ON THE SPIN-DOWN AND MAGNETIC FIELD OF THE X-RAY PULSAR 1E 1207.4-5209

We analyze all of the archival X-ray timing data from the years 2000-2008 on the weakly magnetized central compact object (CCO) pulsar 1E 1207.4-5209 in an attempt to measure its dipole magnetic field strength via spin-down. Because most of these observations were not planned for the purpose of phase-coherent timing, the resulting ephemeris is not unique, but is restricted to two comparably good timing solutions that correspond to B-s = 9.9 x 10(10) G or 2.4 x 10(11) G, respectively, assuming dipole spin-down. One of these should be the correct value and the other one an alias. There are no spinning-up solutions. The smaller value of Bs is close to the surface field of 8 x 10(10) G that is measured independently from the unique absorption lines in the X-ray spectrum of 1E 1207.4-5209, assuming that the lowest-energy line at 0.7 keV is the electron-cyclotron fundamental. We suggest that 1E 1207.4-5209 has the strongest magnetic field among CCOs, which would account for the unique presence of its cyclotron absorption spectrum, while other CCOs likely have even weaker fields for which the cyclotron fundamental falls below the observable soft X-ray band.