Evolution of magnetic field in X-ray emitting radio-quiet M7 neutron stars and the RX J0420.0−5022 & RX J1605.3+3249 anomalies

The intense magnetic fields present in neutron stars are closely linked to their observed temperature and spectral characteristics, timing properties, including spin period and its derivatives. Therefore, a comprehensive theoretical analysis of magnetic field evolution is essential for understanding how the strength of the magnetic field changes over time. The decay rate of magnetic field in isolated, non-accreting neutron stars can be assessed by evaluating the second derivative of the spin frequency. Another method to estimate this rate involves monitoring an increase in thermal emission beyond what is expected from standard cooling processes, assuming no additional heating mechanisms are present. Our findings indicate that for X-ray emitting isolated neutron stars, the evolution rate of spin period derivative aligns with the dissipation rate of magnetic energy from the dipolar field, provided that a substantial portion of the released energy is emitted as X-rays. Except for the RX J0420.0[Formula: see text]5022 and RX J1605.3+3249, for the rest of the M7 stars, the time scale of magnetic field decay is found to be much shorter than typical age of radio pulsars. For these five stars, as the rotational energy loss is about two orders of magnitude less than the X-ray luminosity, it can be attributed to the decay of magnetic field, implying likely evolutionary relationships with magnetars. Consequently, the magnetic field decay times for these five M7 stars are a few orders of magnitudes smaller than the characteristic or spin-down ages of the order of Myr.