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We present a study of the vertical magnetic field of the Milky Way towardsthe Galactic poles, determined from observations of Faraday rotation towardmore than 1000 polarized extragalactic radio sources at Galactic latitudes |b|> 77 degs, using the Westerbork Radio Synthesis Telescope and the AustraliaTelescope Compact Array. We find median rotation measures (RMs) of 0.0 +/- 0.5rad/m^2 and +6.3 +/- 0.7 rad/m^2 toward the north and south Galactic poles,respectively, demonstrating that there is no coherent vertical magnetic fieldin the Milky Way at the Sun's position. If this is a global property of theMilky Way's magnetism, then the lack of symmetry across the disk rules out puredipole or quadrupole geometries for the Galactic magnetic field. The angularfluctuations in RM seen in our data show no preferred scale within the range ~0.1 to 25 degs. The observed standard deviation in RM of ~ 9 rad/m^2 thenimplies an upper limit of ~1microGauss on the strength of the random magneticfield in the warm ionized medium at high Galactic latitudes.

A Survey of Extragalactic Faraday Rotation at High Galactic Latitude: The Vertical Magnetic Field of the Milky Way towards the Galactic Poles