Introduction

One of the most important advances in neutron star (NS) astrophysics in the last decade has been the detection and detailed studies of surface (or near-surface) X-ray emission from a variety of isolated NSs. This has been made possible by X-ray telescopes such as Chandra and XMM-Newton. Such studies can potentially provide invaluable information on the physical properties and evolution of NSs (e.g. equation of state at super-nuclear densities, cooling history, surface magnetic fields and compositions, different NS populations). The inventory of isolated NSs with detected surface emission includes: (i) radio pulsars: e.g. the phase-resolved spectroscopic observations of the ‘three musketeers’ revealed the geometry of the NS polar caps; (ii) magnetars (AXPs and SGRs): e.g. the quiescent emission of magnetars consists of a black body at T ∼ 0.5 keV with a power-law component (index 2.7–3.5), plus significant emission up to ∼ 100 keV; (iii) central compact objects (CCOs) in SNRs: these now include six to eight sources, several have P, measurements and two have absorption lines; (iv) thermally-emitting isolated NSs: these are a group of seven nearby (≲1 kpc) NSs with low (∼1032 erg s−1) X-ray luminosities and long (3–10 s) spin periods, and recent observations have revealed absorption features in many of the sources.