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ABSTRACT 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. 

Up to now, more than 62 of the 115 X-ray sources of low-mass-X-ray binaries have been identified as photospheric radius expansion (PRE) bursters [1]. Galloway and collaborators expect more PRE bursters in their near future analysis [2]. Although more than half of the discovered X-ray sources are PRE bursters, the bursting mechanism of PRE burster is still not adequately understood. This is because of the complicated hydrodynamics and variable accretion rates. An example is the accretion-powered millisecond pulsar SAX J1808.4–3658 [3, 4] that powered up the brightest Type-I X-ray burst (XRB) recorded by NICER in recent history [5]. The first 1D multi-zone model of SAX J1808.4–3658 was recently constructed [6, 7]. The pioneering model offers a first concurrent and direct comparison with the observed light curves, fluences, and recurrence times. With the three observables, a comparison between theory and observations could be more sensitive than the previous studies of the clocked burster and post-processing models. We perform a sensitivity study on ( α ,p), ( α , γ ), (p, α ), and (p, γ ) reactions with a total up to ~1,500 reactions. Our current result indicates that the observables are more sensitive to the competition between the reactions involving alpha-capture, e.g., the 22 Mg( α , p) and 22 Mg(p, γ ) reactions competing at the 22 Mg branch point [8].