Astron. Astrophys. 344, 687-695 (1999)

3. An example: L483

To test the temperature model we have carried out a multitransition CO excitation study of the outflow from the young protostellar source IRAS 18148-0440 in the Lynds 483 dark cloud. This bipolar outflow was first detected in ¹²CO 2-1 by Parker et al. (1991) in a survey of IRAS sources in dark clouds. The outflow is associated with the infrared source IRAS 18148-0440 and a coincident radio source (at (B1950); Anglada et al., priv. comm.). The estimated distance to the source is 200 pc. The infrared and radio source is classified as a `Class 0' source, a young, deeply embedded protostar. The source is centred in a dense core which has been observed in NH₃ and HC₃N, C¹⁸O and in the mm and submm continum (Fuller & Myers 1992; Ladd et al. 1991; Fuller & Wooten 1999). The visual extinction along the line of sight to the source is  mag.

Fuller et al. (1995) mapped the molecular outflow in ¹²CO 3-2 at J, H and K infrared bands, and in 2.12 µm molecular hydrogen emission. These observations show the outflow to be compact, bipolar with a high degree of symmetry and highly collimated. The simple structure, along with the identification of the driving source as extremely young make this outflow an excellent candidate for testing outflow models.

The observations consist of a fully-sampled map of the outflow in ¹²CO 4-3 plus spectra at selected positions in ¹²CO 2-1 and ¹³CO 2-1. The transition lies 55 K above ground and the ratio of this line to lower energy transitions can be sensitive to temperatures up to  K. We use the line ratios to constrain the temperature at several positions in the outflow,compare the results with the shell heating predictions of Sect. 2, and look for any temperature gradients along the outflow lobes, which might differentiate between outflow acceleration models.

The observations were taken at the James Clerk Maxwell Telescope (JCMT) during July 1996, May 1997 and August 1998 using the common user heterodyne receivers A2 and C2. Transitions and observing parameters are given in Table 2. Positions observed in each transition are given in Table 3. All spectra are corrected for the forward scattering and spillover efficiency to give in kelvin. We position switched to cancel sky emission using an off position of (600", 200") in 1996 and 1997 and (0",1800") in 1998. We checked these off positions for emission in ¹²CO 2-1 by comparing with a number of other positions: (600",200") showed a small amount of emission between 2 and 7 km s^-1 with a line brightness of up to 2 K; this was less at (0",1800") (the systemic velocity of L483 is . In ¹²CO 4-3 we made an `on-the-fly' raster map, in which the telescope scanned in right ascension at succesive declinations, storing the result every 5" to build up a map of the source (Fig. 4).

Fig. 4. Integrated intensity maps of 12CO 4-3. Redshifted emission (top ) is integrated from 5.5 to 15.5 km s-1 and blueshifted (bottom ) from -4.5 to 5.5 km s-1. Contours are every from . The position of the VLA source is marked with a star. Positions at which 12CO 2-1 spectra were taken are marked with crosses, and positions where 13CO spectra were taken with circles. There is strong H2 emission at the position marked with the square and arrow, which may mark the jet head. Offsets are (RA, Dec) in arcseconds from (B1950). Note that the coordinates of the H2 emission have changed substantially from that shown in Fuller et al. 1995: the coordinates were checked during the 1997 observations and are now correct to within 1".

Table 2. Observing parameters in L483: frequency, beam FWHM, efficiency, typical system temperature, bandwidth and integration time.

Table 3. Positions observed in L483. Offsets are (RA, Dec) in arcseconds from (B1950).

Fig. 4 shows the positions at which we observed and in addition to . Fig. 4 also shows that both outflow lobes show evidence for redshifted and blueshifted gas, suggesting an inclination close to the plane of the sky. We refer to the lobe at negative RA offset, which shows the strongest blueshifted emission, as the blue lobe, and the lobe at positive RA offset as the red lobe.

3.1. Temperature measurements from CO ratios

To estimate the gas temperature from the CO observations we use the ¹²CO  line as a high excitation line, as a low excitation line, and ¹³CO to determine the optical depth in the ¹²CO. ¹³CO is less abundant than ¹²CO and we take it to be optically thin in outflows. The ¹²CO/¹³CO ratio gives the optical depth in ¹²CO. The CO 4-3/CO 2-1 ratio gives the excitation temperature . This is a good estimate of the kinetic temperature if the gas density is above the critical density of the higher energy transition, for . We assume throughout.

First we find the excitation temperature from the ¹²CO 4-3/¹²CO 2-1 line ratio. Differences in beam filling factors between the CO  and observations are taken into account by convolving the maps of the higher resolution transition to the lower resolution beam. This eliminates the beam filling factor from the equations. The excitation temperature which corresponds to a particular line ratio depends on the optical depth as shown in Fig. 5, calculated under the LTE assumption.

Fig. 5. (12CO 4-3)/(12CO 2-1) as a function of for various .

The optically thin limit (), shown as a solid line on the graph, gives lower limits on the excitation temperatures for a given line ratio. For higher optical depths the line ratio becomes less sensitive to temperature, and must be more accurately known to find the temperature.

Spectra extracted from the interpolated ¹²CO 4-3 map are overlaid on ¹²CO 2-1 spectra in Fig. 6. Ratio spectra of the ¹²CO 4-3/¹²CO 2-1 ratio are also shown in Fig. 6. The ratios are well determined in both red and blueshifted components of each spectrum out to velocities of a few km s^-1 from ambient.

Fig. 6. Top: 12CO 4-3 (light) spectra interpolated to a 21" beam overlaid on 12CO 2-1 spectra (heavy) at selected positions. Bottom: 4-3/2-1 quotients. Corresponding temperature lower limits are given on the right hand side of the plot, assuming optically thin emission. Errorbars are 1 and do not include the systematic 20% calibration uncertainty between frequency bands. The vertical lines mark the extent of emission from the ambient cloud.

The 4-32-1 line ratios in the dominant wings (blueshifted gas in the blue lobe and redshifted gas in the red lobe) are typically . The ratios are similar at different positions within the outflow, with the range in the ratio () due to scatter rather than to obvious velocity trends. In the optically thin limit, line ratios of 0.9 and 1.8 correspond to temperatures of 26 and 48 K, respectively. Such temperatures are much less than our outflow shell model predicts, particularly at (-45",10") which is only 0.025 pc from the end of the outflow.

The range in ratios is sensitive to the relative calibration of the CO 4-3 and 2-1 bands, a source of uncertainty which could push the ratios up or down by as much as 20%, resulting in correspondingly higher or lower temperatures. However, even for a 20% increase in ratios, the temperature range rises to only 33-48 K, in the optically thin lower limit, still lower than the shell model predicts for the outer parts of the outflow.

However, the same line ratios correspond to much higher temperatures if the optical depth is significant, as indicated in Fig. 5. If the optical depth is significant, of order 2 or more, then even a ratio as low as 0.9 could correspond to a temperature  K once the 20% calibration uncertainty is taken into account. Only if the optical depth is much less than 1 can the temperatures be as low as the lower limits suggest.

We can estimate the ¹²CO 2-1 optical depth in the usual way from the ¹²CO 2-1/¹³CO 2-1 ratio. Assuming that the ¹³CO line is optically thin, and that the ¹²CO and ¹³CO have similar beam filling factors (as the beamsizes are similar) and the same excitation temperature, the ratio of the brightness temperatures is given by

where subscripts of 12 and 13 indicate ¹²CO and ¹³CO transitions of the same J, respectively. Wilson & Rood (1994) derive a mean value of 77, and Langer (1997) gives 67 for in the local interstellar medium: we assume an average value of 72 in our calculation of .

Fig. 7 shows the ¹³CO 2-1 spectra at (40", -5"),(-30", 5") and (-45",10") overlaid with the ¹²CO 2-1 spectra at the same positions but with the line intensities divided by 30, and the resulting optical depth as a function of velocity. The ¹²CO/¹³CO ratio is small in the velocity range of emission from the ambient cloud, 4-7 km s^-1, and increases to values of 20-40 in the inner line wings. The ratio remains fairly constant over the whole range of velocities, suggesting that outside the ratios are little affected by ambient cloud contamination, as this would raise at lower velocities.

Fig. 7. Top: (13CO 2-1) (light) spectra overlaid with (12CO 2-1) spectra divided by 30 (heavy). Bottom: calculated from the 12CO/13CO ratio. Errorbars are . Note the different velocity scales. The vertical lines mark the extent of emission from the ambient cloud.

It is clear from Fig. 7 that is significantly greater than 1 in the inner line wings at all three positions. At low velocities, therefore, we do measure the significant optical depths that are required to reconcile the high temperatures predicted by the shell model with the measured 4-3/2-1 ratios. For , the temperature lower limits for 4-3/2-1 ratios of 1.0 and 1.5 rise to 33 and 150 K, respectively. These temperatures are much more in line with what is expected from the shell model (Fig. 3). Most of the mass in the outflow is at these low velocities, as can be seen from the ¹²CO 4-3 spectra (Fig. 6) which are insensitive to cold quiescent cloud material, so it is relatively unimportant that at higher velocities the uncertainties due to noise on the ¹³CO spectrum are too great for to be usefully determined. The temperature estimates rise further for the higher measured at some positions and velocities.

Unfortunately, with , the measured CO 4-3/CO2-1 line ratios do not place strong constraints on the temperature. The 20% calibration uncertainty between bands is a significant source of uncertainty in the temperature determination, as the 4-3/2-1 ratio becomes less sensitive to temperature at higher optical depths (Fig. 5).

3.2. Evidence for temperature gradients?

Returning to the 4-3/2-1 line ratios, is there any evidence for temperature gradients along the outflow lobes, which might differentiate between outflow acceleration models? In fact the 4-3/2-1 ratios are similar at the different positions along the lobes, with possibly a slight rise towards the end of the blue lobe. In addition, comparing the positions (-30",5") and (-45",10") in the blue lobe (Fig. 7), the optical depths are also similar. This suggests that temperatures do not change by much along the length of the outflow.

The shell model predicts that the temperature should rise and the optical depth drop towards the end of the outflow. The temperatures rise towards the end of the jet because this is where the energy input is greatest, but the optical depth falls because further out from the star the shell has swept up less mass, particularly if the density gradient is steep. (The shell column density largely reflects the ambient density distribution). Therefore, for steep density gradients, the shell model predicts that the 4-3/2-1 ratios should increase steeply towards the end of the outflow. In the shell model, only shallow density gradients can produce the similar or slightly rising 4-3/2-1 ratios observed in L483.

A shallow density gradient in the outer half of the outflow is consistent with observations of the environment of L483. The central source is embedded in a high density ridge which is at to the outflow axis. In the central 0.02 pc around the star, the density falls at least as steeply as but at larger radii in the outflow direction, the distribution flattens out (Fuller et al. 1995; Fuller & Wooten 1999). Buckle et al. (1999) show that the infrared extinction drops by a factor of 3 between a position 0.015 pc from the star and a position midway along the jet but then stays roughly constant up to the bow shock, again indicating that the steep power law gives way to a more flat density distribution further from the star.

Alternatively, mixing layer models predict decreasing optical depth combined with decreasing temperature, as more gas is swept up near the star and heated to hotter temperatures. These conditions could also produce constant or slightly rising 4-3/2-1 ratios, if the optical depth falls slowly with distance from the star. However, there is no evidence for falling optical depth between the two positions observed in the blue lobe. It may be possible to reconcile some of the highest observed line ratios with the extreme temperatures ( K) predicted by the mixing layer models, if filling factors are very small. But it is hard to see how enough CO can be entrained to produce the observed column densities in these low-J transitions, given that only small fractions of the CO population would be in the low-J states (1% in at 1000 K). Unrealistically high ambient densities of more than 0.05 pc from the source would be required to produce an optical depth of 1 in , given that the outflow is only a few arcseconds (a few  pc) wide and the mixing layer material is assumed to originate from the ambient cloud.

In order to test the temperature predictions of the shell model further, we need to find better temperature probes than optically thick ¹²CO lines, and observe transitions which trace material from a few tens to a few hundred kelvin. Ratios of optically thin high-J ¹³CO lines would be useful in this respect. Unfortunately, point-by-point mapping of weak transitions in the submillimetre is too time consuming to be feasible with current single dish telescopes, and current interferometers are not sensitive enough and lack capability at higher frequencies. The large collecting area proposed for the next generation of millimetre interferometers is needed to achieve sufficient sensitivity to map optically thin high excitation transitions at high resolution on reasonable timescales. Array receivers on single-dish telescopes may also speed up data collection times. In addition, IR observations of higher excitation CO lines, such as those carried out with ISO (Liseau et al. 1996), provide strong constraints on average outflow temperatures although with satellite instruments the resolution is too low to study the gradients in any detail. In the meantime, it would be valuable to observe outflows which propagate into low ambient densities and have smaller optical depths in ¹²CO, as the ¹²CO 4-3/2-1 ratio is sensitive to temperature in the optically thin case.

© European Southern Observatory (ESO) 1999

Online publication: March 18, 1999
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