Soft X-ray Transients (SXRTs) have long been suspected to contain old,
weakly magnetic neutron stars that have been spun up by accretion tor
ques, After reviewing their observational properties, we analyse the d
ifferent regimes that likely characterise the neutron stars in these s
ystems across the very large range of mass inflow rates, from the peak
of the outbursts to the quiescent emission, While it is clear that cl
ose to the outburst maxima accretion onto the neutron star surface tak
es place, as the mass inflow rate decreases, accretion might stop at t
he magnetospheric boundary because of the centrifugal barrier provided
by the neutron star. For low enough mass inflow rates (and sufficient
ly short rotation periods), the radio pulsar mechanism might turn on a
nd sweep the inflowing matter away. The origin of the quiescent emissi
on, observed in a number of SXRTs at a level of similar to 10(32) - 10
(33) erg s(-1) plays a crucial role in constraining the neutron star m
agnetic field and spin period. Accretion onto the neutron star surface
is an unlikely mechanism for the quiescent emission of SXRTs, as it r
equires very low magnetic fields and/or long spin periods. Thermal rad
iation from a cooling neutron star surface in between the outbursts ca
n be ruled out as the only cause of the quiescent emission. We find th
at accretion onto the neutron star magnetosphere and shock emission po
wered by an enshrouded radio pulsar provide far more plausible models,
In the latter case the range of allowed neutron star spin periods and
magnetic fields is consistent with the values recently inferred from
the properties of kHz quasi-periodic oscillation in low mass X-ray bin
aries. If quiescent SXRTs contain enshrouded radio pulsars, they provi
de a missing link between X-ray binaries and millisecond pulsars.