  Radiative transfer (RT) simulations are a powerful tool that enables the
calculation of synthetic images of a wide range of astrophysical objects. These
simulations are often based on the Monte Carlo (MC) method, as it provides the
needed versatility that allows the consideration of the diverse and often
complex conditions found in those objects. However, this method faces
fundamental problems in the regime of high optical depths which may result in
noisy images and underestimated flux values. In this study, we propose an
advanced MCRT method, i.e., an enforced minimum scattering order that is aimed
at providing a minimum quality of determined flux estimates. For that purpose,
we extended our investigations of the scattering order problem and derived an
analytic expression for the minimum number of interactions that depends on the
albedo and optical depth of the system, which needs to be considered to achieve
a certain coverage of the scattering order distribution. The method is based on
the utilization of this estimated minimum scattering order and enforces the
consideration of a sufficient number of interactions during a simulation.
Moreover, we identified two notably distinct cases that shape the kind of
complexity that arises in MCRT simulations: the albedo-dominated and the
optical depth-dominated case. Based on that, we analyzed implications regarding
the best usage of a stretching method as a means to alleviate the scattering
order problem. We find that its most suitable application requires taking into
account the albedo and the optical depth. Then, we argue that the derived
minimum scattering order can be used to assess the performance of a stretching
method with regard to the scattering orders its usage promotes. Finally, we
stress the need for developing advanced pathfinding techniques to fully solve
the problem of MCRT simulations in the regime of high optical depths.
