Annual Report 2011 Max Planck Institute for Astronomy

50 III. Selected Research Areas
N / N peak
Log (N / N peak )
1
0.1
0.01
0.001
0
–1
–2
–3
Taurus
Av [mag]
1 10
0
–4
0 5
1
ln (A v / A v )
10
A v [mag]
be described efficiently with the help of the mass distribution
data derived using the dust extinction mapping
technique. This topic has been pursued actively in MPIA
recently. The frequency at which density fluctuations occur
in a molecular cloud can be expressed through the
so-called probability density function (PDF, hereafter)
of volume densities in the cloud. This function describes
the probability of a volume dV to have a density between
[ρ, ρ dρ]. The PDF function forms a cornerstone for
many analytic star formation theories, in which its role
is to describe the basic statistics of the density field. In
these theories, the function is directly linked to the formation
rate of self-gravitating dense cores, and hence, to
the rate at which new stars form.
Theoretical and numerical works predict that the volume
density PDF takes a log-normal shape in isothermal,
turbulent media not significantly affected by the
self-gravity of gas or magnetic fields. However, in the
presence of strong gravitational forces, non-isothermal
equation of state, or strong magnetic field support, deviations
(usually an excess) to this shape can develop,
especially at the high-density side of the PDF. Since the
functional form of the PDF is directly linked to the abil-
2
star-forming clouds
quiescent clouds
15 20
N / N peak
1
0.1
0.01
0.001
Lupus V
Av [mag]
1 10
0
1
ln (A v / A v )
Fig. III.2.2: Top: Column density PDFs for the Taurus and Lupus
V molecular clouds. Taurus is an active star forming cloud,
but Lupus V shows very little signs of star formation. Left:
Cumulative mass distributions of 23 nearby molecular clouds.
The star-forming clouds are shown with blue curves and nonstar-forming
clouds with red curves. The figure shows that the
star-forming clouds contain greatly more material at high column
densities compared to the non-star-forming clouds.
ity of the media to form dense cores, it is crucially important
to constrain the PDF through observational data.
However, because of the observational restrictions such
works have been rare in the past.
Observations are always performed in the two-dimensional
plane of the sky and they can only recover
column densities, not directly three-dimensional volume
densities. However importantly, some properties
of the volume density PDFs can be derived through observations
of their column density PDFs. For example,
a log-normal shape of the volume density PDF should
remain invariant in transformation to column densities.
Similarly, under certain conditions, it is possible to derive
the shape parameters of the volume density PDF,
i.e., mean and dispersion, from the column density PDF.
In other words, by measuring accurately the column density
PDFs in molecular clouds it is possible to present
constraints to both processes that regulate structure formation
in molecular clouds and the theories that use the
function as an input in predicting star-forming rates and
-efficiencies in the clouds.
What do the column density PDFs in molecular
clouds then look like? The MPIA scientists performed
recently the first systematic study of the column density
PDFs in molecular clouds (Kainulainen et al. 2009,
A&A, 508, L35; Kainulainen et al. 2011, A&A, 530,
A64). This study presented mass distribution data for 23
nearby molecular clouds, derived using the NIR dust extinction
mapping technique. Most importantly, the work
showed that the PDFs of star-forming and non-star-forming
clouds are fundamentally different from each others,
so that only non-star-forming clouds have column density
PDFs that are consistent with a log-normal shape.
2
Credit: J. Kainulainen