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Triggered Star Formation models The chemical model we have used to simulate the collapse process is an extension to that used by Nelson & Langer (ApJ 20 Oct 1999 issue) in collapse calculations for isolated molecular clouds. This models a 3D cloud of arbitrary geometry, and includes the essentials of the carbon and oxygen chemistry responsible for the majority of the cooling in the cloud. It has already been used to look at the generation of cometary cloud structures by anisotropic heating by the FUV component of the interstellar radiation field (ISRF) (Nelson & Langer in prep). In the model, the following species are evolved: CO, CI, CII, HCO+, OI, He+, H3+, H2O, OH, O2, CH2, CH, M+ and electrons. Both the chemical reaction network and the model are fully time-dependent, and model include the effects of pressure forces, self-gravity, and an artificial viscosity that allows shocks to be modelled. The thermal evolution is modelled by calculating cooling due to CII, CI, OI and CO and other molecules, and heating by cosmic ray ionisation and the FUV component of the ISRF. For the Eagle Nebula we evolved the chemistry of the clouds for 2 Myr until a steady state was attained, then switched on the OB star UV field, and evolved the chemistry for a further 105 years.
The top figure pair shows at left the density and temperature, and at right the chemical abundance profiles along a cut across the finger located 0.1 pc behind the photo-ionised outer edge of the fingertip at 105 years after the switch-on of the UV field. The temperature tends towards a value of ~ 20 K inside the dense clump. This follows since the dust and gas are strongly coupled at these relatively high densities. The chemical profiles show that CO is dominant throughout the Finger, with CI and CII becoming prominent towards the edges of the cloud. Other species such as H2O, O2, and OH become very abundant in the cloud interior. The lower pair shows our [A5] 2D RDI velocity simulation and data across for the edge of Rosette Cometary Globule 1. A substantial amount of theoretical work has already been carried out to model the evolution of dense, gaseous clumps subject to the ionising radiation of nearby OB stars. These include radiatively driven implosion (RDI) (Bertoldi ApJ 346, 735, 1989, Lefloch & Lazareff A&A 289, 559, 1994), and cometary globule models (Bertoldi & McKee ApJ 354, 529, 1990). However, these do not adequately include self-gravity (and do not address the issue of star formation), or treat the chemistry and thermal evolution in a self-consistent way. Similarly, the work by Bertoldi's group did not include full simulations of their non-linear evolution In particular our programme seeks to extend on previous work by specifically addressing the issue of star-formation. The ignition of an OB star causes an R-type ionisation front to propagate out rapidly through the inter-clump medium to the Strömgren radius. The ionised gas leads is heated to Ti ~ 104 K, and sound speeds of ci ~ 11.4 km s-1. When the R-type front reaches a dense clump, it stalls and drives a shock into the clump (RDI) until it is sufficiently compressed for a steady D-type ionisation front to be maintained.There are two distinct types of ionisation fronts, characterised by their propagation speed. The R-type (`Rarified') ionisation fronts travel through a low density medium with a velocity of uIF > 2 ci, where ci = sound speed of the ionised medium. Typically, ci ~ 11.4 km s-1. D-type (`Dense') fronts travel through denser gas with a velocity of uIF < (cI2 / 2 ci), where cI = the sound speed in the pre-ionised material and cI << ci . An intermediate front is called M-type, and results in a shock being driven into the clump (RDI stage), compressing the gas until pressure equilibrium between the ionisation front and the cloud interior is attained. Under these circumstances, the gas just ahead of the ionisation front is compressed initially by the preceding shock wave so that an approximately D-critical ionisation front is able to form (i.e. uIF = cI2 / 2 ci) behind the shock front which continues to compress the cloud ahead of it. The structure of the cloud during this implosion stage, moving from the cloud surface towards its interior, consists of a hot, photoevaporating, ionised region; an approximately D-critical ionisation front; a dense, neutral post-shock region; a shock front; and then a pre-shocked neutral region composed of the undisturbed gas in its original state. Provided that the implosion does not induce the cloud to collapse, the post-implosion cloud evolves slowly as the ionisation front slowly propagates into the cloud. In the case of the Eagle Nebula, we showed [62] that the presence of a shock front currently propagating into the fingers indicates that the dense clumps located towards their tips are not the result of RDI. When an IS-shock front propagates into a cloud, the shock front precedes the ionisation front (located at the optical surface of the cloud) by a small distance. This would preclude it from traversing the top r ~ 0.2 pc of a finger structure such as those on the Eagle Nebula, and forming the clump there. Instead, it seems likely that the dense clumps located towards the tips of the fingers are part of a larger, dense structure that pre-existed the expansion of the HII region. These have now come into stark contrast against their local environment due to the photoionisation of the surrounding, lower density material. The pre-existence of these dense structures, and their associated shadowing effects, have probably contributed to the formation and appearance of the fingers, and the fact that they point towards the external O-stars Although the physics of star forming regions remains poorly understood, the picture developed by Shu et al (ARAA, 25,23,1987) remains, where, following removal of the magnetic field in a core by ambipolar diffusion, the core r distribution changes from r a r-2 (for an isothermal sphere in pressure equilibrium), to r a r-1.5. A crucial observational test is to measure the density profiles, using the mm and submm thermal continuum emission, and to solve for the density profile which we can determine this from our SCUBA maps. These observational data therefore provides information on a) the morphology of dust and gas emission; b) the SED's and energy budgets of the protostellar cores; and c) the density and temperature profiles of the clumps. These can be used to compare with quite specific modelling which will be made with our proposed dynamics and collapse model. It was clear early from our work, that the RDI model can simulate the velocity fields and density structures in the heads and tails closely matching our observations. The ionised boundary layer at the edges of globules hold the key to understanding induced star formation, since it traces the interaction directly. Such induced star-formation has for many years been advocated as the panacea to the formation of clusters, but based only on circumstantial evidence. We therefore believe that extending the model to include the dynamics of the ionised gas, coupled with our new data will allow us to understand the physics of the photoevaporative flows that surround globules - and the role of the shock in inducing collapse and triggering star formation. Our objective is to model of the molecular-ionised gas interface to simulate the pressures, densities and excitation of the gas, and to understand how it is associated with the collapse of the molecular core just inside the neutral gas. This very important astrophysical area is just becoming accessible to modern instrumentation.
Optical line ratios and photoionisation modelling of the photoevaporative flow at the edge of a UV illuminated cloud from [D23, 37]: a) [left] Emission line intensities for [CII] 158 µm, [OI] 63 µm and [OI] 145 µm from PDR models described in our photoionisation code [D23, 36]. The line intensities are shown as a function for four values of the density; [middle left] PDR model of the for n(H) =2 104 cm- 3 and Go = 75. In both graphs, the abscissa represents the column density of hydrogen nuclei, N(H), in cm-2. The upper panel shows gas and dust temperatures into the PDR. The lower panel displays the abundance distribution of hydrogen, electrons and molecules into the PDR. The abundances shown are relative to the number of H-nuclei; [Middle right] Diagnostic line ratio diagram for [CII] 158 µm, [OI] 63 µm and [OI] 145 µm for the PDR models described in the text. n(H) increases top-down and right-left. The logarithmic mesh of the web is 0.25 dex and parameter values are indicated at full decades. Whereas plausible models predict [OI] 63 µm/[OI] 145 µm ratios >> 10, the LWS observations, enclosed by dotted box, fall short of the theoretical values
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