An analysis of the JAGB method from the perspective of the asymptotic giant branch evolution

Context. The JAGB method has been proposed over the last years as a possible distance indicator for the galaxies in the Local Group and possibly beyond. The nature of the stars populating the J region, as well as the conditions of the star formation history and the structural properties of the galaxies for the straight application of this method, still need to be investigated. Aims. We studied the populations of the J region of the colour-magnitude (J - K, J) plane of the Large and Small Magellanic Clouds (LMC and SMC, respectively) to relate the shape of the J luminosity function (JLF) to the details of the formation histories of the two galaxies. Our aim is to try and distinguish the general aspects of the JLF to those more sensitive to the stellar population of the specific galaxy considered. Methods. We used a population synthesis approach, based on the combined results from stellar evolution and dust formation modelling, to find the expected distribution of the stars within the J region. We then compared the outcome with results derived from observations of LMC and SMC stars. Some physical assumptions, mostly related to the modelling of the red giant branch (RGB) and asymptotic giant branch (AGB) phases of stars, were tuned until a satisfactory agreement between the expectations from synthetic modelling and the observational evidence was reached. Results. The sources observed within the J region were characterised as stars that recently reached the C-star stage and have not yet accumulated the extremely large amounts of carbon required to make the evolutionary track to evolve off the J region. Generally speaking, 2 - 3 M-circle dot stars stay within the J region longer, while lower mass objects evolve there for at most a couple of inter-pulse phases. The analysis of the JLF of the LMC, peaking at the J magnitudes expected for these stars, confirms this understanding. In the SMC, the distribution of the J fluxes is shifted to higher J magnitudes when compared to the LMC, which we interpret as the signature of a generally older population, with lower mass progenitors.