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Asymmetric mass ejection in the early phase of supernova (SN) explosions canimpart a kick velocity to the new-born neutron star (NS). For neutrino-drivenexplosions the NS acceleration was shown to be mainly caused by thegravitational attraction of the anisotropically expelled inner ejecta, whilehydrodynamic forces contribute on a subdominant level, and asymmetric neutrinoemission plays only a secondary role. Two- and three-dimensional hydrodynamicsimulations demonstrated that this gravitational tug-boat mechanism can explainthe observed space velocities of young NSs up to more than 1000 km/s. Here, wediscuss how the NS kick depends on the energy, ejecta mass, and asymmetry ofthe SN explosion, and which role the compactness of the pre-collapse stellarcore plays for the momentum transfer to the NS. We also provide simple analyticexpressions for the NS velocity in terms of these quantities. Referring toresults of hydrodynamic simulations in the literature, we argue why within thediscussed scenario of NS acceleration, electron-capture SNe, low-mass Fe-coreSNe and ultra-stripped SNe can be expected to have considerably lower intrinsicNS kicks than core-collapse SNe of massive stellar cores. Our basic argumentsremain valid also if progenitor stars possess large-scale asymmetries in theirconvective silicon and oxygen burning layers. Possible scenarios for spin-kickalignment are sketched. Much of our discussion remains on a conceptual andqualitative level and more work is needed on the numerical modeling side todetermine the dependences of involved parameters, whose prescriptions will beneeded for recipes that can be used to better describe NS kicks in binaryevolution and population synthesis studies.

Neutron star kicks by the gravitational tug-boat mechanism in asymmetric supernova explosions: progenitor and explosion dependence