The structure function of Galactic \HI opacity fluctuations on AU scales based on MERLIN, VLA and VLBA data

TL;DR

This study measures the structure function of Galactic ext{HI} opacity fluctuations on AU scales using multiple radio telescopes, revealing a power-law behavior consistent across six orders of magnitude and suggesting a very small dissipation scale related to turbulence.

Contribution

The paper introduces a bias-free estimator for the ext{HI} opacity structure function and extends measurements to AU scales, confirming a power-law behavior over a broad range of scales.

Findings

The structure function slope is approximately 0.81, similar to parsec-scale observations.

The amplitude of the structure function is consistent with larger-scale measurements.

The dissipation scale of turbulence is smaller than a few AU, indicating specific physical conditions.

Abstract

We use MERLIN, VLA and VLBA observations of Galactic \HI absorption towards 3C~138 to estimate the structure function of the \HI opacity fluctuations at AU scales. Using Monte Carlo simulations, we show that there is likely to be a significant bias in the estimated structure function at signal-to-noise ratios characteristic of our observations, if the structure function is constructed in the manner most commonly used in the literature. We develop a new estimator that is free from this bias and use it to estimate the true underlying structure function slope on length scales ranging $5$ to $40$~AU. From a power law fit to the structure function, we derive a slope of $0.81^{+0.14}_{-0.13}$, i.e. similar to the value observed at parsec scales. The estimated upper limit for the amplitude of the structure function is also consistent with the measurements carried out at parsec scales. Our measurements are hence consistent with the \HI opacity fluctuation in the Galaxy being characterized by a power law structure function over length scales that span six orders of magnitude. This result implies that the dissipation scale has to be smaller than a few AU if the fluctuations are produced by turbulence. This inferred smaller dissipation scale implies that the dissipation occurs either in (i) regions with densities $\gtrsim 10^3 $cm$^-3$ (i.e. similar to that inferred for "tiny scale" atomic clouds or (ii) regions with a mix of ionized and atomic gas (i.e. the observed structure in the atomic gas has a magneto-hydrodynamic origin).