Models of Bright Rim Clouds

The evolution of bright rim clouds are primarily determined by two dimensionless parameters: the ratio of the ionised gas and the initial cloud's densities, and the fraction of UV photons absorbed in a thin ionised boundary layer at the front of the cloud. Additionally the dynamics of gas in the head of the globule will be influenced by the propagation of an isothermal shock. After about 105 years, a dense core will be formed inside the head, whilst the compression continues deeper into the cloud, eventually forming small ansae along the major axis of the cloud (i.e. aligned with the direction of the illuminating stars responsible for the RDI). At this stage the density contrast between the core and the initial cloud material will be about one order of magnitude. Finally, the cloud enters a quasi-equilibrium state, when the cometary head becomes confined by over-pressure of the ionised gas. The globule, and its now well developed tail structure, will ultimately acquire a bulk velocity away from the external radiation source at velocities of typically 10kms-1.
The effect of external radiation on a globule has been shown to lead to the Radiation Driven Implosion (RDI) of a cloud, followed by the formation of a dense core extended along the cloud's axis. This process occurs in two phases; an early collapse phase as the effect of the ionising radiation compresses and ionises the globule, and a cometary phase in which the external ionised gas shields the tail from ionising radiation and pressure confines the head, leading to a long-lived head-tail morphology. During this latter phase of the globule's evolution, it moves away from the illuminating source at a velocity of kms-1 . We have modelled the observationally constrained characteristics of the head of Globule 1.
This 2-D hydrodynamical simulation describes the formation and evolution of a cometary globule as a consequence of a radiatively driven implosion. In this model, the cloud is treated as an isothermal sphere of cold dense gas, surrounded by a hot ambient medium initially in pressure equilibrium. Its evolution is primarily determined by two dimensionless parameters: the ratio of the ionised gas and the initial cloud's densities, and the fraction of UV photons absorbed in a thin ionised boundary layer at the front of the cloud. Additionally the dynamics of gas in the head of the globule will be influenced by the propagation of an isothermal shock. After about 105 years, a dense core will be formed inside the head, whilst the compression continues deeper into the cloud, eventually forming small ansae along the major axis of the cloud (i.e. aligned with the direction of the illuminating stars responsible for the RDI). At this stage the density contrast between the core and the initial cloud material will be about one order of magnitude. Finally, the cloud enters a quasi-equilibrium state, when the cometary head becomes confined by over-pressure of the ionised gas. The globule, and its now well developed tail structure, will ultimately acquire a bulk velocity away from the external radiation source at velocities of typically 10kms-1.
The evolution of the cloud is not very sensitive to the ionisation parameters. We selected model 2 of LL94 for its evolutionary stage, by looking for the best kinematical and morphological match with the observations. Note that in our simulation, we adopt a planar illumination, perpendicular to the cloud's major axis. This means that we neglect any possible influence of the UV flux from the Rosette Nebula when comparing the results with Globule 1 (this point is discussed further below). To facilitate comparison between the simulations and the data, we scaled the numerical results to match the radii of the simulated globule and of Globule 1 (see LL94).
The figure opposite shows an RDI simulation of the major axis position velocity data. The model assumes a velocity dispersion of 1.5km s-1 , equivalent to a half-power linewidth of 3.5kms-1 (with a viewing angle of 20 degrees from the normal). The contour levels follow the style of LL94, and are in arbitrary units of density following the relationship log = m/2, where m is an integer in the range -1 to 4.
Rather than calculating a series of velocity-channel maps which attempt to match all of the details of the gas kinematics, we found it more interesting to simulate the on-axis position velocity diagram. We have integrated this across the globule's width to lay stress on the main kinematical features, rather than try to model every small detail of the kinematics. The RDI model successfully simulates the large velocity gradient in the main body of the globule, as well as recovering the kinematics of the blue and red wings. The characteristics of the simulated globule are compared with the observed characteristics inferred for Globule 1 in Table 1, in which we have adopted a value for the illuminating flux from Patel et al. (1993). The simulated density distribution of the globule is shown below. The contour levels are in arbitrary units following the style of LL94.
There is thus reasonably good agreement between the model predictions and the observed characteristics of Globule 1. The simulation suggests that Globule 1 has nearly reached the maximum compression stage following the initial collapse phase, just prior to entering the quasi-static cometary phase.
The model used in this paper is based on the simplest hypothesis; the description of the finer details seen in the observations would have been at the cost of making assumptions about many more parameters (such as the initial density profile), and therefore might have appeared less convincing in this respect. It is no wonder that the model fails to reproduce some of the kinematic features of Globule 1 - as mentioned above, our boundary conditions are different for the UV flux, since we cannot accurately take into account the illumination from the Rosette Nebula stars, although these must these have an effect on the evolution of the globule, as can be seen from the figure opposite. The sign of the velocity gradient in the tail suggests that the head of the globule points out of the plane of the sky at an angle of 20 degrees - explaining why the blue wing is seen to be slightly ahead of the redshifted component.
The differences between the velocity gradient predicted by the model and that observed in the data, and in the shape of the observed/simulated tail are the likely consequences of simplifications in our model. In particular, the observed 'bending' of the redshifted tail component and the 'hole' produced in the faintest part of the tail of the simulated cloud are not simultaneously matched to the data and simulation. Nevertheless, the relatively good agreement between the other observations and the simulation suggests either that the globule has rotated significantly after the initiation of RDI, or more likely that the collapse is being influenced by one or more of the nearby IRAS sources. It is not clear how the bulk velocity of the ambient material in Globule 1 is related to the larger scale kinematics of the surrounding gas. Blitz & Stark (1986) averaged together 3000 13 CO spectra of the Rosette Molecular Cloud, finding gas velocities ranging from km s . The 13 CO maps of Blitz & Thaddeus (1980) indicated that the mean velocity of the extended gas near to the globule has a similar range to that found by Blitz and Stark (1986), meaning that Globule 1 has a mean velocity difference of km s relative to nearby (i.e. line of sight or background) gas. Velocity differences of this magnitude are similar to those modelled by Bertoldi & McKee (1990) and LL94 for cometary globules in the pre-cometary phase at an age of 200,000 years.
Patel et al. (1993) have noted that the column densities and ionising flux at the surface of Globule 1 are well described by the Bertoldi (1989) model, for a cloud which is compressed by an ionisation front-driven shock, with a thin external ionisation boundary layer around the head. Our derived column densities are similar to those estimated by Patel et al. (1993), and support their general conclusions. The present results do however go much further in suggesting the presence of excited material around the leading edge of the globule The most likely explanation of this is that it lies close to the ionised boundary layer, and may trace the precursor shock to the ionisation front.