  The group of thermally emitting isolated neutron stars (INSs) known as the
"Magnificent Seven" (M7) is unique among the various neutron star populations.
Crustal heating by means of magnetic field decay and an evolutionary link with
magnetars may explain why these objects rotate more slowly and have higher
thermal luminosities and magnetic field intensities than standard pulsars of
similar age. The third brightest INS, RX J1605.3+3249, is the only object
amidst the seven still lacking a detected periodicity. We observed the source
with the XMM-Newton Observatory for 60 ks aiming at unveiling the neutron star
rotation rate and investigating its spectrum in detail. A periodic signal at
P=3.387864(16) s, most likely the neutron star spin period, is detected at the
4-sigma confidence level. The coherent combination of the new data with a past
XMM-Newton EPIC-pn observation of the source constrains the pulsar spin-down
rate at the 2-sigma confidence level, implying a dipolar magnetic field of
B~7.4e13 G. If confirmed, RX J1605.3+3249 would be the neutron star with the
highest dipolar field amongst the M7. The spectrum of the source shows evidence
of a cool blackbody component, as well as for the presence of two broad
absorption features. Furthermore, high-resolution spectroscopy with the RGS
cameras confirms the presence of a narrow absorption feature at energy 0.57 keV
in the co-added spectrum of the source, also seen in other thermally emitting
isolated neutron stars. Phase-resolved spectroscopy, as well as a dedicated
observing campaign aimed at determining a timing solution, will give invaluable
constraints on the neutron star geometry and will allow one to confirm the high
value of spin down, which would place the source closer to a magnetar than any
other M7 INS.
