  Thermal X-ray radiation from neutron star soft X-ray transients in quiescence
provides the strongest constraints on the cooling rates of neutron stars, and
thus on the interior composition and properties of matter in the cores of
neutron stars. We analyze new (2006) and archival (2001) XMM-Newton
observations of the accreting millisecond pulsar SAX J1808.4-3658 in
quiescence, which provide the most stringent constraints to date. The X-ray
spectrum of SAX J1808.4-3658 in the 2006 observation is consistent with a
power-law of photon index 1.83\pm0.17, without requiring the presence of a
blackbody-like component from a neutron star atmosphere. Our 2006 observation
shows a slightly lower 0.5-10 keV X-ray luminosity, at a level of
68^{+15}_{-13}% that inferred from the 2001 observation. Simultaneous fitting
of all available XMM data allows a constraint on the quiescent neutron star
(0.01-10 keV) luminosity of L_{NS}<1.1*10^{31} erg/s. This limit excludes some
current models of neutrino emission mediated by pion condensates, and provides
further evidence for additional cooling processes, such as neutrino emission
via direct Urca processes involving nucleons and/or hyperons, in the cores of
massive neutron stars.
