Power spectrum of small-scale density irregularities in the interstellar medium

Interstellar scintillation (ISS) observations of 17 pulsars are used to place new limits on the spectrum of small-scale electron density irregularities in the interstellar medium. The time-dependent radio frequency spectrum of ISS is the observed quantity; from this we determine the ISS scintillation index (rms intensity/mean intensity) and a precisely defined ISS frequency-correlation scale based on the autocorrelation function in radio-frequency of the ISS fluctuations. Measurements were made at 340, 408 and 450 MHz and in the dispersion measure range 3–57 cm⁻³ pc. Limits to the scintillation parameters were obtained for pulsars with $$89\leqslant DM\leqslant 158\enspace \text {cm}^{-3}\enspace \text {pc}$$. The observations are compared with model interstellar medium spectra of the power-law form (spectrum proportional to wavenumber^−α, $$2\leqslant \alpha\leqslant 4$$) and the Gaussian (or square-law structure function) form. The dispersion-measure dependence of the ISS frequency-correlation scale, B, is consistent with either the Gaussian model or power-law models having $$3.0\lesssim\alpha\leqslant4$$. Although data were taken over only a limited range of centre frequencies, the radio-frequency scaling of B is consistent with power-law models having $$2.8\lesssim\alpha\lesssim3.9$$. However, by comparing the shape of the radio-frequency autocorrelation function with model (thin screen) calculations, we only find good agreement with power-law models having large ($$\alpha \gtrsim 3.6$$) spectral indices. Our data are consistent with the level of the local three-dimensional density spectrum at q = 10⁻⁹ m⁻¹ of 3 × 10²⁸ to 3 × 10²⁹ m⁻³.