  We present a simple, unified model which accounts for properties of the X-ray
emission from the three middle-aged pulsars PSR 1055-52, PSR 0656+14 and PSR
0630+18 (Geminga). The X-ray radiation from these objects is pulsed more
strongly at energies above a transition point around 0.5 keV. In addition, the
phase of the pulses shifts by about 80-100 degrees around the same point.
Geminga also has the peculiarity that its pulsed fraction decreases in the
0.3-0.5 keV energy range, attaining a minimum near 0.5 keV. We show that a
two-component hydrogen atmosphere is able to account for these disparate
features. In our model, the hotter component is powered by particle bombardment
and is restricted to the polar regions, while the cooler one covers the entire
stellar surface. The two components also differ in their emission patterns,
with the hard and soft contributions coming from areas radiating into fan and
pencil beams, respectively.
