Helical fields and filamentary molecular clouds – I

We study the equilibrium of pressure truncated, filamentary molecular clouds that are threaded by rather general helical magnetic fields. We first apply the virial theorem to filamentary molecular clouds, including the effects of non-thermal motions and the turbulent pressure of the surrounding ISM. When compared with the data, we find that many filamentary clouds have a mass per unit length that is significantly reduced by the effects of external pressure, and that toroidal fields play a significant role in squeezing such clouds.
We also develop exact numerical MHD models of filamentary molecular clouds with more general helical field configurations than have previously been considered. We examine the effects of the equation of state by comparing 'isothermal' filaments, with constant total (thermal plus turbulent) velocity dispersion, with equilibria constructed using a logatropic equation of state.
Our theoretical models involve three parameters: two to describe the mass loading of the toroidal and poloidal fields, and a third that describes the radial concentration of the filament. We thoroughly explore our parameter space to determine which choices of parameters result in models that agree with the available observational constraints. We find that both equations of state result in equilibria that agree with the observational results. Moreover, we find that models with helical fields have more realistic density profiles than either unmagnetized models or those with purely poloidal fields; we find that most isothermal models have density distributions that fall off as r ^−1.8 to r ⁻², while logatropes have density profiles that range from r ⁻¹ to r ^−1.8. We find that purely poloidal fields produce filaments with steep radial density gradients that are not allowed by the observations.     

Formation of interstellar clouds: Parker instability with phase transitions

We numerically follow the nonlinear evolution of the Parker instability in the presence of phase transitions from a warm to a cold H  i interstellar medium in two spatial dimensions. The nonlinear evolution of the system favours modes that allow the magnetic field lines to cross the galactic plane. Cold H  i clouds form with typical masses  ≃10⁵ M_⊙  , mean densities  ≃20 cm⁻³  , mean magnetic-field strengths  ≃4.3 μG  (rms field strengths  ≃6.4 μG  ), mass-to-flux ratios  ≃0.1–0.3  relative to critical, temperatures  ≃50 K  , (two-dimensional) turbulent velocity dispersions  ≃1.6 km s⁻¹  and separations  ≃500 pc  , in agreement with observations. The maximum density and magnetic-field strength are  ≃10³ cm⁻³  and  ≃20 μG  , respectively. Approximately 60 per cent of all H  i mass is in the warm neutral medium. The cold neutral medium is arranged into sheet-like structures both perpendicular and parallel to the galactic plane, but it is also found almost everywhere in the galactic plane, with the density being highest in valleys of the magnetic field lines. 'Cloudlets' also form whose physical properties are in quantitative agreement with those observed for such objects by Heiles. The nonlinear phase of the evolution takes ≲30 Myr, so that, if the instability is triggered by a nonlinear perturbation such as a spiral density shock wave, interstellar clouds can form within a time suggested by observations.     

Driven waves in a two-fluid plasma

We study the physics of wave propagation in a weakly ionized plasma, as it applies to the formation of multifluid, magnetohydrodynamics (MHD) shock waves. We model the plasma as separate charged and neutral fluids which are coupled by ion–neutral friction. At times much less than the ion–neutral drag time, the fluids are decoupled and so evolve independently. At later times, the evolution is determined by the large inertial mismatch between the charged and neutral particles. The neutral flow continues to evolve independently; the charged flow is driven by and slaved to the neutral flow by friction. We calculate this driven flow analytically by considering the special but realistic case where the charged fluid obeys linearized equations of motion. We carry out an extensive analysis of linear, driven, MHD waves. The physics of driven MHD waves is embodied in certain Green functions which describe wave propagation on short time-scales, ambipolar diffusion on long time-scales and transitional behaviour at intermediate times. By way of illustration, we give an approximate solution for the formation of a multifluid shock during the collision of two identical interstellar clouds. The collision produces forward and reverse J shocks in the neutral fluid and a transient in the charged fluid. The latter rapidly evolves into a pair of magnetic precursors on the J shocks, wherein the ions undergo force-free motion and the magnetic field grows monotonically with time. The flow appears to be self-similar at the time when linear analysis ceases to be valid.     

Collapse and fragmentation of rotating magnetized clouds – I. Magnetic flux–spin relation

We discuss the evolution of the magnetic flux density and angular velocity in a molecular cloud core, on the basis of three-dimensional numerical simulations, in which a rotating magnetized cloud fragments and collapses to form a very dense optically thick core of  >5 × 10¹⁰ cm⁻³  . As the density increases towards the formation of the optically thick core, the magnetic flux density and angular velocity converge towards a single relationship between the two quantities. If the core is magnetically dominated its magnetic flux density approaches  1.5( n /5 × 10¹⁰ cm⁻³)^1/2 mG  , while if the core is rotationally dominated the angular velocity approaches  2.57 × 10⁻³ ( n /5 × 10¹⁰ cm⁻³)^1/2 yr⁻¹  , where n is the density of the gas. We also find that the ratio of the angular velocity to the magnetic flux density remains nearly constant until the density exceeds  5 × 10¹⁰ cm⁻³  . Fragmentation of the very dense core and emergence of outflows from fragments will be shown in the subsequent paper.     

Temporal evolution of MHD shocks in the interstellar medium

We undertake calculations of the time-dependent structure of shock waves propagating in dark and diffuse interstellar clouds. The results of the time-dependent model are compared with those obtained by means of an independent steady-state code and found to agree well at sufficiently late times. Discontinuities in the flow of the neutral fluid are handled by introducing a pseudo-viscosity. Special procedures are adopted to correct for the associated widening of the discontinuity, in order not to distort the role of inelastic collision processes. We find that, in dark clouds, C shocks will tend to predominate, but are unlikely to have attained steady state in the cloud lifetime. On the other hand, in diffuse clouds, steady state may be reached but the discontinuity in the flow of the neutral fluid remains. We find no evidence for the existence of C* shocks, in which the neutral fluid undergoes a continuous transition from supersonic to subsonic flow (in the reference frame of the shock wave). Attention is drawn to the possible importance of these results for the interpretation of H₂ rovibrational line intensities.     

The possibility of nitrogen isotopic fractionation in interstellar clouds

The possibility of nitrogen isotopic fractionation owing to ion–molecule exchange reactions involving the most abundant N-containing species in dense interstellar clouds has been explored. We find that exchange reactions between N atoms and N-containing ions have most influence on the fractionation, although the extent of fractionation is too small to be readily detectable.     

A study of interstellar Na i D absorption lines towards the Lupus molecular clouds

Intermediate-resolution (60 000 R 120 000) observations of interstellar Na  i lines towards 29 stars in the general direction of the Lupus molecular clouds (330°≲ l ≲350°; 0°≲ b ≲25°) are presented. Previously published spectra towards an additional seven stars are also included. Based on the Hipparcos distances to these stars, and the minimum distance at which strong interstellar Na  i lines appear in the spectra, I obtain a distance of ~150±10 pc to the Lupus molecular complex. While in agreement with a number of other independent estimates, this result is at odds with the value of 100 pc recently obtained by Knude & Høg from a Hipparcos -based study of interstellar extinction. A possible explanation for this discrepancy is discussed, and it is concluded that the value of 150±10 pc obtained here is to be preferred. In addition, these observations have some other implications for the structure of the interstellar medium in this direction, and these are briefly considered.     

Statistical assessment of shapes and magnetic field orientations in molecular clouds through polarization observations

We present a novel statistical analysis aimed at deriving the intrinsic shapes and magnetic field orientations of molecular clouds using dust emission and polarization observations by the Hertz polarimeter. Our observables are the aspect ratio of the projected plane-of-the-sky cloud image and the angle between the mean direction of the plane-of-the-sky component of the magnetic field and the short axis of the cloud image. To overcome projection effects due to the unknown orientation of the line-of-sight, we combine observations from 24 clouds, assuming that line-of-sight orientations are random and all are equally probable. Through a weighted least-squares analysis, we find that the best-fitting intrinsic cloud shape describing our sample is an oblate disc with only small degrees of triaxiality. The best-fitting intrinsic magnetic field orientation is close to the direction of the shortest cloud axis, with small  (∼24°)  deviations towards the long/middle cloud axes. However, due to the small number of observed clouds, the power of our analysis to reject alternative configurations is limited.     

Starlight polarization and CO observations towards the Lupus clouds

We performed an observational study of the dark filaments Lupus 1 and Lupus 4 using both polarimetric observations of 190 stars and a sample of 72 ¹²CO profiles towards these clouds. We have estimated lower limits to the distances of Lupus 1 and Lupus 4 (≳ 140 and ≳ 125 pc, respectively). The observational strategy of the survey allows us to compare the projected magnetic field in an extended area around each cloud with the magnetic field direction observed to prevail along the clouds. Lupus 4 could have collapsed along the magnetic field lines, while in Lupus 1 the magnetic field appears to be less ordered, having the major axis of the filaments parallel to the large-scale projected magnetic field. These differences would imply that both filaments have different pattern evolutions. From the CO observations we have probed the velocity fields of the filaments and the spatial extension of the molecular gas with respect to the dust.     

Three-dimensional simulations of molecular cloud fragmentation regulated by magnetic fields and ambipolar diffusion

We employ the first fully three-dimensional simulation to study the role of magnetic fields and ion–neutral friction in regulating gravitationally driven fragmentation of molecular clouds. The cores in an initially subcritical cloud develop gradually over an ambipolar diffusion time while the cores in an initially supercritical cloud develop in a dynamical time. The infalling speeds on to cores are subsonic in the case of an initially subcritical cloud, while an extended (≳0.1 pc) region of supersonic infall exists in the case of an initially supercritical cloud. These results are consistent with previous two-dimensional simulations. We also found that a snapshot of the relation between density (ρ) and the strength of the magnetic field ( B ) at different spatial points of the cloud coincides with the evolutionary track of an individual core. When the density becomes large, both the relations tend to   B ∝ρ^0.5  .     

Dense and diffuse gas in dynamically active clouds

We investigate the chemical and observational implications of repetitive transient dense core formation in molecular clouds. We allow a transient density fluctuation to form and disperse over a period of 1 Myr, tracing its chemical evolution. We then allow the same gas immediately to undergo further such formation and dispersion cycles. The chemistry of the dense gas in subsequent cycles is similar to that of the first, and a limit cycle is reached quickly (2–3 cycles). Enhancement of hydrocarbon abundances during a specific period of evolution is the strongest indicator of previous dynamical history. The molecular content of the diffuse background gas in the molecular cloud is expected to be strongly enhanced by the core formation and dispersion process. Such enhancement may remain for as long as 0.5 Myr. The frequency of repetitive core formation should strongly determine the level of background molecular enhancement.
We also convolve the emission from a synthesized dark cloud, comprised of ensembles of transient dense cores. We find that the dynamical history of the gas, and therefore the chemical state of the diffuse intercore medium, may be determined if a sufficient sample of cores is present in an ensemble. Molecular ratios of key hydrocarbons with SO and SO₂ are crucial to this distinction. Only surveys with great enough angular resolution to resolve individual cores, or very small groupings, are expected to show evidence of repetitive dynamical processing. The existence of non-equilibrium chemistry in the diffuse background may have implications for the initial conditions used in chemical models. Observed variations in the chemistries of diffuse and translucent regions may be explained by lines of sight which intersect a number of molecular cloud cores in various stages of evolution.     

The formation of molecular clouds

In a recent paper, Elmegreen has made a cogent case, from an observational point of view, that the lifetimes of molecular clouds are comparable to their dynamical time-scales. If so, this has important implications for the mechanisms by which molecular clouds form. In particular, we consider the hypothesis that molecular clouds may form not by in situ cooling of atomic gas, but rather by the agglomeration of the dense phase of the interstellar medium, much, if not most, of which is already in molecular form.     

The interstellar clouds of adams and blaauw revisited: An HI absorption study-I

This investigation is aimed at clarifying the nature of the interstellar gas seen in absorption against bright O and B stars. Towards this end we have obtained for the first time HI absorption spectra towards radio sources very close to the lines of sight towards twenty five bright stars previously studied. In this paper we describe the selection criteria, the details regarding our observations, and finally present the absorption spectra. In the accompanying paper we analyse the results and draw conclusions.