Statistical properties of Faraday rotation measure in external galaxies -- I: intervening disc galaxies

Deriving the Faraday rotation measure (RM) of quasar absorption line systems, which are tracers of high-redshift galaxies intervening background quasars, is a powerful tool for probing magnetic fields in distant galaxies. Statistically comparing the RM distributions of two quasar samples, with and without absorption line systems, allows one to infer magnetic field properties of the intervening galaxy population. Here, we have derived the analytical form of the probability distribution function (PDF) of RM produced by a single galaxy with an axisymmetric large-scale magnetic field. We then further determine the PDF of RM for one random sight line traversing each galaxy in a population with a large-scale magnetic field prescription. We find that the resulting PDF of RM is dominated by a Lorentzian with a width that is directly related to the mean axisymmetric large-scale field strength $\langle B_0 \rangle$ of the galaxy population if the dispersion of $B_0$ within the population is smaller than $\langle B_0 \rangle$. Provided that RMs produced by the intervening galaxies have been successfully isolated from other RM contributions along the line of sight, our simple model suggests that $\langle B_0 \rangle$ in galaxies probed by quasar absorption line systems can be measured within $\approx50$ per cent accuracy without additional constraints on the magneto-ionic medium properties of the galaxies. Finally, we discuss quasar sample selection criteria that are crucial to reliably interpret observations, and argue that within the limitations of the current database of absorption line systems, high-metallicity damped Lyman-$α$ absorbers are best suited to study galactic dynamo action in distant disc galaxies.