3.1. Identification of the sources NGC 6334 I, NGC 6334 I(N)w and NGC 6334 I(N)e
Although the map in Fig. 2 seems to be consistent with the presence of a single source centered in NGC 6334 I(N), high resolution observations (JHH88; Kraemer & Jackson 1999) showed the existence of at least two ammonia features, with angular sizes of the order and smaller than 1´, centered at the positions of the continuum sources NGC 6334 I(N) and NGC 6334 I respectively. Taking into account the half-power beam width of the Itapetinga radio telescope, we find that the expected contribution of these two sources at the position () = (2´,6´) [hereafter, just (2´,6´)] should fall below the detection limit given by the rms of the observations. Since this is not the case, as can be seen in Fig. 1d, we conclude that another source is present in the region. We will describe, in the following paragraphs, the procedure used to separate the contribution of each component.
NGC 6334 I, when observed with high resolution (JHH88), exihibts two main structures, with velocities centered in -6.6 and -9.4 km s-1 and widths of 2.0 and 3.5 km s-1 respectively. The maximum flux densities of these structures are 0.42 and 0.48 Jy beam-1 respectively which, once diluted into the 4.2´ Itapetinga radio telescope beam, correspond to antenna temperatures of 0.20 and 0.23 K respectively. We calculated the contribution of this source to the NH3(J,K) = (1,1) spectra in our map as the convolution of the antenna beam and two point sources, with the characteristics mentioned above. The intensity of the hyperfine satellite lines was calculated assuming LTE in an optically thin source. Although the antenna temperature of NGC 6334 I is small compared to the intensity of NGC 6334 I(N), its effect on the line-width is significant, and its subtraction decreased the observed gradient along the map.
Since the high resolution observations of Kraemer & Jackson (1999) have revealed NGC 6334 I(N) as an extended source, although smaller than the Itapetinga radio telescope beam, it was difficult to subtract its contribution to expose the third and much weaker source. For this reason we used the spectrum at position (2´,6´), where we did not expect any contribution from the strongest source, as representative of the spectrum of the weakest. We labeled these sources as NGC 6334 I(N)w and NGC 6334 I(N)e [hereafter, I(N)w and I(N)e] respectively. We assumed no velocity gradients and subtracted a fraction of the (2´,6´) spectrum from all the others. This fraction was chosen in such a way that the resultanting spectra had the same departure from LTE as found at position (0´,0´). Moreover, since there is a velocity gradient along the region, the subtracted fraction was also limited in order to avoid fake absorptions in the resulting spectra.
In Fig. 3, we show the superimposed antenna temperature maps of the three regions, NGC 6334 I, I(N)w and I(N)e. We can see that I(N)w is aproximately 2.5 and 6.5 times brighter than I(N)e and NGC 6334 I, respectively. The source I(N)w turned out to be smaller than the beam size, as expected from the observations of Kraemer & Jackson (1999). On the other hand, the I(N)e region looks more elongated in declination.
The subtraction procedures affected the magnitude of the gradients of velocity and line-width, but not their directions. In fact, the gradients became softer than before, showing that the other sources were responsible in some amount for the variations of these properties along the region I(N)w. As it can be seen in Fig. 4, the velocity gradient is aproximately perpendicular to the Galactic plane. According to the model adopted here, the gradient in line-width is related to gradient in turbulence, which turned out to be larger in the direction of the more evolved sources.
3.2. The physical parameters of I(N)w and I(N)e regions in non-LTE conditions
We used the antenna temperature of the hyperfine satellites relative to the main line in the NH3(J,K) = (1,1) spectrum and the ratio between the antenna temperatures of the main lines of NH3(J,K) = (2,2) and (1,1), shown in Table 2, to calculate the relevant physical parameters for the I(N)w and I(N)e regions. We applied the model of SW85 to obtain the NH3 column density (), the kinetic temperature () and the H2 density () of the clumps in the two regions. In region I(N)w we used the spectrum from the (0´,0´) position, which corresponds to the highest intensity, and in I(N)e we used the (2´,6´) position, where we believe there is not important contribution from I(N)w.
Table 2. Ratio between the observed antenna temperatures of each hyperfine satellite in relation to the (1,1) main line , besides the ratio between the antenna temperature of the (2,2) and (1,1) main lines.
To determine the physical parameters of the clumps we looked into the (, , ) space for the point at which, according to the model of SW85, the curves representing the observed line intensity ratios intercept themselves. We had to extrapolate these curves up to H2 densities of 108 cm-3 to obtain a good crossing point, which occured at cm-3.
In Fig. 5, we show the curves of constant ratio between the hyperfine satellites and the main line in the NH3(J,K) = (1,1) spectrum, as well as the ratio between the main line intensities of the NH3(J,K) = (2,2) and (1,1) transitions for a kinetic temperature of 24 K, which corresponds to the best fit in both regions. In Table 3, we present the values of the physical parameters extracted from this figure: the brightness temperature for the NH3(J,K) = (1,1) and (2,2) transitions [ and , respectively], the kinetic temperature, the NH3 column density and the H2 density. We can see that the physical conditions of the clumps in both regions are pratically the same. It is important to stress that the values listed in Table 3 would not change substantially if we use the original spectra, including the contribution of the three sources, since I(N)w is much brighter than the others. On the other hand, the dispersion of the contours around the intersection point in Fig. 5(a) decreased appreciably after the separation of the three components, resulting in a better accuracy in the determination of the physical parameters of the region.
Table 3. The physical parameters determined from the Fig. 5 for I(N)w and I(N)e regions.
3.3. Physical parameters of the individual clumps
As it was previously mentioned, to explain the hyperfine structure intensity anomalies in the NH3(J,K) = (1,1) transition by the superposition of individual clump spectra, their dispersion velocities must be small, implying that they should be gravitationally stable. Therefore, their individual masses () cannot be larger than the Jeans mass () and their diameters () must be smaller or equal than the Jeans length (). Arguments in favor of these hypotheses have been presented by Curry & McKee (2000) based on numerical simulations. Assuming spherical clumps with a ratio of helium to molecular hydrogen of 0.25, we calculated their diameter and mass, using the following expressions:
where k is the Boltzmann's constant, the mass of hydrogen atom and G the gravitational constant.
The beam filling factor () can be calculated from the brightness temperature, , derived from the model and , obtained from the observations, which is proportional to the antenna temperature:
where is the half-power beam width of the telescope and A is the ratio between flux density and antenna temperature of a continuum point source. In this work, we used the radio galaxy Virgo A as the calibrating source.
Using the definition of beam filling factor, we can determine the number of clumps inside the beam's solid angle:
where D is the distance from the cloud.
To obtain the density of clumps (), we can consider two different situations. The first one corresponds to the clumps spread over a solid angle larger than the beam. In this case, the density of clumps is given by:
where and are, respectively, the extension of the region in right ascension and declination. In the second one, if the source is smaller than the antenna beam, we can only estimate either an upper limit, considering that the clumps are grouped side by side and without superposition, or a lower limit, supposing they are spread over the whole beam:
Once the density of clumps and their diameters are known, we can calculate their collision time ():
We can also calculate the mean H2 density (), which is the density of an homogeneous cloud with mass equal to the total mass of the clumps filling the telescope beam:
The ammonia abundance is calculated from the following expression:
where it was assumed that there is not superposition between the clumps, so that the line of sight extension is equal to the diameter of each clump (SW85).
The physical parameters of the clumps in regions I(N)w and I(N)e and their respective uncertainties are listed in Table 4. The quoted errors for the mass and diameter of the clumps represent the uncertainties in the kinetic temperature and H2 density.
Table 4. The physical parameters for I(N)w and I(N)e regions calculated in non-LTE conditions. The uncertainties are given in parenthesis.
The clumps in both regions have similar diameters (0.007 pc), masses (0.2 ) and ammonia abundances (710-9). They also seem to be gravitationally bounded, since the total virial mass is about a factor of ten lower than the total mass of the clumps which are contained in the beam's solid angle [7600 and 2100 for I(N)w and I(N)e respectively]. The 36000 clumps of I(N)w are spread in such a way that their density is between 6000 and 33000 clumps per pc-3, much larger than the 720 clumps per pc-3 in the I(N)e region.
The beam filling factor for the I(N)w region is larger than expected from the NH3(J,K) = (3,3) data presented in Kraemer & Jackson (1999) (around 0.10 for a beam size of 4´). The reason is that we had assumed no superposition between the clumps along the line of sight. The physical superposition required by the smaller filling factor is small enough to guarantee very little velocity superposition, in which case the spectra of the superposed clumps can be simply added.
© European Southern Observatory (ESO) 2000
Online publication: October 2, 2000