High-precision timing of millisecond pulsars (MSPs) over years to decades is a promising technique for direct detection of gravitational waves at nanohertz frequencies. Time-variable, multi-path scattering in the interstellar medium is a significant source of noise for this detector, particularly as timing precision approaches 10 ns or better for MSPs in the pulsar timing array. For many MSPs the scattering delay above 1 GHz is at the limit of detectability; therefore, we study it at lower frequencies. Using the LOFAR (LOw-Frequency ARray) radio telescope we have analyzed short (5-20 min) observations of three MSPs in order to estimate the scattering delay at 110-190 MHz, where the number of scintles is large and, hence, the statistical uncertainty in the scattering delay is small. We used cyclic spectroscopy, still relatively novel in radio astronomy, on baseband-sampled data to achieve unprecedented frequency resolution while retaining adequate pulse phase resolution. We detected scintillation structure in the spectra of the MSPs PSR B1257+12, PSR J1810+1744, and PSR J2317+1439 with diffractive bandwidths of $6pm 3$, $2.0pm 0.3$, and $sim 7$ kHz, respectively, where the estimate for PSR J2317+1439 is reliable to about a factor of 2. For the brightest of the three pulsars, PSR J1810+1744, we found that the diffractive bandwidth has a power-law behavior $Delta u_d propto u^{alpha}$, where $ u$ is the observing frequency and $alpha = 4.5pm 0.5$, consistent with a Kolmogorov inhomogeneity spectrum. We conclude that this technique holds promise for monitoring the scattering delay of MSPs with LOFAR and other high-sensitivity, low-frequency arrays like SKA-Low.
Download