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Scaling relations for molecular gas in the
Large Magellanic Cloud
By A r t o H e i kk i l ¨a
e­mail: arto@oso.chalmers.se
Onsala Space Observatory, S­43992 Onsala, SWEDEN
We have studied scaling relations (virial mass versus CO luminosity, luminosity versus size,
linewidth versus size) for molecular clouds in the 30 Dor and N 159 regions in the Large Magel­
lanic Cloud. The analysis is based on CO J = 1 ! 0 observations with the SEST (Swedish­ESO
Submillimeter Telescope). A comparison with corresponding relations for Galactic clouds is
made. At this stage of the analysis our conclusions are: (1) 30 Dor, N 159 and Galactic clouds
obey the same linewidth­size relation, (2) Virial mass­luminosity and luminosity­size scalings
are different in 30 Dor and N 159, but similar in N 159 and the Galaxy, and (3) 30 Dor clouds
are less luminous than N 159 and Galactic clouds.
1. Introduction
The Large Magellanic Cloud (LMC), the nearest neighbour of the Milky Way, is a
small, irregular galaxy at a distance of 50 kpc. LMC provides a hostile environment
for molecular gas. The environment differs from that in the Galaxy in several aspects.
Relative to Galaxy, LMC exhibits a lower metallicity, stronger radiation fields and a
higher gas­to­dust ratio. This implies less shielding and higher photodissociation rates
and is expected to lead to smaller and more clumpy clouds, lower molecular and dust
abundances, higher temperatures and lower optical depths for the molecular gas. The
proximity of the LMC enables detailed studies of the molecular gas in an environment
differing from that in quiescent spiral galaxies such as the Milky Way.
The study of molecular clouds in the Galaxy has resulted in a number of scaling rela­
tions between global cloud properties such as mass, density, luminosity, size and velocity
dispersion (e.g. Larson (1981), Scoville & Sanders (1987), Solomon et al. (1987), Myers
& Goodman (1988a), Myers & Goodman (1988b)). Of these quantities the luminosity
and the velocity dispersion are well defined and directly measurable. On the other hand
cloud mass cannot be measured directly and the cloud size has to be defined. Attempts
have been made to ``explain'' the scalings in terms of virial equilibrium, turbulence,
equipartition of energies (Larson (1981), Solomon et al. (1987), Chieze (1987), Fleck
(1988), Myers & Goodman (1988a), Myers & Goodman (1988b), Henriksen (1991)), but
so far no explanation is fully satisfactorily.
Star formation is believed to take place mainly inside molecular clouds. Thus, it is
important to be able to estimate the masses of molecular clouds. However, molecular
clouds consist mainly of molecular hydrogen, but being a symmetric molecule it lacks ra­
diation at suitable frequencies. Therefore, masses are estimated by relating the intensity
(I) of a ``tracer'' to the column density (N ) of molecular hydrogen using an empirical
``conversion factor'' X:
N = X \Theta I: (1.1)
Such tracers are, for example, other molecules (notably CO and its isotopomers), dust
and gamma­rays.
The CO to H 2 conversion factor has been calibrated through observations of molecu­
lar clouds in the Galactic molecular ring (e.g. Scoville & Sanders (1987), Solomon &
1

2 Arto Heikkil¨a: Scaling relations in the LMC
Barrett (1991), Wolfendale (1991)). X is usually taken as constant and frequently used
to estimate molecular gas masses in external galaxies. The constancy of X is question­
able; both theoretical considerations (e.g. Kutner & Leung (1985), Maloney & Black,
(1988), Elmegreen (1989)) and observations of the outer parts of the Galaxy (Sodroski
(1991)) and irregular galaxies (e.g. Israel et al. (1986), Cohen et al. (1988), Johansson
(1991), Rubio et al. (1993)) indicate that X depends on the environment.
2. Observations
Observations of the CO J = 1 ! 0 transition in the 30 Dor and N 159 regions in
the LMC were made within the SEST Key project ``CO in the Magellanic Clouds'' using
the SEST (Swedish­ESO Submillimeter Telescope) at La Silla, Chile. The FWHP beam
width at 115 GHz is 45 00 , which corresponds to about 10 pc at the distance of the LMC.
3. Analysis
The CO emission in the 30 Dor and N 159 regions can be decomposed into 25 and 13
individual clouds, respectively. The cloud radii range up to 23 pc (which is considerably
less than for the largest cloud complexes found in the Galaxy, 50 to 100 pc). As mass
estimate we use the so called virial mass (which follows from the simplest form of the
virial theorem, see e.g. MacLaren et al. (1988)):
M vir
= Koe s oe 2
v
(3.2)
where K is a coefficient depending on the density distribution, oe s is a measure of the
cloud size (``radius'') and oe v is the one­dimensional velocity dispersion.
If M vir is expressed in M fi , oe s in parsecs, oe v in km s \Gamma1 and a radially symmetric density
profile ae(r) = ae 0 r \Gamma1 is used, then K = 1046. We define the cloud radius as oe s = p oe x oe y ,
where oe x and oe y are the spatial dispersions from a two­dimensional Gaussian fit to the
integrated intensity contour map of the cloud. The velocity dispersion is determined
from a Gaussian fit to the global line profile of the cloud.
4. Results
Scatterplots of the resulting scalings are shown in Figures 1, 2 and3. The filled circles
are for the N 159 region, the empty circles are for the 30 Dor region and the line is a
fit for Galactic clouds taken from Solomon et al. (1987). For the N 159 clouds good
correlations are found for the different quantities. Data for the 30 Dor clouds show a
larger scatter, which is probably due to lower signal­to­noise ratios and difficulties in
defining cloud sizes. The scatter plots indicate (despite of the large scatter in the 30 Dor
data) that the same line width--size relation holds in 30 Dor, N 159 and Galactic clouds.
The luminosity--size and virial mass--luminosity scalings are however different for 30 Dor
and N 159. A clear offset is evident in the plots. This suggests that the line width--size
relation is fundamental and that differences in the physical conditions of the clouds and
their environments play a role for the two other relations. Maloney (1990) showed that
the virial mass--luminosity relation likely is an artifact of the line width--size relation.
Our data support this suggestion. Further more, our study shows that the clouds in the
30 Dor region are underluminous compared with those in the N 159 area. Differences in
optical depths and/or volume filling of CO gas may provide an explanation.
This work has been done in collaboration with my supervisors Lars E.B. Johansson
and Roy Booth.

Arto Heikkil¨a: Scaling relations in the LMC 3
Figure 1. Log--log scaling of the line width versus the size.
Figure 2. Log--log scaling of the luminosity versus the size.
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