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The observed correlations, between the characteristic ages and dipole surfacemagnetic field strengths of all pulsars, can be well explained by magneticfield decay with core temperatures of $~2\times10^{8}$ K, $\sim2\times10^{7}$K, and $\sim10^{5}$ K, for magnetars, normal radio pulsars, and millisecondpulsars, respectively; assuming that their characteristic ages are about twoorders of magnitude larger than their true ages, the required core temperaturesmay be reduced by about a factor of 10. The magnetic decay follows a power-lawand is dominated by the solenoidal component of the ambipolar diffusion mode.In this model, all NSs are assumed to have the same initial magnetic fieldstrength, but different core temperature which do not change as the magneticfield decays. This suggests that the key distinguishing property betweenmagnetars and normal pulsars is that magnetars were born much hotter thannormal pulsars, and thus have much longer magnetic field decay time scales,resulting in higher surface magnetic field strength even with the same ages ofnormal pulsars. The above conclusion agrees well with the observed correlationsbetween the surface temperatures of magnetars and other young NSs, which do notagree with the cooling dominated evolution of neutron stars. This suggests apossible scenario that heating, perhaps due to magnetic field decay, balancesneutron star cooling for observed pulsars.

Power-law Magnetic Field Decay and Constant Core Temperatures of Magnetars, Normal and Millisecond Pulsars