Pulsar Cyclic Spectroscopy in the Partial-deconvolution Regime: Benefits and Limitations

Abstract We explore possible advantages of cyclic spectroscopy for observations of pulsars in instances where full cyclic deconvolution is not possible. We compute cyclic merits and full-deconvolution regime boundaries for pulsars observed by NANOGrav and discuss which sources stand to benefit the most from using cyclic spectroscopy when observed with the Green Bank Telescope and DSA-2000 in a given frequency range. We compare data products, namely the wavefield, in both full-deconvolution and partial-deconvolution regimes to demonstrate what can be accomplished with incomplete phase retrieval. Additionally, we show how some phase retrieval can still be achieved in the partial-deconvolution regime and how this allows for additional information in scintillation-based data products, like the dynamic wavefield power, compared to what can be found in traditional dynamic spectra. An examination of dynamic wavefield phase as a function of observing frequency reveals more complete phase retrieval is achieved the closer one gets to the full-deconvolution regime, agreeing with the expectations of cyclic merit. While we demonstrate that fragmentary recovery of the secondary wavefield can be accomplished in the partial-deconvolution regime, we advocate for a synergistic approach with phase retrieval methods like the θ − θ transform, although we also provide discussion about shortcomings of this strategy. Finally, we use the combination of modest cyclic merit and lack of discernible results for PSR J1903+0327 to motivate the creation of an updated “cyclic merit 2.0,” which relies on scintillation bandwidth instead of observing bandwidth.