Constraining the date of the martian dynamo shutdown by means of craters' magnetization signatures

Mars is characterized by a strong crustal magnetic field, particularly over its southern hemisphere, which is the remnant of ancient core dynamo. The dynamo ceased operating approximately 4 Gyr ago, although the exact time is still under debate. The scope of this study is to introduce constraints on the possible timing of its cessation by studying the magnetization signatures over some craters which have reliable crater retention ages and are large enough for the impact to have reset the crustal magnetization within. It is well known that inverting magnetic field data for a magnetization distribution suffers from inherent non-uniqueness. However, the study of Gubbins et al. (2011) has shown that vector spherical harmonics allow the separation of a magnetization distribution into the part that generates the magnetic field observed in source-free regions, hereafter called the visible magnetization, and the null space, which does not contribute to the observed magnetic field. In the first step of our study, under the assumption of a 40 km thick magnetic layer and of a magnetization distribution that varies only laterally, we propose a model of the visible magnetization of Mars based on the lithospheric magnetic field model of Morschhauser et al. (2014). In the second step of our study, by means of a Monte Carlo approach, we generate various magnetization distributions that span its null space as this is described by the vector Spherical Harmonic bases. For this, we make the assumption that the visible part of the magnetization and its null-space are characterized by the same properties, e.g., concerning their intensity and their coherence wavelength. By adding the visible magnetization to these null space samples, we intend to infer the probability of a given crater to be magnetized, partially magnetized or demagnetized. Combining these probabilities with the date of each crater can lead to a probabilistic history for the martian dynamo.