  The spectra of many X-ray pulsars show, in addition to a power law, a
low-energy component that has often been modeled as a blackbody with kT ~ 0.1
keV. However the physical origin of this soft excess has remained a mystery. We
examine a sample of well-studied, bright X-ray pulsars, which have been
observed using ROSAT, ASCA, Ginga, RXTE, BeppoSAX, Chandra, and XMM-Newton. In
particular we consider the Magellanic Cloud pulsars SMC X-1, LMC X-4, XTE
J0111.2-7317, and RX J0059.2-7138 and the Galactic sources Her X-1, 4U 1626-67,
Cen X-3, and Vela X-1. We show that the soft excess is a very common if not
ubiquitous feature intrinsic to X-ray pulsars. We evaluate several possible
mechanisms for the soft emission, using theoretical arguments as well as
observational clues such as spectral shapes, eclipses, pulsations of the soft
component, and superorbital modulation of the source flux. We find that
reprocessing of hard X-rays from the neutron star by the inner region of the
accretion disk is the only process that can explain the soft excess in all the
pulsars with Lx > 10^38 ergs/s. Other mechanisms, such as emission from diffuse
gas in the system, are important in less luminous objects.
