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Neutron stars are very dense media in which axions may be produced. Such a link leads to stringent limits on the axion characteristic energy scale by imposing restrictions on the neutron star cooling. In this presentation, I will show our current study on the dependence of this limit with respect to the particle composition of the neutron star core. We will do so by recalculating the limits on KSVZ and DFSZ axions using equations of state that assume different particles to be present within the neutron star.