The Pressure Structure of Molecular Clouds


Abstract. Broadly, we seek to understand the role of pressure in star forming molecular clouds. We examine molecular line data of the Perseus region from the COMPLETE survey alongside radiative transfer-processed ‘observations’ of the turbulent simulations of S. Offner to try to (1) understand to what extent we can actually measure pressure through observations, and (2) study how pressure changes within a cloud’s substructure.


  1. Internal pressure in GMCs acts to resist collapse locally and is an important part of the force balance equation controlling the efficiency of star formation

  2. Pressure of the ambient ISM “external” to clouds may act to help confine them against dissipation on short timescales – i.e. clouds may be in pressurized virial equilibrium even if unbound according to simple virial analysis (Field, Blackman & Keto 2011).

  3. Clouds are complex, turbulent entities that contain hierarchical structure and both large- and small-scale features (in density, velocity, possibly magnetic fields).

  4. Molecular line observations of clouds reveal some of this structure but are limited to a small dynamic range in density (for a single tracer) and one dimension of the velocity field. Observations also represent only a snapshot in what is in reality a dynamic system. Simulations have the advantage of allowing the time evolution within clouds to be followed, and including the full (“true”) six-dimensional phase space information, but are heavily reliant on the (necessarily limited) input physics.

  5. Dendrograms represent a powerful tool for probing hierarchical structure and can be applied to real and simulated data to make progress on understanding the pressure structure within and external to clouds.

  6. We have analyzed data from COMPLETE and synthetic cubes from radiative transfer-processed turbulent simulations to attempt to clarify the role of pressure within clouds and in the star formation process.

\(^{13}\)CO integrated intensity map of IC348 in Perseus.

Expectations from Simple Scaling Laws


Pressure scaling: \[P \propto \rho \sigma_v^2\]

Density and velocity scale as power laws: \[\begin{aligned} \rho &\propto& L^{-a} \\ \sigma_v &\propto& L^b\end{aligned}\] Here \(\sigma_v\) is the 3d velocity dispersion, related to the 1d dispersion for isotropic fields by \(\sigma_{v,{\rm 1d}} = \sqrt{3} \sigma_{v,{\rm 3d}}\).

What values do we expect for the exponents \(a\) and \(b\)? Table \ref{tab:scaling} gives some possible examples. Combining these equations, we see that pressure scales as \[P \propto L^c; c=2b-a\] where \(-2 \lapprox c \lapprox 1\), with the lowest value for the exponent for thermal gas in a SIS envelope, and the highest value for turbulent, constant density gas. (Is the latter realistic? Probably not, limiting exponent to \(c < 0\)). Note Larson’s relations (updated for modern observations, and focusing on scales larger than core scales) give \(b \sim 0.5\) (Larson 1981, Solomon 198?, Goodman 199?, others?).

Upshot: we expect pressure to decrease toward small scales in clouds. We will test this with our data and simulations.

to do: think about: wouldn’t scaling expectations change as a function of size sampled? a cloud as a whole does NOT have the same density structure as a core – swiss cheese vs. bbs