We investigate an interesting new class of high-mass X-ray binaries ( HMXBs ) with long orbital periods ( P _ { orb } > 30 { d } ) and low eccentricities ( e \lesssim 0.2 ) .
The orbital parameters suggest that the neutron stars in these systems did not receive a large impulse , or “ kick , ” at the time of formation .
After considering the statistical significance of these new binaries , we develop a self-consistent phenomenological picture wherein the neutron stars born in the observed wide HMXBs receive only a small kick ( \lesssim 50 { km s ^ { -1 } } ) , while neutron stars born in isolation , in the majority of low-mass X-ray binaries , or in many of the well-known HMXBs with P _ { orb } \lesssim 30 { d } receive the conventional large kicks , with a mean speed of \sim 300 { km s ^ { -1 } } .
Assuming that this basic scenario is correct , we discuss a physical process that lends support to our hypothesis , whereby the magnitude of the natal kick to a neutron star born in a binary system depends on the rotation rate of its immediate progenitor following mass transfer — the core of the initially more massive star in the binary .
Specifically , the model predicts that rapidly rotating pre-collapse cores produce NSs with relatively small kicks , and vice versa for slowly rotating cores .
If the envelope of the NS progenitor is removed before it has become deeply convective , then the exposed core is likely to be a rapid rotator .
However , if the progenitor becomes highly evolved prior to mass transfer , then a strong magnetic torque , generated by differential rotation between the core and the convective envelope , may cause the core to spin down to the very slow rotation rate of the envelope .
Our model , if basically correct , has important implications for the dynamics of stellar core collapse , the retention of neutron stars in globular clusters , and the formation of double neutron star systems in the Galaxy .