2025ApJ...989L..34M

We report a direct measurement of the electron density turbulence parameter C₁, enabled by 550-750 MHz baseband observations with the upgraded Giant Metrewave Radio Telescope. The parameter C₁ depends on the power-law index of the wavenumber spectrum of electron density inhomogeneities in the ionized interstellar medium. Radio waves propagating through the inhomogeneous ionized medium suffer multipath propagation, as a result of which the pulsed emission from a neutron star undergoes scatter broadening. Consequently, interference between the delayed copies of the scatter-broadened electric field manifests as scintillation. We measure a scintillation bandwidth Δν_d = 149 ± 3 Hz as well as a scatter-broadening timescale τ_d = 1.22 ± 0.09 ms at 650 MHz. These two quantities are related through the uncertainty relation C₁ = 2πΔν_dτ_d, using which we directly measure C₁ = 1.2 ± 0.1. We describe the methods employed to obtain these results and discuss their implications in general, as well as for the magnetar XTE J1810-197, toward which the measurements have been made. We also discuss how such effectively in situ measurements of C₁ can aid in inferring the wavenumber spectrum power-law index and hence quantitatively discriminate between the various possible scattering scenarios in the ionized medium. Finally, using the fact that C₁ ∼ 1, we nominally constrain the emission size to less than a few thousand kilometers for a screen very close to the magnetar and to within the magnetosphere for all screen distances.