A cosmic-ray positron anisotropy due to two middle-aged, nearby pulsars?

Geminga and B0656 + 14 are the closest pulsars with characteristic ages in the range of 100 kyr to 1 Myr. They both have spin-down powers of the order 3 x 1034 ergs s(-1) at present. The winds of these pulsars had most probably powered pulsar wind nebulae (PWNe) that broke up less than about 100 kyr after the birth of the pulsars. Assuming that leptonic particles accelerated by the pulsars were confined in the PWNe and were released into the interstellar medium ( ISM) on breakup of the PWNe, we show that, depending on the pulsar parameters, both pulsars make a nonnegligible contribution to the local cosmic ray (CR) positron spectrum, and they may be the main contributors above several GeV. The relatively small angular distance between Geminga and B0656 + 14 thus implies an anisotropy in the local CR positron flux at these energies. We calculate the contribution of these pulsars to the locally observed CR electron and positron spectra depending on the pulsar birth period and the magnitude of the local CR diffusion coefficient. We further give an estimate of the expected anisotropy in the local CR positron flux. Our calculations show that within the framework of our model, the local CR positron spectrum imposes constraints on pulsar parameters for Geminga and B0656 + 14, notably the pulsar period at birth, and also the local interstellar diffusion coefficient for CR leptons.