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We present a phase-coherent timing solution for RX J0420.0-5022, the coolest(kT=45 eV) and fastest-spinning (P=3.45 s) of the seven so-called isolatedneutron stars (INSs). Using 14 observations with the XMM-Newton spacecraft in2010-2011, we were able to measure a spin-down rate nudot=(-2.3+/-0.2)e-15 Hz/s(Pdot=(2.8+/-0.3)e-14 s/s), from which we infer a dipolar magnetic field of1.0e13 G. With reasonable confidence we were able to extend the timing solutionback to archival XMM-Newton from 2002 and 2003, giving the same solution butwith considerably more precision. This gives RX J0420 the lowest dipolemagnetic field of the INSs. Our spectroscopy does not confirm the broadabsorption feature at 0.3 keV hinted at in earlier observations, althoughdifficulties in background subtraction near that energy make conclusionsdifficult. With this, all 6 of the INSs that have confirmed periodicities nowhave constrained spin-downs from coherent solutions. The evidence that the INSsare qualitatively different from rotation-powered pulsars now appears robust,with the likely conclusion that their characteristic ages are systematicallyolder than their true ages, because their fields have decayed. The field decayprobably also causes them to be systematically hotter than pulsars of the same(true) age.

A Coherent Timing Solution for the Nearby, Thermally Emitting Isolated Neutron Star RX J0420.0-5022