On early Solar System chronology: Implications of an heterogeneous spatial distribution of $^{26}$Al and $^{53}$Mn

Early Solar System chronology is usually built with the assumption that the distribution of short-lived radionuclides was homogeneous through the solar accretion disk. At present, there is no unambiguous evidence for a homogeneous distribution of short-lived radionuclides in the solar accretion disk, while some data point to a heterogeneous distribution of short-lived radionuclides. In this paper, we explore a possible chronology based on a heterogeneous distribution of $^{26}$Al and $^{53}$Mn in the accretion disk. Our basic assumption is that the different abundances of extinct short-lived radionuclides in calcium-aluminium-rich inclusions (CAIs) and chondrules are due to spatial rather than temporal differences. We develop a simple model where CAIs and chondrules form contemporaneously, in different spatial locations, and are characterised by distinct initial $^{26}$Al and $^{53}Mn abundances. In this model, all evolved bodies are supposed to be originally chondritic, i.e., to be made of a mixture of CAIs, chondrules, and matrix. This mixture determines the initial content in $^{26}$Al and $^{53}$Mn of a chondritic parent-body as a function of its CAI and chondrule abundance fraction. This approach enables us to calculate coherent $^{26}$Al and $^{53}$Mn ages from the agglomeration of the parent-body precursors (CAIs and chondrules) until the isotopic closure of $^{26}$Al and $^{53}$Mn, thereafter called $^{26}$Al-$^{53}$Mn age. We calculate such $^{26}$Al-$^{53}$Mn ages for a diversity of evolved objects, with the constraint that they should be found for realistic chondritic parent-body precursors, i.e., objects having similar or identical petrograpy to the existing chondrite groups. The so defined age of the d'Orbigny angrite is 4.3 $\pm$ 1.1 Myr, for the Asuka-881394 eucrite 2.8 $\pm$ 1.0 Myr, for the H4 chondrite Sainte Marguerite $\sim 3 Myr, and for H4 Forest Vale $\sim$ 5 Myr. The calculated $^{26}$Al-$^{53}$Mn ages give timescales for the evolution of the respective parent-bodies/meteorites that can be investigated in the light of further petrographic studies. We anchor the calculated relative chronology to an absolute chronology using absolute Pb-Pb ages and relative Hf-W ages of the objects under scrutiny. The precursors of Sainte Marguerite and Forest Vale agglomerated at the same time ($\sim$ 4565.8 $\pm$ 1.2 Ma ago). The precursors of eucrites (Asuka-881394) agglomerated 4564.8 $\pm$ 1.2 Ma ago. The precursors of angrites agglomerated late (4561.5 $\pm$ 1.8 Ma ago). Our model provides a fully compatible Al-Mg/Mn-Cr/Pb-Pb chronology, and is shown to be robust to reasonable changes in the input parameters. The calculated initial $^{26}$Al/$^{27}$Al ratios are high enough to have $^{26}$Al as a possible heat source for differentiation