Slow pulsar scintillation and the spectrum of interstellar electron density fluctuations1

Intensity fluctuations in pulsars are commonly ascribed to scintillations produced by electron density inhomogeneities in the interstellar medium. The power spectrum of the inhomogeneities is believed to be a power law, q−β with β = 11/3 (Kolmogorov spectrum). The spectrum of intensity fluctuations produced by a thin phase-changing screen has already been worked out for the case 2<β<4 and shows that two length-scales exist – a fast variation due to diffractive scintillation and a slow variation due to refractive effects. In this paper the theory is worked out for 4<β<6 and asymptotic expressions are developed for the intensity fluctuation spectrum in various regimes. Two major differences emerge. First, the magnitude of the refractive intensity fluctuations is much larger for β>4 than for β<4. Secondly, for β>4, the intensity fluctuations are essentially independent of the strength of the phase fluctuations on the screen and thus independent of the wavelength of observation λ or the distance D of the pulsar. In contrast, for β<4, there is a dependence on both λ and D. The available observations on slow refractive intensity fluctuations seem to support a spectrum for the interstellar medium with β>4. Several arguments have been presented in the past, based on the observed wavelength dependence of decorrelation bandwidth, image size, scintillation time-scale, etc. to support the Kolmogorov value β = 11/3. We show that these observations are equally consistent with β>4. If β>4, the observations require the power-law spectrum to extend over only a small range of scales ∼1012–1015 cm compared to ∼109–1015 cm required in the case of a Kolmogorov spectrum.