  We compute the classes of universal theta divisors of degrees zero and g-1
over the Deligne-Mumford compactification of the moduli space of curves, with
various integer weights on the points, in particular reproving a recent result
of M\"uller.
  We also obtain a formula for the class in the Chow ring of the moduli space
of curves of compact type of the double ramification locus, given by the
condition that a fixed linear combination of the marked points is a principal
divisor, reproving a recent result of Hain.
  Our approach for computing the theta divisor is more direct, via test curves
and the geometry of the theta divisor, and works easily over the entire
Deligne-Mumford compactification. We use our extended result in another paper
to study the partial compactification of the double ramification cycle.
