Refraction and diffraction of incoming radio waves by the ionosphere induce time variability in the angular positions, peak amplitudes and shapes of radio sources, potentially complicating the automated cross-matching and identification of transient and variable radio sources. In this work, we empirically assess the effects of the ionosphere on data taken by the Murchison Widefield Array (MWA) radio telescope. We directly examine 51 hours of data observed over 10 nights under quiet geomagnetic conditions (global storm index Kp < 2), analysing the behaviour of short-timescale angular position and peak flux density variations of around ten thousand unresolved sources. We find that while much of the variation in angular position can be attributed to ionospheric refraction, the characteristic displacements (10-20 arcsec) at 154 MHz are small enough that search radii of 1-2 arcmin should be sufficient for cross-matching under typical conditions. By examining bulk trends in amplitude variability, we place upper limits on the modulation index associated with ionospheric scintillation of 1-3% for the various nights. For sources fainter than ~1 Jy, this variation is below the image noise at typical MWA sensitivities. Our results demonstrate that the ionosphere is not a significant impediment to the goals of time-domain science with the MWA at 154 MHz.
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