Bonnor-Ebert Sphere Research Articles

Reliability of NH3as the temperature probe of cold cloud cores

The temperature is a central parameter affecting the chemical and physical properties of dense cores of interstellar clouds and their evolution to star formation. The chemistry and the dust properties are temperature dependent and the interpretation of observation requires the knowledge of the temperature and its variations. Measurement of the gas kinetic temperature is possible with molecular line spectroscopy, the ammonia molecule, NH3, being the most commonly used tracer. We want to determine the accuracy of the temperature estimates derived from ammonia spectra. The normal interpretation of NH3 observations assumes that all the hyperfine line components are tracing the same gas volume. In the case of temperature gradients they may be sensitive to different layers and cause errors in the optical depth and gas temperature estimates. We examine a series of spherical cloud models, 1.0 and 0.5 M_Sun Bonnor-Ebert spheres, with different radial temperature profiles. We calculate synthetic NH3 spectra and compare the derived column densities and temperatures to the true values. For high signal-to-noise observations, the estimated gas kinetic temperatures are within ~0.3 K of the real mass averaged temperature and the column densities are correct to within ~10%. When the S/N ratio of the (2,2) spectrum decreases below 10, the temperature errors are of the order of 1K but without a significant bias. When the density of the models is increased by a factor of a few, the results begin to show significant bias because of the saturation of the (1,1) main group. The ammonia spectra are found to be a reliable tracer of the mass averaged gas temperature. Because the radial temperature profiles of the cores are not well constrained, the central temperature could still differ from this value. If the cores are optically very thick, there are no guarantees of the accuracy.

Radiation hydrodynamics of triggered star formation: the effect of the diffuse radiation field

We investigate the effect of including diffuse field radiation when modelling the radiatively driven implosion of a Bonnor-Ebert sphere (BES). Radiation-hydrodynamical calculations are performed by using operator splitting to combine Monte Carlo photoionization with grid-based Eulerian hydrodynamics that includes self-gravity. It is found that the diffuse field has a significant effect on the nature of radiatively driven collapse which is strongly coupled to the strength of the driving shock that is established before impacting the BES. This can result in either slower or more rapid star formation than expected using the on-the-spot approximation depending on the distance of the BES from the source object. As well as directly compressing the BES, stronger shocks increase the thickness and density in the shell of accumulated material, which leads to short, strong, photo-evaporative ejections that reinforce the compression whenever it slows. This happens particularly effectively when the diffuse field is included as rocket motion is induced over a larger area of the shell surface. The formation and evolution of 'elephant trunks' via instability is also found to vary significantly when the diffuse field is included. Since the perturbations that seed instabilities are smeared out elephant trunks form less readily and, once formed, are exposed to enhanced thermal compression.

On the stability of non-isothermal Bonnor-Ebert spheres

Aims: We aim to derive a stability condition for non-isothermal Bonnor-Ebert spheres and compare the physical properties of critical non-isothermal and isothermal gas spheres. These configurations can serve as models for prestellar cores before gravitational collapse. Methods: A stability condition for non-isothermal spheres is derived by constructing an expression for the derivative of boundary pressure with respect to core volume. The temperature distribution is determined by means of radiative transfer calculations. Based on the stability analysis, we derive the physical parameters of critical cores for the mass range 0.1 - 5.0 M_sun. In addition, the properties of roughly Jupiter-mass cores are briefly examined. Results: At the low-mass end the critical non-isothermal sphere has lower central density and a slightly larger physical radius than the corresponding isothermal sphere (i.e. one with the same mass and average temperature). The temperature decrease towards the core centre becomes steeper towards smaller masses as the central density becomes higher. The slope depends on the adopted dust model. We find that the critical dimensionless radius increases above the isothermal value xi_0 = 6.45 for very low-mass cores (< 0.2 M_sun). However, in the mass-range studied here the changes are within 5% from the isothermal value. Conclusions: The density structures of non-isothermal and isothermal Bonnor-Ebert spheres for a given mass are fairly similar. However, the present models predict clear differences in the average temperatures for the same physical radius. Especially for low-mass cores, the temperature gradient probably has implications on the chemistry and the observed line emission. We also find that hydrostatic Jupiter-mass cores with radii less than 100 AU would have very high boundary pressures compared with typical pressures in the interstellar space.

A DYNAMICS CODE FOR A DUSTY INTERSTELLAR CLOUD EMBEDDED IN AN INTER-CLOUD MEDIUM

To study the internal dynamics of dusty interstellar clouds bound by an inter-cloud medium, we have written a one-dimensional numerical code for dusty gas dynamics in two-phase media. The governing equations for both cloud and inter-cloud media are solved using a Godunov-type scheme. The interface between the cloud and inter-cloud media is tracked by a mesh in the arbitrary Lagrangian-Eulerian frame. The dust component is treated as either a pressureless continuum or super-particles. The dust-gas drag is described by either the Epstein law or the Baines relation. To minimize errors from source terms, we utilize (in time integration) an explicit fourth-order Runge-Kutta scheme. This code is specially designed and tuned for simulating the complicated dynamics of dusty interstellar clouds. We have run three sets of test problems: the first set comprises shock-tube tests. The resulting shocks are resolved with two or three grid points. The second set is to examine the degree of error convergence. The results at various spatial resolutions demonstrate the second-order spatial accuracy of our code. The third set involves the Bonnor-Ebert sphere. From a number of simulations, we could numerically determine the Bonnor-Ebert criterion with errors less than 6%. As an example of utilizing our code, we simulate the collapse of dusty clouds embedded in a radiation field. Inside the cloud, the dust grains drift inward by radiation field and the dust-to-gas ratio at the intermediate radius increases by a factor of 20.

Protostellar collapse of rotating cloud cores

Aims. We investigate the influence of turbulent viscosity on the collapse of a rotating molecular cloud core with axial symmetry, in particular, on the first and second collapse phase, as well as the evolution of the second (protostellar) core during its first accretion period. By using extensive numerical calculations, we monitor the intricate interactions between the newly formed protostar and the surrounding accretion disk (the first core) in which the star is embedded.Methods. We use a grid-based radiation-hydrodynamics code with a spatial grid designed to meet the high resolution required to study the second core. The radiative transfer is treated in the flux-limited diffusion approximation. A slightly supercritical Bonnor-Ebert sphere of 1 M ⊙ and uniform rotation according to a fixed centrifugal radius of 100 AU serves as the initial condition without exception. In a parameter study, we vary the β -viscosity driving the angular momentum transport.Results. Without viscosity (β = 0), a highly flattened accretion disk forms that fragments into several “cold” rings. For β = 10-4 , a single “warm” ring forms that undergoes collapse due to hydrogen dissociation. For β = 10-3 , ring formation is suppressed completely. The second collapse proceeds on the local thermal timescale, which is in contrast to the current view of a generally dynamical second collapse. During the first accretion period of the second core, the first core heats up globally and, as a consequence, a nearly spherical outflow occurs, destroying the structure of the former accretion disk completely. Finally, for β = 10-2 , we see the classical dynamical second collapse and a shorter but more rapid accretion phase. The impact on the surrounding accretion disk is even more pronounced. We follow the resulting massive outflow up to several kyr after the second collapse, where the central parts (R < 0.7 AU) are now cut out and replaced with an appropriate inner boundary condition. Matter is found to turn back to the center at a radius of 500 AU after about 4 kyr and to reach the protostar again after approximately 7 kyr. The results suggest that the star formation process consists of short and rapid accretion phases (lasting on the order of 100 yr) between long and quiet outflow periods (lasting several kyr).

MODELING COLLAPSE AND ACCRETION IN TURBULENT GAS CLOUDS: IMPLEMENTATION AND COMPARISON OF SINK PARTICLES IN AMR AND SPH

We implemented sink particles in the adaptive mesh refinement (AMR) hydrodynamics code FLASH. Sink particles are created in regions of local gravitational collapse, and their trajectories and accretion can be followed over many dynamical times. We perform a series of tests including the time integration of circular and elliptical orbits, the collapse of a Bonnor-Ebert sphere and a rotating, fragmenting cloud core. We compare the collapse of a highly unstable singular isothermal sphere to the theory by Shu (1977), and show that the sink particle accretion rate is in excellent agreement with the theoretical prediction. To model eccentric orbits and close encounters of sink particles accurately, we show that a very small timestep is often required, for which we implemented subcycling of the N-body system. We emphasize that a sole density threshold for sink particle creation is insufficient in supersonic flows, if the density threshold is below the opacity limit. In that case, the density can exceed the threshold in strong shocks that do not necessarily lead to local collapse. Additional checks for bound state, gravitational potential minimum, Jeans instability and converging flows are absolutely necessary for a meaningful creation of sink particles. We apply our new sink particle module for FLASH to the formation of a stellar cluster, and compare to a smoothed particle hydrodynamics (SPH) code with sink particles. Our comparison shows encouraging agreement of gas properties, indicated by column density distributions and radial profiles, and of sink particle formation times and positions. We find excellent agreement in the number of sink particles formed, and in their accretion and mass distributions.

THE VELA CLOUD: A GIANT H I ANOMALY IN THE NGC 3256 GROUP

We present Australia Telescope Compact Array (ATCA) observations of a galaxy-sized intergalactic HI cloud (the Vela Cloud) in the NGC 3256 galaxy group. The group contains the prominent merging galaxy NGC 3256, which is surrounded by a number of HI fragments, the tidally disturbed galaxy NGC 3263, and several other peculiar galaxies. The Vela Cloud, with an HI mass of 3-5 * 10**9 solar masses, resides southeast of NGC 3256 and west of NGC 3263, within an area of 9' x 16' (100 kpc x 175 kpc for an adopted distance of 38 Mpc). In our ATCA data the Vela Cloud appears as 3 diffuse components and contains 4 density enhancements. The Vela Cloud's properties, together with its group environment, suggest that it has a tidal origin. Each density enhancement contains ~10**8 solar masses of HI gas which is sufficient material for the formation of globular cluster progenitors. However, if we represent the enhancements as Bonnor-Ebert spheres, then the pressure of the surrounding HI would need to increase by at least a factor of 6 in order to cause the collapse of an enhancement. Thus we do not expect them to form massive bound stellar systems like super star clusters or tidal dwarf galaxies. Since the HI density enhancements have some properties in common with High Velocity Clouds, we explore whether they may evolve to be identified with these starless clouds instead.

Protostellar discs formed from rigidly rotating cores

Abridged: We use three-dimensional SPH simulations to investigate the collapse of low-mass prestellar cores and the formation and early evolution of protostellar discs. The initial conditions are slightly supercritical Bonnor-Ebert spheres in rigid rotation. The core mass and initial radius are held fixed at M_O=6.1 M_sun and R_O=17,000 AU, and the only parameter that we vary is the initial angular speed \Omega_O. Protostellar discs forming from cores with \Omega_O<1.35 10d-13 1/s have radii between 100 and 300 AU and are quite centrally concentrated; due to heating by gas infall onto the disc and accretion onto the central object, they are also quite warm, T>100 K, and therefore stable against gravitational fragmentation. In contrast, more rapidly rotating cores form discs which are less concentrated and cooler, and have radii between 400 and 1000 AU; as a consequence they are prone to gravitational fragmentation and the formation of multiple systems. We derive a criterion that predicts whether a rigidly rotating core having given M_O, R_O and \Omega_O will produce a protostellar disc which fragments whilst material is still infalling from the core envelope. We then apply this criterion to core samples for which M_O, R_O and \Omega_O have been estimated observationally. We conclude that the observed cores are stable against fragmentation at this stage, due to their low angular speeds and the heat delivered at the accretion shock where the infalling material hits the disc.

A TWO MICRON ALL SKY SURVEY ANALYSIS OF THE STABILITY OF SOUTHERN BOK GLOBULES

We used near-infrared Two Micron All Sky Survey data to construct visual extinction maps of a sample of Southern Bok globules utilizing the NICE method. We derived radial extinction profiles of dense cores identified in the globules and analyzed their stability against gravitational collapse with isothermal Bonnor-Ebert spheres. The frequency distribution of the stability parameter (ξmax) of these cores shows that a large number of them are located in stable states, followed by an abrupt decrease of cores in unstable states. This decrease is steeper for globules with associated IRAS point sources than for starless globules. Moreover, globules in stable states have a Bonnor-Ebert temperature of T = 15 ± 6 K, while the group of critical plus unstable globules has a different temperature of T = 10 ± 3 K. Distances were estimated to all the globules studied in this work and the spectral class of the IRAS sources was calculated. No variations were found in the stability parameters of the cores and the spectral class of their associated IRAS sources. On the basis of 13CO J = 1 – 0 molecular line observations, we identified and modeled a blue-asymmetric line profile toward a globule of the sample, obtaining an upper limit infall speed of 0.25 km s–1.

Protostellar discs formed from turbulent cores

We investigate the collapse and fragmentation of low-mass, trans-sonically turbulent prestellar cores, using SPH simulations. The initial conditions are slightly supercritical Bonnor-Ebert spheres, all with the same density profile, the same mass (M_O=6.1 Msun) and the same radius (R_O=17,000 AU), but having different initial turbulent velocity fields. Four hundred turbulent velocity fields have been generated, all scaled so that the mean Mach number is M=1. Then a subset of these, having a range of net angular momenta, j, has been evolved. The evolution of these turbulent cores is not strongly correlated with j. Instead it is moderated by the formation of filamentary structures due to converging turbulent flows. A high fraction (~ 82%) of the protostars forming from turbulent cores are attended by protostellar accretion discs, but only a very small fraction (~16%) of these discs is sufficiently cool and extended to develop non-linear gravitational instabilities and fragment.

Supersonic cloud collision. I.

It has long been suggested that shocks might play an important role in altering the form of the interstellar medium (ISM). Shocks enhance gas density and sufficiently dense regions may become self gravitating. Potential star forming clouds within larger molecular clouds, move randomly at supersonic speeds. Depending on the precollision velocity, colliding molecular clouds produce a slab that is either shock compressed or pressure confined. In a sequel of two papers (I & II), we simulate molecular cloud collision and investigate the dynamical evolution of such slabs. Shocked slabs are susceptible to hydrodynamic instabilities and in the present paper (I) we study the effect of strong shear between slab layers on the dynamic evolution of a shock compressed gas slab. Both, head-on and off-centre cloud collisions have been examined in this work. We include self gravity in all our simulations. Simulations presented here, are performed using the smoothed particle hydrodynamics (SPH) numerical scheme. Individual, pre-collision clouds are modelled as pressure confined Bonnor-Ebert spheres. However, in the interest of brevity the thermodynamic details of the problem are simplified and the gas temperature is simply evolved by a barytropic equation of state. Obviously, the gas, to some extent suffers from thermal inertial effects. However, we note that the dynamical timescale is much smaller than the local sound crossing time so that such effects should have minimum influence.

THE INEVITABLE FUTURE OF THE STARLESS CORE BARNARD 68

Dense, small molecular cloud cores have been identified as the direct progenitors of stars. One of the best studied examples is Barnard 68 which is considered a prototype stable, spherical gas core, confined by a diffuse high-pressure environment. Observations of its radial density structure however indicate that Barnard 68 should be gravitationally unstable and collapsing which appears to be inconsistent with its inferred long lifetime and stability. We argue that Barnard 68 is currently experiencing a fatal collision with another small core which will lead to gravitational collapse. Despite the fact that this system is still in an early phase of interaction, our numerical simulations imply that the future gravitational collapse is already detectable in the outer surface density structure of the globule which mimicks the profile of a gravitationally unstable Bonnor-Ebert sphere. Within the next 200,000 years Barnard 68 will condense into a low-mass solar-type star(s), formed in isolation, and surrounded by diffuse, hot interstellar gas. As witnessed in situ for Barnard 68, core mergers might in general play an important role in triggering star formation and shaping the molecular core mass distribution and by that also the stellar initial mass function.

An analytic column density profile to fit prestellar cores

We present a new analytical three-parameter formula to fit observed column density profiles of prestellar cores. It represents a line-of-sight integral through a spherically symmetric or disc-like isothermal cloud. The underlying model resembles the Bonnor–Ebert model in that it features a flat central region leading into a power-law decline ∝r−2 in density, and a well-defined outer radius. However, we do not assume that the cloud is in equilibrium, and can instead make qualitative statements about its dynamical state (expansion, equilibrium, collapse) using the size of the flat region as a proxy. Instead of having temperature as a fitting parameter, our model includes it as input, and thus avoids possible inconsistencies. It is significantly easier to fit to observational data than the Bonnor–Ebert sphere. We apply this model to L1689B and B68. We show that L1689B cannot be in equilibrium but instead appears to be collapsing, while our model verifies that B68 is not far from being a hydrostatic object.

Ionization front-driven turbulence in the clumpy interstellar medium

We present 3D radiation-gas dynamical simulations of an ionization front running into a dense clump. In our setup, a B0 star irradiates an overdensity which is at a distance of 10 pc and modelled as a supercritical Bonnor–Ebert sphere. The radiation from the star heats up the gas and creates a shock front that expands into the interstellar medium. The shock compresses the clump material, while the ionizing radiation heats it up. The outcome of this ‘cloud-crushing’ process is a fully turbulent gas in the wake of the clump. In the end, the clump entirely dissolves. We propose that this mechanism is very efficient in creating short-living supersonic turbulence in the vicinity of massive stars.

Simulating hydromagnetic processes in star formation: introducing ambipolar diffusion into an adaptive mesh refinement code

Given the importance of simulating hydromagnetic processes that impact star formation, we have earlier developed a 3D adaptive mesh approach that allows us to include hydromagnetic processes during the formation and evolution of cores, discs and stars in observed regions of star formation. In this paper, we take the next step in this program – namely – to develop a modified version of the 3D adaptive mesh refinement (AMR) code flash in which the ambipolar diffusion of the magnetic field in poorly ionized molecular gas is implemented. We approach the problem using a single-fluid approximation to simplify numerical calculations. In this paper, we present a series of test cases including oblique isothermal and non-isothermal C-shocks. We also present a study of the quasi-static collapse of a uniform, self-gravitating, magnetized sphere that is initially supported by its magnetic field against collapse (i.e. magnetically subcritical). Applications to the collapse of a pre-stellar Bonnor–Ebert sphere are presented in a companion paper.

Formation and Collapse of Quiescent Cloud Cores Induced by Dynamic Compressions

We present numerical hydrodynamic simulations of the formation, evolution, and gravitational collapse of isothermal molecular cloud cores in spherical geometry. A compressive wave is set up in a constant sub-Jeans density distribution of radius r = 1 pc. As the wave travels through the simulation grid, a shock-bounded spherical shell is formed. The inner shock of this shell reaches and bounces off the center, leaving behind a central core with an initially almost uniform density distribution, surrounded by an envelope consisting of the material in the shock-bounded shell, which at late times develops a logarithmic slope close to -2, even in noncollapsing cases. The central core and the envelope are separated by a mild shock. The central core grows to sizes of ~0.1 pc and resembles a Bonnor-Ebert (BE) sphere, although it has significant dynamical differences: its self-gravity is initially negligible, and it is confined by the ram pressure of the infalling material, thus growing continuously in mass and size. With the appropriate parameters, the core mass eventually reaches an effective Jeans mass, at which time the core begins to collapse. Thus, the core evolves from a stable regime to an unstable one, implying the existence of a time delay between the appearance of the core and the onset of its collapse, but due to its growth in mass, rather than to the dissipation of its internal turbulence, as is often believed. These results suggest that prestellar cores may approximate BE structures, which are, however, of variable mass and may or may not experience gravitational collapse, in qualitative agreement with the large observed frequency of cores with BE-like profiles.

Large‐Area Mapping at 850 μm. V. Analysis of the Clump Distribution in the Orion A South Molecular Cloud

We present results from a 2300 arcmin^2 survey of the Orion A molecular cloud at 450 and 850 micron using the Submillimetre Common-User Bolometer Array (SCUBA) on the James Clerk Maxwell Telescope. The region mapped lies directly south of the OMC1 cloud core and includes OMC4, OMC5, HH1/2, HH34, and L1641N. We identify 71 independent clumps in the 850 micron map and compute size, flux, and degree of central concentration in each. Comparison with isothermal, pressure-confined, self-gravitating Bonnor-Ebert spheres implies that the clumps have internal temperatures T_d ~ 22 +/- K and surface pressures log (k^-1 P cm^-3 K) = 6.0 +/- 0.2. The clump masses span the range 0.3 - 22 Msun assuming a dust temperature T_d ~ 20 K and a dust emissivity kappa_850 = 0.02 cm^2 g^-1. The distribution of clump masses is well characterized by a power-law N(M) propto M^-alpha with alpha = 2.0 +/- 0.5 for M > 3.0 Msun, indicating a clump mass function steeper than the stellar Initial Mass Function. Significant incompleteness makes determination of the slope at lower masses difficult. A comparison of the submillimeter emission map with an H_2 2.122 micron survey of the same region is performed. Several new Class 0 sources are revealed and a correlation is found between both the column density and degree of concentration of the submillimeter sources and the likelihood of coincident H_2 shock emission.

Oscillations of Starless Cores

If the split, asymmetric molecular spectral line profiles that are seen in many starless cores are interpreted as indicative of global collapse or expansion of the core then one possible implication is that most starless cores have short lifetimes on the order of the collapse or sound crossing time scale. An alternative interpretation of the line profiles as indicative of perturbations on an underlying equilibrium structure leads to the opposite implication, that many cores have long lifetimes. While evidence suggests that some cores are collapsing on a free-fall time scale, we show that observations of some other starless cores can be reproduced by a model of non-radial oscillations about the equilibrium configuration of a pressure-bounded, thermally-supported sphere (Bonnor-Ebert sphere). We model the oscillations as linear perturbations following a standard analysis developed for stellar pulsations and compare the column densities and molecular spectral line profiles predicted from a particular model to observations of the Bok globule B68.

The Large‐ and Small‐Scale Structures of Dust in the Star‐forming Perseus Molecular Cloud

We present an analysis of ~3.5 deg2 of submillimeter continuum and extinction data of the Perseus molecular cloud. We identify 58 clumps in the submillimeter map, and we identify 39 structures ("cores") and 11 associations of structures ("super cores") in the extinction map. The cumulative mass distributions of the submillimeter clumps and extinction cores have steep slopes (α ~ 2 and 1.5-2, respectively), steeper than the Salpeter initial mass function (IMF; α = 1.35), while the distribution of extinction super cores has a shallow slope (α ~ 1). Most of the submillimeter clumps are well fit by stable Bonnor-Ebert spheres with 10 K < T < 19 K and 5.5 <(Pext/k) < 6.0. The clumps are found only in the highest column density regions (AV > 5-7 mag), although Bonnor-Ebert models suggest that we should have been able to detect them at lower column densities if they exist. These observations provide a stronger case for an extinction threshold than that found in analysis of less sensitive observations of the Ophiuchus molecular cloud (Johnstone et al.). The relationship between submillimeter clumps and their parent extinction core has been analyzed. The submillimeter clumps tend to lie offset from the larger extinction peaks, suggesting that the clumps formed via an external triggering event, consistent with previous observations.

Convection during the formation of gaseous giants and stars

AbstractConvection theories for star and planet formation studies have to be (1) simple, to allow a self-consistent solution with other relevant processes, (2) time-dependent, because convection often starts in collapse-flows, and (3) robust, i.e. physically well-behaved under a wide range of conditions ranging from the quiet protoplanetary nebula to supercritical protostellar accretion-shocks with Mach-numbers of a few hundred. I describe how the equations of radiation fluid-dynamics can be augmented by a one-equation convection model in order to construct a system of equations that contains the Sun, brown dwarfs and planets as well as their nearly isothermal parent-clouds. The system of equations is calibrated to the Sun and tested by the solar convection zone and the pulsations of RR-Lyrae stars. I discuss the following applications: (1) star formation as the collapse of Bonnor-Ebert spheres of masses ranging from the stellar domain to the brown dwarf region, (2) the approach to the main sequence, (3) companion mass determinations for direct imaging searches for exoplanets, with GQ Lupi as an example, and (4) the formation of Pegasi-planets, and the “large core” exoplanet, HD 149 026, in particular.