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Two recent papers reconsider the possibility that the excess of microwaveemission from a region within $\sim 20^0$ of the galactic center (the {\it WMAPhaze}), measured by WMAP, can be due to the synchrotron emission originated byneutralino self-annihilation; on the basis of this possible occurrence, alsoupper bounds on the neutralino self-annihilation cross--section are suggested.In the present note, we show that in the common case of thermal WIMPs in astandard cosmological model, when the rescaling of the galactic WIMP density isduly taken into account for subdominant WIMPs, the upper bound applicablegenerically to {\it any} signal due to self-conjugate WIMPs is more stringentthan the ones obtained from analysis of the WMAP haze. We also argue that anexperimental upper bound, which can compete with our generic upper limit, canrather be derived from measurements of cosmic antiproton fluxes, for somevalues of the parameters of the astrophysical propagation model. Finally, wecomment on the possible impact of our generic upper bound on the interpretationof the WMAP haze in terms of thermal neutralinos in a standard cosmologicalscheme.

Upper bounds on signals due to WIMP self--annihilation: comments on the case of the synchrotron radiation from the galactic center and the WMAP haze