the production of brown dwarfs and core rotation, but the uncertainties are large enough that we are not able to conclude whether observations favor one or the other.

Star formation through gravitational collapse and competitive accretion

Competitive accretion, a process to explain the origin of the IMF, occurs when stars in a common gravitational potential accrete from a distributed gaseous component. We show that concerns recently raised on the efficiency of competitive accretion are incorrect as they use globally averaged properties which are inappropriate for the detailed physics of a forming stellar cluster. A full treatment requires a realistic treatment of the cluster potential, the distribution of turbulent velocities and gas densities. Accreting gas does not travel at the global virial velocity of the system due to the velocity-sizescale relation inherent in turbulent gas and due to the lower velocity dispersion of small-N clusters in which much of the accretion occurs. Stars located in the gas-rich centres of such systems initially accrete from low relative velocity gas attaining larger masses before needing to accrete the higher velocity gas. Stars not in the centres of such potentials, or that enter the cluster later when the velocity dispersion is higher, do not accrete significantly and thus retain their low-masses. In competitive accretion, most stars do not continue to accrete significantly such that their masses are set from the fragmentation process. It is the few stars which continue to accrete that become higher-mass stars. Competitive accretion is therefore likely to be responsible for the formation of higher-mass stars and can explain the mass distribution, mass segregation and binary frequency of these stars. Global kinematics of competitive accretion models include large-scale mass infall, with mean inflow velocities of order 0.5 km/s at scales of 0.5 pc, but infall signatures are likely to be confused by the large tangential velocities and the velocity dispersion present.

The formation of stars by gravitational collapse rather than competitive accretion

There are two dominant models of how stars form. Under gravitational collapse, star-forming molecular clumps, of typically hundreds to thousands of solar masses (M(o)), fragment into gaseous cores that subsequently collapse to make individual stars or small multiple systems. In contrast, competitive accretion theory suggests that at birth all stars are much smaller than the typical stellar mass (approximately 0.5M(o)), and that final stellar masses are determined by the subsequent accretion of unbound gas from the clump. Competitive accretion models interpret brown dwarfs and free-floating planets as protostars ejected from star-forming clumps before they have accreted much mass; key predictions of this model are that such objects should lack disks, have high velocity dispersions, form more frequently in denser clumps, and that the mean stellar mass should vary within the Galaxy. Here we derive the rate of competitive accretion as a function of the star-forming environment, based partly on simulation, and determine in what types of environments competitive accretion can occur. We show that no observed star-forming region can undergo significant competitive accretion, and that the simulations that show competitive accretion do so because the assumed properties differ from those determined by observation. Our result shows that stars form by gravitational collapse, and explains why observations have failed to confirm predictions of the competitive accretion model.

Accretion in stellar clusters and the initial mass function

We present a simple physical mechanism that can account for the observed stellar mass spectrum for masses M∗≳0.5 M⊙. The model depends solely on the competitive accretion that occurs in stellar clusters where each star's accretion rate depends on the local gas density and the square of the accretion radius. In a stellar cluster, there are two different regimes depending on whether the gas or the stars dominate the gravitational potential. When the cluster is dominated by cold gas, the accretion radius is given by a tidal-lobe radius. This occurs as the cluster collapses towards a ρ ∝ R−2 distribution. Accretion in this regime results in a mass spectrum with an asymptotic limit of γ=−3/2 (where Salpeter is γ=−2.35). Once the stars dominate the potential and are virialized, which occurs first in the cluster core, the accretion radius is the Bondi–Hoyle radius. The resultant mass spectrum has an asymptotic limit of γ=−2 with slightly steeper slopes (γ≈−2.5) if the stars are already mass-segregated. Simulations of accretion on to clusters containing 1000 stars show that, as expected, the low-mass stars accumulate the majority of their masses during the gas-dominated phase whereas the high-mass stars accumulate the majority of their masses during the stellar-dominated phase. This results in a mass spectrum with a relatively shallow γ≈3/2 power law for low-mass stars and a steeper power law for high-mass stars −2.5≲γ≤−2. This competitive accretion model also results in a mass-segregated cluster.