Frequency-dependent Template Profiles for High-precision Pulsar Timing

Abstract

Pulsar timing experiments require high fidelity template profiles in order to minimize the biases in pulse time-of-arrival (TOA) measurements and their uncertainties. Efforts to acquire more precise TOAs given fixed effective area of telescopes, finite receiver noise, and limited integration time have led pulsar astronomers to the solution of implementing ultra-wideband receivers. This solution, however, has run up against the problem that pulse profile shapes evolve with frequency, which raises the question of how to properly measure and analyze TOAs obtained using template-matching methods. This paper proposes a new method for one facet of this problem, that of template profile generation, and demonstrates it on the well-timed millisecond pulsar J1713+0747. Specifically, we decompose pulse profile evolution into a linear combination of basis eigenvectors, the coefficients of which change slowly with frequency such that their evolution is modeled simply by a sum of low degree piecewise polynomial spline functions. These noise-free, high fidelity, frequency-dependent templates can be used to make measurements of so-called "wideband TOAs" simultaneously with an estimate of the instantaneous dispersion measure. The use of wideband TOAs is becoming important for pulsar timing array experiments, as the volume of datasets comprised of conventional, subbanded TOAs are quickly becoming unwieldly for the Bayesian analyses needed to uncover latent gravitational wave signals. Although motivated by high precision timing experiments, our technique is applicable in more general pulsar observations.

Dual-frequency single-pulse study of PSR B0950+08

“…The earliest VHF observation was aligned against a four-component Gaussian model in which the amplitudes and widths were all allowed to vary as a function of a frequency, but their positions were fixed (Pennucci 2015); this alignment permits a frequency-dependent separation between the two observed profile components while maintaining the usual assumption of a fixed-in-frequency fiducial point, such as the mid-point between the observed components. We then model the profile evolution in this aligned VHF observation following Pennucci (2019), in which a principal component analysis is used to reproduce the frequency dependent shape, resulting in a higher fidelity, noise-free template than when using a Gaussian component decomposition. The DM from each VHF observation was then determined by effectively measuring the ν −2 dependence of the delays of the profiles relative to this template (Pennucci et al 2014).…”

The NANOGrav 12.5 yr Data Set: Observations and Narrowband Timing of 47 Millisecond Pulsars

“…The usage of wideband TOAs and their associated DM measurements requires special attention and new techniques, which are detailed later. For this reason, up until now, there has been no published, large-scale application of wideband timing for PTAs or other projects, although early, proof-of-concept demonstrations on NG9 can be found in Pennucci (2015).…”

“…The measurement of TOAs from pulsar data with a large instantaneous bandwidth was first developed in Liu et al (2014) and Pennucci et al (2014), and further explored in Pennucci (2015) and Pennucci (2019). We refer the reader to those works for details and here briefly summarize the important points.…”

An ultra-wide bandwidth (704 to 4 032 MHz) receiver for the Parkes radio telescope

“…Not only such files are difficult to transfer to local computer systems, our current astronomical software suites for single-dish telescopes are ill-equipped to deal with these data volumes. In addition, traditional calibration procedures such as feed rotation and frequency switching cannot be applied and new methods will be required to extract the required scientific results from the wideband data (such as new wideband timing methods, e.g., Pennucci 2019).…”