Noise in the Cross-Power Spectrum of the Vela Pulsar

We compare the noise in interferometric measurements of the Vela pulsar from ground- and space-based antennas with theoretical predictions. The noise depends on both the flux density and the interferometric phase of the source. Because the Vela pulsar is bright and scintillating, these comparisons extend into both the low and high signal-to-noise regimes. Furthermore, our diversity of baselines explores the full range of variation in interferometric phase. We find excellent agreement between theoretical expectations and our estimates of noise among samples within the characteristic scintillation scales. Namely, the noise is drawn from an elliptical Gaussian distribution in the complex plane, centered on the signal. The major axis, aligned with the signal phase, varies quadratically with the signal, while the minor axis, at quadrature, varies with the same linear coefficients. For weak signal, the noise approaches a circular Gaussian distribution. Both the variance and covariance of the noise are also affected by artifacts of digitization and correlation. In particular, we show that gating introduces correlations between nearby spectral channels.