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Anomalies of the J = 1 , 0 HCN hyper ne structure and clumpiness of dense molecular cloud cores. Implications for S140 IRS1
L. Pirogov
Institute of Applied Physics of Russian Academy of Sciences, Uljanov st. 46, 603600 Nizhny Novgorod, Russia

Introduction J =1 , 0 HCN observations toward dense molecular cloud cores associated with Galactic
high-mass star forming regions Pirogov, 1999 reveal prominent anomalies of hyper ne component intensities R12 = T F = 1 , 1=T F = 2 , 1 0:4 and R02 = T F = 0 , 1=T F =2 , 1 0:2 in many cases. A standard explanation of this e ect includes thermal line overlaps in higher HCN transitions Guilloteau and Baudry, 1981, hereafter GB, yet, the observed line widths in the sources demonstrating anomalies are highly suprathermal 2 km s. It is shown Pirogov, 1999 that microturbulent models with local line pro les having both thermal and microturbulent contributions fail to reproduce J = 1 , 0 HCN anomalies together with high line widths. These models often produce saturated or self-reversed HCN pro les which are rarely observed in that kind of ob jects.

On the other hand, there are many indications that molecular clouds and their cores are clumpy on all spatial scales down to telescope resolution limits see Goldsmith, 1995. One might expect that in the case of small-scale clumpiness the anomalies of the J =1 , 0 HCN hyper ne structure can originate in clumps with nearly thermal local line widths. If the clump's volume lling factor is su ciently small, the emission from a single clump can escape from the cloud without signi cant scattering thus providing information about its parameters. Observed line widths in this case re ect velocities of interclump motions.

A clumpy model
We developed a program that calculates HCN excitation parameters as well as emergent J = 1 , 0 HCN pro les within a spherically-symmetric model that can consist of many clumps unresolved by a telescope beam. The model utilizes the multi-zone radiative transfer code developed earlier for a cloud with smooth density distribution Turner et al., 1997. Model cloud consists of a set of concentric zones, each of which is divided into cells having dimensions lower or equal to zone's width. Each cell can be lled with gas or be empty according to integer random number generator which gives 1 with probability P clump or 0 empty cell with probability1 , P The probability P which has the same statistical meaning as clump volume lling factor can be varied from zone to zone, thus changing number of clumps in each zone. No interclump gas is assumed. Clumps are considered to be homogeneous isothermal balls of the same size without internal structure. Clump parameters kinetic temperature, density and microturbulentvelocity as well as velocity of bulk motions of clump ensemble can be varied from zone to zone.


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HCN excitation is computed for one representative clump per zone using GB approach and assuming constant excitation conditions within the clump. All clumps in the zone are assumed to be identical to the given clump. Local line pro le for each clump is assumed to be Gaussian with both thermal and microturbulent contributions to its width. Angular integration while computing mean radiation eld is calculated by summing radiation coming along numberofrays separated by a xed angular step. Radiation along particular ray summarizes contributions from clumps crossed by this ray. Each clump has randomly oriented velocity component. Its absolute value called velocityof interclump bulk motions is the same for each clump in the given zone. A pro jection of random velocity component on a given ray gives particular Doppler shift for emission coming from distant clump. Spatial distribution of clumps is kept xed during calculation of HCN excitation for given clump in the zone. Because next representative clump can take arbitrary place in the next zone, new spatial distribution of clumps is considered because all possible clumps con gurations are statistically equivalent see Pagani, 1998. Iteration process is similar to the one described byTurner et al. 1997. After the iteration process converges, emergent line pro les are calculated for all independent lines of sights separated by angular size of single clump. To reduce statistical uctuations, the resultant pro les are averaged over independent lines of sight within pro jection of each zone on a plane of a sky. These pro les can be convolved with telescope beam to be compared with real spectra.

L1204 S140 IRS1 dense core implications for clumpy structure
The clumpy model was examined by tting model pro les to the HCN and H13 CN spectra observed toward the bright infrared source S140 IRS1. This well-known high-mass star forming region demonstrates very strong HCN lines with prominent anomalies. S140 IRS1 has been widely observed and modeled in various lines giving a possibility to compare with the parameters found by other authors. The dense core of the L1204 molecular cloud is located northeast of the S140 optical H II region and contains a cluster of three infrared sources, IRS 1-3, which are identi ed with high-mass stars of spectral type B Evans et al., 1989. The multitransitional CS observations of the core Zhou et al., 1994 reveal two di erent components on a subarcminute spatial scale: a spherical one centered on IRS1 and an arc component being closer to the photon-dominated interface region between the H II region and molecular cloud. The arc component demonstrates resolved clumpy structure Hayashi and Murata, 1992 while the spherical component shows a central disk surrounded by a cavity embedded in an inhomogeneous dense envelope Wilner and Welch, 1994; Minchin et al., 1993; Harker et al., 1997. The J =1 , 0 HCN observations toward S140 IRS1 performed at RT-22 Pirogovet al., 1995 and at 20-m OSO Pirogov, 1999 reveal the following line parameters: TMB F = 2 , 1 = 10 K, V =2:6 km s and R12 =0; 37, R02 =0:24. The J =1 , 0 H13 CH line parameters are the following: TMB F =2 , 1=1:2 K, V =2:2 km s and R12 0; 6, R02 0:2 Pirogov et al., 1995. Our observations with 40 beam toward IRS1 covered most of the spherical component and, probably, a part of the arc component. In order to reproduce the observed J =1 , 0 HCN and H13 CH spectra toward S140 IRS1


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we performed detailed model calculations of the spherical component. We took 0.44 pc for the outer radius Zhou et al., 1994 and divided the model core into 17 zones, each zone having 0.026 pc width. Clump parameters: number density, kinetic temperature as well as volume lling factor and velocity of bulk motions were kept constant within each zone and could be varied from zone to zone as power-law functions of a zone's radius. Microturbulent velocity was set to zero in order to obtain the e ect of thermal line overlaps alone. The velocity of bulk interclump motions was set to 1.3 km s according to the optically thin H13CN line width. Following Zhou et al. 1994 we assumed the central zone to be empty in order to account for the cavity around IR sources. The HCN abundance was assumed constant and its value was varied in order to t the calculated F =2 , 1 intensity to the observed value. The resulted spectrum was calculated byaveraging individual spectra for all independent lines of sight within the pro jection of each zone on the plane of the sky and then convolving the averaged model spectra corresponding to di erent pro jections with a 4000 beam. The quality of tting was controlled by the sum of squares of residual between model and observed values of line pro le temperatures. A clump's number density and volume lling factor were set to be power-law functions of radius: n = n0 r=R, and P = P0r=R, respectively, where n0 and P0 corresponds to the second zone and R is the outer radius. While searching for suppressed R12 ratios together with R02 0:2we found that the best ts occur at kinetic temperatures 20 K. This could be related to the fact that the overlaps of the second pair of closely located components in the J = 2 , 1 transition F =2 , 2 and F =1 , 0, see GB which lead to suppressed R02 ratio are still e ective at temperatures higher than 20 K. We set the following law for kinetic temperature dependence: TKIN = 30r=R,0:4 which gives 30 K in the second zone and 10 K at the edge of the cloud. The best t parameters correspond to n0 = 1:8 106 cm,3, = 0:6, P0 = 0:2, and = 0:3. Microturbulent CS modeling performed by Zhou et al. 1994 resulted in the following radial dependence of number density: n = 1:4 106r=R,0:8 which has a power-law index close to the total nr and P r index from our results. Lower kinetic temperatures e.g. 13 K for all zones can give even better ts, yet, low temperatures contradict with high HCO+ line intensities observed toward S140 IRS1 with 2000 resolution Hasegawa et al. 1991. The number of clumps within the rst 4 zones which give the main contribution to the resulting spectrum is 16000 with an average volume lling factor of 0.11 which is somewhat lower than estimates made by other authors Zhou et al., 1994; Spaans and Dishoeck, 1997. The HCN abundance is 5 10,9. The H13 CN lines are nearly optically thin and the R12 and R02 ratios are approximately equal to 0.6 and 0.2, respectively, being insensitive to particular forms of density and volume lling factor laws. We used the power-law parameters from the HCN tting and t only the F =2 , 1 peak intensityvarying H13 CN abundance. The best H13 CN t was found at X H13 CN 1:8 10,10. The HCN and H13 CN spectra are shown in Fig. 1 together with the best tting curves. The results of recent HCN and H13 CN observations toward S140 IRS1 obtained at OSO with high spectral resolution are also discussed.


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Figure 1: The J = 1 , 0 HCN and H13 CN pro les toward S140 IRS1 Pirogov et al., 1995. Smooth curves correspond to the clumpy model results

Conclusions
Anomalies of the J = 1 , 0 HCN hyperfne structure R12 0:4 and R02 0:2 are often observed toward dense molecular cloud cores associated with high-mass star forming regions where line widths are highly suprathermal Pirogov, 1999. These e ects can be explained if the cores are clumpy on scales unresolved by telescope beam. Detailed clumpy model calculations give good ts between model and observed HCN and H13 CN spectra toward the bright infrared source S140 IRS1 con rming that well-known HCN hyper ne intensity anomalies observed in regions of high-mass star formation can be an indicator of small-scale clumpiness.
The research was supported by the INTAS grant 93-2168-ext and the Russian Foundation for Basic Research grants 96-02-16472 and 99-02-16556 in part.

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