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Whether and how magnetic fields influence the formation and evolution of galaxies is still unknown. Most numerical models of the interstellar medium in galaxies ignored magnetic fields. Magneto-hydrodynamical (MHD) models of evolving galaxies are computationally challenging and require various simplifications (Wang & Abel 2009; Pakmor & Springel 2013; Pakmor et al. 2014).

Much more is known about magnetic fields in the interstellar medium (ISM) of nearby galaxies and the Milky Way, thanks to modern radio telescopes, the construction of sensitive and wide-band receiving systems and the development of new methods of observation and data analysis in the radio range. Major progress was also achieved in numerical modelling of the magnetized ISM (e.g. de Avillez & Breitschwerdt 2005; Gissinger et al. 2009; Hill et al. 2012; Gressel et al. 2013; Gent et al. 2013; Machida et al. 2013), using a variety of codes and assumptions. Not surprisingly, the results differ and are not always consistent with observations, which calls for further efforts on both sides.

A widespread argument to neglect galactic magnetic fields in the past was based on assuming field strengths of a few µG taken from Faraday rotation data in our Milky Way, which trace only a small component of the total field. The dynamical importance of galactic fields, with typical strengths of 15 µG, is now widely appreciated in many fields of astrophysics. Magnetic and cosmic-ray pressures control the overall star-formation rate (Birnboim et al. 2015). Magnetic fields are important for the gas dynamics of molecular clouds (Planck Collaboration et al. 2015a). With stronger fields fewer cloud cores are formed but with larger masses (Vázquez-Semadeni et al. 2005; Price & Bate 2008). Magnetic fields control the density and propagation of cosmic rays. Together with cosmic rays they can provide the pressure to drive fast outflows of hot gas, in particular in galaxies with high star-formation rates in the early Universe (Hanasz et al. 2013). Cosmic rays propagating along the field lines in galaxy halos may heat the warm ionized gas and explain the optical line ratios (Wiener et al. 2013). Outflows from starburst galaxies may have magnetized the intergalactic medium (Bertone et al. 2006).

The detection of ultrahigh-energy cosmic rays (UHECRs) reaching the Earth with the AUGER observatory and the possibly anisotropic distribution of their arrival directions (Aab et al. 2015) calls for a proper model of particle propagation. As UHECR particles are deflected by large-scale regular fields and scattered by turbulent fields, the structure and the extent of the fields in the disk and halo of the Milky Way need to be known, but are hard to measure from our inside location. The view onto external spiral galaxies can help.

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