We show that the soft X-ray spectra and light curves observed with the
ROSAT and EUVE from the closest known millisecond pulsar J0437-4715 c
an be interpreted as thermal radiation from two hot polar caps whose e
mitting layers (atmospheres) are comprised of hydrogen. The simplest m
odel yields a uniform temperature of (0.8 - 0.9) x 10(6) K within a ca
p radius of 0.7 - 0.9 km. The spectral fits indicate that the temperat
ure may be nonuniformly distributed along the cap surface. The distrib
ution can be approximated by a central core heated up to (1 - 2) x 10(
6) K within a radius of 0.2 - 0.4 km, surrounded by a colder rim with
temperatures (3 - 5) x 10(5) K extending out to 2 - 6 km. The polar ca
p interpretation implies low column densities, (1 - 3) x 10(19) cm(-2)
, and a high degree of ionization, > 20%, of the interstellar hydrogen
towards the pulsar. The inferred bolometric luminosity of the polar c
aps, (1.0 - 1.6) x 10(30) erg s(-1), is in excellent agreement with th
e predictions of the slot-gap model of radio pulsars developed by Aron
s and his coworkers. Similar polar cap radiation should be emitted by
other millisecond pulsars, although in some of them (e. g., PSR B1821-
24) the soft X-ray flux is dominated by the nonthermal radiation from
pulsar magnetospheres.