  A new hierarchy of lasting gravitational-wave effects (the higher memory
effects) was recently identified in asymptotically flat spacetimes, with the
better-known displacement, spin, and center-of-mass memory effects included as
the lowest two orders in the set of these effects. These gravitational-wave
observables are determined by a set of temporal moments of the news tensor,
which describes gravitational radiation from an isolated source. The moments of
the news can be expressed in terms of changes in charge-like expressions and
integrals over retarded time of flux-like terms, some of which vanish in the
absence of radiation. In this paper, we compute expressions for the flux-like
contributions to the moments of the news in terms of a set of multipoles that
characterize the gravitational-wave strain. We also identify a part of the
strain that gives rise to these moments of the news. In the context of
post-Newtonian theory, we show that the strain related to the moments of the
news is responsible for the many nonlinear, instantaneous terms and "memory"
terms that appear in the post-Newtonian expressions for the radiative multipole
moments of the strain. We also apply our results to compute the leading
post-Newtonian expressions for the moments of the news and the corresponding
strains that are generated during the inspiral of compact binary sources. These
results provide a new viewpoint on the waveforms computed from the multipolar
post-Minkowski formalism, and they could be used to assess the detection
prospects of this new class of higher memory effects.
