probing the structure of molecular cloud cores: observations and modelling of c i and c18o in...

Probing the structure of molecular cloud cores: observations and modellingof C I and C18O in HH24–26

A. G. Gibb*† and L. T. Little*Electronic Engineering Laboratory, University of Kent at Canterbury, Canterbury, Kent CT2 7NT

Accepted 1997 September 24. Received 1997 September 9; in original form 1997 February 17

A B S T R A C TWe describe observations of the C18O J ¼ 2 → 1, 3 → 2 and C I

3P1→3P0 lines towards theHH24–26 molecular cloud core. The C18O traces the north–south molecular ridge, but thedense clumps identified by previous high-resolution HCOþ and dust continuum data do notstand out. Using H2 column densities estimated from dust continuum measurements, we findthat the CO abundance may be reduced by factors of at least 10 towards three positions (two ofwhich are Class 0 protostars). Depending on the assumptions employed, the reduction may beas high as ,50 towards the clump positions. The magnitude of the reduced abundances is ingood agreement with chemical models of collapsing clouds in which molecules accrete on todust grains. Alternative interpretations, retaining normal abundances, and relying on subtleoptical depth and beam filling effects, are considered, but shown to be less likely.

The contrast in C I line intensity is low across the source. The greater part of the emissionprobably arises from the outer surface of the cloud, but it is impossible to determine the exactcontribution from C atoms deeper into the core as their emission cannot be separated from thatarising at the surface.

Non-LTE radiative transfer modelling of the C18O emission towards the two Class 0 sourcesHH24MMS and HH25MMS confirms a widespread reduction of the CO abundance by a factorof greater than 10 within a radius of 0.3 pc and not just close to the clumps. In HH24MMS, theabundance is required to rise again towards the centre of the model clouds in accordance withthe rise in temperature near to the central embedded object where CO is desorbed from grains.Application of the same radiative transfer model to the C I emission provides little constrainton the carbon abundance profile, although fits can be obtained for reasonable forms.The depletion of CO in the core, coupled with the lack of an infrared cluster, suggests thatHH24–26 may be in the process of forming its first generation of stars.

Key words: line: profiles – stars: formation – ISM: clouds – ISM: individual: HH24–26 –ISM: molecules – radio lines: ISM.

1 I N T RO D U C T I O N

The rarer isotopomers of carbon monoxide, such as C18O, arewidely used as tracers of molecular hydrogen column density indense molecular cloud cores. The abundance of C18O relative to H2,denoted by X(C18O), has been estimated to be ,2 × 10¹7 (Frerking,Langer & Wilson 1982), some 500 times lower than that of 12CO.Within dense cores in molecular clouds, the observed intensity ofC18O is assumed to be directly proportional to the column density ofH2 (provided that the emission is optically thin).

The implicit assumption is that the C18O abundance remainsconstant along the line of sight. During the early 1980s, there was

little evidence for the depletion of CO on to dust grains (Leger1983), notwithstanding the prediction that it should freeze out attemperatures less than ,20 K (Nakagawa 1980). As a consequence,many early chemical models have treated CO as an ‘anchor’ andfixed its abundance at a constant value. However, there is nowmounting evidence for the removal of CO from the gas phase in coldclouds (e.g. B5-IRS1: Teixeira & Emerson 1995; Kelly, Macdonald& Millar 1996).

The chemical evolution of collapsing gas clouds has yet to befully explored, with only a few treatments published (e.g. Prasad,Heere & Tarafdar 1991; Rawlings et al. 1992; Ceccarelli, Hollen-bach & Tielens 1996; Bergin & Langer 1997). Rawlings et al.(1992) predict a decrease in XðCOÞ towards the centre of acollapsing clump. Within these compact regions of high density,the time-scale for removal of molecules from the gas phase is but afew thousand years. This is similar to the lifetime inferred for the

Mon. Not. R. Astron. Soc. 295, 299–311 (1998)

q 1998 RAS

*E-mail: [email protected] (AGG); [email protected] (LTL)† Present address: Department of Astronomy, University of Leeds, LeedsLS2 9JT.

Class 0 phase of protostellar evolution (Andre & Montmerle 1994).Therefore, in Class 0 and similar objects, the variation of chemicalabundances over short spatial scales is to be expected. To detectdepletion, the depletion time-scale must be less than the star-forming (collapse) time-scale. The molecules remain on the dustgrains until the protostar warms the environment sufficiently toremove the mantle material, and abundances gradually return tonormal (Mundy, McMullin & Blake 1995).

Neutral atomic carbon is predicted to be abundant in regions oflow visual extinction where UV radiation can penetrate anddissociate CO (Langer 1976; Meixner & Tielens 1993). Simplisti-cally it would be expected that the abundance of C would be highonly at cloud surfaces subjected to a far-UV radiation field (Langer1976). In reality, the emission from the fine-structure line of carbonat 492 GHz is observed to be widespread, even in clouds where thereare no strong sources of UV radiation, such as TMC-1 (Schilke et al.1995). The widespread observation of C0 in molecular clouds hasbeen shown to have significant contributions to the emission fromatoms deep within the cloud where AV is as high as 50–100(Frerking et al. 1989; Little et al. 1994).

HH24–26 is a dense, star-forming core located in the L1630molecular cloud at an estimated distance of 400 pc (Anthony-Twarog 1982). It has been shown to be an active region of ongoingstar formation, with a highly fragmented appearance on small scalesand numerous outflows (Zealey et al. 1992; Gibb & Heaton 1993,hereafter GH93; Gibb et al. 1995, hereafter GLHL95; Verdes-Montenegro & Ho 1996). Within its bounds is HH24MMS, aClass 0 continuum source and one of the strongest protostellarcandidates (Ward-Thompson et al. 1995).

As part of a programme investigating the small-scale structure ofHH24–26, we present here observations of C18O J ¼ 2 → 1 and C I3P1→3P0 transitions. The outline of this paper is as follows. Section2 describes the observational details. Section 3 presents the resultsin the form of maps and spectra. In Section 4 we compute columndensities for C18O and C I. In Section 5 we discuss whether the C18Odepletions that we deduce are genuine. In Section 6 we model theradiative transfer within the framework of recent theoretical modelsfor collapsing cores, to determine the C18O and C abundancedistribution. Section 7 relates these distributions to models ofcloud chemistry, while Section 8 summarizes our conclusions.

2 O B S E RVAT I O N S

All data were recorded at the James Clerk Maxwell Telescope(JCMT) on Mauna Kea, Hawaii, on 1994 January 29 to February 1.The common-user receivers A2 and C2 were employed along withthe digital autocorrelation spectrometer (DAS) as backend. Thezenith atmospheric opacity as determined by the Caltech Submilli-meter Observatory (CSO) radiometer at 225 GHz was typically 0.05during the observing run. System parameters for the respectivetransitions are listed in Table 1. All observations were made

employing position-switching, and OMC-1 was observed tocheck calibration which is estimated to be uncertain by < 10 percent at 220 GHz and ,20–25 per cent at 492 GHz. The meanpointing error was of order 3 arcsec. The forward scattering andspillover efficiency, hfss, was taken from the JCMT userguide andhas been used to convert T¬

A into T¬R values. All line intensities are

reported on the T¬R scale. The adopted map-centre coordinates are

a1950 ¼ 5h43m33:s0, d1950 ¼ ¹0◦130000: 0. The off-source referenceposition was (¹1800,0) arcsec relative to this centre.

The core was mapped in C18O, covering the same area as theHCOþ emission observed by GH93, but centred 10 arcsec south ofthe nominal (0, 0) position. Neutral carbon spectra were observedtowards the centre positions of the six clumps listed by GH93, inaddition to an east–west cross-scan made at the declination of themost massive clump (clump E). The cross-scan extended toapproximately 3 arcmin in either direction. More recently, on1996 September 19, two C18O J ¼ 3 → 2 spectra were alsoobtained towards the positions of HH24MMS and clump E(HH25MMS) at the JCMT although the integration time waslimited, giving a relatively high noise level of DT¬

A = 0.5 K inthese spectra.

3 R E S U LT S

3.1 C18O emission

The spatial distribution of C18O T¬R integrated from 8 to 11 km s¹1

is shown in Fig. 1(a). The emission delineates a north–south ridge,with a gradient in intensity along it. Immediately striking oncomparison with the HCOþ 4 → 3 and 800-mm continuum data(Fig. 1(b)) is the lack of clear emission maxima: rather, the trend ismore akin to the HCOþ 1→0, although it must be admitted that thelatter resolution is somewhat lower (GLHL95). In the north of Fig.1(a), HH24MMS can be clearly identified, as can an elongatedfeature coincident with HH24D and clump A of GH93. The south-ernmost contour levels mark the position of clump E. The intensityfalls off rapidly further south, and there is little or no significantemission near clump F and SSV59. Neither is there significantemission near the position of the projected centre of the northernCO outflow at (¹20, ¹15) (GH93). Unfortunately the area coveringthe centre of the HH26 outflow was not mapped.

3.2 Neutral carbon

The neutral carbon spectra observed at the clump positions of GH93are presented alongside corresponding C18O 2→1 spectra in Fig. 2.The most intense C18O 2→1 emission is observed towards positionsthat display the most intense C I emission. However, the intensity ofthe C I lines remains high (T¬

R > 3 K) towards the clumps, even whenthe C18O falls to less than 1 K. The line profiles have a flat-toppedappearance near (15, –95) and (30, –135), although given the noiselevel it is unclear whether or not this is due to saturation.

300 A. G. Gibb and L. T. Little

q 1998 RAS, MNRAS 295, 299–311

Table 1. Observational parameters listing the transition, SSB system noise temperature, integration time per point,estimated noise level, forward scattering and spillover efficiency, spectral resolution, equivalent velocity resolution,angular and spatial resolution and number of spectra observed.

Transition Tsys tint DT¬A hfss dn dv vFWHM Number of

(K) (s) (K) (kHz) (km s¹1) (arcsec/pc) points

C18O J ¼ 2→1 450 300 0.2 0.8 378 0.52 23/0.04 109C I 3P1→3P0 6000 900 0.4 0.5 1134 0.69 10/0.02 15

Fig. 3 shows the C I spectra observed in the east–west scan acrossthe core. Aweak east–west gradient in intensity is evident but thesefigures otherwise demonstrate the general lack of contrast in the C I

emission: T¬R values of ,4 K are still observed up to 3 arcmin off the

main north–south ridge. Unfortunately the C18O data do not extendthis far for comparison. The 12CO 2→1 intensities at these positionsare typically T¬

R,8–9 K (GH93). The C I and the 12CO intensities atthis declination are consistent with optically thick emission fromgas with a temperature of 12–13 K.

3.3 Line parameters

Parameters for Gaussian fits to the C18O and C I spectra observedtowards the clump positions are listed in Table 2. The broadeningeffect of the phase instability on receiver A2 on these measurements isnegligible, contributing only 0.05 km s¹1 to the linewidth, and canthus be ignored (H. E. Matthews, private communication). Owing tothe high noise level, the presence of extended line wings on the C I

spectra would not be distinguished. Towards HH24MMS (clump B),however, a few C18O 2→1 spectra have low-level line wings. Despitethe recent discovery of what appears to be a compact jet-like featurewithin HH24MMS (Bontemps, Ward-Thompson & Andre 1996;Davis et al. 1997), it cannot be determined whether this wing emissionis associated with HH24MMS, owing to the confusing presence ofseveral flows (Krugel & Chini 1994, hereafter KC94).

From the Gaussian fits to the C18O lines, there is little evidencefor a velocity gradient. The most prominent feature is a slight

C I and C18O in HH24–26 301

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Figure 2. Comparison of C I and C18O 2→1 spectra observed towards theclump positions of GH93. The clump labels are listed in the left-hand panelwhile the offsets given in the top right of each frame are in arcsec withrespect to the map centre (Section 2). The difference in velocity between theC18O and C I lines is due to an offset in tuning of the C I line – 492.1623 GHzcompared with the recommended value of 492.1607 GHz (Frerking et al.1989). The line centre velocities given in Table 2 have been corrected for thisdifference.

+A

+B

+ C

+ D

+E

+F

*

*

*

*

*

. ...

.

.

+A

+B

+ C

+ D

+E

+F

*

*

*

*

*

. ...

.

.100 50 0 -50 100 50 0 -50

R.A. offset(arcsec) from 05 43 33.00 R.A. offset(arcsec) from 05 43 33.00

-200

2

1.5

1

0.5

0

Figure 1. (a, left) Grey-scale with contours superimposed of C18O 2→1 T¬R integrated between 8 and 11 km s¹1. Contours start at 2.5 K km s¹1 with interval 0.8

K km s¹1. (b, right) 800-mm emission (grey-scale) and 4→3 HCOþ (thick contours) superimposed. The clumps of GH93 are labelled (A–F), as are knowninfrared (asterisks) and HH objects (filled squares). The crosses mark the peak positions of the clumps where C I spectra were observed.

blueward shift in the peak velocity near the location of the opticaljet G (Solf 1987), which is also detected in HCOþ (GH93). Thelinewidths also appear to be marginally enhanced towards theclumps that appear along a line of sight to a CO outflow (clumpsC, E and F), although there is no wing emission observable in C18O.Also, the neutral carbon linewidths are significantly greater thanthose of the corresponding C18O lines, and closer to those of the COJ=2→1 lines (GH93).

Clump B (HH24MMS) does not exhibit any enhancement in theFWHM linewidth as predicted for a collapsing clump, and observedin L1527 (Myers et al. 1995). This fact may suggest that it is indeedvery young – perhaps less than one free-fall time. Alternatively, theC18O emission does not arise from the (innermost) region mostaffected by collapse.

4 LT E A N A LY S I S

In this section we attempt to estimate abundances for CO and C,assuming that the species are distributed in local thermodynamicequilibrium (LTE). We first estimate excitation temperatures andthen go on to derive column densities. The molecular hydrogen

column densities are estimated from existing dust continuumemission measurements.

4.1 Excitation temperatures

An appropriate choice of excitation temperature is important forestimating column densities. To assist us in this choice for HH24–26, we have rotation temperatures derived from ammonia observa-tions (Harju, Walmsley & Wouterloot 1993), and minimum valuesbased on the observed brightnesses of 12CO and 4→3 HCOþ

(GH93) lines which are likely to be optically thick. 12CO iswidely distributed, so estimates derived from it are likely to pertainto the outer regions of the core, while NH3 and HCOþ have a morecompact distribution following the HH24–26 ridge, yielding esti-mates more likely to be appropriate for the inner regions. Further-more, the molecular hydrogen density required to excite the J=4→3HCOþ line (nH2

, 107 cm¹3) is much greater than that required forJ=2→1 CO (nH2

, 103 cm¹3). Thus the HCOþ is more likely to besub-thermally excited than CO.

Table 3 lists the values for Tex inferred from previous observa-tions. The HCOþ-derived values are, as expected, systematicallylower than the other two. The CO values are generally slightlyhigher than the NH3 ones (although substantially so for clump B).The C18O excitation temperatures would be expected to be similarto those listed in Table 3 for 12CO and NH3. The values that we haveadopted are listed in Table 4.

Assuming that the C18O is optically thick, our observed C18Obrightnesses can be used, with appropriate correction for theRayleigh–Jeans approximation, to set minimum values for Tex.The minimum Texs derived in this way for the clumps are given inTable 4. They lie between 4 and 9 K. It is most unlikely that thesouthern clumps have a true beam-averaged brightness temperatureas high as 15 K, yet their densities (derived from dust observations –GLHL95) suggest that the C18O 2→1 line should not be sub-thermally excited. Therefore, assuming that the beam-fillingfactor is unity, it is likely that they are optically thin, althoughC17O observations are needed to provide unambiguous confirma-tion of this. The two northern clumps, however, could be opticallythick (within the errors) as their minimum excitation temperaturesare somewhat higher. Table 4 lists for C18O the line centre opticaldepths implied by the peak T¬

R assuming the excitation temperaturegiven in column 3 of Table 4.

The difference between the CO 2→1- and NH3-derived tempera-tures suggests that some of the clumps may be externally heated.


q 1998 RAS, MNRAS 295, 299–311

Figure 3. C I spectra observed at ambient cloud positions in the east–westscan. The offsets in arcsec with respect to the map centre are shown in the topright of each frame. The velocity scale assumed a rest frequency of 492.1623GHz (see caption for Fig. 2).

Table 2. Parameters of C18O 2→1 and C I3P1→3P0 spectra observed

towards the clump positions. Brightness temperatures are in K; linewidthsand centre velocities (relative to the LSR) are in km s¹1.

C18O C I

T¬R Dv vcen T¬

R Dv vcen

(K) (km s¹1) (km s¹1) (K) (km s¹1) (km s¹1)

A 4.6 1.6 9.5 7.8 2.6 9.7B 3.9 1.3 9.5 7.0 2.5 9.7C 1.5 1.9 9.4 4.4 2.8 9.6D 1.4 1.6 9.6 4.4 3.7 9.9E 2.0 1.5 9.8 3.6 2.1 10.3F 0.9 2.1 9.7 3.4 3.2 9.8

Table 3. Excitation temperatures in kelvin inferredfrom previous observations. Those from HCOþ andCO are from GH93, except for clumps A and B, forwhich CO data are from KC94. The ammonia valueslisted are the kinetic temperatures estimated fromthe (1,1)–(2,2) rotation temperature (Harju et al.1993).

Position 12CO HCOþ NH3

2→1 4→3 (1,1)–(2,2)

A – 9 12B 27 9 11–15C 16 10 14D 17 9 14E 18 12 17F 17 10 15

Given a scenario in which the neutral carbon is confined to a ‘skin’bounded by AV < 4 while the CO exists at AV > 4, we might expectthe C I excitation temperature to be higher than that of the CO. Theexcitation requirements for 12CO and C I are rather similar (e.g.Phillips & Huggins 1981), so that if the two are well-mixed then weexpect that the C I excitation temperature can be taken as similar tothat for 12CO. We may compare the values for 12CO (left-handcolumn of Table 3) with the minimum excitation temperatures forC I from the brightness of the C I lines, again corrected upwards totake account of the Rayleigh–Jeans approximation (Table 5). Sincethe C I is more extended than the 40-arcsec source (Jupiter) used inderiving hfss ¼ 0:5, we do not expect the true values of theminimum Tex to be greater than those given in Table 5 as a resultof incomplete beam filling. None the less the C I values are less thanthose of 12CO, but not so much that taking errors into account wecan rule out the possibility that the C I lines are optically thick.Therefore the column densities for neutral atomic carbon should beregarded as lower limits.

4.2 Column densities

Beam-averaged column densities have been computed from theC18O and C I using the result derived under the assumption of lowoptical depth, multiplied by a correction factor which takes accountof finite opacity:

N ¼ 1:94 × 103n2

�T¬

Rdv

Aul fu

t

1 ¹ e¹tcm¹2 ð1Þ

(e.g. Irvine, Goldsmith & Hjalmarson 1987), where n is in GHz,�T¬

Rdv is in K km s¹1, fu is the fraction of molecules in the upper

level, Aul ¼ 7:9 × 10¹7 s¹1 for the C I3P1→3P0 transition (Nuss-

baumer 1971) or calculated from, for example, equation (11) ofIrvine et al. (1987) for C18O assuming m0 ¼ 0:1 D, and t is the linecentre optical depth.

Tables 4 and 5 present the column densities of C18O and neutralatomic carbon so calculated towards the clump positions of GH93.The moderate opacities of the observed lines suggest that providedLTE applies, and that the beam-filling factor is unity, our determi-nations of C18O column density should be reasonably accurate, atleast for the southern clumps.

The errors quoted for the column densities in Table 4 includecontributions from calibration and noise uncertainties and theeffects of varying the excitation temperature between 10 and 17K. In general, the largest contribution to the uncertainty arises fromthe uncertainty in Tex, since a low assumed Tex leads to a highoptical depth and correspondingly high N(CO). The errors quotedin Table 4 are extreme values representing a range of Tex from 10 to17 K.

4.3 C18O abundances

Converting the C18O column densities into abundances relative tomolecular hydrogen has made use of the 800-mm data fromGLHL95. H2 column densities (in cm¹2) were calculated followingHildebrand (1983) using the flux densities from GLHL95:

NðH þ H2Þ ¼ 1:38 × 1023 Fn

n5v2 ðe48n=Td ¹ 1Þ;

where Fn is in Jy, n is in THz and v is the full width at half-maximumbeamsize for the observations, 15 arcsec for the data of GLHL95. Adust temperature equal to the corresponding C18O excitationtemperature was assumed. Although our C18O data represent anaverage over a 22-arcsec beam, we can still derive valid abundanceson the assumption that the dust emission is uniformly distributed.By contrast, if all the dust emission is concentrated in an unresolvedcomponent, the dust-derived H2 column densities, averaged over a22-arcsec beam for comparison with C18O, should be reduced by afactor of (22/15)2=2.2. This represents the maximum correctionpossible due to beamsize alone and would raise the C18O abun-dances by the same factor, simultaneously reducing the apparentlevels of depletion. The clumps are probably centrally condensed tosome degree.

4.4 C I column densities

The neutral carbon column densities evaluated towards the clumps


q 1998 RAS, MNRAS 295, 299–311

Table 4. Excitation temperatures, optical depths and column densities for C18O and H2. The C18O column densitiesrepresent an average over a 22-arcsec beam. The minimum excitation temperatures listed in column 2 are derived from theobserved C18O line brightnesses. The H2 column densities were derived from the 800-mm data of GLHL95 and represent anaverage over a 15-arcsec beam. The abundance of C18O has been estimated from the ratio of columns 5 and 6 (the standardC18O abundance is ,2 × 10¹7: Frerking et al. 1982). The depletion factor should be decreased by a factor of 2.2 if it isassumed that the dust emission comes from a central unresolved component. The notation aðbÞ indicates a × 10b.

Position Min. Tex Adopted Tex t NC18O NH2XðC18OÞ Depletion

(K) (K) (implied) (cm¹2) (cm¹2) factor

A 8.8 12 >1.0 >5.6þ4:1¹1:9(15) 3.7þ1:6

¹1:7(23) >2.0þ0:7¹0:6(–8) <10þ4

¹3

B 8.0 12 >0.8 >4.6þ1:7¹1:0(15) 9.9þ4:4

¹4:6(23) >4.6þ2:2¹0:2(–9) <43þ2

¹14

C 5.1 15 0.2 1.8þ0:5¹0:2(15) 1.9þ2:1

¹0:4(23) 9.5þ2:7¹3:9(–9) 21þ15

¹5

D 4.9 15 0.2 1.4þ0:4¹0:2(15) 0.9þ1:1

¹0:3(23) 1.6þ0:4¹0:7(–8) 12þ10

¹2

E 5.7 17 0.2 1.9þ0:7¹0:2(15) 3.4þ5:8

¹0:2(23) 5.6þ0:3¹2:8(–9) 36þ35

¹2

F 4.1 16 0.1 1.2þ0:2¹0:2(15) 1.9þ2:7

¹0:2(23) 6.3þ0:7¹3:3(–9) 32þ35

¹3

Table 5. Excitation temperatures and column densities for neutral carbon.The minimum excitation temperatures listed in column 2 are derived fromthe observed C I line brightnesses. The ratio of C to CO column densities islisted in the final column. The notation aðbÞ indicates a × 10b.

Position Min. Tex Adopted Tex NC NC=NCO

(K) (K) (cm¹2)A 17 20 >2.7(17) —B 16 20 >2.3(17) —C 13 15 >2.0(17) >0.19D 13 15 >2.6(17) >0.27E 12 15 >1.2(17) >0.13F 11 15 >1.6(17) >0.26

lie within a factor of about 2 of ,1:9 × 1017 cm¹2. Combining thesewith the corresponding H2 column densities suggests column-averaged abundances of 0.1–1.1×10¹6. There is little or no correla-tion between the neutral carbon column densities and those ofhydrogen, although the C I and C18O column densities tend to behigher in the north near HH24. Away from the clumps, the columndensity of carbon is ,2.7×1017 cm¹2, very similar to that towardsthe clumps. This indicates that there is a significant amount ofneutral carbon in the outer regions of the core. However, we cannotdetermine whether it is solely confined to an outer shell or whethercontributions from material deeper within the core are merelymasked by high optical depths. A useful complementary tracer toclarify the distribution of C and CO might be 13CO 2→1, whichappears to have a similar optical depth and line shape to the C I

(Little et al. 1994; Schilke et al. 1995).

5 E V I D E N C E F O R C O D E P L E T I O N ?

What is immediately clear from Table 4 is the widespread reductionof the derived C18O abundances towards all the clump positions byfactors of 10 to 43 compared with the canonical value of 2×10¹7

(Frerking et al. 1982).In view of the chemical significance of the apparent depletion,

suggested by the simple model presented in Section 6, it isimportant to look for other explanations for our observations,which retain normal abundance. Three other possibilities bearconsideration.

(1) The properties of the dust, e.g. gas/dust ratio, dust emissivity,may be abnormal in the HH24–26 clumps. The absorption coeffi-cient may be enhanced within dense clumps due to processes suchas coagulation (e.g. Krugel & Siebenmorgen 1994), and this is oftenallowed for by the introduction of a parameter b in column densitycalculations. Employing the expression given by Mezger (1994) fordark clouds (b=3.4) results in column densities which are 33 percent lower than those of Hildebrand (1983), consequently reducingthe apparent levels of depletion by one-third. Correcting further by afactor of 2.2 for the difference in beamsize and assuming point(dust) sources brings the levels of depletion down to a factor of 17 orless – somewhat lower than in Table 4 but still significant (>10)towards clumps E and F (and possibly towards clump B), evenallowing for the uncertainties due to calibration and noise. Thus,towards these clumps, it appears that the C18O abundance is stilllower than the canonical value by a factor of at least 10, unless thedust emissivity is enhanced by *10 times.

Furthermore, the dust emission-derived masses in the clumps arein good agreement with the virial masses (GLHL95). Thus abnor-mal dust parameters do not appear to explain the apparent abun-dances.

(2) Another possibility is that the dust emission arises fromunresolved sub-clumps which are optically thick in C18O. Deple-tion need not then be invoked as we are simply not detecting all theC18O. The most convincing example of depletion, clump E, isresolved by the dust and HCOþ observations, and would require tobe composed of two or more sub-clumps for this explanation to bevalid. The structure within the clumps can be tested via interfero-metric observations of C18O and of dust continuum emission, and/or beam-matched observations of C17O 2→1 to estimate the opticaldepth of the C18O 2→1 line.

It is of interest to examine the implications of sub-clumpingwithin the clumps, by constructing a simple model for the content ofthe antenna beam.

Suppose that the beam is filled with two components: ‘envelope’and ‘sub-clump’ material. In 12CO both components are opticallythick, while in a less abundant CO isotopomer the envelope(component 1) is optically thin, and the sub-clump material (com-ponent 2) is optically thick. For convenience we neglect Rayleigh–Jeans effects and suppose that both components are at the sametemperature (T degrees above the background). The beam fillingfactor of component 2 is denoted fc, while that of component 1 iseffectively (1–fc). The components 1 and 2 have linewidths Dv1 andDv2 respectively.

The contribution of component 1 to the integrated line intensityof the weaker CO isotopomer is

ðTADvÞ1 ¼ ð1 ¹ fcÞt1TDv1

(since t1 p 1), while that of component 2 is

ðTADvÞ2 ¼ fcTDv2

since it is optically thick (t2 > 1). The beam-averaged integratedintensity is

TADv ¼ ðTADvÞ1 þ ðTADvÞ2:

If component 1 is extended so that it subtends an angle much greaterthan the beam dimension, it may be possible to make an estimate ofthe relative contributions of components 1 and 2, by making anobservation on and off the core:

R12 ¼ ðTADvÞ1=ðTADvÞ2 ¼ ð1 ¹ fcÞt1Dv1=ðfcDv2Þ

so that fc ¼ t1Dv1=ðR12Dv2 þ t1Dv1Þ.The 4→3 HCOþ emission is closely correlated with the con-

tinuum dust emission, rather than the C18O, but has a linewidthsimilar to the C18O. We take Dv1 ¼ Dv2. Clump E is barelydetectable as an independent source on the north–south ridge of2→1C18O emission. The integrated intensity on the ridge istypically 3.3 K km s¹1 (Fig. 1a) while clump E does not addmore than about 0.3 K km s¹1 to it. Thus R12 ¼ TA1=TA2 $ 10.Also, for clump E, t1 , 0:2 (Table 4) so that fc # 0:02. The sub-clumps would thus have a very small beam filling factor in the 22-arcsec JCMT beam and would require an extremely high C18Ooptical depth.

There is a serious problem with this ‘sub-clump’ interpretation,which lies in a comparison of the 4→3 HCOþ and 2→1 C18O lineemission. The peak HCOþ T¬

R value towards clump E is 5.5 K whilethat of C18O is only 2.0 K (of which only a small fraction appears tobe associated with the sub-clumps). The HCOþ intensity followsthe submillimetre dust continuum emission well, rather than theenvelope observable in C18O, and is thus associated with the sub-clumps. Yet its line brightness is so high that it must have a beamfilling factor near unity, which is much greater than that deduced forthe sub-clumps, from C18O. Its filling factor is similar to that of theenvelope but its distribution is different. It is also surprising that thesub-clumps and the envelope material have similar linewidths,given their extremely large density contrast. Although it is possibleto construct a model that ‘hides’ matter in sub-clumps that areoptically thick in C18O, the model does not seem to work well whena consideration of the HCOþ observations is included.

(3) Another possibility is that C18O emission is absorbed by anoptically thick C18O envelope of low excitation temperature, so thatinterior clumps observable in 4→3 HCOþ and 5→4 CS cannot bedistinguished. In this case we would expect the CO optical depth tobe very much greater than that of C18O, so that the C18O emissionwould arise from deeper in the cloud than the CO. If the C18O isoptically thick then in clump E its excitation temperature is 5.7 Kcompared with 17 K for CO (from Tables 2 and 3). The excitation


q 1998 RAS, MNRAS 295, 299–311

temperature must thus be much less within the cloud. However, thetemperatures inside the cloud deduced from NH3 show littleevidence of any such decrease, so this explanation appears improb-able.

It therefore seems likely that the CO abundance is truly reducedrelative to hydrogen molecules, most probably as a result ofdepletion on to grains in the cold dense clumps. We prefer thisinterpretation and emphasize it in this paper both for simplicity andbecause of the problems with the alternative interpretationsdescribed above.

We thus assume that the depletion at the clump positions isgenuine, but what about positions well away from the clumps?Unfortunately, the more extended emission has not been detected inthe continuum observations. A crude estimate may be made fromthe flux density towards a position away from any clump emission.For example, at the position offset (45, –30) arcsec, the 800-mmflux density is 0.26 Jy (corresponding to a 3j measurement:GLHL95). Assuming that the excitation temperature lies between10 and 17 K (as above), the hydrogen column density is then< 1:1 × 1023 or < 4:1 × 1022 cm¹2. The corresponding C18O columndensities are 2.160:2 × 1015 and 1:6 6 0:2 × 1015 cm¹2. Thus theC18O abundance is > 2:0 × 10¹8 or > 3:9 × 10¹8, factors of ,5–10lower than the standard value. Therefore CO may also be depletedaway from the clumps as well, but probably by no more than a factorof 10. However, given the upper limit in N(H2) this is a highlyuncertain result and needs to be further constrained by moresensitive continuum observations.

6 R A D I AT I V E T R A N S F E R M O D E L L I N G O FC I A N D C 1 8O E M I S S I O N

In an attempt to study the distribution of C18O and C I within thecore, we have employed a spherically symmetric non-LTE radiativetransfer model. This program is based on the Stenholm–Rybickicomoving frame, core-saturation technique (CCT), and has beensuccessfully employed in modelling C I and CO line emission fromG34.3+0.2 (Little et al. 1994). We seek to model HH24MMS andclump E (HH25MMS in the notation of Bontemps, Andre & Ward-Thompson 1995). Since there are significant differences betweenthem, we model the two regions separately. Each object is modelledby a spherical cloud, the radius, density and velocity structure ofwhich are the same for both sources. Only the temperature andabundance differ between them. A model cloud typically contains30 shells with an inner radius of 1–3×10¹3 pc, and shell thicknesses

corresponding to a change in density of a factor of roughly 2between successive shells.

We have chosen to model the core structure in three ways. Model1: a model with velocity and density variation similar to thatproposed by Crutcher et al. (1994) on the basis of magnetohydro-dynamic (MHD) simulations. Model 2: a freefall collapse modelwhere nH2

~ r¹1:5 and vs ~ r¹0:5. Model 3: a modified singularisothermal sphere (SIS) with density ~r¹2 beyond an ‘infall radius’(rinf ), within which the density and velocity variation is like thefreefall model (Shu 1977). Model 1 corresponds to a cloud that isevolving on an ambipolar diffusion time-scale rather than in freefallcollapse. In this model, we have approximated the density and‘turbulent’ velocity profiles as a two-power-law function.

Table 6 summarizes the basic parameters of each model whichare kept constant – the temperature and abundance profiles arethen varied. The outer radius is chosen to be 1.5 pc. The densityis assigned on two pieces of evidence: (1) that the density at adistance of 0.02 pc is of order 105 –106 cm¹3 since the HCOþ

4→3 line is clearly detected towards both clumps; and (2) thatthe masses of the model clouds are matched as closely aspossible to the dust and/or virial masses of the clumps. Sub-sequent investigation reveals that the exact density variation isrelatively unimportant and our conclusions hold for all reason-able forms.

The clouds are also assumed to be simultaneously internallyand externally heated using a radial temperature variation takenfrom the results of Scoville & Kwan (1976). The outermosttemperature is assigned on the strength of observed 12CO lineintensities (see Table 3). The temperature variation withinthe clouds is TK ¼ 13:0R0:33 þ 2:0R¹0:33 for HH25MMS, and17:1R0:33 þ 2:9R¹0:33 for HH24MMS, where R ¼ r=r0 is the ratioof the shell radius to the outer radius of the cloud.

6.1 Carbon monoxide

For C18O, we have maps for the J=2→1 transition and on-sourcepoints for J=3→2 in both HH24MMS and HH25MMS, whichpermit us to constrain the structure of each model cloud.

The effect of an embedded heating source is simulated by a radialdecrease in temperature from the central shell at a radius of 0.003pc, producing the net profile shown in Fig. 4 (see previous sectionalso). The innermost temperature in the HH24MMS model (seeChandler et al. 1995) is higher than in HH25MMS. This difference,if genuine, probably reflects a difference in mass (and henceluminosity) between the two Class 0 sources, rather than a


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Table 6. Summary of model parameters – molecular hydrogen number density (nH2), systematic

velocity (vs) and ‘turbulent’ velocity (vt). The radial parameter, R ¼ r=r0, is the ratio of the shellradius to the outer radius (=1.5 pc). SIS corresponds to the model of a (truncated) collapsing singularisothermal sphere of Shu (1977).

Parameter Magnetic Freefall SIS

nH2(cm¹3) 2.5×103R¹1:3 r > 0:05 pc 2.5×103R¹1:5 300 R¹2 r > 0:01 pc

2.0×105R¹1:7 r < 0:05 pc 5.5×106R¹1:5 r < 0:01 pc

vs (km s¹1) 0.0 –0.17 R¹0:5 0.0 r > 0:01 pc–0.17 R¹0:5 r < 0:01 pc

vt (km s¹1) 1.75 R0:9 r > 0:5 pc 1.5 1.250.74 R0:14 0:02 < r < 0:5 pc

1.0 r < 0:02 pc

difference in age. HH25MMS has a well-developed, highly colli-mated bipolar CO outflow (Gibb & Davis 1998), whereas the flowfrom HH24MMS is somewhat more compact (Bontemps et al.1996). The temperature affects the abundance of C18O close to thecentre (see below). The J=3→2 line (with an upper energy level of31.6 K) provides a sensitive means to estimate the effect of a rise intemperature towards the centre.

The velocity variation in each cloud (both turbulent and systema-tic) has a subtle but important effect on the line shapes andintensities. In the freefall collapse model (2), the systematic(collapse) velocity produces extended line wings. Since suchwings are not observed, the only way to reproduce this is tomaintain a low C18O abundance close to the cloud centre. However,in so doing it becomes impossible to model the centre and off-centrespectra simultaneously. It is therefore unlikely that these clumps arein freefall collapse.

The turbulent component is, in general, the dominant source ofline broadening. It is necessary to increase the turbulent velocity toapproximately 1 km s¹1 for radii less than about 0.02 pc (for allthree models). This may be a crude representation of the effect of an

outflow on the gas nearest the centre of the cloud, which of course isnot accounted for here.

The C18O abundance variation is taken from Schilke et al. (1995)for the outer regions (AV < 4, which corresponds roughly to radiigreater than 1.1 pc) but forced to fall off towards the centre to mimicthe effects of accretion on to dust grains. The rate at which theabundance decreases into the cloud is varied to fit the observedintensities at the centre, and 20- and 40-arcsec offsets. A constantC18O abundance results in lines that were too bright in the 2→1 and3→2 transitions (both on- and off-centre). Therefore an inwardlydecreasing abundance is necessary to reduce the line optical depths.However, if the C18O abundance falls off too steeply then there is novariation in intensity with radial offset from the cloud centre, andthe line intensities are too low. If the fall-off is too shallow then theintensities of the off-centre points are too high.

To obtain a fit for HH24MMS, the C18O abundance needs to riseagain towards the centre to raise the optical depth and hencebrightness temperature along the central line of sight. This simu-lates the evaporation of CO from grain mantles as a consequence ofthe rise in temperature. It is assumed that the rate at which thisoccurs is proportional to temperature as a crude way of permittingthe slow release of molecules into the gas phase. This ‘slow release’is found to be necessary – no good fits can be achieved if the CO isreturned instantly to the gas phase. One might expect the abundanceto return instantly to its standard value once the sublimationtemperature is exceeded (given the exponential dependence of theevaporation rate on temperature). However, if the CO molecules areembedded in a water or CO2 matrix then even if the dust grains arewarmer than the CO sublimation temperature given by Nakagawa(1980), some CO molecules will remain trapped in the mantle (alsosee, e.g., Blake et al. 1995). The proportion of other grain mantlecomponents must be roughly equal to that of the CO to bind itefficiently. An outflow will also return grain mantle material to thegas phase, although we have found it unnecessary to include such aneffect separately.

The most notable result, which applies irrespectively of theassumed model, is the widespread reduction in the C18O abundance(compared with the nominal value of 2 × 10¹7) required to fit theobserved profiles (which confirms our earlier LTE analysis). Quan-titatively, the model requires that the C18O abundance must be afactor of 10 lower than the standard value throughout the innermost0.25 pc of the core. Furthermore, to fit the spatial variation in lineintensity towards HH24MMS, the abundance of C18O is increasedagain near the centre of the model cloud. Such a rise is unnecessarytowards HH25MMS, although Fig. 4 shows the maximum level thatthis could attain without influencing the output profile. We stressthat this rise towards the centre is necessary to obtain a good fit forHH24MMS. The best-fitting solution involves a variation such thatXðC18OÞ ¼ 1:7 × 10¹7R1:6 þ 1:2 × 10¹9R¹0:33 (which is roughly~1=nH2

in the outer regions of the cloud). Fig. 5 compares thebest-fitting model lines with those observed towards HH24MMSand HH25MMS.

Overall, the best model fits are obtained using the quasi-staticmagnetic model (1) with a (negligibly) small systematic velocity,and a turbulent velocity which decreased inwards from the cloudedge in the manner given by Crutcher et al. (1994) until a radius of0.02 pc is reached where vt is set to a constant (Fig. 4). Table 7summarizes the properties of the observed and resultant best-fittingmodel lines for each model cloud. Model 3 (SIS) tends to produceline profiles that are broader at the base (larger full-width-at-zero-intensity) and more sharply peaked at the centre then those frommodel 1, although the fall-off in intensity for the SIS model is a


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Figure 4. Radial variation of cloud parameters for HH24MMS andHH25MMS. These are the inputs for model 1. The profiles for H2 numberdensity, systematic velocity and turbulent velocity are identical for the twoclouds. The vertical dotted line at 0.02 pc represents the JCMT beam radiusat 220 GHz.

slightly better fit to that observed than the magnetic model (1). Thevalue of the infall radius required for the SIS model is not especiallywell constrained but appears to be less than the beam radius,consistent with a protostellar source with an age of approximately2×104 yr.

These results have been derived assuming a cloud radius of 1.5pc, somewhat larger than the observed largest dimension of thecore. This value is chosen to include the contribution to the CO andC I lines from the low-density envelope. The effect of assumingsmaller values of r0 has been investigated. It is found that the C18Oabundance must fall off more rapidly towards the centre than givenabove. This is easily explained because the observed lines areoptically thin and so directly measure column density. Reducing theouter radius gives rise to a larger value for the outer density, wherethe C18O abundance is set to its nominal value. Therefore theobserved column density of C18O is reached within a shorter pathlength into the cloud and so the abundance must fall off morequickly to compensate.

6.2 Neutral carbon

Since we have only a single transition of neutral carbonand the mapping is incomplete, our results are not particularly

well-constrained. In the case of HH24MMS, we only have a singleposition, whereas several off-source spectra were recorded nearHH25MMS (Figs 2 and 3).

The neutral carbon abundance depends most strongly on thevisual extinction from the outer surface of the cloud uponwhich the dissociating far-UV radiation is presumed to impinge.Accordingly we have assumed initially that it falls off with AV

from the outer radius following a profile similar to that ofSchilke et al. (1995), but with the value at the outer radius ofthe cloud adjusted to give a good fit to the line intensity. Theirvariation of carbon abundance with visual extinction is para-metrized as follows:

XC ¼ 4:0 × 10¹5AV1:5 AV < 2;

¼ 1:1 × 10¹4AV¹9:8 2 < AV < 6;

¼ 2:6 × 10¹12AV¹2:3 AV > 6;

where AV ¼ 1:06 × 10¹21NH (Bohlin, Savage & Drake 1978) is thevisual extinction measured from the edge of the cloud (at r0 ¼ 1:5pc) inwards to a radius r. The column density of hydrogen iscalculated from NH ¼ 2

� rr0

nH2dr, the factor of 2 converting from

molecular hydrogen column density to total H column density. Atno position is the C abundance greater than the cosmic value(3 × 10¹4: Allen 1973). The maximum abundance is 1.1×10¹4,about 6 times higher than in TMC-1, from the model of Schilke etal. (1995). The modelling shows that this abundance variationresults in line intensities and shapes similar to those observed,and that there is no noticeable difference between the magnetic (1),freefall (2) or SIS (3) model. This is perhaps not surprising giventhat the first two models are physically very similar in the regionwhere most of the carbon resides. Typical resultant lines are shownin Fig. 6. Since the majority of the neutral carbon is located in theoutermost 2–3 mag of the cloud, it is also unsurprising that themodel easily reproduces the observed lack of contrast in C I spectrafrom the east–west scan (Fig. 3).

Similar fits can be obtained over a fairly small range ofparameters for HH25MMS. For example, fits can be obtained


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Figure 5. Comparison of observed and modelled C18O spectra from the central position of HH24MMS (top) and HH25MMS (bottom).

Table 7. Summary of observed and best-fitting model C18O spectral linebrightnesses (T¬

R) in K towards HH24MMS and HH25MMS. The values for20 and 40 arcsec off-source have been derived for azimuthally-averagedspectra. The uncertainty in the observed line temperatures is the 1j noiselevel given in Table 1.

HH24MMS HH25MMSTransition Observed Model Observed Model

2→1 (centre) 3.960.2 3.9 1.860.2 2.02→1 (2000 off) 3.260.2 3.4 1.560.2 1.82→1 (4000 off) 2.360.2 3.2 1.560.2 1.83→2 (centre) 2.660.5 2.6 < 2.060.5 0.8

for clouds with higher exterior temperatures (25–30 K) if thecarbon abundance is reduced (by a factor of ,2). However, forHH24MMS no satisfactory fits are possible if the carbonabundance is reduced below the value adopted above, regardlessof temperature. This is easily explained because the model linesare optically thin and the fractional population of the J ¼ 1 levelchanges by less than 10 per cent between 16 and 100 K. Sincethe C I emission is optically thin then NC ~

�TRdv=f1ðTÞ, and the

observed integrated intensity will also change by less than 10 percent. The low optical depths of the model lines are surprisinggiven the saturated appearance of the observed lines.

6.2.1 Alternative carbon distributions

The above discussion has assumed that the neutral carbon abun-dance varies with AV in the manner of the model of Schilke et al.(1995), which is tantamount to placing the carbon in an outer shell.However, a wide variety of abundance profiles can be made to fit thedata. For example, a constant abundance can be fitted for models 1and 3, but not model 2: therefore, if the clumps are in freefallcollapse then a rapid inward decrease in the neutral carbonabundance must exist or else the predicted lines are too broad.Another alternative is the radial dependence that we derived forG34.3+0.2 (Little et al. 1994) in which XC ~ r0:9. This profile iseasily fitted by all three models, demonstrating the difficulty inconstraining the abundance variation within the cloud with only asingle transition and a sparsely sampled map. To summarize,models 1 and 3 can be fitted with almost any abundance profile(subject to an upper limit of approximately 2 × 10¹5 at the cloudedge for shallower profiles), while the freefall model (2) requires aninwardly decreasing abundance, either in the form of Schilke et al.(1995) or as typically ,r1:75. The external temperature is slightlybetter constrained: at least 20 K towards HH24MMS, and 15 Ktowards HH25MMS. In all of these models, the C I lines havegreater optical depths than those derived from the Schilke et al.abundance profile, a result which is more in keeping with observedappearance of the lines (Fig. 2). A good fit has been achievedwithout the necessity of heavy saturation of the C I lines, which, ifassumed, would increase the derived C abundance further.

6.3 Justifying a spherically symmetric model

A major approximation involved in the modelling is clearly that ofspherical symmetry. We can justify this assumption on the groundsthat both of the sources we are modelling are of Class 0 status andare therefore not appreciably flattened except on scales smaller thanour beam (and also on scales smaller than the innermost shellemployed in the models). For example, Chandler et al. (1995) didnot resolve any flattening of HH24MMS with 2.5-arcsec resolution(1000 au at 400 pc), while in the prototype Class 0 sourceVLA1623, the circumstellar disc is estimated to be 175 au or less(Pudritz et al. 1996). The presence of bipolar outflows from bothsources also questions the assumption of spherical clouds. How-ever, outflows from Class 0 objects tend to be highly collimated andthus the propagation of such a flow only affects a small volume ofthe whole cloud. In both cases, therefore, it seems that the assump-tion of spherical symmetry is reasonable.

7 D I S C U S S I O N A N D I N T E R P R E TAT I O N

7.1 The N(C)/N(CO) ratio

The ratio of C and CO LTE-derived, beam-averaged columndensities lies in the range 0.13 to 0.27 (with a mean value of 0.21– Tables 4 and 5). The effect of depletion in the inner core is to boostthe N(C)/N(CO) ratio, while high optical depths in the C I line causethe true C/CO ratio to be underestimated. Unfortunately we have noC18O data away from the main ridge so the N(C)/N(CO) ratio isunknown off-source. The behaviour of the N(C)/N(CO) ratio withinthe cloud is complicated by the depletion of CO on to dust grainsinside the clumps and the removal of free atomic carbon viareactions with Hþ

3 , the efficiency of which increases as the COabundance drops (Gredel, Lepp & Dalgarno 1987). This should leadto a very rapid decrease in the C abundance towards the cloudcentre, which would show up as a nearly unchanging neutral carbon


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Figure 6. Comparison of model C I spectra with those observed towardsHH24MMS (top) and HH25MMS (bottom), using the abundance profile ofSchilke et al. (1995) and model 1.

column density (or integrated intensity) across the source, as weobserve (Fig. 3).

In the low-ionization phase (LIP) model for TMC-1 by Schilke etal. (1995) the neutral carbon is located predominantly on the outsideof the cloud and decreases rapidly inwards. This model predicts anearly constant carbon column density as a function of visualextinction above a value of about 2 mag. With no carbon in theinterior there is clearly no contribution to the integrated intensity.The values of NC (Table 5) in HH24–26 all lie above the LIP modelline (their fig. 2b). If the C I lines are optically thick, then the carboncolumn densities will be higher still.

The most likely explanation for our greater C column densitiesis a greater gas-phase carbon abundance. For example, Hollen-bach, Takahashi & Tielens (1991) demonstrate that N(C) is onlya weak function of the incident UV radiation field strength.Therefore it seems most likely that the reason our estimatedN(C) values lie above the line of Schilke et al. is that morecarbon is present in the gas phase than assumed in their model.This is also borne out by the radiative transfer model, whichrequires a higher neutral carbon abundance to fit the C I lineintensities (in the models that employ the Schilke et al. Cabundance profile). Furthermore, the models of Hollenbach etal. (1991) also tend to have higher peak gas-phase abundances ofC than that of Schilke et al.

7.2 Chemistry in cold collapsing cores

CO is relatively volatile, only freezing out at temperatures of order17 K (Nakagawa 1980). Bergin, Langer & Goldsmith (1995) haveexamined the chemistry in static clouds, allowing for depletion onto grains and including a number of desorption mechanisms. Theyshowed that for CO to freeze out significantly, the grain mantlesmust be primarily composed of H2O. However, they also showedthat the binding of CO in the mantle is weak and that the CO isremoved within a very short period of time (of order 100 yr) oncethe dust temperature has increased above ,22 K. Given our resultthat the C18O abundance must rise more gradually than expected,one possible explanation is that the CO takes part in grain surfacereactions so that there is less to release into the gas phase once thesublimation temperature is exceeded.

Within collapsing clumps, the chemistry has been modelled byRawlings et al. (1992) who demonstrate that, in the isothermal stageof collapse, the CO freezes out on to the dust grains. Referring totheir fig. 3, the CO abundance at an age of 1.3×105 yr and within aradius of 0.02 pc is ,2 × 10¹6, corresponding to a C18O abundanceof 4 × 10¹9. Comparing this with the values in Table 3, we see thattowards the clump positions there is good agreement between thevalues of Rawlings et al. (1992) and our C18O abundances to withina factor of ,2. The length of time that the chemical model requiresto produce such low abundances is an order of magnitude greaterthan the inferred ages of the two Class 0 sources. This suggests thatthe parent cloud remains in a (quasi-) static configuration for aconsiderable time before becoming unstable to forming a proto-stellar core, as expected if the evolution of the cloud is controlledby magnetic fields (e.g. Ciolek & Mouschovias 1994). Theseresults are also borne out by more recent work by Bergin &Langer (1997), who conclude that water-ice mantles are necessaryto produce large levels of depletion, and predict that HCOþ, CS andSO will be highly depleted from the gas phase. Given the largedepletions inferred within HH24MMS and HH25MMS, we con-clude that the dust grain mantles should contain a significantamount of water ice.

7.3 The evolutionary status of HH24–26

Molecular depletion has now been observed towards severalsources (e.g. NGC 1333-IRAS4 – Blake et al. 1995), althoughhigh levels inferred throughout the core have only been identified ina few (e.g. IRAS 05338–0624 – McMullin, Mundy & Blake 1994).The high level of CO depletion inferred within HH24–26 suggeststhat there have been no stellar sources to influence the chemistryand return grain mantle material to the gas phase, so that moleculesare continuously accreting on to the dust grains. Thus the core maybe forming its first generation of stars. If the bulk of the core hasbeen contracting quasi-statically through the action of ambipolardiffusion for 106 yr (e.g. Crutcher et al. 1994) then there has beensufficient time for CO to accrete on to grains even in the lower-density regions. This interpretation is reinforced by the lack of anear-IR cluster compared with the other high-mass cores in L1630(Lada et al. 1991). We would not, therefore, expect to see such highlevels of depletion towards these other cores.

Is this interpretation supported by other observations in HH24–26? The 4→3 HCOþ data of GH93 were the original tracers of theclumps, so we need to address why 4→3 HCOþ traces the clumpsand C18O does not – i.e. why HCOþ does not appear to besignificantly depleted. There is some evidence for the depletionof HCOþ – the large velocity gradient (LVG) modelling ofGLHL95 required a modest reduction in the HCOþ abundance tofit the observed line intensities. Chemical models of cloud evolutionshow that HCOþ may actually rise in abundance for a time duringthe collapse of a clump because the species that destroy HCOþ areremoved from the gas phase more quickly than HCOþ itself(Rawlings et al. 1992). This seems to be true for all molecularions (Blake et al. 1995). In addition, the HCOþ 4→3 line becomesoptically thick relatively quickly and so masks any evidence ofinternal depletion (GH93).

While the HCOþ emission can be explained by collapse-phasechemistry, CS is also seen to trace some of the clumps (GH93),contrary to the results of Bergin & Langer (1997). However, closerinspection reveals that the CS emission is observed towards regionswhere shocks are likely to be the dominant source of excitation. Forexample, HH25MMS is located exactly at the centre of the HCOþ

4→ 3 emission but the CS 5→4 peaks about 10 arcsec north-east ofHH25MMS and is strong in the south-east. Given that there is abipolar outflow being driven by HH25MMS and that its shape isnearly identical to the distribution of CS 5→4, it seems probablethat the outflow is responsible for the enhanced CS emission (Gibb& Davis 1998).

8 C O N C L U S I O N S

We have presented observations of C18O (J ¼ 2→1 and 3→2) andneutral atomic carbon (3P1→3P0) towards the HH24–26 molecularcloud core, made at the JCMT. The core was mapped in the 2→1line of C18O, with single 3→2 spectra recorded at the peak positionof the two clumps harbouring Class 0 protostar candidates(HH24MMS and HH25MMS). C I spectra were observed at theposition of each of the clumps identified by GH93, together with aneast–west cross-scan which was made at the declination of clumpE/HH25MMS.

The C18O distribution is markedly different from theprevious maps of HCOþ and dust continuum, and displayslittle evidence of the substructure in the core. Estimates ofthe column density towards clumps B (HH24MMS), E(HH25MMS) and F suggest that there is very little CO in the


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gas phase. Alternative explanations, retaining normal abun-dances and relying on optical depth effects (as discussed inSection 5), seem to be less likely.

The clump temperatures are sufficiently low to permit CO tofreeze out on to grains. Comparison with chemical models ofcollapsing clumps, such as Rawlings et al. (1992), reveals reason-ably good agreement with the depletion interpretation, suggestingthat these clumps are still in the collapse phase of evolution and thatembedded young stellar objects have not yet been able to warm theirsurroundings sufficiently to liberate ices significantly. This effectshould therefore be observable in many other species which willrequire further observations to confirm.

Non-LTE radiative transfer modelling of the C18O emission cangive a quite satisfactory description of the C18O and C I line shapesand intensities with a fairly simple model for the core. The modelsrequire a significant reduction in the CO abundance, and show that itis widespread throughout the core and not just confined to theimmediate environs of the clumps. In the case of HH24MMS, it hasbeen deduced that the CO abundance begins to rise again within0.05 pc, suggesting that this source is warming up the grains andreturning mantle material into the gas phase. To the south,HH25MMS shows no evidence for this level of internal heating,which suggests that HH24MMS may be the more massive andluminous young stellar object of the two. In the context of recentchemical models by Bergin & Langer (1997), the grain mantlesmust contain a significant amount of water ice to permit such levelsof depletion.

The neutral carbon displays very low contrast across the source,although both it and C18O tend to be brighter towards the HH24complex in the northern part of the core. The C I spectra show weakevidence for broadening towards the clumps, indicating that theremay be neutral carbon deep within the core and not just on thesurface. Application of a non-LTE radiative transfer model showsthat the difference in intensity between the northern and southernregions of HH24–26 is consistent with a difference in temperatureand not necessarily abundance, although the results are poorlyconstrained.

We conclude with the following picture of HH24–26. The corehas dimensions of approximately 1.0×0.5 pc, elongated roughlynorth–south. In the north of HH24–26, the envelope temperaturesare 20–25 K (from C I and CO line intensities), indicating anexternal heating source located to the north and east such as thenear-IR cluster in NGC 2068 (Lada et al. 1991). Within the core, alinear filament has formed (seen in ammonia: Harju et al. 1993)which has fragmented into numerous clumps (seen in HCOþ anddust continuum: GH93; GLHL95). The filament and clumps havelower temperatures: typically 10–15 K. The clumps are the sites ofcurrent or future star formation, and some of them have embeddedinfrared and or radio continuum sources. Significantly reducedabundances of C18O suggest that these clumps are still in thecollapse phase of evolution, and, coupled with the observationthat the core does not contain an infrared cluster, this indicates thatHH24–26 may be in the process of forming its first generation ofstars.

AC K N OW L E D G M E N T S

The authors thank the PPARC for financial support, Chris Davis forproviding data in advance of publication, Robin Phillips for makingthe C18O J ¼ 3→2 observations, Duncan MacKay and DavidHollenbach for discussions regarding accretion/desorption ofgrain mantle material, and an anonymous referee for helpful

comments and criticism. The JCMT is operated by the JointAstronomy Centre on behalf of the Particle Physics and AstronomyResearch Council of the United Kingdom, The Netherlands Orga-nization for Scientific Research and the National Research Councilof Canada.

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