On the Relative Abundance of C 18 OandC 17 O in the Taurus Molecular Cloud

Transcription

1 Submitted: 23 February 2004 Revised: March 24, 2004 On the Relative Abundance of C 18 OandC 17 O in the Taurus Molecular Cloud E. F. Ladd Physics Department, Bucknell University, Lewisburg, PA ladd@bucknell.edu ABSTRACT We present measurements of the [C 18 O]/[C 17 O] abundance ratio based on observations of J = 1 0 lines of these isotopomers toward star-forming cores in the Taurus molecular cloud. Our data set includes measurements along 648 lines of sight through these clouds, covering both low and high column density regions. We compare the integrated intensity ratio for each line of sight with a simple model of emission from a dense cloud to determine this abundance ratio. Using this model, we find a [C 18 O]/[C 17 O] abundance ratio of 4.0 ± 0.5 is consistent with the data. However, at low column densities, it appears that a higher abundance ratio may be more appropriate. We examine ways in which the abundance ratio might be changed in the outer parts of molecular clouds and conclude that selective photodissociation of C 17 O by external ultraviolet light can increase the abundance ratio. A two-phase model, incorporating a C 17 O-free sheath of cloud material surrounding a self-shielded inner cloud region, is fit to the data. Using this model and an assumed sheath H 2 column density of cm 2, we find a lower abundance ratio of 2.8±0.4 for the material in the shielded inner cloud. This new result is consistent with recent results from ultraviolet absorption spectroscopy through translucent clouds and measurements of the [ 13 C 18 O]/[ 13 C 17 O] ratio in the Ophiuchus molecular cloud. Subject headings: ISM: clouds ISM: individual (Taurus molecular cloud) ISM: molecules astrochemistry radio lines: ISM 1. Introduction Carbon monoxide is the second most abundant molecular constituent in star-forming clouds, and because the most abundant constituent, H 2, does not ordinarily emit in the cold

2 2 conditions characteristic of these clouds, observations of CO emissions provide a primary probe of cloud column density, mass, and dynamics. The low rotational energy levels of CO are easily excited under typical molecular cloud conditions (n 10 4 cm 3,T 10 K), and emission from transitions between these levels has wavelengths in the millimeter range. Because of its relatively high abundance, the main isotopomer, 12 C 16 O, produces emission with high optical depth, making measurements of this tracer s lines less suitable for determining column densities and dynamical characteristics. The rare isotopomers of CO offer many of the same advantages of the main isotopomer (e.g., substantial excitation under typical molecular cloud conditions, and emission lines at accessible wavelengths), but with emission lines of lower optical depth. C 18 O, which is approximately 500 times less abundant than 12 C 16 O (Wilson & Rood (1994)), has been used by many authors as a probe of mass and dynamics in star-forming clouds. In most cases, authors have assumed that the C 18 O emission from clouds has low optical depth, but newer observations indicate that especially toward dark clouds with small velocity dispersions, C 18 O emission lines may have optical depths of order unity (e.g., Lada et al. (1994), Ladd, Fuller & Deane (1998)), and therefore corrections for line saturation are necessary to obtain accurate column densities (Wilson et al. (1981)). The line optical depth can be directly measured with observations of a pair of rare CO isotopomers, provided that the abundance ratio between the isotopomers is known. Myers et al. (1983) used observations of 13 C 16 OandC 18 OtoestimatetheC 18 Ooptical depth and subsequently the CO and H 2 column density toward a number of dark clouds. These authors assumed that both isotopomers are excited under the same physical conditions and compared the observed intensity ratio with an abundance ratio derived from previous measurements. The 13 CO emission is often optically thick toward many of these sources, and so this technique essentially reduces to using the 13 CO emission to deduce the excitation temperature and then applying that temperature to the C 18 O emission to measure the C 18 O optical depth. A potential shortcoming of this technique is that the excitation temperature determined from the 13 CO emission may not be indicative of the excitation temperature along the entire line of sight, simply because of optical depth effects. In addition, the use of a doubly-substituted isotopomer (i.e., 13 C for 12 C and 16 O for 18 O) makes estimation of the abundance ratio difficult. Moreover, exchange reactions involving 12 Cand 13 C can alter the abundances of species containing these isotopes (e.g., Watson, Anicich, & Huntress (1976), Wilson et al. (1981), Langer et al. (1984), van Dishoeck & Black (1988), & Federman et al. (2003)) so that their abundance ratio may vary within a cloud or even along a line of sight. More recently, Ladd, Fuller & Deane (1998) and Fuller & Ladd (2002) have used the

3 3 same technique with observations of C 18 O and the even less abundant isotopomer C 17 Oto determine column densities toward forming stars in the Taurus molecular cloud. However, because C 17 O emission has an even lower optical depth than that from C 18 O, emission from both isotopomers is produced along the entire line of sight, and the assumption that the emission from both isotopomers arises from the same material is better justified. Furthermore, these isotopomers differ only in that their oxygen isotopes differ. Chemical fractionation of molecules containing oxygen isotopes does not occur in dark cloud environments ((Langer et al. 1984)) and so the abundance ratio of these isotopomers is directly related to the isotope abundance ratio. The relative abundances of rare oxygen isotopes are thought to be set by stellar nucleosynthesis processes, most notably in the post-main Sequence phase for low and intermediate mass stars where substantial production of 17 O may take place ((Boothroyd & Sackmann 1999)). 18 O, on the other hand, may be produced by stars of both high and low mass. Because of the different timescales for the evolution of low and high mass stars, one might expect the [ 18 O]/[ 17 O] ratio to decrease with time as a stellar population ages. This effect may explain why the solar abundance ratio (which may be indicative of the interstellar medium 4.5 billion years ago) is higher than the values found in the interstellar medium today ((Wilson & Rood 1994)). The success of these techniques for determining cloud column densities depends critically on pre-existing determinations of the isotopomer abundance ratio. The ratio of intensities in the two lines is compared to this abundance ratio in order to determine the optical depth of the more abundant species. Ladd, Fuller & Deane (1998) and Fuller & Ladd (2002) assumed a [C 18 O]/[C 17 O] abundance ratio of 3.65 based on the work of Penzias (1981). However, other studies of different molecular cloud environments have found values ranging from 2.9 to 4.2. Penzias (1981) value was measured toward massive star formation regions throughout the galactic disk; he found an average abundance ratio of 3.65 ± 0.15 with no evidence for variation as a function of galactocentric radius. Wilson et al. (1981) examined nearby dark cloud environments and found an abundance ratio of 3.2 ± 0.2 for a selection of sources. More recently, Bensch et al. (2001) have detected 13 C 18 Oand 13 C 17 Otowardthe Ophiuchus cloud complex, and have used these measurements to determine an abundance ratio of 4.15 ± 0.52(stat) ± 0.59(sys). Sheffer et al. (2002) have measured ultraviolet absorption due to these isotopomers through a translucent molecular cloud. They find an abundance ratio of 2.9 ± 1.2 in this environment. Each of the above studies is based on one line of sight, or at best single lines of sight through several different clouds. In this work, we present observations of more than 600 lines of sight through five dark clouds in the Taurus molecular cloud complex. We measure the

4 4 C 18 OandC 17 O intensities through regions of varying column density in the same clouds, and can therefore construct curve of growth -type plots which show explicitly the saturation of the C 18 O intensity due to increasing optical depth. Using a simple parametric model for the emitting cloud, we assess the range of abundance ratios which are consistent with the dataset. Because the dataset contains spectra taken toward many positions in several clouds, we can evaluate whether the abundance ratio varies with column density. We consider the observable effects chemical fractionation and selective photodissociation might have on our data, and construct a simple two phase model consisting of a selectively-dissociated sheath region surrounding an unaffected cloud interior. For reasonable values of the sheath thickness, we find that our observations are consistent with a cloud interior abundance ratio of 2.8 ± 0.5. We compare our results with previous determinations published in the literature, many of which were derived without explicit consideration of the effects of selective photodissociation. We discuss how these results might change if such effects were considered, and conclude that all of the observations may be consistent with the cloud interior abundance ratio derived in this work. We present our observations in 2 and delineate our method for extracting the abundance ratio from the observations in 3. In 4 we compare the data with a simple model for the emitting cloud, and examine the effects of chemical fractionation and selective photodissociation on our results. We present our conclusions in Observations We observed the J = 1 0 rotational transition of C 18 O ( GHz) and C 17 O ( GHz) with the 14-m telescope of the Five College Radio Astronomy Observatory (FCRAO) 1 during the observing season toward five regions containing forming stars in the Taurus molecular cloud. The data were obtained with the FCRAO 15 beam QUARRY receiver array Erickson et al. (1992) and the 1024 channel FAAS autocorrelator, with channel spacing of 19.5 khz, which with uniform weighting produced a full width at half maximum (FWHM) velocity resolution of 0.06 km s 1. The pointing of the telescope 1 The Five College Radio Astronomy Observatory is operated with support from the National Science Foundation under grant AST and with permission of the Metropolitan District Commission of Massachusetts.

5 5 was updated with observations of Mars and the strong stellar SiO maser IK Tau several times per observing session. Typical pointing corrections were less than 10 in azimuth and elevation. All observations were calibrated onto an antenna temperature scale by a chopper wheel technique that allowed switching between the sky and an ambient temperature load. Data were obtained by frequency switching, with an offset frequency of 4 MHz. System temperatures were K at both frequencies, and typical integration times were 30 minutes in C 18 O and 120 minutes in C 17 O, yielding root mean square (rms) noise levels of 0.15 and 0.07 K, respectively. The half-power beam width (Θ B =48 ) was determined from observations of Mars, and the forward scattering and spillover efficiency (η fss =0.72) was determined from observations of the Moon. Half-beam sampled footprint maps were obtained toward five regions containing forming stars in Taurus. The coordinates of these forming stars are given in Table 1. Each footprint covers a region of with 120 observations on a 25 grid. Observations toward the L1551 region were extended eastward to map the region surrounding the forming star L1551NE; this extended map contains 168 observations. Taken together, the maps provide 648 observations of dense gas in the Taurus molecular cloud. 3. Results Typical spectra for each region of shown in Figure 1. Peak C 18 O antenna temperatures range from 1 2 K, and most lines have FWHM velocity widths of 0.7 kms 1. Single component, somewhat gaussian C 18 O lines are seen toward L1527, L1551, and L1489, while two velocity components are more typically present toward I04381 and TMR1. All C 17 O spectra show three emission components resulting from the hyperfine splitting of the J = 1 rotational energy level. In all cases, the frequency separation and relative intensities of the measured components is consistent with a single velocity component and low optical depth in the line. The data were reduced with the CLASS data package (Forveille, Guilloteau, & Lucas (1989)). The frequency-switched data were rectified, after which a linear baseline was subtracted. Integrated intensities were obtained for both C 18 OandC 17 O by summing line intensities over a specified velocity interval. The FWHM velocity width of the C 18 O emission was measured via one of two methods: 1) with a gaussian fit using the GAUSS routine in CLASS if the spectral line was reasonably gaussian, or 2) by direct calculation of the second moment of the emission as a function of velocity. In the latter case, the effective FWHM line width assigned to the spectrum was the FWHM line width of a gaussian with the same second moment. This technique produces an intensity weighted effective width and proved

6 6 useful for quantifying the velocity width of a small number of multi-peaked and non-gaussian intensity distributions Extracting the Abundance Ratio from the Data The abundance ratio R can be extracted from a comparison between observed intensities of the two isotopomers, assuming that the emission from both tracers arises from the same material under the same excitation conditions. R is then the ratio of the column densities in each of the species, and the ratio of the total optical depth in the two J = 1 0 lines differs from the abundance ratio R only by a factor η which arises because of the frequency dependence the relationship between column density and optical depth. For the optical depth in the J = 1 0 line for this pair of isotopomers, η =0.98. Thus, we can express the line-integrated C 18 O optical depth in terms of the line-integrated C 17 O optical depth as follows: The C 18 O optical depth as a function of velocity is then τ 18,o = ηrτ 17,o. (1) τ 18 (v) =τ 18,o Φ(v) (2) where Φ(v) is a normalized function describing the velocity distribution of the optical depth. The C 17 O optical depth as a function of velocity is complicated by the hyperfine splitting of the J = 1 0 transition into three components, but it can be written as τ 17 (v) =τ 17,o Σ 3 i=1 g i Φ(v v i )= τ 18,o ηr Σ3 i=1 g i Φ(v v i ) (3) where g i and v i are the statistical weight and velocity offset of the i th C 17 O hyperfine component, and we assume the same shape for the distribution of optical depth with velocity for each hyperfine component. With these relationships for the optical depths of the two tracers, one can calculate the integrated intensities of both lines: I 18 v T 18 = [J 18 (T x ) J 18 (T bg )](1 e τ18(v) ) dv (4) v

7 7 I 17 v T 17 = [J 17 (T x ) J 17 (T bg )](1 e τ17(v) ) dv (5) v where T x is the excitation temperature of the J = 1 0 transition, T bg is the temperature of the cosmic background radiation. Using Eqs. 2 and 3 above, we can parametrize Eqs. 4 and 5intermsofτ 18,o, R, T x,andφ(v) allowing us to create models of how these intensities vary with optical depth for input values of R, T x,andφ(v). Modeling the integrated intensities, rather than line peak temperatures, has the advantage that the ratio of the intensities is somewhat insensitive to the velocity distribution of the emission (Ladd, Fuller & Deane 1998), and therefore this ratio, and how it changes with optical depth, is dominated by the value of R chosen for each model (see discussion below). In the limit of low optical depth in both lines, the intensity ratio reduces to I 18 I 17 = ηr. For all larger optical depths, the intensity ratio decreases, and for very high optical depths, the ratio can be less than one, since the presence of three C 17 O hyperfine components allows the C 17 O emission to saturate over a large velocity range Comparing with Data With a large number of observations toward each region, we can construct plots of I 18 vs. I 17 and compare the data with models for different values of R and T x. The result is a classic curve of growth plot where I 17 essentially measures column density (since τ 17,o << 1 along all lines of sight), and I 18 saturates as τ 18,o ηr τ 17,o approaches and exceeds unity. Models of the emission, given input values of R, T x, and a gaussian FWHM line width V, can be compared with these data, and the values of these parameters can be constrained. However, the role line width plays in this analysis can be minimized by plotting the integrated intensity divided by the measured line width, rather than the integrated intensity alone. Observations with identical integrated intensity but different line width have differing peak C 18 O optical depths, and so are saturated to different degrees. Since it is this saturation that produces the turnover in the I 18 vs. I 17 curve, spectra of differing line widths produce a broadening in the distribution of (I 17,I 18 ) points, particularly for higher values of I 18. The difference between the two modes of data presentation is illustrated in Figure 2. In the left panel, the C 18 OandC 17 O integrated intensities are plotted against one another, while in the right panel, the intensities are divided by the FWHM line width as determined from the C 18 O emission. Overplotted on both panels are models for the emission assuming

8 8 an abundance ratio (R) of 4.0, an excitation temperature (T x ) of 8 K, and several choices for FWHM line width ranging from 0.3 to 1.0 km s 1. By normalizing the dataset with the line width, we substantially reduce the scatter in the dataset, particularly in the direction orthogonal to the model curves. Furthermore, the models themselves become indistinguishable from one another, removing the line width as a relevant parameter. The data for all five regions, in integrated intensity divided by FWHM line width (hereafter II/lw) format, is displayed in Figure 3. Overplotted on each panel is a model assuming R =4.0andT x = 8 K. The plots for all five regions are quite similar in that the data cluster around the model curve. However differences are evident: the I04381 data have on average values of II/lw in both tracers which are lower than those found toward other regions. In addition, the L1489 data typically have more C 17 O emission than predicted by the model, while the L1527 data tend to have less C 17 O emission than predicted by this model. Nonetheless, the distribution of the combined dataset, shown in the leftmost panel, appears centered on the model curve. 4. Analysis To estimate the best values of R and T x, we created models for a range of input values andthenusedaχ 2 minimization technique to select the group of models which best fit the data. We considered values of T x ranging from 5 to 10.5 K and R values from 1.8 to 8.0. To calculate the reduced χ 2, we considered both the statistical uncertainties derived from the noise level in each spectrum, and a 10% systematic uncertainty contribution. A plot of the reduced χ 2 as a function of R and T x is shown in Figure 4 for models fit to the entire data set. This figure shows that the best-fit abundance ratio is relatively insensitive to the excitation temperature of the emission, except perhaps in cases of very low excitation temperature. Both I 18 and I 17 scale with T x in similar ways, so that changes in the value of this parameter have little effect on the slope of the model curve through the (I 17,I 18 ) plane. The main difference between a high-t x model and a low-t x model occurs at large values of I 18,where low T x implies a large optical depth, while a higher T x model has a lower optical depth. Therefore, to fit the turnover in the in the data distribution at high values of I 18,high- T x models require a slightly lower value of R, while low-t x models replicate the turnover because of saturation effects due to increasing C 18 O optical depth. The minimum reduced χ 2 of 1.56 occurs for an excitation temperature of 8.5 K and

9 9 an abundance ratio of 3.9. However, the excitation temperature of the minimum is poorly constrained; for temperatures ranging from 7 K to 10 K, similar values of χ 2 can be found at approximately the same values of R, and cuts through the χ 2 surface at constant values of T x produce very similar χ 2 vs. R plots for all temperatures in this range. This insensitivity to excitation temperature allows us to reduce the number of fitted parameters without substantially biasing our results. Therefore, we adopt an excitation temperature of 8 K for the analysis presented below. Figure 5 show the reduced χ 2 as a function of R for each of the regions considered in this paper, along with a curve for the combined dataset. Each of the curves has a minimum χ 2 between R = 3.1 and R = 4.3, and all curves are steeper in the low-r regime and flatter in the high-r regime. One sigma uncertainties in the best-fit value of R can be determined from the width of the χ 2 minimum. Assuming gaussian statistics for the uncertainties in the data, the onesigma uncertainty in R can be measured from the range of models with χ 2 <χ 2 min +1. Table 2 contains the best-fit values for R and the uncertainties determined from the data presented in Figure 5. Based on the best-fit abundance ratios, the regions appear to divide into two groups: a low-r group consisting of L1489 and I04381 whose best-fit models have R 3.3, and a high-r group consisting of L1527, L1551, and TMR1 whose best fit models have R 4.3. However, the uncertainties in all of the best-fit values are sufficiently large that this difference is likely not significant. Also included in Table 2 are values determined from the combined dataset and an average of the R values obtained from each region. The Combined Dataset value and uncertainties were determined from a model fit to all of the observed data, while the Region Average value and uncertainties were determined from a weighted mean of the values obtained for each region using a Monte Carlo sampling process which accounts for the unequal positive and negative error bars. Using both techniques, we find similar results, with R 4. This value is well within the one-sigma uncertainty ranges of our estimates from each of the individual regions Photodissociative Effects The analysis presented thus far presumes that the abundance ratio is constant throughout each molecular cloud. However, this need not be the case. Chemical fractionation via exchange reactions and selective photodissociation can substantially alter the relative abundance of CO isotopomers in environments that favor these processes.

10 10 Chemical fractionation of carbon in CO is a rather well-documented and well-understood process. It is likely driven by an exchange reaction with C+, resulting in an overabundance of 13 CO relative to 12 CO,whencomparedwiththe[ 13 C]/[ 12 C] abundance ratio (see e.g., Langer et al. (1984), van Dishoeck & Black (1988), & Federman et al. (2003)). An equivalent chemical fractionation of oxygen isotopes does not occur, largely due to the lack of ionized oxygen in molecular cloud environments (Sheffer et al. (2002)) and the fact that no other exchange mechanism (e.g., using atomic oxygen) is favored in molecular cloud environments (Langer et al. (1984)). Based on these findings, we conclude that oxygen fractionation does not significantly affect the abundance ratio R. On the other hand, selective photodissociation can substantially alter the relative abundance of C 18 OandC 17 O, particularly in regions with high ultraviolet flux (Bally & Langer (1982)). Photodissociation of CO is primarily a line process, where the absorption of ultraviolet photons elevates molecules to excited states from which dissociation can easily occur (van Dishoeck & Black (1988)). In regions forming low mass stars, the predominant source of ultraviolet radiation is the external interstellar radiation field, which permeates those parts of the cloud with low ultraviolet optical depth, when measured from the cloud edge. The ultraviolet optical depth into the cloud is governed in part by broadband absorption due to dust, but predominantly through self-shielding by each molecular species. C 18 Oand C 17 O are not well shielded by the more abundant isotopomers of CO because of differences in the wavelengths of their ultraviolet absorption lines (Warin et al. (1996)), so these species can only be protected by their own kind, and the physical depth to which dissociating radiation can penetrate into the cloud depends on the column density of each species to that point. Since C 18 O is more abundant than C 17 O there exist regions within the cloud in which C 18 O molecules are shielded while C 17 O molecules are still subjected to dissociating radiation. In these zones, the abundance ratio R will be significantly higher than that found deep within the cloud where both species are well-shielded. The data show some evidence of this effect. Figure 6 shows the ratio of C 18 OtoC 17 O integrated intensities as a function of C 17 O integrated intensity for the entire dataset, along with model predictions for various parameters. The solid line depicts the best-fit model described in the previous section with R = 4. Note that this model correctly predicts the decrease in the intensity ratio with increasing C 17 O intensity, which occurs because of the saturation of the C 18 O line. Prominent in Figure 6 is the substantial increase in the intensity ratio for some low values of the C 17 O integrated intensity. Though the R = 4 model does not replicate this strong increase in the intensity ratio at low C 17 O intensities, it is statistically a very good fit to the entire dataset, primarily because there are relatively few high intensity ratio points

11 11 and because the uncertainties on these data points are quite large. Still, the fact that these high intensity ratio points occur only for low values of C 17 O intensity suggest that selective photodissociation is acting to reduce the C 17 O abundance. To assess the effects of selective photodissociation on our dataset, we have created a simple two-phase model for cloud material. The first phase is an outer sheath of material where C 18 O is present, but C 17 O has been dissociated. The second phase represents the inner part of the cloud, where both C 17 OandC 18 O are present with abundance ratio R. The thickness of the sheath region is parametrized by a C 18 O optical depth A, so that for any line of sight, the C 18 O optical depth is defined by τ 18,o = A + ηrτ 17,o (6) This model is a vast oversimplification of the complex photodissociation environments in the outer parts of clouds, but it captures the essential feature that C 17 O will be underabundant compared to C 18 O in the outer sheath region. For any realistic molecular cloud model, the abundances of both species will vary rapidly with depth in the sheath region as both dissociation and formation processes compete. However, regardless of the actual abundances as a function of depth, the contribution to the total line of sight C 18 O optical depth from the photodissociation region, τ 18,pdr, will be greater than ηr times the C 17 O optical depth through this region (i.e., τ 18,pdr >ηrτ 17,pdr ). In this more realistic picture, the parameter A is then A τ 18,pdr ηrτ 17,pdr, and the relation between C 18 OandC 17 O total optical depths given in Eq. 6 can be used to describe this environment as well. The prediction for the two phase model is displayed in Figure 6. The dashed line indicates a model with R = 4 and A = 0.2. It shows behavior similar to that of the dataset, and tracks particularly well the increase in the intensity ratio for I(C 17 O) 0.2 K kms 1. However, this model does not correctly predict the intensity ratio for high column density regions. A reduced value of the abundance ratio R produces a model which matches the high column density intensity ratios and still predicts higher intensity ratios for low column density regions. The highest intensity ratios measured at the lowest column densities are not predicted by this model; these high values might arise if the excitation temperature in the sheath region is higher than that in the rest of the cloud material. Unfortunately, the uncertainties of the data in this regime are quite large, and the data quality does not justify the addition of another parameter (i.e., T sheath ) to the current model. In fact, the introduction of even the sheath optical depth A produces a degeneracy where many pairs of A and R can produce essentially the same observable behavior. One can see this degeneracy by examining the similarity between the R = 2.8, A = 0.2 model

12 12 (dot-dashed line) and the R = 2.2, A = 0.3 model (dotted line) in Figure 6. In general, lower values of R can be fit to the data if one chooses larger values of A. Though this dataset alone does not provide substantial constraints on A, published observational and theoretical studies appear consistent with a non-zero value of approximately 0.2. A peak C 18 O optical depth of 0.2 corresponds to a total C 18 O column density of cm 2, assuming a thermalised population with a temperature of 8 K, and a line width of 0.5 km s 1. With an estimate of the [H 2 ]/[C 18 O] abundance ratio, we can convert this C 18 O column density into an H 2 column density; this column density is the extra amount required to provide self-shielding for the C 17 O molecule, over and above that required to provide self-shielding for C 18 O. If both isotopomers self-shield in the same way, then the ratio of the column density required to shield C 17 O to the column density required to shield C 18 O should be equal to the abundance ratio R. In their observational study of CO emission versus visual extinction in Taurus molecular clouds, Frerking, Langer, & Wilson (1982) concluded an H 2 column of cm 2 is required to produce sufficient self-shielding to protect the C 18 O molecule. They also concluded that the [H 2 ]/[C 18 O] abundance ratio is Using this value, we find that a sheath with A = 0.2 has an H 2 column density of cm 2, implying a total column density of cm 2 to shield C 17 O about three to four times the column required to shield C 18 O. Warin et al. (1996) calculated the photodissociation expected in the outer portions of dark clouds due to external ultraviolet radiation. They assume an [H 2 ]/[C 18 O] abundance ratio of , and find that a total column required for C 18 O self-shielding of cm 2. Using their abundance ratio, we find that a sheath with A = 0.2 has an H 2 column density of cm 2, implying a total column density of cm 2 to shield C 17 O again approximately three times the column required to shield C 18 O. Therefore, we conclude that a model with A = 0.2 is consistent with observational results and theoretical expectations. A = 0.3 models imply larger than expected column densities for the sheath region, and also predict that lines of sight with relatively strong C 18 O lines (T A 0.5 K) will have no associated C17 O emission. This is not generally seen in our dataset, and so we conclude that while A = 0.3 models can fit the dataset, models with smaller values of A are to be preferred. Including a sheath region with thickness parameter A = 0.2 in the calculations results in best-fit models with lower values of R. Figure 7 displays the reduced χ 2 as a function of R for T = 8 K and A = 0.2. Best-fit R values range from 2 to 3 for individual regions, and the best-fit model for the combined dataset has R = The weighted average of the

13 13 value for the individual regions yields R = 2.8 ± 0.4. These results are tabulated in Table Comparing the Derived Value for R with Other Determinations The value of R determined with A = 0.2 is similar to those found by Wilson et al. (1981) toward the deeply embedded protostellar sources and by Sheffer et al. (2002) through translucent clouds, even though neither group explicitly included the effects of selective dissociation in deriving their values. It s possible that in both of these cases, selective photodissociation does not play a pivotal role, though for very different reasons. Toward protostellar sources such as B 335, the total cloud column density is very high and the contribution from a thin sheath of selectively photodissociated material may be very small. One can see this effect in Figure 6, which shows that only for the smallest column densities is the intensity ratio an overestimate of the abundance ratio. In contrast, translucent clouds likely have so little column density that both isotopomers may be unshielded throughout. Unshielded molecule photodissociation rates are similar for both isotopomers (Warin et al. 1996), so in translucent clouds the abundances of both species should be reduced by the same fraction, and therefore the abundance ratio should be same as that found in cloud interiors. Along lines of sight which include a substantial sheath component, the intensity ratio may be substantially greater than R, and the abundance ratio derived for these observations will be an overestimate of the true cloud interior value. This may help explain the higher abundance ratios derived by Penzias (1981) from observations of giant molecular cloud cores, where the ultraviolet radiation field is likely quite high. The value of R determined by Bensch et al. (2001) from observations of the doublyrare isotopomers 13 C 18 Oand 13 C 17 O, is also higher than the result presented in this work. Along a line of sight containing an H 2 column density of cm 2 (A V > 200) in the Ophiuchus molecular cloud, they find R = 4.15 ± 0.52(stat) ± 0.59(sys). Because these doubly-rare isotopomers have abundances nearly two orders of magnitude lower than those of C 18 OandC 17 O, they are likely to provide inefficient self-shielding from photodissociating ultraviolet radiation until deep within the cloud. Instead, it is likely that mutual shielding from other CO isotopomers, H 2, and broadband absorption by dust may play a greater role than self-shielding for these isotopomers. Without detailed models of the ultraviolet absorption spectra for these isotopomers, it is impossible to asses whether a selectively photodissociated sheath can be responsible for the higher measured value of R. While the Bensch et al. (2001) value for R is larger than the value presented in this work, we note that the uncertainties in both measurements are sufficiently large that these results are formally consistent.

14 14 5. Summary and Conclusions 1. We present C 17 OandC 18 OJ=1 0 observations of 648 lines of sight toward five star-forming regions in the Taurus molecular cloud complex. Our C 18 O spectra have peak antenna temperatures in the range 1 2 K and typical FWHM line widths of km s 1. Many spectra are multi-peaked, indicating the several cloud components lie along the line of sight. The C 17 O emission is divided into three spectral components due to hyperfine splitting; the peak antenna temperature of the brightest component was typically in the range K, and FWHM line widths are comparable to the C 18 O line width along the same line of sight. 2. Assuming that the C 18 OandC 17 O emission arise from the same cloud material under the same excitation conditions, we construct a simple model to measure the abundance ratio R between the two isotopomers. We derive R for each of the regions individually, and for the the entire dataset. By combining the results for the individual regions, we conclude R =4.0± By examining the observed intensity in both lines as a function of column density, we find some evidence that the abundance ratio at low column densities may differ from that at high column densities. We consider the effects of selective photodissociation due to the differing abundances of the two isotopomers, and conclude that in parts of the cloud illuminated by dissociating ultraviolet radiation, C 18 O is overabundant relative to C 17 O due to the former isotopomer s ability to self-shield more effectively. 4. We modify our model to include two distinct phases within the cloud: a deep-cloud region where both species are adequately shielded from ultraviolet radiation and where the abundance ratio is R, and a sheath of cloud material where C 17 O has been destroyed by dissociating radiation but C 18 O has not. We parametrize the thickness of this sheath in terms of its C 18 O optical depth, A. While models for a range of values for A (including A = 0) adequately fit the data, we argue that a small non-zero value (A 0.2) is the most reasonable choice. Using this value in our model, we find that the data are best-fit with R =2.8± The effects of selective photodissociation may help explain the variety of values for R which have appeared in the literature. Larger values of R found by some authors may be explained with a small-r deep cloud region surrounded by a C 17 O-free sheath. Indeed, many of the results suggesting higher values for R have been derived from observations of clouds in regions of stronger external ultraviolet radiation. In contrast, smaller values of R are found for observations toward isolated high column density clouds, where the ratio of sheath column density to deep-cloud column density may be very low, and also toward regions of very low

15 15 column density, where neither isotopomer is well-shielded from dissociating radiation. 6. We conclude that for material in the Taurus complex, R = 2.8 ± 0.4, a value approximately half the accepted [ 18 O]/[ 17 O] value for the solar system. This value is consistent with the results of Wilson et al. (1981), Sheffer et al. (2002), and Bensch et al. (2001), and may be consistent with the observations of Penzias (1981) if selective photodissociation plays a large role toward the sources this author examined. This work was supported in part by NSF grant AST E.F.L. gratefully acknowledges the hospitality and financial support provided by the Australia Telescope National Facility (ATNF) during his sabbatical leave from Bucknell University. The ATNF is a division of the Commonwealth Scientific and Industrial Research Organization, funded by the federal government of Australia. E.F.L. also acknowledges financial support from the Bucknell University Office of the Dean of Arts & Sciences.

16 16 Table 1. Regions Studied Source RA(J2000.0) Dec(J2000.0) L h 04 m 43.1 s L h 31 m 34.1 s TMR1 04 h 39 m 13.8 s L h 39 m 54.3 s I h 41 m 12.5 s Table 2. Abundance Ratios Derived from Individual Regions Region R L L L TMR I Combined Dataset Region Average 4.1 ± 0.5 Table 3. Abundance Ratios Derived from Individual Regions for A = 0.2 Region R L L L TMR I Combined Dataset Region Average 2.8 ± 0.4

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18 18 This preprint was prepared with the AAS L A TEX macros v5.2.

19 19 Fig. 1. Sample C 18 OandC 17 OJ=1 0spectra toward the five regions studied. The C 18 O spectra have been displaced vertically by 1 K in each panel. Velocity structure in these lines reflects line of sight motions in the cloud material. The C 17 O intensities have been multiplied by a factor of two for this display. Note that hyperfine splitting of the J = 1 energy level produces three emission components, two of which are closely spaced in velocity, and one of which occurs displaced by km s 1. The bottom right panel contains the average of all spectra obtained toward the L1489 region. This panel shows clearly the three C 17 O hyperfine components. The velocity scale for all C 17 O spectra is referenced to the strongest hyperfine component, which is the middle one in the pattern.

20 20 Fig. 2. Integrated intensities in C 18 OandC 17 O are plotted against one another for the L1527 region in the left panel. Overlaid are models for the emission assuming an abundance ratio (R) of 4.0 and excitation temperature (T x ) of 8 K. From top to bottom, the models assume FWHM line widths of 1.0, 0.7, 0.5, and 0.3 kms 1, respectively. The right panel shows the same data and models, though in this case, both data and models are normalized by the FWHM line width. The line widths for the data were determined from the C 18 O emission, and were applied to both the C 18 OandC 17 O emission. Note that the models with different line widths are nearly indistinguishable in this presentation.

21 21 Fig. 3. Integrated intensity divided by FWHM line width for the five regions studied. The leftmost panel contains all of the data, while panels to the right display data for each individual region. Over plotted is a model assuming R =4andT x =8K.Onesigma statistical error bars are plotted for a few points in a few panels to provide an indication of the typical uncertainties in the data.

22 22 Fig. 4. Plot of reduced χ 2 as a function of R and T x for the combined II/lw dataset. The minimum χ 2 value of 1.56 occurs at R =3.9andT x =8.5K. Squares indicate the parameters used in the model calculations. Contours delineate reduced χ 2 values of 2.16, 2.56, 3.56, and 4.56 (i.e., χ 2 min +0.5, χ2 min +1,χ2 min +2,χ2 min +3). Theχ2 min + 1 contour is in bold.

23 23 Fig. 5. Plots of reduced χ 2 as a function of R with T x = 8 K for the II/lw datasets of each of the regions studied. The curve representing the combined dataset is in bold.

24 24 Fig. 6. Plot of abundance ratio R vs. C 17 O integrated intensity. Error bars are plotted for a few representative data points. The solid line indicates the prediction of a model with R = 4 and no selective photodissociation zone. The long dashed line indicates the prediction for a model with R = 4 and a selective photodissociation zone whose C 18 O optical depth (i.e., A) is 0.2. The dot-dash line indicates the prediction for a model with R = 2.8 and A = 0.2, and the dotted line indicates the prediction for a model with R = 2.2 and A = 0.3.

25 25 Fig. 7. Plots of reduced χ 2 as a function of R with T x =8KandA=0.2 for the II/lw datasets of each of the regions studied. The curve representing the combined dataset is in bold.