Photoelectron energy degradation

One of my current activities is to investigate the non-thermal heating, excitation and ionization of gases of atmospheric interest. Towards that end, I have recently built a Monte Carlo (MC) model that solves the energy degradation of the photoelectrons. The model is thoroughly described in a paper published in the journal Icarus, 2023:

You can find the fortran version of the MC model here:

This v1 version runs for gas mixtures of H, He and thermal electrons. The above link provides access to cross sections at 1 eV resolution. Cross sections at higher resolution (0.1, 0.01 eV) have also been calculated, but are not posted through the link because they take too much memory. If needed, drop me an email. 

Future versions of the code will include other atoms and molecules of interest in aeronomy.

A newer version, including oxygen chemistry is available through:


Radiative transport of polarized light in planetary atmospheres

In 2015, I and collaborator Frank Mills from the Australian National University published a paper in A&A on backward Monte Carlo (BMC) algorithms to solve the polarization radiative transfer equation in planetary atmospheres. We identified a numerical inconsistency in past implementations of BMC algorithms, which neglect the polarization state when identifying the next direction the simulated photons are moved to and that leads to unreliable solutions when the medium is highly polarizing. We proposed an alternative way of sampling the photon directions that, by taking into account the polarization state, eliminates the numerical problem altogether. We tested our algorithm against more than 30,000 analytical and non-analytical solutions and demonstrated that our sampling scheme provides solutions that are accurate to within 0.01% or better for all elements of the Stokes vector provided that enough photons are simulated. To my knowledge, this is the most thorough validation exercise ever for a Monte Carlo algorithm.

Our so-called Pre-conditioned BMC algorithm is well suited for the interpretation of both spatially-resolved and disk-integrated measurements. The algorithm is particularly efficient when only the disk-integrated signal of the planet is required. It has been used in the interpretation of the phase curves of hot Jupiters, Earth, Venus and Titan. The figures and animations below demonstrate some of its applications.

A one-slab, plane-parallel version of the PBMC algorithm is freely available at the CDS via anonymous ftp to (

or via


The two figures above were prepared by a former summer student, Tom Enstone, who spent a summer working with Kate Isaak (ESA/ESTEC, the Netherlands) and me. They are based on published work (García Muñoz, International Journal of Astrobiology, 2015) that investigates the brightness modulation of the Earth during a 24-hr rotational period. The Earth surface albedo (top, left) and cloud fraction (bottom, left) impact significantly the brightness light curves (right). The three curves are specific to three different wavelengths and compare well with observations made by the NASA/Messenger spacecraft in a 2005 flyby. Accurate measurements of multi-wavelength brightness modulations will enable the investigation of Earth-like planets. As predicted in our work, the modulation of the linear polarization level of the Earth during a 24-hr period is on the order of a few percents.


Phase curve of Kepler-7b: Modeling and observations (black dots, unbinned; pink symbols, binned). Our interpretation of the Kepler-7b phase curve is unique in that it solves the multiple scattering problem in the atmosphere. This work was published in PNAS (García Muñoz & Isaak, 2015). The interpretation of the phase curves is susceptible to various degeneracies (see below), but we could robustly conclude that Kepler-7b’s atmosphere is made of poorly-absorbing, small cloud particles, and that the cloud is shifted towards the morning terminator.


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