Abstract
The small periods and period derivatives of millisecond pulsars permit interesting upper bounds to be placed on the strength of multipole components in their magnetic fields if the loss of rotational energy may be approximated by vacuum electromagnetic radiation formulas. The surface field strength of millisecond pulsars may be as high as about 10 to the 12th G if the dominant multipole component is l not less than 3. Significant multipole moments may help explain the unusual pulse morphology of millisecond pulsars. If the magnetic fields in gamma-ray burst sources (old neutron stars?) have the same evolutionary history as in millisecond pulsars, the about 10 to the 12th G local fields observed in several gamma-ray bursts must be due to multipole moments with l not less than 3.
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