  Phase self-calibration (or selfcal) is an algorithm often used in the
calibration of interferometric observations in astronomy. Although a powerful
tool, this algorithm presents strong limitations when applied to data with a
low signal-to-noise ratio. We analyze the artifacts that the phase selfcal
algorithm produces when applied to extremely noisy data. We show how the phase
selfcal may generate a spurious source in the sky from a distribution of
completely random visibilities. This spurious source is indistinguishable from
a real one. We numerically and analytically compute the relationship between
the maximum spurious flux density generated by selfcal from noise and the
particulars of the interferometric observations. Finally, we present two simple
tests that can be applied to interferometric data for checking whether a source
detection is real or whether the source is an artifact of the phase
self-calibration algorithm.
