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Most models for the central engine of gamma-ray bursts involve a stellar massblack hole surrounded by a thick disk formed after the merging of a system ofcompact objects or the collapse of a massive star. Energy released from theaccretion of disk material by the black hole or from the rotation of the holeitself extracted by the Blandford-Znajek mechanism powers a relativistic windalong the system axis. Lorentz factors of several hundreds are needed to solvethe compactness problem in the wind which implies the injection of a tremendouspower into a very small amount of matter. The Blandford-Znajek mechanism, wherethe outflow follows magnetic field lines anchored to the black hole is probablythe best way to prevent baryonic pollution and can even initially produce apurely leptonic wind. In this paper we rather study the wind emitted from theinner part of the disk where the risk of baryonic pollution is much largersince the outflow originates from high density regions. We show that thebaryonic load of this wind sensitively depends on the disk temperature andmagnetic field geometry and that the outflow can become ultra-relativistic(Lorentz factor Gamma>100) under quite restrictive conditions only. Conversely,if Gamma remains of the order of unity the dense wind emitted from the innerdisk could help to confine the central jet but may also represent a source ofbaryon contamination for the Blandford-Znajek mechanism.Comment: 13 pages, 8 figures, to be published in A&

Baryonic pollution in gamma-ray bursts: The case of a magnetically driven wind emitted from a disk orbiting a stellar mass black hole