Magnetic field tomography in two clouds towards Ursa Major using HI fibers

The atomic interstellar medium (ISM) is observed to be full of linear structures that are referred to as "fibers". Fibers exhibit similar properties to linear structures found in molecular clouds known as striations. Suggestive of a similar formation mechanism, both striations and fibers appear to be ordered, quasi-periodic, and well-aligned with the magnetic field. The prevailing formation mechanism for striations involves the excitation of fast magnetosonic waves. Based on this theoretical model, and through a combination of velocity centroids and column density maps, Tritsis et al. (2018) developed a method for estimating the plane-of-sky (POS) magnetic field from molecular cloud striations. We apply this method in two H\textsc{I} clouds with fibers along the same line-of-sight (LOS) towards the ultra-high-energy cosmic-ray (UHECR) hotspot, at the boundaries of Ursa Major. For the cloud located closer to Earth, where Zeeman observations from the literature were also available, we find general agreement in the distributions of the LOS and POS components of the magnetic field. We find relatively large values for the total magnetic field (ranging from $\sim$$\rm{10}$ to $\sim$$\rm{20} ~\rm{\mu G}$) and an average projection angle with respect to the LOS of $\sim$ 50$^\circ$. For the cloud located further away, we also find a large value for the POS component of the magnetic field of $15^{+8}_{-3}~\rm{\mu G}$. We discuss the potential of our new magnetic-field tomography method for large-scale application. We consider the implications of our findings for the accuracy of current reconstructions of the Galactic magnetic field and on the propagation of UHECR through the ISM.