Helioseismology, the science that studies the Sun's interior using its acoustic oscillations, has revolutionized our understanding of solar physics. The frequency precisions of a few tens of parts per million have paved the way over the years to improve the solar modeling, which now reaches an accuracy of 0.1% in most of the Sun. This is opens the possibility to use the Sun as a laboratory to test plasma opacities, nuclear reaction rates, and even neutrino physics. It was also used to map the radial and latitudinal dependences of the solar differential rotation – a 2D dependence in the convection zone and a solid-body rotation below, in the radiative zone. This knowledge is crucial as a key ingredient in magnetic dynamo theories. However, acoustic modes are not efficient at extracting information from the nuclear core – the first 20% in radius – since they have too low amplitudes there. This leaves solar physicists unable to discriminate between fast and slow core rotations. The measurement of differential core rotation – an imprint of past angular momentum transport inherited from the primitive Sun – would offer crucial insights into the physical processes at work in the central regions and constraints on the Sun's past evolution. 

In this respect, the long-awaited gravity modes, trapped in the deep interior, could in principle provide valuable information on the core. For these reasons, they have been the subject of extensive searches over the years, but none have been conclusively detected, despite the almost 30-year-long time series from the GOLF (SOHO/ESA) spectrograph. Their very small amplitudes at the surface leave them hidden in the convective noise.

In order to overcome this convective barrier and sound the deepest layers of the Sun, we propose a radically new strategy. Considering that the radiative zone represents 98% of its mass, we suggest that time-dependent processes occurring in the solar core, like the differential – centrifugally distorted and possibly inclined – rotation produces gravitational signals that can be detected outside the Sun. The objective of our project is to detect the gravitational signals emitted by the Sun’s core into Solar System planetary orbits. We predict that these perturbations are at the centimeter level, which can nowadays be detected using planetary ephemerides like INPOP. 

This numerical integration is known to reach remarkable precision through a combined effort of collecting radar tracking data over the years from spacecraft in the Solar System, together with comprehensive physical modeling including all possible effects known to affect these data – tidal deformations, asteroid perturbations, body shapes, solar plasma – within the General Relativity (GR) framework. With this model, the Solar System becomes a laboratory where gravitational physics is tested over baselines of decades, using planetary positions as high-precision "clocks" that allow GR tests, such as Mercury's perihelion precession, the Equivalence Principle, alternative theories (MOND), dark matter, and the mass of the graviton. Two approaches can be used to test new gravitational physics with ephemerides. The first one consists of adding the new physics to INPOP, and checking whether it lowers the residuals with observations. We used this approach for the preparation of the BepiColombo (ESA) mission to study the influence of solar differential rotation on Mercury's orbit. The second approach consists of using the residuals from INPOP and finding the signature of the missing process.

Using this second approach, the PhD project will focus on the analysis of Mars’ orbit, since the planet has so far the best constrained planetary orbit of the Solar System due to the numerous missions that have visited it. Using the 20-year-long data from Mars Express (ESA), we will be able to detect the signal of differential rotation and possibly other processes of solar interior. The student will have to complete an analytical formalism developed by our team in GR formalism to calculate the impacts of time-dependent physical processes in the Sun’s core onto gravitational signals. Since the geometry of the system, with different planets and radar signals traveling from the spacecraft to Earth, makes the problem difficult to solve analytically, the PhD student will have to make a numerical code that accounts for the couplings, phase shifts, and possible amplifications by resonances in multi-body interactions. He/she will also conduct an in-depth analysis of the Mars Express data to detect the signatures of solar core processes. Finally, the detected processes will be integrated by the student into the INPOP modeling. This will quantitatively improve the accuracy of the INPOP’s predictions for future studies. The project will serve as the basis for future studies of the upcoming Bepicolombo mission, which will start to deliver cm-level precision positions from the mid-2027.

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For more Information about the topics and the co-financial partner (found by the lab!); contact Directeur de thèse - lbigot@oca.eu

Then, prepare a resume, a recent transcript and a reference letter from your M2 supervisor/ engineering school director and you will be ready to apply online before March 13th, 2026 Midnight Paris time!