Synchrotron radiation from the Galactic center in the decaying dark matter scenario

We discuss the synchrotron radiation flux from the Galactic center in the unstable dark matter scenario. Motivated by the anomalous excess of the positron fraction recently reported by the PAMELA Collaboration, we consider the case that the dark matter particle is unstable (and long-lived) and that energetic electrons and positrons are produced by the decay of dark matter. Then the emitted e(+/-) becomes the source of the synchrotron radiation. We calculate the synchrotron radiation flux for models of decaying dark matter, which can explain the PAMELA positron excess. Taking the lifetime of the dark matter of O(10(26) sec), which is the suggested value to explain the PAMELA anomaly, the synchrotron radiation flux is found to be O(1 kJy/str) or smaller, depending on the particle-physics and cosmological parameters.