For many years, photoionization codes have been used to numerically solve the equations of radiative transfer by making the assumption of spherical symmetry. However, very few HII regions or planetary nebulae (PNe) show spherical symmetry. Many images of PNe and HII regions show complex structures such as knots of higher density which can cause the regions behind them to be protected from direct starlight. In such regions the diffuse radiation field will dominate causing an enhancement of lower ionization species.

NGC 6302
Figure 1. HST WFC3 image of the bipolar planetary nebula NGC 6302.

MOCASSIN is a self-consistent, three-dimensional radiative transfer code that uses Monte Carlo techniques to build realistic models of photoionised nebulae. The code is capable of treating arbitrary geometries, density distributions and multiple exciting stars at non-central locations (Ercolano et al. 2003). MOCASSIN has been benchmarked against established one-dimensional spherically symmetric codes for a number of standard cases, as defined by the Lexington / Meudon photoionization workshops.

MOCASSIN uses a cuboidal Cartesian grid to model the gaseous region. Within each grid cell, the thermal equilibrium and ionization balance equations are solved to determine the physical conditions. The primary and secondary radiation fields are calculated self-consistently by locally simulating the individual processes of ionization and recombination.


Almost all nebulae contain dust. Some PNe and protostars have toroidal dust rings that can constrain the flow of ejected material, creating biconical structures. These dust grains can have a significant effect on the radiative transfer (RT) in an ionised plasma and can influence the physical conditions of the gas. The dust is heated by the absorption of UV photons and nebular resonance line radiation emitted by the gas.

Dusty MOCASSIN was the first 3D Monte Carlo photoionization code to include a fully self-consistent treatment of dust radiative transfer within a photoionised region. It introduces the vital coupling, in the RT, between the co-existing dust and gas, incorporating the scattering, absorption and emission of radiation by dust particles mixed within the gas (Ercolano, Barlow and Storey 2005).

Clumpy SN
Figure 2. A 3-dimensional representation of the dust number density in a clumpy supernova ejecta model.

MOCASSIN uses standard Mie scattering theory to calculate the effective absorption and scattering efficiences. The code can determine accurate dust temperature and spectral energy distributions (SEDs) by treating multiple grain species and distributions, compared to the frequently used approximation of having a single grain as representative of an ensemble of grains. It also calculates emission line spectra, the 3D ionization structure and the electron temperature and density profiles of the nebula.

Dusty MOCASSIN has also been adapted to treat non-central energy sources and regions where gas and dust is highly clumped. Such conditions can be encountered in the ejecta of supernova remnants, where dust which has condensed in dense clumps is heated by the decay products of radioactive elements. Figure 2, from Ercolano, Barlow and Sugerman 2007, illustrates how such a situation can be treated by MOCASSIN using higher resolution meshes for the clumped zones.

For more information about MOCASSIN, please visit its website.

UCL contact: Dr Roger Wesson (rwesson AT

Page last modified on 11 apr 17 11:45 by Roger Wesson