Line transfer

In the case of molecules the observed radiation is released in spontaneous transitions where a molecule moves to a lower energy state (energy level). When line emission is simulated for a model cloud one must first know the number of molecules on initial level of the transition. This is also called the level population. Molecules are moved to other energy levels by collisions with other particles and by radiation. The radiation that excites molecules in one part of the cloud may have been emitted by molecules elsewhere. It is this self-coupling which makes the computations so complicated. Lines are relatively narrow in frequency and this leads to another important difference compared with continuum radiative transfer. If there is a large velocity difference between two regions photons emitted in one place can no longer be absorbed in the other. This means that velocity field is very important for excitation of molecules and in part determines the observed line intensities.

Radiative transfer calculations start with an assumption of how molecules are distributed on different energy levels in each position of the cloud. Next one calculates how much radiation is emitted and how this radiation is transferred inside the cloud. Together with local density and temperature this information is used to re-compute level populations. The whole process (simulation of radiation field and re-solving of excitation) is repeated until there are no more changes. Finally, one can solve equation of radiative transfer for selected lines-of-sight through the model cloud and the final result is a set of line spectra that can be compared with observations.

I have developed a radiative transfer program, Cppsimu, which can be used to solve the radiative transfer problem in three-dimensional model clouds which are divided into small, cubic cells. The program is based on Monte Carlo simulation. This means that the stregth of radiation field is computed by actually simulating emission and propagation of photons. One selects a random position in the cloud and sets up a photon package that represents all photons emitted from that region. Next one selects a random direction for the package and follows the package until it exits the cloud. While the package moves through the cloud one calculates how many photons from the package are absorbed in each cell that the package passes through. The simulation is repeated many times so that emission from all parts of the cloud is taken into account. The number of photons absorbed in a cell represents the local field strength and this information is used when new level populations are solved for that particular cell.

The program has been used to predict spectral lines from 3D model clouds that are based on magnetohydrodynamical simulations. Statistical properties of spectral lines carry information on various cloud properties. Simulated spectral line maps can be compared with observations, and this enables us learn something about, for example, the nature of turbulence in interstellar clouds.

Below are examples of simulated spectral line maps.

spectra for a MHD model cloud
Spectral lines simulated for one MHD model cloud (MHD simulation by P. Padoan, UCSD). Each little frame shows a spectrum computed for a different line-of-sight through the cloud. In many spectra one can see several peaks at different radial velocities. These correspond to filaments that are moving at different velocities with respect to the observer. There is also an animated gif (2MB!) that shows how line profiles change continuously as one shifts the line-of-sight.

spectra for a MHD model cloud
Another example of line spectra calculated for a MHD simulation. The MHD simulation defines the underlying density and velocity structure of the cloud, while radiative transfer calculations are needed to solve the molecular excitation in each position of the cloud and, finally, to calculate the observed line profiles and intensities. The corresponding animation is available in divx format (4.5MB). In the movie the cloud is rotated and one sees, consecutively, the column density map, and maps of line profiles and line area.