Survival of fossil fields during the pre-main sequence evolution of intermediate-mass stars

Chemically peculiar Ap and Bp stars host strong large-scale magnetic fields in the range of $200$~G up to $30$~kG, which are often considered to be the origin of fossil magnetic fields. We assess the evolution of such fossil fields during the star formation process and the pre-main sequence evolution of intermediate stars, considering fully convective models, models including a transition to a radiative protostar and models with a radiative core. We also examine the implications of the interaction between the fossil field and the core dynamo. We employ analytic and semi-analytic calculations combined with current observational constraints. For fully convective models, we show that magnetic field decay via convection can be expected to be very efficient for realistic parameters of turbulent resistivities. Based on the observed magnetic field strength - density relation, as well as the expected amount of flux loss due to ambipolar diffusion, it appears unlikely that convection could be suppressed via strong enough magnetic fields. On the other hand, a transition from a convective to a radiative core could very naturally explain the survival of a significant amount of flux, along with the presence of a critical mass. We show that in some cases, the interaction of a fossil field with a core dynamo may further lead to changes in the surface magnetic field structure. In the future, it will be important to understand in more detail how the accretion rate evolves as a function of time during the formation of intermediate-mass protostars, including its impact on the protostellar structure. The latter may even allow to derive quantitative predictions concerning the expected population of large scale magnetic fields in radiative stars.