RXTE observation of NGC 6240: a search for the obscured active nucleus

We present new data taken at 850 μm with SCUBA at the James Clerk Maxwell Telescope for a sample of 19 luminous infrared galaxies. Fourteen galaxies were detected. We have used these data, together with fluxes at 25, 60 and 100 μm from IRAS , to model the dust emission. We find that the emission from most galaxies can be described by an optically thin, single temperature dust model with an exponent of the dust extinction coefficient ( k _λ ∝ λ ^{− β} ) of β ≃1.4–2. A lower β ≃1 is required to model the dust emission from two of the galaxies, Arp 220 and NGC 4418. We discuss various possibilities for this difference and conclude that the most likely is a high dust opacity. In addition, we compare the molecular gas mass derived from the dust emission, M _850 μm, with the molecular gas mass derived from the CO emission, M _CO, and find that M _CO is on average a factor 2–3 higher than M _850 μm.     

A submillimetre survey of the kinematics of the Perseus molecular cloud – I. Data

We present submillimetre observations of the   J = 3 → 2  rotational transition of ¹²CO, ¹³CO and C¹⁸O across over 600 arcmin² of the Perseus molecular cloud, undertaken with the Heterodyne Array Receiver Programme (HARP), a new array spectrograph on the James Clerk Maxwell Telescope. The data encompass four regions of the cloud, containing the largest clusters of dust continuum condensations: NGC 1333, IC348, L1448 and L1455. A new procedure to remove striping artefacts from the raw HARP data is introduced. We compare the maps to those of the dust continuum emission mapped with the Submillimetre Common-User Bolometer Array (SCUBA; Hatchell et al.) and the positions of starless and protostellar cores (Hatchell et al.). No straightforward correlation is found between the masses of each region derived from the HARP CO and SCUBA data, underlining the care that must be exercised when comparing masses of the same object derived from different tracers. From the ¹³CO/C¹⁸O line ratio the relative abundance of the two species  ([¹³CO]/[C¹⁸O]∼ 7)  and their opacities (typically τ is 0.02–0.22 and 0.15–1.52 for the C¹⁸O and ¹³CO gas, respectively) are calculated. C¹⁸O is optically thin nearly everywhere, increasing in opacity towards star-forming cores but not beyond  τ₁₈∼ 0.9  . Assuming the ¹²CO gas is optically thick, we compute its excitation temperature, T _ex (around 8–30 K), which has little correlation with estimates of the dust temperature.     

The initial conditions of isolated star formation – V. ISOPHOT imaging and the temperature and energy balance of pre-stellar cores

ISO data taken with the long-wavelength imaging photo-polarimeter ISOPHOT are presented of 18 pre-stellar cores at three far-infrared wavelengths, 90, 170 and 200 μm. Most of the cores are detected clearly at 170 and 200 μm, but only one is detected strongly at 90 μm, indicating that mostly they are very cold, with typical temperatures of only ∼     . Colour temperature images are constructed for each of the cores. Most of the cores are seen either to be isothermal, or to have associated temperature gradients from the core centres to their edges, with all except one being cooler at the centre. We compare the data with previous ISOCAM absorption data, and calculate the energy balance for those cores in common between the two samples. We find that the energy radiated by each core in the far-infrared is similar to that absorbed at shorter wavelengths. Hence there is no evidence for a central heating source in any of the cores – even those for which previous evidence for core contraction exists. This is all consistent with external heating of the cores by the local interstellar radiation field, confirming their pre-stellar nature.     

Dust coagulation in star formation with different metallicities

Dust grains coagulate into larger aggregates in dense gas. This changes their size distribution and possibly affects the thermal evolution of star-forming clouds. We here investigate dust coagulation in collapsing pre-stellar cores with different metallicities by considering the thermal motions of grains. We show that coagulation does occur even at low metallicity  ∼10⁻⁶ Z_⊙  . However, we also find (i) that the H₂ formation rate on dust grains is reduced only after the majority of H₂ is formed and (ii) that the dust opacity is modified only after the core becomes optically thick. Therefore, we conclude that the effects of dust coagulation can safely be neglected in discussing the temperature evolution of the pre-stellar cores for any metallicity as long as the grain motions are thermal.     

Comparison of 13CO line and far-infrared continuum emission as a diagnostic of dust and molecular gas physical conditions – I. Motivation and modelling

Determining temperatures in molecular clouds from ratios of CO rotational lines or from ratios of continuum emission in different wavelength bands suffers from reduced temperature sensitivity in the high-temperature limit. In theory, the ratio of far-infrared (FIR), submillimetre or millimetre continuum to that of a ¹³CO (or C¹⁸O) rotational line can place reliable upper limits on the temperature of the dust and molecular gas. Consequently, FIR continuum data from the COBE /Diffuse Infrared Background Experiment (DIRBE) instrument and Nagoya 4-m  ¹³CO  J = 1 → 0  spectral line data were used to plot  240 μm/¹³CO  J = 1 → 0  intensity ratios against 140/240 μm dust colour temperatures, allowing us to constrain the multiparsec-scale physical conditions in the Orion A and B molecular clouds.
The best-fitting models to the Orion clouds consist of two components: a component near the surface of the clouds that is heated primarily by a very large scale (i.e. ∼1 kpc) interstellar radiation field and a component deeper within the clouds. The former has a fixed temperature and the latter has a range of temperatures that vary from one sightline to another. The models require a dust–gas temperature difference of 0 ± 2 K and suggest that 40–50 per cent of the Orion clouds are in the form of dust and gas with temperatures between 3 and 10 K. The implications are discussed in detail in later papers and include stronger dust–gas thermal coupling and higher Galactic-scale molecular gas temperatures than are usually accepted, and an improved explanation for the N (H₂)/ I (CO) conversion factor. It is emphasized that these results are preliminary and require confirmation by independent observations and methods.     

Accounting for the foreground contribution to the dust emission towards Kepler's supernova remnant

Whether or not supernovae contribute significantly to the overall dust budget is a controversial subject. Submillimetre (sub-mm) observations, sensitive to cold dust, have shown an excess at 450 and 850 μm in young remnants Cassiopeia A (Cas A) and Kepler. Some of the sub-mm emission from Cas A has been shown to be contaminated by unrelated material along the line of sight. In this paper, we explore the emission from material towards Kepler using sub-mm continuum imaging and spectroscopic observations of atomic and molecular gas, via H  i , ¹²CO( J = 2–1) and ¹³CO( J = 2–1). We detect weak CO emission (peak   T *_A  = 0.2–1 K, 1–2 km s⁻¹ full width at half-maximum) from diffuse, optically thin gas at the locations of some of the sub-mm clumps. The contribution to the sub-mm emission from foreground molecular and atomic clouds is negligible. The revised dust mass for Kepler's remnant is  0.1–1.2 M_⊙  , about half of the quoted values in the original study by Morgan et al., but still sufficient to explain the origin of dust at high redshifts.     

The far-infrared signature of dust in high-latitude regions

We present ISOPHOT observations of eight interstellar regions in the 60–200 μm wavelength range. The regions belong to mostly quiescent high-latitude clouds and have optical extinction peaks from   A_V ∼1–6 mag  . From the 150- and 200-μm emission, we derived colour temperatures for the classical big grain component which show a clear trend of decreasing temperature with increasing 200-μm emission. The 200-μm emission per unit   A_V   , however, does not drop at lower temperatures. This fact can be interpreted in terms of an increased far-infrared (FIR) emissivity of the big grains. We developed a two-component model including warm dust with the temperature of the diffuse interstellar medium (ISM) of   T = 17.5 K  , and cold dust with   T = 13.5 K  and FIR emissivity increased by a factor of >4. A mixture of the two components can reproduce the observed colour variations and the ratios   I ₂₀₀/ A_V   and  τ₂₀₀/ A_V   . The relative abundance of small grains with respect to the big grains shows significant variations from region to region at low column densities. However, in lines of sight of higher column density, our data indicate the disappearance of small grains, perhaps a signature of adsorption/coagulation of dust. The larger size and porous structure could also explain the increased FIR emissivity. Our results from eight independent regions suggest that these grains might be ubiquitous in the galactic ISM.     

The spatial variation of the 3-μm dust features in Circinus

We report spatially resolved variations in the 3.4-μm hydrocarbon absorption feature and the 3.3-μm polycyclic aromatic hydrocarbon (PAH) emission band in the Circinus galaxy over the central few arcsec. The absorption is measured towards warm emitting dust associated with Coronal line regions to the east and west of the nucleus. There is an absorption optical depth  τ_3.4 μm∼ 0.1  in the core which decreases to the west and increases to the east. This is consistent with increased extinction out to ∼40 pc east of the core, supported by the Coronal emission line intensities which are significantly lower to the east than the west. PAH emission is measured to be symmetrically distributed out to ±4 arcsec, outside the differential extinction region. The asymmetry in the 3.4-μm absorption band reflects that seen in the 9.7-μm silicate absorption band reported by Roche et al., and the ratio of the two absorption depths remains approximately constant across the central regions, with  τ_3.4 μm/τ_9.7 μm∼ 0.06 ± 0.01  . This indicates well-mixed hydrocarbon and silicate dust populations, with no evidence for significant changes near the nucleus.     

A multiwavelength infrared study of NGC 891

We present a multiwavlength infrared (IR) study of the nearby, edge-on, spiral galaxy NGC 891. We have examined 20 independent, spatially resolved IR images of this galaxy, 14 of which are newly reduced and/or previously unpublished images. These images span a wavelength regime from  λ 1.2 μ  m in which the emission is dominated by cool stars, through the mid-IR, in which emission is dominated by polycyclic aromatic hydrocarbons (PAHs), to λ 850 μm, in which emission is dominated by cold dust in thermal equilibrium with the radiation field. The changing morphology of the galaxy with wavelength illustrates the changing dominant components. We detect extraplanar dust emission in this galaxy, consistent with previously published results, but now show that PAH emission is also in the halo, to a vertical distance of   z ≥ 2.5 kpc  . We compare the vertical extents of various components and find that the PAHs (from λ 7.7 and 8 μm data) and warm dust (λ 24 μm) extend to smaller z heights than the cool dust (λ 450 μm). For six locations in the galaxy for which the signal-to-noise ratio was sufficient, we present spectral energy distributions (SEDs) of the IR emission, including two in the halo – the first time a halo SED in an external galaxy has been presented. We have modelled these SEDs and find that the PAH fraction, f _PAH, is similar to Galactic values (within a factor of 2), with the lowest value at the galaxy's centre, consistent with independent results of other galaxies. In the halo environment, the fraction of dust exposed to a colder radiation field, f _cold, is of the order of unity, consistent with an environment in which there is no star formation. The source of excitation is likely from photons escaping from the disc.     

Submillimetre continuum images of the NGC 2024 star-forming ridge

We present 450- and 800-μm images, made with the James Clerk Maxwell Telescope, of the NGC 2024 molecular ridge. The seven previously known compact cores, FIR1–7, have been detected, and FIR5 has been resolved into a compact object and an associated extended source to the east. The estimated masses of the dense cores vary between 1.6 and 5.1 M⊙ per 14-arcsec beam, assuming a dust temperature of 30 K and a dust opacity of κ_800 μm = 0.002 m² kg⁻¹. A spectral index map made from the 450- and 800-μm images shows spatial variations, with the spectral index, α ( F _ν ∝ ν^α), being systematically lower towards the dense cores. We interpret this as evidence for a lower value of the frequency dependence of the dust opacity, β, towards the denser cores relative to the surrounding molecular material. This may indicate that grain growth is occurring in the cores, prior to planetesimal formation. By comparing the high-resolution 450-μm image with interferometer maps of the integrated CS(2–1) emission, the previously reported discrepancy between dust continuum emission and molecular line emission is found to be very localized. Depletion and temperature variations are discussed as possible explanations.     

Microwave polarization in the direction of galaxy clusters induced by the CMB quadrupole anisotropy

Electron scattering induces a polarization in the cosmic microwave background (CMB) signal measured in the direction of a galaxy cluster owing to the presence of a quadrupole component in the CMB temperature distribution. Measuring the polarization towards distant clusters provides the unique opportunity to observe the evolution of the CMB quadrupole at moderate redshifts, z ∼0.5–3. We demonstrate that for the local cluster population the polarization degree will depend on the cluster celestial position. There are two extended regions in the sky, which are opposite to each other, where the polarization is maximal, ∼0.1( τ /0.02) μK in the Rayleigh–Jeans part of the CMB spectrum ( τ being the Thomson optical depth across the cluster). This value exceeds the polarization introduced by the cluster transverse peculiar motion if v _t<1300 km s⁻¹. One can hope to detect this small signal by measuring a large number of clusters, thereby effectively removing the systematic contribution from other polarization components produced in clusters. These polarization effects, which are of the order of ( v _t c )² τ , ( v _t c ) τ ² and ( kT _e m _e c ²) τ ², as well as the polarization owing to the CMB quadrupole, were previously given by Sunyaev and Zel'dovich for the Rayleigh–Jeans part of the spectrum. We fully confirm their earlier results and present exact frequency dependences for all these effects. The polarization degree is considerably higher in the Wien region.     

SCUBA polarization observations of the magnetic fields in the pre-stellar cores L1498 and L1517B

We have mapped linearly polarized dust emission from the pre-stellar cores L1498 and L1517B with the James Clerk Maxwell Telescope (JCMT) using the Submillimetre Common User Bolometer Array (SCUBA) and its polarimeter (SCUBAPOL) at a wavelength of 850 μm. We use these measurements to determine the plane-of-sky magnetic field orientation in the cores. In L1498, we see a magnetic field across the peak of the core that lies at an offset of ∼19°± 12° to the short axis of the core. This is similar to the offsets seen in previous observations of pre-stellar cores. To the south-east of the peak, in the filamentary tail of the core, we see that the magnetic field has rotated to lie almost parallel to the long axis of the filament. We hypothesize that the field in the core may have decoupled from the field in the filament that connects the core to the rest of the cloud. We use the Chandrasekhar–Fermi (CF) method to measure the plane-of-sky field strength in the core of L1498 to be ∼10 ± 7 μG.
In L1517B, we see a more gradual turn in the field direction from the northern part of the core to the south. This appears to follow a twist in the filament in which the core is buried, with the field staying at a roughly constant ∼25°± 6° offset to the short axis of the filament, consistent with previous observations of pre-stellar cores. Hence these two clouds in an apparently similar evolutionary state, that exhibit similar masses, morphologies and densities, have very different magnetic field configurations. We again use the CF method and calculate the magnetic field strength in L1517B to be ∼30 ± 10 μG. Both cores appear to be roughly virialized. Comparison with our previous work on somewhat denser cores shows that, for the denser cores, thermal and non-thermal (including magnetic) support are approximately equal, while for the lower density cores studied here, thermal support dominates.     

Photoionized Hβ emission in NGC 5548: it breathes!

Emission-line regions in active galactic nuclei (AGNs) and other photoionized nebulae should become larger in size when the ionizing luminosity increases. This 'breathing' effect is observed for the Hβ emission in NGC 5548 by using Hβ and optical continuum light curves from the 13-yr (1989–2001) AGN Watch monitoring campaign. To model the breathing, we use two methods to fit the observed light curves in detail: (i) parametrized models and, (ii) the memecho reverberation-mapping code. Our models assume that optical continuum variations track the ionizing radiation, and that the Hβ variations respond with time-delays τ due to light travel-time. By fitting the data using a delay-map  Ψ(τ, F _c)  that is allowed to change with continuum flux F _c, we find that the strength of the Hβ response decreases and the time-delay increases with ionizing luminosity. The parametrized breathing models allow the time-delay and the Hβ flux to depend on the continuum flux so that,  τ∝ F ^β_c  and   F _Hβ∝ F ^α_c  . Our fits give  0.1 < β < 0.46  and  0.57 < α < 0.66. α  is consistent with previous work by Gilbert and Peterson, and Goad, Korista and Knigge. Although we find β to be flatter than previously determined by Peterson et al. using cross-correlation methods, it is closer to the predicted values from recent theoretical work by Korista and Goad.     

Collapse and fragmentation of rotating magnetized clouds – II. Binary formation and fragmentation of first cores

Subsequent to Paper I, the evolution and fragmentation of a rotating magnetized cloud are studied with use of three-dimensional magnetohydrodynamic nested grid simulations. After the isothermal runaway collapse, an adiabatic gas forms a protostellar first core at the centre of the cloud. When the isothermal gas is stable for fragmentation in a contracting disc, the adiabatic core often breaks into several fragments. Conditions for fragmentation and binary formation are studied. All the cores which show fragmentation are geometrically thin, as the diameter-to-thickness ratio is larger than 3. Two patterns of fragmentation are found. (1) When a thin disc is supported by centrifugal force, the disc fragments into a ring configuration (ring fragmentation). This is realized in a rapidly rotating adiabatic core as  Ω > 0.2τ⁻¹_ff  , where Ω and  τ_ff  represent the angular rotation speed and the free-fall time of the core, respectively. (2) On the other hand, the disc is deformed to an elongated bar in the isothermal stage for a strongly magnetized or rapidly rotating cloud. The bar breaks into 2–4 fragments (bar fragmentation). Even if a disc is thin, the disc dominated by the magnetic force or thermal pressure is stable and forms a single compact body. In either ring or bar fragmentation mode, the fragments contract and a pair of outflows is ejected from the vicinities of the compact cores. The orbital angular momentum is larger than the spin angular momentum in the ring fragmentation. On the other hand, fragments often quickly merge in the bar fragmentation, since the orbital angular momentum is smaller than the spin angular momentum in this case. Comparison with observations is also shown.     

Molecular hydrogen in damped Lyα systems: clues to interstellar physics at high redshift

In order to interpret H₂ quasar absorption-line observations of damped Lyα systems (DLAs) and subDLAs, we model their H₂ abundance as a function of dust-to-gas ratio, including H₂ self-shielding and dust extinction against dissociating photons. Then, we constrain the physical state of the gas by using H₂ data. Using H₂ excitation data for DLAs with H₂ detections, we derive a gas density  1.5 ≲ log n (cm⁻³) ≲ 2.5  , temperature  1.5 ≲ log T (K) ≲ 3  , and an internal ultraviolet (UV) radiation field (in units of the Galactic value)  0.5 ≲ log χ≲ 1.5  . We then find that the observed relation between the molecular fraction and the dust-to-gas ratio of the sample is naturally explained by the above conditions. However, it is still possible that H₂ deficient DLAs and subDLAs with H₂ fractions less than  ∼10⁻⁶  are in a more diffuse and warmer state. The efficient photodissociation by the internal UV radiation field explains the extremely small H₂ fraction  (≲10⁻⁶)  observed for  κ≲ 1/30  (κ is the dust-to-gas ratio in units of the Galactic value); H₂ self-shielding causes a rapid increase in, and large variations of, H₂ abundance for  κ≳ 1/30  . We finally propose an independent method to estimate the star formation rates of DLAs from H₂ abundances; such rates are then critically compared with those derived from other proposed methods. The implications for the contribution of DLAs to the cosmic star formation history are briefly discussed.     

Global velocity field and bubbles in the blue compact dwarf galaxy Mrk 86

We have studied the velocity field of the blue compact dwarf galaxy Mrk 86 (NGC 2537) using data provided by 14 long-slit optical spectra obtained in 10 different orientations and positions. This kinematical information is complemented with narrow-band ([O  iii ]5007 Å and H α ) and broad-band ( B , V , Gunn r and K ) imaging. The analysis of the galaxy global velocity field suggests that the ionized gas could be distributed in a rotating inclined disc, with projected central angular velocity of Ω=34 km s⁻¹ kpc⁻¹. The comparison between the stellar, H  i and modelled dark matter density profile indicates that the total mass within its optical radius is dominated by the stellar component. Peculiarities observed in its velocity field can be explained by irregularities in the ionized gas distribution or local motions induced by star formation.
Kinematical evidences for two expanding bubbles, Mrk 86–B and Mrk 86–C, are given. They show expanding velocities of 34 and 17 km s⁻¹, H α luminosities of 3×10³⁸ and 1.7×10³⁹ erg s⁻¹, and physical radii of 374 and 120 pc, respectively. The change in the [S  ii ]/H α , [N  ii ]/H α , [O  ii ]/[O  iii ] and [O  iii ]/H β line ratios with the distance to the bubble precursor suggests a diminution in the ionization parameter and, in the case of Mrk 86–B, an enhancement of the shock-excited gas emission. The optical–near-infrared colours of the bubble precursors are characteristic of low‐metallicity star‐forming regions (∼0.2 Z_⊙) with burst strengths of about 1 per cent in mass.     

A burst of outflows from the Serpens cloud core: wide-field submillimetre continuum, CO J=2–1 and optical observations

Wide-field mapping of Serpens in submillimetre continuum emission and CO J =2–1 line emission is here complemented by optical imaging in [S  ii ] λλ 6716, 6731 line emission. Analysis of the 450- and 850-μm continuum data shows at least 10 separate sources, along with fainter diffuse background emission and filaments extending to the south and east of the core. These filaments describe 'cavity-like' structures that may have been shaped by the numerous outflows in the region. The dust opacity index, β , derived for the identifiable compact sources is of the order of 1.0±0.2, with dust temperatures in excess of 20 K. This value of β is somewhat lower than for typical class I YSOs; we suggest that the Serpens sources may be 'warm', late class 0 or early class I objects.
With the combined CO and optical data we also examine, on large scales, the outflows driven by the embedded sources in Serpens. In addition to a number of new Herbig–Haro flows (here denoted HH 455–460), a number of high-velocity CO lobes are observed; these extend radially outwards from the cluster of submillimetre sources in the core. A close association between the optical and molecular flows is also identified. The data suggest that many of the submillimetre sources power outflows. Collectively, the outflows traced in CO support the widely recognized correlation between source bolometric luminosity and outflow power, and imply a dynamical age for the whole protostellar cluster of ∼3×10⁴ yr. Notably, this is roughly equal to the proposed duration of the 'class 0' stage in protostellar evolution.     

Desorption from interstellar ices

The desorption of molecular species from ice mantles back into the gas phase in molecular clouds results from a variety of very poorly understood processes. We have investigated three mechanisms: desorption resulting from H₂ formation on grains, direct cosmic ray heating and cosmic ray-induced photodesorption. Whilst qualitative differences exist between these processes (essentially deriving from the assumptions concerning the species selectivity of the desorption and the assumed threshold adsorption energies, E _t), all the three processes are found to be potentially very significant in dark cloud conditions. It is therefore important that all three mechanisms should be considered in studies of molecular clouds in which freeze-out and desorption are believed to be important.
Employing a chemical model of a typical static molecular core and using likely estimates for the quantum yields of the three processes, we find that desorption by H₂ formation probably dominates over the other two mechanisms. However, the physics of the desorption processes and the nature of the dust grains and ice mantles are very poorly constrained. We therefore conclude that the best approach is to set empirical constraints on the desorption, based on observed molecular depletions – rather than try to establish the desorption efficiencies from purely theoretical considerations. Applying this method to one such object (L16 89B) yields upper limits to the desorption efficiencies that are consistent with our understanding of these mechanisms.     

The initial conditions of isolated star formation – VII. Spitzer mapping of pre-stellar cores

We have retrieved Spitzer archive data of pre-stellar cores taken with the Multiband Imaging Photometer for Spitzer (MIPS) at a wavelength of 160 μm. Seventeen images, containing 18 cores, were constructed. Flux densities were measured for each core, and background estimates were made. Mean off-source backgrounds were found to be 48 ± 10 MJy sr⁻¹ in Taurus and 140 ± 55 MJy sr⁻¹ in Ophiuchus. Consistency was found between the MIPS 170-μm and ISOPHOT 160-μm calibrations. Fourteen cores were detected both by MIPS and by our previous submillimetre surveys. Spectral energy distributions were made for each core, using additional 24- and 70-μm data from the Spitzer data archive, as well as previous infrared and submillimetre data. Previous temperature estimates were refined, and new temperature estimates were made where no Infrared Space Observatory ( ISO ) data exist. A temperature range of 8–18 K was found for the cores, with most lying in the range 10–13 K. We discount recent claims that a large number of pre-stellar cores may have been misclassified and in fact contain low-luminosity protostars detectable only by Spitzer . We find no new protostars in our sample other than that previously reported in L1521F. It is shown that this has a negligible effect on pre-stellar lifetime estimates.     

The initial conditions of isolated star formation – IV. C18O observations and modelling of the pre-stellar core L1689B

We present C¹⁸O observations of the pre-stellar core L1689B, in the J =3→2 and 2→1 rotational transitions, taken at the James Clerk Maxwell Telescope in Hawaii. We use a λ -iteration radiative transfer code to model the data. We adopt a similar form of radial density profile to that which we have found in all pre-stellar cores, with a 'flat' inner profile, steepening towards the edge, but we make the gradient of the 'flat' region a free parameter. We find that the core is close to virial equilibrium, but there is tentative evidence for core contraction. We allow the temperature to vary with a power-law form and find that we can consistently fit all of the CO data with an inverse temperature gradient that is warmer at the edge than at the centre. However, when we combine the CO data with the previously published millimetre data we fail to find a simultaneous fit to both data sets without additionally allowing the CO abundance to decrease towards the centre. This effect has been observed qualitatively many times before, as the CO freezes out on to the dust grains at high densities, but we quantify the effect. Hence we show that the combination of millimetre/submillimetre continuum and spectral line data is a very powerful method of constraining the physical parameters of cores on the verge of forming stars.