A Direct Measurement of the Electron Density Turbulence Parameter C1 and Implications for the Emission Size of Magnetar XTE J1810-197 - Visweshwar Ram Marthi; Yogesh Maan (The Astrophysical Journal Letters)
We report a direct measurement of the electron density turbulence parameter C _1 , enabled by 550–750 MHz baseband observations with the upgraded Giant Metrewave Radio Telescope. The parameter C _1 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 Δ ν _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 C _1  = 2 π Δ ν _d τ _d , using which we directly measure C _1  = 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 C _1 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 C _1  ∼ 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.