  We use the theory of logarithmic line bundles to construct compactifications
of spaces of roots of a line bundle on a family of curves, generalising work of
a number of authors. This runs via a study of the torsion in the tropical and
logarithmic jacobians (recently constructed by Molcho and Wise). Our moduli
space carries a `double ramification cycle' measuring the locus where the given
root is isomorphic to the trivial bundle, and we give a tautological formula
for this class in the language of piecewise polynomial functions (as recently
developed by Molcho-Pandharipande-Schmitt and Holmes-Schwarz).
