  Understanding the natal kicks received by neutron stars (NSs) during
formation is a critical component of modelling the evolution of massive
binaries. Natal kicks are an integral input parameter for population synthesis
codes, and have implications for the formation of double NS systems and their
subsequent merger rates. However, many of the standard observational kick
distributions that are used are obtained from samples created only from
isolated NSs. Kick distributions derived in this way overestimate the intrinsic
NS kick distribution. For NSs in binaries, we can only directly estimate the
effect of the natal kick on the binary system, instead of the natal kick
received by the NS itself. Here, for the first time, we present a binary kick
distribution for NSs with low-mass companions. We compile a catalogue of 145
NSs in low-mass binaries with the best available constraints on proper motion,
distance, and systemic radial velocity. For each binary, we use a
three-dimensional approach to estimate its binary kick. We discuss the
implications of these kicks on system formation, and provide a parametric model
for the overall binary kick distribution, for use in future theoretical
modelling work. We compare our results with other work on isolated NSs and NSs
in binaries, finding that the NS kick distributions fit using only isolated
pulsars underestimate the fraction of NSs that receive low kicks. We discuss
the implications of our results on modelling double NS systems, and provide
suggestions on how to use our results in future theoretical works.
