The structure of molecular cloud cores

The interstellar medium is composed of material in various thermal and chemical phases, including cool atomic gas inside, or mixed with cold molecular clouds; cool and warm atomic gas on the envelopes of molecular clouds; cold molecules in dark, dense or translucent clouds; warm molecules in dense clouds near embedded luminous sources; dense photoionised gas near O- and B-stars; and hot, shocked gas near supernova remnants and molecular outflow sources.

The measurable properties using mm and submm spectroscopy include temperature, density, and kinematics of the various phases, allowing the initial mass function, chemical evolution, masses and physics of star forming clumps and ultimately the star forming history of the cloud to be studied. A growing concern amongst many workers in this field is the (in)accuracy of mass determination in the ISM. The generally poor angular resolution, combined with computational inadequacies has led to the widespread use of approximate methods such as LTE and escape probability to calculate level populations and line intensities. The simple, fundamental objective in this project is to improve techniques used to estimate the masses of gas and dust in several typical regions, using a wide range of data from the optical, IR, submm/mm spectral regions, which can critically constrain radiative transfer modelling.
NGC6334 molecular cloud observed by Glenn White, Bill McCutcheon and Henry Matthews in the CO J = 2-1 molecular line with the JCMT

Most workers have used either observations of interstellar dust, or of interstellar molecules, to estimate the properties of interstellar material. For interstellar dust, the seminal work of Hildebrand (QJRAS, 24, 267, 1983), led to a 'standard' relationship widely used to estimate interstellar dust masses. Converting from submm flux to dust mass depends on the submm opacity at various wavelengths, an adopted benchmark 400 mm opacity, k400 and a power law dependence of the dust opacity b, as well as making corrections for spectral line contamination and the dust temperature. The absolute values of k 400 and b are each uncertain by factors of at least 2 (Gear et al MNRAS 231, 55p, 1988, Richardson et al A&A 221, 95, 1995, Goldsmith et al ApJ 491, 615, 1997, Visser et al, MN, 585, 1998, [62]), and many regions are known to have strong temperature gradients and to suffer line contamination - all often poorly constrained.

For interstellar gas, two methods are widely used to infer gas masses i) by the use of a luminosity-mass relationship (Solomon et al ApJ 319, 730, 1987), and ii) by indirect inference of H2 column densities by scaling 13CO or in some cases C18O or C17O observations or even the dust continuum intensity. ii) is the most commonly used for individual clouds, but is highly questionable, despite the literature ibeing permeated with 'authoritative' values of molecular cloud masses based on such data. In reality, problems with isotope selective photodissociation (ISP), depletion, fractionation, and the interpretation of a complex radiative transfer situation for combinations of lines with varying degrees of opacity are scantily treated, rendering the derived masses to be of limited reliability (Minchin et al A&A 301, 894, 1995, Minchin & White A&A 302, 25, 1995, White & Sandell A&A 299, 179, 1995). Many workers also adopt a 'canonical' gas to dust ratio (typically 100 - 200) to infer the total masses of molecular clouds. Such multiplicative factors, although widely used, are also poorly constrained. A further (uncertain) multiplicative factor, the molecular abundance, is then used to convert from the column density of the trace molecule to that of molecular hydrogen. Because the determination of interstellar masses is fundamental to almost all investigations of the ISM, we wish to start a programme to put the measurement techniques on a more rigorous footing, using a combination of ISO, IRAS, SCUBA, FCRAO, JCMT, CSO, Nobeyama and VLA data which sample the full SED's of SF regions to constrain radiative transfer modelling techniques we have already developed. The availability of large format, multi-transition molecular maps give data well suited to understanding these problems - and importantly, to constraining the modelling techniques.

A first objective for our programme is to measure the properties of dust. In particular we will use the data to study the power law dependence of the dust opacity b. This is important since the flux from an object, Fn nb Bn(Td) is conventionally used to estimate dust masses through the relationship Md = Fn D2 / (kn Bn(Td ). The masses of interstellar clouds are however still estimated by assuming a dust-to-gas mass ratio, despite few real measurements of the ratio. The reality is that solving for dust masses in real sources is a non-trivial inverse problem which is frequently glossed over. Recent observations with SCUBA use maps at several wavelengths to make first order estimates of b values, however determining this factor, which is principle should be calculable from the ratios of fluxes at two wavelengths, is riddled with hazards for the data analyst, because of the difficulty of accurately correcting for the error pattern of the telescope. We have studied the observational difficulties of this inverse problem, and convincingly show systematic variations to dust emissivity throughout two test star formation regions [184].

To accurately estimate b we have a) developed a technique which accurately allows b to be estimated across SCUBA submm maps, and b) using a 2D radiative transfer code (a ray tracing technique we have developed for the solution of the frequency dependent radiative transfer equation [Men'shchikov et al A&A, 318, 879, 1997, White et al L1551 2001]). This has allowed us to accurately constrain, for arbitrary geometries, the measured fluxes, to derive accurate b 's, and hence dust masses. The mass errors are checked by estimating the self-consistent energy conservation in the model, and are believed to be at the 5 - 10% level - providing us with the most accurate determinations of interstellar dust masses currently available. An objective of our work will be to measure reliable clump-mass distributions, in particular to resolve the problem of understanding why prestellar clump-mass functions and the IMF differ (Scalo Fund Cosmic Phys 11, 1, 1986, Motte et al A&A 336, 150, 1998). Despite observational advances, the errors are dominated by mass estimate (in)accuracies. It appears that some as yet poorly understood fragmentation process is required to reconcile matters, but few observational data exist to help constrain modelling.

[left] SCUBA observations of the Eagle Nebula, [middle] The vertical and horizontal axes show ratios of fluxes S450/S850 and S850/S1300 respectively, the dotted and solid lines are constant greybody emissivity indexes and Td respectively, and the crosses show experimantal uncertainties, [right] 3D radiative transfer modelling L1551, fitting the optical - radio spectral region.

Other recent work has concentrated on the use and application of CO isotopomers to trace mass and abundances in large area high angular resolution multi-isotope/transition mappings of GMC's. We have examined the importance of isotope selective photodissociation / fractionation to gas mass estimation in molecular clouds. There are strong indications that many masses determined using CO isotope data may in fact have large systematic errors (see also White & Sandell, A&A 299, 179, 1995, Gibb & Little, MN, 295, 299, 1998, Plume et al Ap J 512, 768, 1999). The figure below shows the variation of 13CO / C18O ratios we have measured towards a sample of objects. This ratio (vertical axes) should have a value close to the terrestial ratio (5.5). The strong variation indicates that isotope selective photodissociation destroys some of the same tracer that is assumed to have a constant abundance, rendering C18O derived masses highly questionable. Additional uncertainty is that despite indications of C18O depletion in a few clouds, little quantitative work has been done to assess the implications of this effect for cloud mass determinations, particularly in light of the fact that photodissociation affect C17O/ C18O observations, on which the evidence for depletion mainly depends.

[left] Variations of 13CO/C18O ratio - in the absence of photodissociation (often neglected by many astronomers), the data should all lie on a horizontal line at a value of ~ 5.5, [middle] Similar plot showing the effect on atomic carbon abundances - which in the absence of C18O photodissociation should also lie close to an horizontal line), [right] large area maps of the Lagoon Nebula being used to measure masses and gas to dust mass ratios - CO (contours) on an 850 mm SCUBA (grey).

Opacity effects also pose a serious problem for mass determination - often rendering the use of the most commonly observed isotopomers such as 13CO questionable. We are involved in a programme to model and understand the limitations of the more commonly used techniques of mass determination (discussions of this theme featured in a Workshop on radiative transfer in molecular lines held in Leiden, May 1999). Inter-comparisons using LTE, LVG and Monte Carlo analysis of the same starting data has convincingly shown [A15] that LTE analyses systematically underestimate masses, while LVG analyses have difficulties in real molecular clouds which are not dominated by velocity gradients. We have developed a fast, 'on-the-fly' LVG analysis technique for use in large scale mapping projects to estimate cloud clump masses. We intend to develop an equivalent Monte Carlo based code to further improve the accuracy - since this is better able to handle realistic geometries and clumpy structures. We believe the development of computationally efficient codes of this kind are better suited to handling the radiative transfer properly, allowing accurate gas mass estimates.

The programme we are carrying out is investigating the range of internal physical conditions within GMCs. A multi-wavelength survey will be proposed of a sample of dense cloud cores spanning the full observed range of core masses, luminosities and LIR / M(H2 ) ratios. Some observations are already available [75]. Composite spectral energy distributions (CSEDs) for these cores will be assembled from IRAS HIRES, ISOPhot C200, SCUBA and SHARC data. A specially-modified implementation of the HIRES resolution enhancement algorithm (Cao et al. 1997 ApJS 111, 387) will be used to produce images and photometry at 12, 25, 60 and 100 mm. Photometry at 150 and 200 mm has already been obtained from a dedicated Guest Observer program, and images and photometry at 850 and 450 mm using SCUBA on the JCMT, and at 350 mm using SHARC on the CSO are planned, or already in hand. The total luminosity, dust temperature and emissivity for each source will be determined, and compared with the molecular gas properties (e.g. column density, excitation temperature, gas density and volume filling factor) as determined from a multi-transition, multi-isotopomer CO survey of the same cores performed at the CSO. We will place emphasis on using the data to determine reliable vales of b and masses from the submm continuum data, and molecular masses from the line data. The latter will involve extensions of the new on-the-fly radiative transfer analysis techniques discussed in this section. The data will be used to determine the gas-to-dust mass ratios, IMF and molecular abundances.

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