4. Results and discussion
The results of our search are summarized in Table 2. In all cases, only upper limits to the emission of the water dimer can be given.
4.1. The interstellar abundance of water dimers
We computed limits to the beam averaged column densities in the lower levels, , of the observed transitions given in Table 2 using
Here, is the integrated line intensity in K km s-1, , is the line frequency in GHz and the dipole matrix element (see Sect. 2.4) is in D2. This equation is valid for optically thin emission (see Rohlfs & Wilson 1996). The values of given in Table 2 correspond to three times the measured RMS and to the expected line width in each source. Using the function and the individual given in Table 1, we estimate limits to the total column density, ; these are typically 5 10. We assumed for Hale-Bopp (Bird et al. 1997) and also for the Galactic hot cores. Although the kinetic temperatures in these hot cores may in some cases exceed 200 K (Mauersberger et al. 1996), our beam probably also picks up emission from a more extended, cooler component. Only for the dark cloud L134 N, we assumed a value of 5 K (Swade 1989).
For each of the sources, we compile the most stringent limits obtained from the individual observations in Table 3. These are compared to the column densities of H2O and H2 obtained with beamsizes similar to that of our water dimer measurements. The abundance of (H2O)2 relative to that of water is typically toward the dense cloud cores; toward Orion-KL an even more stringent limit of 8 10-6 is derived. The abundance of (H2O)2 relative to H2 is typically .
It is interesting that the 91.087 GHz line frequency used in our search happens to be in the spectrometer band used by Allen et al. (1997) to search for CO-H2. In none of their sources (TMC 1, L 1157, 2013+370 and L 134 at a position different than ours) did they detect a signal. The typical noise they quota for a 1 MHz channel was 5 mK for the dark clouds. This is similar to the limit we report for L134 N, although our velocity resolution is much finer to search for narrow lines, which are characteristic for such cold clouds, and we conclude that the column densities of (H2O)2 are , as in L 134N.
We summarize that water dimers apparently make up only a small fraction of the water in the dense interstellar medium, even in hot cores where complex molecules have recently evaporated from grains and where chemical equilibrium still has not been reached. It is not clear whether this is due to a lack of such complexes in evaporating interstellar ice, whether the bonds are destroyed in the process of evaporation or whether the chemical timescales in which water dimers react and recondense into larger clusters are just too short.
4.2. Water dimers toward comet Hale-Bopp
Molecules are destroyed by the solar UV field within typically several 1000 s after they have evaporated from the surface of a comet. Murad & Bochsler (1987) estimated that the lifetime of the water dimer in the solar radiation field is 10 at a distance of 1 AU, which is an order of magnitude smaller than the lifetime of water.
For an unresolved source, the molecular production rate Q is related to the beam averaged column density N by
(Snyder 1982). Here, is the geocentric distance (in cm), is the heliocentric distance of the comet in AU, is the beam width of the telescope in radian. This can be written in more convenient units:
where is the beamwidth in arcseconds, Q is in s-1 and N in cm-2. From our March 1997 observation, the upper limit of the production rate of the water dimer in Comet Hale-Bopp was (with , =1.35 AU, r=0.97 AU, ). The water production rate at that time is still debated. Schleicher et al. (1997) and Dello Russo et al. (1997) estimate a value of 4-5 10, while a value of 1 s-1 has been proposed from radio observations of OH (Colom et al. 1998). Assuming that the radio data give a more reliable estimate of , an upper limit for the relative production rate of the water dimer is therefore 6%.
This does not necessarily reflect the conditions at the cometary surface, since (H2O)2 can be chemically produced and destroyed in the coma after the evaporation process, and water dimers will partly recondense into large clusters as pointed out by Crifo & Slanina (1991). Our limit casts doubt on the suggestion by Krasnopolsky et al. (1988) that water dimers make up 25% of cometary parent molecules; it is consistent with the models by Crifo & Slanina (1991), which predict an abundance of 10-5.
Note that for excitation temperatures around 100 K the lines in the 3 mm range are much more sensitive indicators of the column density of water dimers than the 24 Ghz line we observed. Unfortunately we had not been granted time at a mm-wave telescope around Hale-Bopp's perihelion. It is, however, worthwhile to investigate other line observations for a serendipitous detection of one of the numerous mm-wave transitions of (H2O)2. For this, we suggest to use the compilation of transition frequencies by Coudert & Hougen (1990). Even a non-detection could yield much lower limits for the relative abundance of the water dimer than we were able to obtain.
We detected the E and A lines of CH3OHCO (methyl formate) toward Orion-KL but not toward comet Hale-Bopp. From this non-detection, the limit to the production rate of this molecule is consistent with the production rate estimated from a mm-wave detection of CH3OHCO by Colom et al. (1997).
© European Southern Observatory (ESO) 1998
Online publication: June 26, 1998