  The unidentified X-ray source RX J0720.4-3125 is a candidate isolated neutron
star showing evidence for pulsed emission with an 8.39 s period and a spectrum
consistent with a blackbody at kT=80 eV (Haberl et al. 1996, 1997). We show
that this source is most likely an old isolated neutron star accreting from
surrounding media. We then argue that unless it was born with a long spin
period (P_i >~ 0.5 seconds) and weak field (B_i <~ 10^10 G), the magnetic field
on this star must have decayed. With B_i ~ 10^12 G, we find decay timescales >~
10^7 yrs for power law decay or >~ 10^8 yrs for exponential decay. A measured
period derivative Pdot <~ 10^{-16} s s^{-1} would be consistent with an old
accreting isolated neutron star. Both power law and exponential decay models
can give a Pdot ~ 10^{-16} s s^{-1}, though a Pdot substantially less than this
would be indicative of exponential field decay.
