Control of Instabilities in Rotating flows Conducting Electricity: dynamo seeds and subcritical transition to MHD turbulence in stellar objects.

Magnetic fields play a central role in the evolution of stellar objects: they drive angular momentum transport in stellar interiors, influence accretion rates in stellar discs, and shape the rotational dynamics that ultimately determine a star's lifetime and fate. Yet, the very origin of these magnetic fields remains poorly understood in many astrophysical environments, particularly in stably stratified radiative stellar layers and in the innermost, weakly ionized regions of stellar discs. In such systems, classical (linear) stability theory predicts that infinitesimal magnetic perturbations cannot be amplified by the flow — a theoretical dead end that stands in contrast with observational evidence of magnetism and angular momentum transport.

The CIRCE project tackles this challenge by developing and applying novel nonlinear stability methodology to the problem of magnetic field generation (dynamo instability) and subcritical transition to turbulence in stellar objects. The key element is that, even when a flow is linearly stable to dynamo action, finite-amplitude magnetic perturbations with a favourable structure may trigger a subcritical dynamo instability through the nonlinear feedback of the Lorentz force. Identifying the least-energy perturbations — or "minimal seeds" — capable of initiating such subcritical magnetic transitions is a problem that no other existing method can address systematically, and which CIRCE proposes to solve using adjoint-based optimal control, a powerful mathematical framework recently proven transformative in hydrodynamic stability research.

The project is structured around four interconnected objectives. The first objective (O1) is methodological and transverse: it consists in building a new, versatile, publicly available software library for performing nonlinear adjoint-based optimisation on magnetohydrodynamic (MHD) flow models relevant to stellar systems. The second objective (O2) targets radiative stellar layers, where the project aims to identify nonlinear magnetohydrodynamic transitions — with a particular focus on the Tayler-Spruit dynamo mechanism —, determine the minimal magnetic seeds that can trigger them, and quantify the resulting angular momentum transport and potential signatures on asteroseismic observations. The third objective (O3) addresses stellar discs, where the project seeks to characterise the conditions for subcritical transition to turbulence in Keplerian flows, and to predict the resulting impact on accretion dynamics and magnetic field generation. Finally, the fourth objective (O4) uses adjoint-based optimisation as a physical diagnostic tool to probe the fundamental mechanisms most favourable to nonlinear dynamo action, with the long-term ambition of informing future laboratory experiments.

By combining cutting-edge mathematical methods from optimal control theory with frontier problems in stellar physics, CIRCE aims to establish a new paradigm for studying nonlinear transitions in MHD systems, with far-reaching implications for stellar evolution modelling and the interpretation of rapidly progressing observational constraints from asteroseismology and spectropolarimetry.

During the first reporting period, a major effort has been dedicated to the methodological and numerical foundations of the project. As part of Objective 1, the team has achieved substantial development in building direct and adjoint solvers for several simulation codes relevant to stellar and disc magnetohydrodynamics, with highly efficient HPC parallelisation. These solvers have been integrated within optimisation pipelines implementing adjoint-based methods, and validated over a range of test cases. The developed software spans different geometries and physical setups, so as to address both the stellar interior models targeted by Objective 2 and the accretion disc models targeted by Objective 3. This transverse development effort, which is central to the project's methodology, will continue to be enriched throughout the project's duration.

Significant progress has been made already concerning the nonlinear stability of Keplerian flows as models for protostellar discs. The newly developed optimisation tools have enabled, for the first time, the computation of nonlinear optimal perturbations in Keplerian flow configurations. These calculations provide new insight into mechanisms of nonlinear energy amplification in such flows, and into the potential for subcritical transition to hydrodynamic turbulence — a long-standing open question in astrophysics. A complementary study, focused on a local, stratified disc model, has also led to the identification of minimal seeds and edge states for subcritical instabilities in an Keplerian shearing box. Ongoing studies are investigating subcritical magnetic transitions in models of radiative stellar layers under increasingly realistic conditions, including the associated angular momentum transport and its potential signatures in asteroseismic observables. This line of research will be a central focus of the next project period.

This project brings adjoint-based nonlinear optimisation methods into the realm of astrophysical flows. The numerical and methodological tools developed during this first period make it now possible to systematically search for nonlinear (magneto)hydrodynamic transitions and their critical perturbations in stellar and disc configurations. For example, the computation of nonlinear optimal perturbations in Keplerian flows has revealed a rich phenomenology of energy amplification scenarios inaccessible to classical linear stability analysis, while the identification of minimal seeds and edge states in an astrophysical shearing-flow model opens a new route to characterising the boundary between laminar and turbulent regimes in accretion discs. These advances establish the methodological basis for the project's core astrophysical objectives.

Periodic Reporting for period 1 - CIRCE (Control of Instabilities in Rotating flows Conducting Electricity: dynamo seeds and subcritical transition to MHD turbulence in stellar objects.)

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