New molecular line observations of the Bok globule Barnard 68 in HCO+ irrefutably confirm the complex pattern of red and blue asymmetric line profiles seen across the face of the cloud in previous observations of CS. The new observations thus strengthen the previous interpretation that Barnard 68 is undergoing peculiar oscillations. Furthermore, the physical chemistry of B68 indicates that the object is much older than the sound crossing time and is therefore long-lived. A model is presented for the globule in which a modest external pressure perturbation is shown to lead to oscillations about a stable equilibrium configuration. Such oscillations may be present in other stable starless cores as manifested by a similar signature of inward and outward motions.
One difficulty in identifying a potential site of future star formation has been to decide whether a dense portion of a molecular cloud is likely to proceed to collapse to form a star, or else is just a transient or a long-lived density enhancement. Models of supersonically turbulent cold molecular clouds readily produce localized density enhancements in colliding gas streams (e.g. Klessen et al. 2000; Padoan & Nordlund 2002; Ballesteros-Paredes et al. 2003). However, in the simulations, the clouds either quickly dissipate on a sound crossing time or, if their density and size are such that the cloud mass exceeds the local Jeans mass, they may collapse to form stars. However, observations that show that the internal structure of some clouds is consistent with self-gravitating equilbrium suggest that the alternative of long-lived clouds should not be excluded. Unbiased observations of large swathes of molecular cloud gas point to cloud survival time-scales of a few sound crossing times, but less than an order of 10 (Visser et al. 2002). Theoretical models of small clouds in equilibrium closely match the observations and suggest that small clouds may be catagorized as either ‘stable starless cores’ or ‘unstable pre-stellar cores’ using the terminology suggested in Keto & Field (2005) (note that the terms ‘starless cores’, ‘pre-protostellar’ and ‘pre-collapse’ cores are commonly used in observational work). Such structures, in which local thermal pressure dominates over larger scale inertial forces, could represent the end point of the turbulent cascade in larger scale molecular clouds. Thus the picture of the interstellar medium as a purely turbulent phenomenon, and all clouds as purely transient, may not be applicable on the scale of the smaller clouds such as Bok globules and starless cores (Fig. 1). Because star formation in regions such as Taurus and Ophiuchus takes place in these small clouds, an understanding of whether equilibrium conditions can prevail is crucial in order to be able to understand the initial conditions of star formation and the firm identification of infall candidates.
Barnard 68 (LDN 57, CB 82 hereafter B68, Figs 1 and 2) is an excellent test case of an object that could either be a stable starless core or an unstable pre-stellar core. Because B68 is nearby (∼125 pc) and fortuitously seen in silouette against the galactic bulge, Alves, Lada & Lada (2001a) were able to directly measure the dust extinction in the core with unprecedented accuracy using deep near-infrared extinction measurements from H and K imaging of background stars. With the assumption of a uniform gas-to -dust ratio, the gas density profile for this core is thus very well constrained as a cloud in hydrostatic equilibrium confined by external pressure: a Bonnor-Ebert Sphere (Bonnor 1956; Ebert 1955) which is a solution of the Lane-Emden equation for a bounded isothermal pressure-balanced sphere. However, we argue below that B68 is not isothermal and is possibly not in hydrostatic pressure balance. The high quality of the absorption data and the precise determination of the column density removes a major source of uncertainty for investigating the internal structure of this possible prestellar core candidate.
The dust obscuration map in fig. 2 of Alves, Lada & Lada (2001b) show that B68 consists of an approximately spherical component of radius 12500 au with a markedly off-centre dust peak. There is also a lower density extension to the south-east. Alves et al. (2001a) estimated that the central density of B68 is ∼2.5 × 105 cm−3, giving a total mass of the cloud of ∼2 M’. Note that Hotzel et al. (2002a) argue that B68 is substantially closer (∼80 pc) than the 125 pc used by Alves et al. (2001a) which would make the cloud smaller and less massive.
The Alves et al. (2001a) paper has led to intense interest in B68 and its basic physical and chemical properties have now become well constrained. Several measurement of the gas and dust temperatures have been made. ISOPHOT observations by Langer & Willacy (2001) indicate a cold central dust temperature of 7K surrounded by a warmer envelope. Hotzel et al. (2002b) use ammonia inversion lines to measure a gas kinetic temperature of 10 ± 1.2 K. Similarly, Lada et al. (2003) find a gas temperature of 10.5 K from 12CO measurements in B68. These results are entirely consistent with continuum submillimetre observations and radiative transfer models of this and other sources of similar evolutionary age (Evans et al. 2001). These models clearly show that the cores possess significant temperature structure, with a warmer (∼10-15 K) envelope surrounding a colder (∼5–8 K) inner region.
The above temperatures are also consistent with molecular observations: The species used for calculating the gas temperature show evidence for heavy depletion due to freeze-out on to dust grains in the central regions of B68. Indeed, dust emissivity measurements by Bianchi et al. (2003) point to ice-covered coagulated grains in the core of B68. The depleted species include H2O, NH3, CO, CS and even N2 H+ (Bergin et al. 2002; Bergin & Snell 2002; Hotzel et al. 2002a; Di Francesco et al. 2002; Lai et al. 2003). For reasons that are still not clear, N2H+ is found to be remarkably resistant to freeze-out and it traces matter to surprisingly high densities in many cloud cores. The chemistry of N2H+ is relatively simple; it is formed by reaction of N2 with H+3 and destroyed by dissociative recombination and reaction with CO. The main loss route for CO itself is reaction with H+3. The high N2H+ abundances that are seen in many regions of moderate to high depletion has previously been ascribed to the low surface binding energies of N2 and related species, but recent laboratory and theoretical work suggests that the binding energies are probably larger than previously thought. In any case, at very high densities and after long periods of time, even N2H+ will freeze out. In B68, Bergin et al. (2002) estimate that N2H+ is depleted by a factor of 2 (between Av∼ 2-17), whilst Di Francesco et al. (2002) suggest that the level of depletion may be an order of magnitude larger. The central density of B68 is not anomalously high, so the obvious conclusion is that the core has been quasi-static for an exceptionally long period of time.
The chemical determination that B68 has a long lifetime is important in understanding the evolution of the cloud because both stable and unstable Bonnor-Ebert spheres have an approximate balance of thermal and gravitational forces, provided the clouds are not in free fall (Keto & Field 2005). Therefore, observations of structure consistent with an approximate balance of forces is an ambiguous indicator of the evolutionary fate of a cloud.
The observations of starless cores such as B68 often show spectral line profiles indicating large-scale gas motions. If interpreted in terms of simple contraction or expansion, the clouds could not have lifetimes longer than a crossing time. If a starless core can exhibit significant internal motions yet not ultimately collapse or evanesce, this would have profound implications for the continuing attempts to firmly identify infalling prestellar cores and test the competing dynamical models of star formation.
The spectral line observations of Lada et al. (2003) show profiles that are all double-peaked and asymmetric but, most remarkably, they alternate between being red asymmetric and blue asymmetric across the core. These observations consist of CS J = 2-1 line profiles and a velocity centroid map of C18O J = 2−1. In this Letter we present additional molecular line observations of HCO+J = 3−2 in a two-dimensional pattern covering the face of B68. In Section 2 these profiles are presented and compared with the data of Bergin et al. (2002). Section 3 describes a dynamical model for this cloud to account for the shapes of the line profiles, and conclusions are drawn in Section 4.
James Clerk Maxwell Telescope (JCMT) observations of the HCO+J = 3−2 line were collected gradually in service observing mode over the year from 2003 August to 2004 August. In addition to observing across the east-west strip of points examined by Lada et al. (2003), data were also gathered from several other strips in order to build up a map of 38 separate pointings. The Lada et al. (2003)CS J = 2-1 data] are reproduced in Fig. 3. Fig. 4 shows the location of the JCMT pointing positions against the Alves et al. (2001a) image of B68. A good signal-to-noise ratio at each point was preferred over additional pointings in order that the substructure of the line profile could be adequetely detected. The data were reduced in the standard manner using the specx package in the starlink suite of astronomical software. A beam efficiency of 0.65 was used to convert the temperatures to the Tmb scale.
Fig. 5 is a map of the HCO+J = 3−2 line profiles. Individual panels are separated by 10 arcsec to the north and/or east. The central east-west profiles are at the same declination as the Lada et al. (2003) profiles reproduced in Fig. 3. Comparing the profiles it is immediately obvious that the pattern of asymmetry changes in the CS J = 2-1 line observed by Lada et al. (2003) is present in exactly the same way in the HCO+J = 3−2 line. The rest of the data show that the distribution of the asymmetric profiles exhibits some overall order in that there are large contiguous blocks of red or blue asymmetric profiles. Lada et al. (2003) also used the difference of the centroid velocities between their C18O and CS J = 2-1 data to construct a map of the asymmetries across the face of B68. Again, the line profiles obtained here match this distribution of red and blue asymmetries closely. The fact that species/transitions with different chemical behaviours and excitation characteristics apparently trace the same kinematics is indicative of bulk motions propagating deep into the core (but traced no deeper than the freeze-out radius: cf. the N 2H+ data of Lada et al. (2003), which exhibit somewhat different kinematics extending to the very centre of the core), rather than disturbances in the surface layers. In this context, it is interesting to note (see Fig. 6) that the velocity of the self-absorption dips does not vary significantly across the source. This would again suggest that the origin of the kinematics and the reversal of the line profile asymmetry is due to dynamical activity extending deep into the cloud.
Discussion and Model
The observed velocity pattern is very hard to explain with simple combinations of infall, outflow or rotation (or depletion). For an optically thick cloud undergoing collapse, blue asymmetric line profiles are expected everywhere. For a rotating cloud with no infall, an ordered set of red asymmetric and blue asymmetric profiles are obtained either side of the rotation axis (Redman et al. 2004). The red and blue asymmetric profiles cannot be caused by an outflow because there is no central source to power the one present in B68. Because the pattern of asymmetry is present in two different tracer species then, as described above, it is likely an effect of gas motion, i.e. a dynamical effect as opposed to an effect which varies by species such as line generation or depletion. So a new mechanism is required that could produce strong enough dynamical activity that the cloud can exhibit such readily observable asymmetric profiles.
Keto & Field (2005) analysed the hydrodynamical response of Bonnor-Ebert spheres to external pressure disturbances. They found that stable starless cores (i.e. those on the stable branch of the Bonnor-Ebert sphere solution curve) can undergo bulk compression or expansion motions that do not tip the core into gravitational collapse, provided the amplitude of the perturbation is not too large. Such a model naturally explains the observed origin of the pulsation as deriving from motions within the inner parts of the core.
We model B68 as a Bonnor-Ebert sphere that is internally supported by thermal pressure and initially in pressure equilibrium with the external medium. The cloud is initially in critical equilibrium and stable against gravitational collapse. The initial conditions of the model cloud are listed in Table 1. We then follow the evolution of the cloud in two different scenarios. In the first case the external pressure increases by a factor of 4 and is held constant thereafter, and in the second case the pressure decreases by a factor of 4. The resultant hydrodynamics are treated one-dimensionally for simplicity, and the density, velocity, pressure and temperature are calculated. To compare the model with observations, a molecular line radiative transfer code (Keto & Field 2005; Redman et al. 2004) is employed to calculate the spectral line profiles of HCO+ across the cloud, assuming constant abundance of HCO+.
Sample results of the calculations are presented in Fig. 7. The results show that the 1D cloud model can exhibit profiles that are either red or blue asymmetric depending on whether contraction or expansion is taking place. The HCO+J = 3−2 spectral line profiles shape closely match our observed spectra and our model also predicts the profiles of the HCO+J = 1-0 and HCO+J = 4-3 lines. We make the firm prediction that observations of Barnard 68 taken in the HCO+J = 1-0 line should reveal an identical asymmetry pattern as pronounced as that in the HCO+J = 3−2 data presented here and that the HCO+J = 4-3 line will be weak and single-peaked. Calculations were also performed for the CS molecule and similar results (not shown here) obtain and match the CS J = 2-1 data of Lada et al. (2003).
The data show a mixture of red and blue asymmetric profiles simultaneously across the cloud rather than a single set of expanding or contracting motions, but it seems reasonable that in a real cloud different portions of the cloud could be in different phases of the cycle. These higher-order non-radial modes may be excited in the cloud by external pressure perturbations, similar to the mechanism envisaged by Lada et al. (2003) to explain their results. Keto et al (in preparation) have calculated the line profiles that would result from an analytic model of modes of oscillation and find that zones of expansion and contraction produce red and blue assymmetric spectra similar to those seen in B68.
It should soon be possible to attempt a fully 3D analysis of B68 in which the hydrodynamics, the dust continuum radiative transfer, chemistry and molecular line radiative transfer are all carried out self-consistently. Most of the ingredients are already available: a 3D hydrodynamic code could be combined with the 3D dust density distribution (recently constrained by J. Steinacker et al, in preparation). Dark cloud chemistry models are available that are beginning to include freeze-out and the radiative transfer can be calculated in three dimensions with our code.
New observational data confirms that B68 exhibits split asymmetric molecular line profiles that indicate significant dynamical activity in the core. We favour a simple model in which the variety of spectral line profiles across the face of the cloud are the result of oscillatory motions about a state of gravitational equilibrium. The oscillations could have been started by a disturbance in the external pressure. A simple numerical hydrodynamic model in one dimensions that follows the evolution of an equilibrium Bonnor-Ebert sphere subject to a change in external pressure reproduces spectral line profiles similar to those observed. This simple model suggests that a more complex model that allowed for three-dimensional oscillations could reproduce the variety of spectral line profiles across the face of the cloud.
At a very general level, this study reinforces the need for caution, as emphasized by Rawlings & Yates (2001) and others, in the interpretation of line profiles observed along single lines of sight. A variety of dynamical activities, including rotation, non-spherical outflows and - as shown in this paper - pulsation, can mimic the characteristics of simple spherically symmetric inflow.
The depletion of molecular species observed toward the centre of the cloud suggests that the cloud must have a lifetime long enough (say, a few million years) to allow collisional processes to deplete the molecules from the gas phase by freeze-out on to grains. Turbulent models for the interstellar medium tend to indicate rapid star formation, as localized dissipation of energy leads to stars ‘condensing’ out of molecular clouds. Typically, in these models the star formation process is not traced beyond the formation of a Jeans mass worth of cloud because of resolution issues; the star is assumed to appear on a collapse time-scale once a suitable prestellar core has formed. This process of density change is not necessarily one way. In another picture, slow-mode magnetohydrodynamical waves allow for the formation and then dissipation of density enhancements Falle & Hartquist (2002), Garrod et al. (2005). The chemistry of some molecular clouds appears to support this latter view, in that the presence of several species is most plausibly explained if the cloud has undergone several such enhancements and contractions.
The combination of the oscillatory motions, an internal structure consistent with equilibrium, and a lifetime greater than several crossing times suggests that long-lived pressure supported clouds may exist in the turbulent ISM. Some part of the inefficiency of star formation may be due to formation of long-lived clouds. Many objects like B68 will promptly condense out of a turbulent medium, marking the endpoint of the supersonic turbulence cascade, but only a subset are destined to continue to collapse all the way to becoming a star. The rest will remain as stable starless cores, eventually to be dissipated or triggered into collapse by external effects due to nearby massive stars and supernovae. The observational challenge is to identify those objects most likely to collapse with the difficulty, shown here, that some stable starless cores may exhibit strong evidence of dynamical activity yet, paradoxically, be perfectly stable against collapse.
We thank the referee, C. Lada, for a helpful report. MPR was supported by the UK PPARC and the Ireland IRCSET during the early stages of this work. We thank the staff of the JCMT and visiting observers for obtaining the observations. The JCMT is operated by the JAC, Hawaii, on behalf of the UK PPARC, the Netherlands NWO, and the Canadian NRC. We thank Gary Stevens for permission to reproduce Fig. 1. Fig. 3 has been reproduced, with permission, from Astrophysical Journal, published by The University of Chicago Press. (© 2003 by the American Astronomical Society. All rights reserved.)