Modelling Martian Moons Surface Temperature – an update

Introduction

The martian moons Phobos and Deimos are the main target of the Martian Moons eXploration mission (MMX). The mission will depart from Earth in October 2026, and arrive around Mars in 2027. Phobos and Deimos orbit Mars at respectively 9400 and 23000 km [2], with low inclinations and eccentricities. The moons present strongly processed surfaces and host a fine regolith [15]. Spectroscopic observations in the Visible and Near-Infrared (Vis-NIR) display dark and red flat spectra [12].
Because of their shape, spectral properties and orbital parameters, their origins is yet to be understood. The proposed hypothesis regarding their formation stipulate that they could result from the capture of D-type asteroids [12] or that they may results from an impact [3, 12].
Despite they share important spectral similarities with D-type asteroids, their peculiar orbits (low inclination and eccentricity) are difficult to reconcile with a gravitational capture scenario; but are compatible with an impact origin.
The mission MMX [10] hence aims to study closely Phobos and Deimos compositions relying on MMX Infrared Spectrometer (MIRS) observing across a spectral range of 0.9 to 3.6µm [1]. At a distance of 1.5 a.u., the moons' surfaces are warm enough [8] to emit a significant thermal flux, especially beyond 2µm resulting in a spectral distortion after 2.5µm. This work presents a method adapted from previous works [6, 10] to characterise the surface temperature of the martian moons in preparation of MIRS data interpretation.

 

Illumination at the moons surface

Because of their small size and the absence of atmosphere, Phobos and Deimos surface temperatures are solely driven by the flux absorbed at the surface.
Thus, we developed a simulation that computes the flux reaching the surface of the moons over one orbit around the Sun. It relies on the SPICE/NAIF toolkit and the shape models by [16] to computes the distance and the viewing geometry at the moons surfaces. Consequently the incident flux at a given location at the surface varies with the solar distance, the eclipses, the orientation of the satellite, and the thermal emission of Mars.

 

Solving heat equations

A thermophysical model [6,10] solves the 1-D time-dependent heat equation for each point of the incident flux map previously computed. The model takes as input the surface properties: the porosity p, the grain size D_g, the bulk density ρ and the thermal conductivity of the non-porous material κ_m. Considering the absence of atmosphere of the martian moons the model does not consider convection, but consider the heat exchange by conduction and radiation inside the surface. This conduction is described by the effective conductivity κ_eff computed from the surface texture (Dg, p,) and thermal (Cp, κ_m) properties with [14] model.

 

Concerning self-heating

This self-heating represents the mutual irradiation between two surface elements as their temperature is warm enough to emit a significant flux in the IR. As the self-heating influences the temperature and thus itself, we simulate this self-heating several times and reinject the previous estimation in the thermal model until the self-heating flux converge – which happens after 2 iterations. This mutual heating is specifically important in the craters and adds up to 35 W.m^-2 to the surface.

 

Thermal emission of a rough surface

We adopted the method from [5] to estimate the flux from a rough surface. Therefore, we compute the temperature of a large number of sub-resolution elements by modulating the incoming flux by a tilting angle estimated from Hapke’s mean slope parameter derived in [7]. The surface emission is thus only the averaged sum of all the sub-resolution elements contribution.

 

Removing thermal emission in NIR spectra

Figure : a) CRISM data and best fitted thermophysical model. b) Comparison of CRISM data corrected with [4] and this work.

To test our model, we simulated NIR synthetic data in the MIRS spectral range using outputs of our models, on which we added a reflective component - estimated from the Hapke model [9], and the solar flux scaled to the martian orbit – and gaussian noise. To remove the thermal emission from a NIR spectrum, the pipeline computes thermal emission, the reflective component and adjust the grain size and the porosity to fit the data. We were able to perfectly remove the thermal emission.
Moreover, when incorporating absorption feature in the synthetic data, we could test the sensitivity of the correction to the presence of bands, which is revealed pretty robust unless the bands lies in the thermal emission range. In addition, this method does not deform the band shape and therefore allows for a precise measurements of their depths. As a second test of the model, we tried to fit the NIR measurement from CRISM hyperspectral observations and compared to another method of iterative black-body fitting from [4]. The residual slope after the corrections is minimal and 4 times smaller than the one after [4], but after 3µm the noise in the data is too large to assess of the presence of any spectral feature.

 

Perspectives

We developed a pipeline to support the analysis of the future MIRS data, dedicated to estimating the surface temperature of martian moons and remove the thermal emission from the spectral observations. This approach is strongly dependent on the surface properties, necessitates a previous knowledge of the surface and is computationally hungry, but gives promising results and is not dependent to the data. Thus it can be used as support to closely monitor the presence of absorption features at Phobos surface. As the model computes the temperature profile down to 10 thermal skin depth (~10m on Phobos), it is potentially possible to derive the sub-surface texture from spectral measurements in the NIR-MIR like PFS data.

 

References

[1]Barucci+2021
[2]Burns+1978
[3]Craddock+2011
[4]David+2024
[5]Davidsson&Rickman2014
[6]Ferrari+2006
[7]Fornasier+2024
[8]Giuranna+2011
[9]Hapke2012
[10]Kuramoto+2022
[11]Leyrat+2011
[12]Rivkin+2002
[13]Rosenblatt+2016
[14]Sakatani+2017
[15]Thomas+1979
[16]Willner+2014