A new method to probe the thermal electron content of the Galaxy through spectral analysis of background sources

We present a new method for probing the thermal electron content of the Galaxy by spectral analysis of background point sources in the absorption-only limit to the radiative transfer equation. In this limit, calculating the spectral index, $\alpha$, of these sources using a natural logarithm results in an additive factor, which we denote $\alpha_\mathrm{EM}$, resulting from the absorption of radiation due to the Galactic thermal electron population. We find that this effect is important at very low frequencies ($\nu\lesssim200$ MHz), and that the frequency spacing is critical. We model this effect by calculating the emission measure across the sky. A (smooth) thermal electron model for the Galaxy does not fit the observed emission measure distribution, but a simple, cloud-based model to represent the clumpy nature of the warm interstellar medium does. This model statistically reproduces the Galactic emission measure distribution as obtained independently from $H_\alpha$ data well. We find that at the lowest frequencies ($\sim10-50$ MHz), the observed spectral index for a large segment of the Galaxy below Galactic latitudes of $\lesssim15^\circ$ could be changed significantly (i.e., $\alpha_\mathrm{EM}\gtrsim0.1$). This method therefore provides a correction to low-frequency spectral index measurements of extragalactic sources, and provides a sensitive probe of the thermal electron distribution of the Galaxy using current and next-generation low-frequency radio telescopes. We show that this effect should be robustly detectable individually in the strongest sources, and statistically in source samples at a level of $\alpha_\mathrm{EM}\gtrsim0.18,0.06$, and 0.02 for source densities of 10, 100 and 1,000 sources per square degree.