Context. Magnetic flux emergence and cancelling in the quiet Sun is a frequently observed phenomenon. The two possible physical flux-removal mechanisms involved in this cancelling process are retraction and reconnection. Aims. We seek to find distinct observational signatures characterising retraction and reconnection. Methods. We carried out three-dimensional non-grey radiative magnetohydrodynamic (MHD) simulations of convection near the solar surface and the solar photosphere using the STAGGER code, and employing different initial conditions: (1) mixed-polarity simulations with alternating horizontal stripes of opposite vertical magnetic field and separated by a zero field stripe, and (2) flux emergence simulations with continuous injection of magnetic flux from the lower boundary. These initial conditions are meant to represent two different situations in the solar photosphere, namely magnetic flux cancelling in the absence or presence of magnetic flux emergence, respectively. Results. We analyse the observational signatures of magnetic flux-removal processes for flux emergence as well as for mixed-polarity MHD simulations. In the flux emergence simulation, we are able to identify ubiquitous reconnection events anywhere from the solar surface to the upper photosphere. For a few of those reconnection events, we can identify supersonic upflow velocities in the upper photosphere as well as strong temperature enhancements. We also see strong electric currents very close to the locations where reconnection takes place, as well as supersonic horizontal velocities leading to sideways plasma compression. In the mixed-polarity simulations, we only detect observational signatures of magnetic field retraction related to large downflow velocities that appear in between regions where opposing horizontal velocities converge. These horizontal velocities are often supersonic, leading to heating due to shock dissipation. We do not see clear signatures of magnetic reconnection in these mixed-polarity simulations. Conclusions. We suggest that, in the emerging flux regions of the quiet Sun, the main flux-removal process is reconnection, while in regions without flux emergence, retraction is the dominant flux-removal process.
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