Multi-million-year cycles in modelled <i>δ</i>¹³C as a response to astronomical forcing of organic matter fluxes

Abstract

Along with 400 kyr periodicities, multi-million-year cycles have been found in δ13C records over different time periods. An ∼ 8–9 Myr periodicity is found throughout the Cenozoic and part of the Mesozoic. The robust presence of this periodicity in δ13C records suggests an astronomical origin. However, this periodicity is barely visible in the astronomical forcing. Due to the large fractionation factor of organic matter, its burial or oxidation produces large δ13C variations for moderate carbon variations. Therefore, astronomical forcing of organic matter fluxes is a plausible candidate to explain the oscillations observed in the δ13C records. So far, modelling studies forcing astronomically the organic matter burial have been able to produce 400 kyr and 2.4 Myr cycles in δ13C but were not able to produce longer cycles, such as 8–9 Myr cycles. Here, we propose a mathematical mechanism compatible with the biogeochemistry that could explain the presence of multi-million-year cycles in the δ13C records and their stability over time: a preferential phase locking to multiples of the 2.4 Myr eccentricity period. With a simple non-linear conceptual model for the carbon cycle that has multiple equilibria, we are able to extract longer periods than with a simple linear model – more specifically, multi-million-year periods.