Temporal evolution of magnetic molecular shocks II. Analytics of the steady state and semi-analytical construction of intermediate ages

In the first paper of this series (Paper I) we computed time dependent simulations of multifluid shocks with chemistry and a transverse magnetic field frozen in the ions, using an adaptive moving grid. In this paper, we present new analytical results on steady-state molecular shocks. Relationships between density and pressure in the neutral fluid are derived for the cold magnetic precursor, hot magnetic precursor, adiabatic shock front, and the following cooling layer. The compression ratio and temperature behind a fully dissociative adiabatic shock is also derived. To prove that these results may even hold for intermediate ages, we design a test to locally characterise the validity of the steady state equations in a time-dependent shock simulation. Applying this tool to the results of Paper I, we show that most of these shocks (all the stable ones) are indeed in a quasi-steady state at all times, i.e. : a given snapshot is composed of one or more truncated steady shock. Finally, we use this property to produce a construction method of any intermediate time of low velocity shocks (u < 20 km/s) with only a steady-state code. In particular, this method allows one to predict the occurrence of steady CJ-type shocks more accurately than previously proposed criteria.Comment: A&A in pres

An Explicit Scheme for Incorporating Ambipolar Diffusion in a Magnetohydrodynamics Code

We describe a method for incorporating ambipolar diffusion in the strong coupling approximation into a multidimensional magnetohydrodynamics code based on the total variation diminishing scheme. Contributions from ambipolar diffusion terms are included by explicit finite difference operators in a fully unsplit way, maintaining second order accuracy. The divergence-free condition of magnetic fields is exactly ensured at all times by a flux-interpolated constrained transport scheme. The super time stepping method is used to accelerate the timestep in high resolution calculations and/or in strong ambipolar diffusion. We perform two test problems, the steady-state oblique C-type shocks and the decay of Alfv\'en waves, confirming the accuracy and robustness of our numerical approach. Results from the simulations of the compressible MHD turbulence with ambipolar diffusion show the flexibility of our method as well as its ability to follow complex MHD flows in the presence of ambipolar diffusion. These simulations show that the dissipation rate of MHD turbulence is strongly affected by the strength of ambipolar diffusion.Comment: 25 pages, 5 figures, ApJS accepte

L1521E: the first starless core with no molecular depletion

L1521E seems unique among starless cores. It stands out in a distribution of a ratio (R) that we define to asses core evolution, and which compares the emission of the easily-depleted C18O molecule with that of the hard to deplete, late-time species N2H+. While all cores we have studied so far have R ratio lower than 1, L1521E has an R value of 3.4, which is 8 times the mean of the other cores. To understand this difference, we have modeled the C18O and N2H+ abundance profiles in L1521E using a density distribution derived from 1.2mm continuum data. Our model shows that the C18O emission in this core is consistent with constant abundance, and this makes L1521E the first core with no C18O depletion. Our model also derives an unusually low N2H+ abundance. These two chemical peculiarities suggest that L1521E has contracted to its present density very recently, and it is therefore an extremely young starless core. Comparing our derived abundances with a chemical model, we estimate a tentative age of 1.5 x 10^5 yr, which is too short for ambipolar diffusion models.Comment: 4 pages, 3 figure

The initial conditions of isolated star formation - VI. SCUBA mapping of prestellar cores

Observations have been carried out with SCUBA at the JCMT of 52 molecular cloud cores that do not contain any sign of protostellar activity. These are all therefore candidate prestellar cores, which are believed to represent the stage of star formation that precedes the formation of a protostar. 29 of the 52 cores were detected at 850 microns at varying levels of signal-to-noise ratio greater than 3 sigma at peak. The detected cores were split into 'bright' cores and `intermediate' cores, depending on their peak flux density at 850 microns. Cores with peak 850 microns flux densities greater than 170 mJy/beam were designated 'bright' (13 cores), while those flux densities below this value were designated 'intermediate' (16 cores). This dividing line corresponds to A_v~50 under typical assumptions. The data are combined with our previously published ISO data, and the physical parameters of the cores, such as density and temperature, are calculated. Detailed fitting of the bright core radial profiles shows that they are not critical Bonnor-Ebert spheres, in agreement with previous findings. However, we find that intermediate cores, such as B68 (which has previously been claimed to be a Bonnor-Ebert sphere), may in fact be consistent with the Bonnor-Ebert criterion, suggesting perhaps that cores pass through such a phase during their evolution. We make rough estimates of core lifetimes based on the statistics of detections and find that the lifetime of a prestellar core is roughly ~3x10^5 years, while that of a bright core is \~1.5x10^5 years. Comparisons with some magnetic and turbulence regulated collapse models show that no model can match all of the data. Models that are tuned to fit the total prestellar core lifetime, do not predict the relative numbers of cores seen at each stage.Comment: 23 pages, 52 figures, accepted by MNRAS, alternate PDF w/all figures available from http://www.astro.cf.ac.uk/pub/Derek.Ward-Thompson/publications.htm

Optical and submillimetre observations of Bok globules -- tracing the magnetic field from low to high density

We present optical and submillimetre polarimetry data of the Bok globule CB3 and optical polarimetry data of the Bok globule CB246. We use each set of polarimetry data to infer the B-field orientation in each of the clouds. The optical data can only be used in the low density, low extinction edge regions of clouds. The submillimetre data can only be used in the high column-density, central regions of the clouds. It has previously been found that near-infrared polarisation mapping of background stars does not accurately trace the magnetic field in dense cloud regions. This may be due to a lack of aligned grains in dense regions. We test this by comparing the field orientations measured by our two independent polarimetry methods. We find that the field orientation deduced from the optical data matches up well with the orientation estimated from the submillimetre data. We therefore claim that both methods are accurately tracing the same magnetic field in CB3. Hence, in this case, there must be significant numbers of aligned dust grains in the high density region, and they do indeed trace the magnetic field in the submillimetre. We find an offset of 40$\pm$14 degrees between the magnetic field orientation and the short axis of the globule. This is consistent with the mean value of 31$\pm$3 degrees found in our previous work on prestellar cores, even though CB3 is a protostellar core. Taken together, the six prestellar cores that we have now studied in this way show a mean offset between magnetic field orientation and core short axis of $\sim30\pm$3 degrees, in apparent contradiction with some models of magnetically dominated star formation.Comment: 8 pages, 3 figures, accepted for publication in MNRA

Submillimeter Studies of Prestellar Cores and Protostars: Probing the Initial Conditions for Protostellar Collapse

Improving our understanding of the initial conditions and earliest stages of protostellar collapse is crucial to gain insight into the origin of stellar masses, multiple systems, and protoplanetary disks. Observationally, there are two complementary approaches to this problem: (1) studying the structure and kinematics of prestellar cores observed prior to protostar formation, and (2) studying the structure of young (e.g. Class 0) accreting protostars observed soon after point mass formation. We discuss recent advances made in this area thanks to (sub)millimeter mapping observations with large single-dish telescopes and interferometers. In particular, we argue that the beginning of protostellar collapse is much more violent in cluster-forming clouds than in regions of distributed star formation. Major breakthroughs are expected in this field from future large submillimeter instruments such as Herschel and ALMA.Comment: 12 pages, 9 figures, to appear in the proceedings of the conference "Chemistry as a Diagnostic of Star Formation" (C.L. Curry & M. Fich eds.

Multifluid, Magnetohydrodynamic Shock Waves with Grain Dynamics II. Dust and the Critical Speed for C Shocks

This is the second in a series of papers on the effects of dust on multifluid, MHD shock waves in weakly ionized molecular gas. We investigate the influence of dust on the critical shock speed, v_crit, above which C shocks cease to exist. Chernoff showed that v_crit cannot exceed the grain magnetosound speed, v_gms, if dust grains are dynamically well coupled to the magnetic field. We present numerical simulations of steady shocks where the grains may be well- or poorly coupled to the field. We use a time-dependent, multifluid MHD code that models the plasma as a system of interacting fluids: neutral particles, ions, electrons, and various ``dust fluids'' comprised of grains with different sizes and charges. Our simulations include grain inertia and grain charge fluctuations but to highlight the essential physics we assume adiabatic flow, single-size grains, and neglect the effects of chemistry. We show that the existence of a phase speed v_phi does not necessarily mean that C shocks will form for all shock speeds v_s less than v_phi. When the grains are weakly coupled to the field, steady, adiabatic shocks resemble shocks with no dust: the transition to J type flow occurs at v_crit = 2.76 v_nA, where v_nA is the neutral Alfven speed, and steady shocks with v_s > 2.76 v_nA are J shocks with magnetic precursors in the ion-electron fluid. When the grains are strongly coupled to the field, v_crit = min(2.76 v_nA, v_gms). Shocks with v_crit < v_s < v_gms have magnetic precursors in the ion-electron-dust fluid. Shocks with v_s > v_gms have no magnetic precursor in any fluid. We present time-dependent calculations to study the formation of steady multifluid shocks. The dynamics differ qualitatively depending on whether or not the grains and field are well coupled.Comment: 43 pages with 17 figures, aastex, accepted by The Astrophysical Journa

Turbulent Control of the Star Formation Efficiency

Supersonic turbulence plays a dual role in molecular clouds: On one hand, it contributes to the global support of the clouds, while on the other it promotes the formation of small-scale density fluctuations, identifiable with clumps and cores. Within these, the local Jeans length \Ljc is reduced, and collapse ensues if \Ljc becomes smaller than the clump size and the magnetic support is insufficient (i.e., the core is ``magnetically supercritical''); otherwise, the clumps do not collapse and are expected to re-expand and disperse on a few free-fall times. This case may correspond to a fraction of the observed starless cores. The star formation efficiency (SFE, the fraction of the cloud's mass that ends up in collapsed objects) is smaller than unity because the mass contained in collapsing clumps is smaller than the total cloud mass. However, in non-magnetic numerical simulations with realistic Mach numbers and turbulence driving scales, the SFE is still larger than observational estimates. The presence of a magnetic field, even if magnetically supercritical, appears to further reduce the SFE, but by reducing the probability of core formation rather than by delaying the collapse of individual cores, as was formerly thought. Precise quantification of these effects as a function of global cloud parameters is still needed.Comment: Invited review for the conference "IMF@50: the Initial Mass Function 50 Years Later", to be published by Kluwer Academic Publishers, eds. E. Corbelli, F. Palla, and H. Zinnecke

Complex Structure in Class 0 Protostellar Envelopes

We use archived IRAC images from the Spitzer Space Telescope to show that many Class 0 protostars exhibit complex, irregular, and non-axisymmetric structure within their dusty envelopes. Our 8 $\mu$m extinction maps probe some of the densest regions in these protostellar envelopes. Many of the systems are observed to have highly irregular and non-axisymmetric morphologies on scales >= 1000 AU, with a quarter of the sample exhibiting filamentary or flattened dense structures. Complex envelope structure is observed in regions spatially distinct from outflow cavities, and the densest structures often show no systematic alignment perpendicular to the cavities. These results indicate that mass ejection is not responsible for much of the irregular morphologies we detect; rather, we suggest that the observed envelope complexity is mostly the result of collapse from protostellar cores with initially non-equilibrium structures. The striking non-axisymmetry in many envelopes could provide favorable conditions for the formation of binary systems. We also note that protostars in the sample appear to be formed preferentially near the edges of clouds or bends in filaments, suggesting formation by gravitational focusing.Comment: 20 pages, 11 figures, 3 Tables, accepted to ApJ. Paper with full resolution figures available at http://www.astro.lsa.umich.edu/~jjtobin/Envelopes.pd

The Degree of CO Depletion in Pre-stellar Cores

We present new results on CO depletion in a sample of nearby pre-stellar cores, based on observations of the millimeter C17O and C18O lines and the 1.3 mm dust emission with the IRAM 30m telescope. In most cases, the distribution of CO is much flatter than that of the dust, whereas other tracers, like N2H+, still probe the latter. In the centre of these objects, we estimate CO to be underabundant by a factor 4-15 depending on the cores. The CO underabundance is more pronounced in the central regions and appears to decrease with increasing distance from the core centre. This underabundance is most likely due to the freezing out of CO onto the dust grains in the cold, dense parts of the cores. We find evidence for an increase of the CO depletion degree with the core density.Comment: 5 pages, 2 figures, A&A Letters, in pres