## Cloud models

First step in the simulation of dust emission or line emission from an interstellar cloud is the creation of a physical model for the object. This defines the density distribution in the source. For calculations of line emission one also must specify the velocity field.

Most models are even this day spherically symmetric. Such models consist of a number of co-centric shells. In these 'one-dimensional' models density depends only on the distance from the cloud centre. For such models simulations are very fast and in many case we do not have enough information so that more accurate and more complicated models could be constructed. It is known, however, that interstellar clouds are very inhomogeneous ('clumpy') and this should affect both dust and molecular line emission. Small scale density fluctuations cannot be taken into account with one-dimensional models where also velocity field must be rather simple.

I have written computer programs for simulation of radiative transfer in three-dimensional clouds. Model clouds consist of a regular, three-dimensional grid where density and velocity can be set separately in each cell. This allows modelling of clouds with arbitrary density and velocity structures. In the beginning of this work I used density distributions created with simple algorithms, and velocity field consisted simply of random motions. The two figures below illustrate density distributions in a fractal cloud and in a cloud created according to a so-called structure-tree algorithm. Such models were used to study the basic effects that inhomogeneities (in density and in velocity) have on computed line spectra.

Two simple models of three-dimensional, clumpy clouds: a fractal cloud (on the left) and a cloud created using the structure-tree description. The drawn surfaces enclose volume where density exceeds a selected value. (Juvela M. 1998, A&A 329, 659-682)

The previous models are based on some observed properties of interstellar clouds. The generated density distributions are, however, not physically accurate and density and velocity fields are independent of each other. It is, however, possible to simulate density and velocity fields self-consistently with magnetohydrodynamic (MHD) calculations. In addition to normal fluid dynamics one must consider the effects that magnetic fields have on gas flow. Strength of magnetic fields in interstellar clouds is one of the things we want to study with cloud modelling.

In these studies I have collaborated with Paolo Padoan (University of California) who has done the MHD-simulations. Below is one example of the filamentary density field produced in such simulations.

Density isocontour in a model cloud produced with MHD-calculations. Simulations produce clumpy and filamentary structures that are similar to what is seen in many real interstellar clouds. (MHD calculations: P. Padoan). There is also an animated gif (2MB!) where this model is rotated 360o.