We present the results of a spectroscopic monitoring campaign of the OB-star companions to the eclipsing X-ray pulsars SMC~X $ - $ 1 , LMC~X $ - $ 4 and Cen~X $ - $ 3 .
High-resolution optical spectra obtained with UVES on the ESO Very Large Telescope are used to determine the radial-velocity orbit of the OB ( super ) giants with high precision .
The excellent quality of the spectra provides the opportunity to measure the radial-velocity curve based on individual lines , and to study the effect of possible distortions of the line profiles due to e.g .
X-ray heating on the derived radial-velocity amplitude .
Several spectral lines show intrinsic variations with orbital phase .
The magnitude of these variations depends on line strength , and thus provides a criterion to select lines that do not suffer from distortions .
The undistorted lines show a larger radial-velocity amplitude than the distorted lines , consistent with model predictions .
Application of our line-selection criteria results in a mean radial-velocity amplitude K _ { opt } of 20.2 \pm 1.1 , 35.1 \pm 1.5 , and 27.5 \pm 2.3 km s ^ { -1 } ( 1 \sigma errors ) , for the OB companion to SMC~X $ - $ 1 , LMC~X $ - $ 4 and Cen~X $ - $ 3 , respectively .
Adding information on the projected rotational velocity of the OB companion ( derived from our spectra ) , the duration of X-ray eclipse and orbital parameters of the X-ray pulsar ( obtained from literature ) , we arrive at a neutron star mass of 1.06 ^ { +0.11 } _ { -0.10 } , 1.25 ^ { +0.11 } _ { -0.10 } and 1.34 ^ { +0.16 } _ { -0.14 } M _ { \sun } for SMC~X $ - $ 1 , LMC~X $ - $ 4 and Cen~X $ - $ 3 , respectively .
The mass of SMC~X $ - $ 1 is near the minimum mass ( \sim 1 M _ { \sun } ) expected for a neutron star produced in a supernova .
We discuss the implications of the measured mass distribution on the neutron-star formation mechanism , in relation to the evolutionary history of the massive binaries .