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We present in this article an overview of the problem of neutron star masses. After a brief appraisal of the methods employed to determine the masses of neutron stars in binary systems, the existing sample of measured masses is presented, with a highlight on some very well-determined cases. We discuss the analysis made to uncover the underlying distribution and a few robust results that stand out from them. The issues related to some particular groups of neutron stars originated from different channels of stellar evolution are shown. Our conclusions are that last centurys paradigm that there a single, $1.4 M_{odot}$ scale is too simple. A bimodal or even more complex distribution is actually present. It is confirmed that some neutron stars have masses of $sim 2 M_{odot}$, and, while there is still no firm conclusion on the maximum and minimum values produced in nature, the field has entered a mature stage in which all these and related questions can soon be given an answer.
Precision mass spectrometry of neutron-rich nuclei is of great relevance for astrophysics. Masses of exotic nuclides impose constraints on models for the nuclear interaction and thus affect the description of the equation of state of nuclear matter,
We investigate remnant neutron star masses (in particular, the minimum allowed mass) by performing advanced stellar evolution calculations and neutrino-radiation hydrodynamics simulations for core-collapse supernova explosions. We find that, based on
X-ray observations of transiently accreting neutron stars during quiescence provide information about the structure of neutron star crusts and the properties of dense matter. Interpretation of the observational data requires an understanding of the n
Half of all the elements in the universe heavier than iron were created by rapid neutron capture. The theory for this astrophysical `$r$-process was worked out six decades ago and requires an enormous neutron flux to make the bulk of these elements.
Observations of thermal radiation from neutron stars can potentially provide information about the states of supranuclear matter in the interiors of these stars with the aid of the theory of neutron-star thermal evolution. We review the basics of thi