Millimetre-wave spectral line observing with Mopra
The history of the Mopra telescope and my inordinately long PhD are intertwined. In the
past seven years Mopra has grown into a fine young telescope. Meanwhile, my PhD, after a long
and difficult confinement, has become a description
of the capabilities and potential of the Mopra telescope. I would now like to share what I
have learned with other potential users.
My PhD has involved observing a large sample of dense cores in southern molecular clouds, in
a variety of molecular transitions at millimetre wavelengths. I have used the observed
line intensities to calculate molecular abundances
and physical conditions in the sample of dense
cores. This type of analysis requires careful
intensity calibration of the Mopra observations. Consequently, calibration has formed a major
part of my thesis.
Intensity Calibration of Mopra Data: Removing the Earth's atmosphere.
The specifics of intensity calibration can be
found on the Mopra website at
http://wwwnar.atnf.csiro.au/mopra/calibration/mm_calibration.html or http://newt.phys.unsw.edu.au/~ramesh/. Alternatively, I am very happy to send
information about Mopra calibration on request to mhunt@atnf.csiro.au. In this article I would like
to concentrate on the efficacy of the intensity calibration.
There seems to be a general belief that a
millimetre site must be high enough to induce altitude
sickness in the unfortunate observer if accurate
line intensities are to be obtained. This is not true in
the 3-mm band at which Mopra operates. The Earth's atmosphere absorbs radiation at
millimetre wavelengths and this effect must be calibrated
out, however it has proved possible at Mopra to formulate a calibration method that does this
quite effectively. This method is a variation on
the "chopper wheel" method commonly used
to calibrate millimetre-wave telescopes (see Mopra web site for more information).
The calibration of Mopra data is a two step process:
1) The effect of atmospheric attenuation must
be removed from the data. This is a most important step as atmospheric attenuation varies with
air temperature, moisture content and zenith angle;
2) Secondly, the data must be tied to a known brightness temperature (intensity) scale. In this
case the Mopra observations have been placed onto
the SEST antenna temperature scale.
How effectively can this be done?
Figure 1 compares SEST observations to Mopra observations for the chosen primary
calibrators Orion A and M 17. Figure 1a shows the
Mopra observations before atmospheric calibration
(QT) and Figure 1b shows the Mopra observations
after atmospheric calibration (TA'). The
Mopra observations were made at a range of
frequencies between 86 and 115 GHz during the period 1995
to 1998, in weather conditions that varied from
clear to heavy cloud cover. The SEST observations
are available on the SEST web site at
http://www.ls.eso.org/lasilla/Telescopes/SEST/SEST.html.
Figure 1: Comparison of SEST and Mopra data before and after calibration of the Mopra data. (a) SEST corrected
antenna temperature (TA*) plotted with Mopra peak antenna temperature before calibration
(QT). The equation for the line of best fit
is (TA* SEST = 4.33(QT MOPRA) + 7.3 and the correlation coefficient is
r2 = 0.87. (b) SEST corrected antenna temperature
(TA*) plotted with corrected peak antenna temperature from Mopra
(TA') for the same data after calibration. The equation for the
line of best fit is (TA* SEST =
1.62(TA' MOPRA) _ 1.1 and the correlation coefficient is
r2 = 0.99.
The atmospheric calibration method clearly removes the attenuation effectively. The
calibrated Mopra observations can then be placed on the
SEST antenna temperature scale using the linear fit
from Figure 1b. This relationship is
TA*(SEST) = (1.62 ±
0.06)TA'(Mopra). (1)
Note that this relationship is only valid for
data collected prior to the resurfacing of the Mopra
dish in 1999.
The correlation coefficient for equation (1) is
r2 = 0.99.
Uncertainties in Mopra Data
The uncertainties in the Mopra data themselves
have been calculated from repeated observations of a
set of secondary calibrators. Once again the Mopra observations were collected during the period 1995
_ 1998 in a variety of weather conditions.
The relative difference of each observation from
the mean for that source (in terms of integrated brightness temperature), at that frequency, is
shown in Figure 2. The observations are plotted
against integrated main-beam brightness
temperature (TMBDv) from calibrated Mopra observations.
The uncertainties have been modelled as consisting of
a flux dependent and a flux independent component
as described in equation 2.
Figure 2: Relative uncertainties computed from equation (2) compared with actual values of relative uncertainties
for calibrated Mopra data, plotted with integrated main-beam brightness temperature. The diamonds show the predicted
values, while the crosses show the values obtained from repeated measurements.
The sum of the two uncertainties can be
represented by
(2)
where TMB is the calibrated Mopra
main-beam brightness temperature.
Figure 2 also shows the uncertainty values
predicted by equation (2).
Calculating the uncertainties in this empirical
way takes into account all sources of error,
including those from the Gaussian fit to the spectral line.
The flux-independent uncertainty of 11.8 per cent compares well with that of the SEST, which
is estimated to be 10 per cent at 3-mm.
Doing Science with Mopra
Of course the proof of the pudding is in the
eating. The rotation diagram in Figure 3 shows that
Mopra can be used just as well as SEST to do science
with 3-mm observations.
Figure 3: Rotation diagram for HC3N in G268.4-0.8.
The rotation diagram (Figure 3) shows the
number of molecules per statistical weight in the upper
level of a transition plotted with the energy of the
level above the ground state. The transitions shown,
in order of increasing energy, are J=10-9,
J=11-10, J=12-11, J=15-14 and J=16-15. The J=10-9
and J=12-11 are from Mopra whereas the others are
from the SEST. The straight line relationship shows
that the MOPRA and SEST observations have been successfully calibrated onto the same scale, as
well as giving information about the excitation in
the G268.4-0.8 molecular cloud.
The capacity of Mopra to provide accurate measurements of molecular line intensities makes
it a valuable tool for investigating the
interstellar medium and evolved stars, either used on its own
or in conjunction with the SEST. The ready
availability of Mopra to Australian astronomers and the
low associated travel costs add to its value.
Studying the Interstellar Medium
Accurate measurements of molecular line
intensities in several transitions of a molecule can be used
to determine molecular abundances, temperatures
and densities within molecular gas. There are a
number of ways to obtain this information, all starting
of course with the crucial business of accurate
well-calibrated observations.
The kinetic temperature and molecular hydrogen column density can be obtained from observing
CO and its isotopomers 13CO,
C18O and C17O. The methods for doing this can be found in Rohlfs
and Wilson (1996). The kinetic temperature is the temperature of the molecular hydrogen in a
dense molecular cloud. CO can be assumed to be thermalised at the kinetic temperature.
Other molecules may have different excitation temperatures, depending on the relative
importance of their interaction with both the
hydrogen molecules and the radiation field within
the molecular cloud. (The radiation field at any frequency will have its own
characteristic temperature as defined by Planck's law.)
A rotation diagram can be used to find the
molecular abundance and excitation temperature of a
molecule, if a straight line fit can be obtained. This type
of local thermodynamic equilibrium (LTE) analysis
can be used if the emission in the observed transitions
is optically thin and if all transitions have the
same excitation temperature (as defined by the
level populations and the Maxwell-Boltzmann
equation). For molecules such as HCN, HCO+
and CS, which are usually optically thick, observations of
13CO isotopomers can be used for the rotation diagram.
A good reference for the use of the rotation diagram
as an analytical tool can be found in Goldsmith
and Langer (1999).
If the conditions of low optical depth and a
single excitation temperature for all transitions are not
met, a large velocity gradient (LVG) analysis can be
used although this is a considerably more complex undertaking. An LVG analysis can give the
kinetic temperature, excitation temperature,
hydrogen spatial density and molecular abundance if at
least four different transitions have been observed. I
have some LVG analysis programs that I would be
happy to provide to interested parties.
Combining Mopra with the SEST
The molecules HC3N and OCS have three
transitions within the range of Mopra, and
CH3OH has six. Mopra observations alone can be sufficient
to determine physical conditions in these sources
if combined with information on the kinetic temperature and molecular hydrogen column
density from observations of CO. Molecular
abundances can also be estimated from observations of a
single molecule if the conditions for an LTE analysis
are met. The optical depth is determined by
observing an optically thin isotopomer of the molecule
in question; however, observing a single transition
does not give information on the excitation
temperature of the molecule and so the accuracy of
the abundance estimate cannot be known without
further information.
The best strategy is to use Mopra to observe
the available transitions of the molecules of interest
and then augment these observations with SEST observations of some 2-mm and 1-mm transitions
of the same molecule.
References
Goldsmith and Langer, 1999. ApJ. 517, 209.
Rohlfs, K., and Wilson, T. L. 1996, Tools of
Radio Astronomy, 2nd Edition. p. 386.
Springer-Verlag, Berlin.
Maria Hunt, University of Western Sydney
(mhunt@atnf.csiro.au)