The observed correlations , between the characteristic ages and dipole surface magnetic field strengths of all pulsars , can be well explained by magnetic field decay with core temperatures of ~ { } 2 \times 10 ^ { 8 } K , \sim 2 \times 10 ^ { 7 } K , and \sim 10 ^ { 5 } K , for magnetars , normal radio pulsars , and millisecond pulsars , respectively ; assuming that their characteristic ages are about two orders of magnitude larger than their true ages , the required core temperatures may be reduced by about a factor of 10 .
The magnetic decay follows a power-law and is dominated by the solenoidal component of the ambipolar diffusion mode .
In this model , all NSs are assumed to have the same initial magnetic field strength , but different core temperature which do not change as the magnetic field decays .
This suggests that the key distinguishing property between magnetars and normal pulsars is that magnetars were born much hotter than normal pulsars , and thus have much longer magnetic field decay time scales , resulting in higher surface magnetic field strength even with the same ages of normal pulsars .
The above conclusion agrees well with the observed correlations between the surface temperatures of magnetars and other young NSs , which do not agree with the cooling dominated evolution of neutron stars .
This suggests a possible scenario that heating , perhaps due to magnetic field decay , balances neutron star cooling for observed pulsars .