## 4. Column densities and abundance ratios## 4.1. Basic assumptionsIn order to derive accurate column densities from the absorption lines, we have to make three assumptions. These are - assume a value for the covering factor
*f*of the absorbing molecular gas with respect to the extent of the radio core in Cen A. - assume a value for the excitation temperature of the absorbing gas.
- assume that each molecular species is in local thermodynamical equilibrium, i.e. that all the rotational levels are characterized by the same excitation temperature (called then the rotational temperature ).
The covering factor
The excitation temperature defines the relative population of two levels and can be derived if the velocity integrated optical depths of two rotational transitions of the same molecule can be determined. This is not the case for Cen A. Furthermore, in order to derive the total column density we must link the fractional level population to all the levels. This is done by invoking a weak LTE-approximation and assuming that , where is a temperature which governs the fractional population of all rotational levels in a given molecule. The LTE approximation is weak in the sense that it does not imply that equals the kinetic temperature and it allows for different molecules to have different . With this approximation we can use the partition function to express the total column density as where is the observed optical depth
integrated over the line for a given transition,
the statistical weight for rotational level
The excitation temperature is most likely low for the gas seen in
absorption. The reason is that a high quickly
depopulates the lower rotational levels and decreases their opacity.
For K, . Hence, along a
line of sight with a mixture of molecular gas components of similar
column density but with different excitation temperatures, absorption
lines of ground transitions will preferentially sample the
excitationally coldest gas. Excitationally cold gas does not
necessarily imply that the kinetic temperature is low.
, HCN and HNC are thermalized at H The detection of a relatively strong absorption of CS(2-1) does not
necessarily imply either a high or a high
density. The J 1 level of CS has an energy
corresponding to 2.35 K and should be significantly populated by the
cosmic microwave background radiation. We searched for the CS(3-2)
line and came up with a very weak detection of the main line at
552 km s Since we have observed molecules with a large electric dipole moment, we will use K for all the lines when deriving column densities. If the excitation temperature is close to the cosmic microwave background temperature, we overestimate the column densities of , HCN and HNC by a factor 2.0. For CS the factor is 1.5. If, on the other hand, the excitation temperature is 10 K, we would underestimate the , HCN and HNC column densities by a factor 3.1 and the CS by a factor 2.5. A low means that only the lowest rotational levels are significantly populated and that the assumption that one single temperature governs the overall population distribution, i.e. is likely to be valid. The abundance ratios are very insensitive to the assumed excitation temperature, only depending on the weak LTE assumption. Hence, the column densities should be accurate to within a factor of 2, while the abundance ratios are very robust estimates. ## 4.2. Qualitative resultsWe calculated column densities for the four absorption lines in the
LV complex by using the gaussian components given in Table 2. For the
HV complex we derived the velocity integrated optical depth directly
from the spectra
where is the rms of the opacity (0.012),
the velocity resolution
(0.15 km s In Table 7 we present column densities and abundance ratios for 4 clearly defined (1-0) components in the High Velocity complex. The components can only be identified in the spectrum and are designated 5a-d. They are defined in a smoothed spectrum and correspond to gaussian components 10, 11-13, 14-16 and 17 as given in Table 5. Integrated optical depths were derived by integrating over the velocity intervals given in Table 7. © European Southern Observatory (ESO) 1997 Online publication: May 26, 1998 |