Generalizing the similitude approach for laboratory astrophysics through equivalence symmetries for the example of radiative waves

For decades, scaling laws have served as the cornerstone of laboratory astrophysics, enabling quantitative comparisons between astrophysical phenomena and laboratory experiments. However, the lack of observational data and some experimental limitations has limited our ability to validate certain theoretical and numerical models when studying some of the most extreme phenomena in the universe. In this work, we present a theoretical framework for a new class of laboratory astrophysics experiments that leverage existing high-power laser facilities to investigate supersonic radiation-dominated waves. By extending Lie symmetry theory, we demonstrate that the stringent constraints imposed by traditional scaling laws can be relaxed. This approach enables the study of astrophysical phenomena in the laboratory, even when the ratio of radiation energy density to thermal energy and the micro-physics of the systems differ. These equivalence symmetry concepts are illustrated through simulations under conditions relevant to Type-I X-ray bursts and through the design of a first equivalent laboratory experiment. These findings pave the way for a broader range of astrophysical systems to be explored using laboratory experiments, marking the birth of a new innovative approach in laboratory astrophysics.