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High-Velocity Clouds (HVCs) are believed to be an important source of gasaccretion for star formation in the Milky Way. Earlier numerical studies havefound that the Galactic magnetic field and radiative cooling strongly affectsaccretion. However, these effects have not previously been included together inthe context of clouds falling through the Milky Way's gravitational potential.We explore this by simulating an initially stationary cloud falling through thehot hydrostatic corona towards the disc. This represents a HVC that hascondensed out of the corona. We include the magnetic field in the corona toexamine its effect on accretion of the HVC and its associated cold gas.Remnants of the original cloud survive in all cases, although a strong magneticfield causes it to split into several fragments. We find that mixing of coldand hot gas leads to cooling of coronal gas and an overall growth with time incold gas mass, despite the low metallicity of the cloud and corona. The role ofthe magnetic field is to (moderately to severely) suppress the mixing andsubsequent cooling, which in turn leads to less accretion compared to when thefield is absent. A stronger field leads to less suppression of condensationbecause it enhances Rayleigh-Taylor instability. However, magnetic tension in astronger field substantially decelerates condensed cloudlets. These havevelocities typically a factor 3-8 below the velocity of the main cloud remnantsby the end of the simulation. Some of these cloudlets likely disperse beforereaching the disc.

The role of the halo magnetic field on accretion through High-Velocity Clouds