The NANOGrav 15 yr Dataset: Modified Functional Forms for Profile-Evolution Time Delays in Pulsar Timing Models
Abstract
Radio pulsars exhibit frequency-dependent variations in the shape of their pulse profiles that introduce systematic delays in the observed pulse times of arrival (TOA) across an observing band. The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) models these delays using a frequency-dependent (FD) log-polynomial function whose coefficients are fit to TOA measurements at different radio frequencies. However, FD parameters are prone to absorbing power from other chromatic effects, such as interstellar dispersion, leading to fitted FD values that overestimate profile evolution and vary significantly across datasets. To separate these effects, we introduce two new mathematical formulations of profile evolution: a monomial expansion (IFD) and a Legendre polynomial expansion (LIFD). We test these models on observations of 11 pulsars in the NANOGrav 15-year dataset and on simulated data, and also compare their performance to that of frequency-resolved pulse templates. We find that Legendre-based models generally predict timing delays that more closely replicate the true profile evolution, reducing the residual offset relative to FD by as much as 85% for the simulated data. Additionally, we find that the choice of profile evolution model can bias the fitted dispersion model, with FD-based models overestimating the injected DM by 0.013 pc cm^-3 compared to 0.0002 pc cm^-3 for LIFD. These results support the use of Legendre bases to mitigate covariances between chromatic effects, directly benefiting targeted timing studies of these effects and the development of advanced noise-modeling techniques for nanohertz gravitational-wave detection.
Related
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BibTeX
@misc{fiscella2026nanograv,
title = {{The NANOGrav 15 yr Dataset: Modified Functional Forms for Profile-Evolution Time Delays in Pulsar Timing Models}},
author = {Sofia V. Sosa Fiscella and Michael T. Lam and Olivia West and Ruggero Valdata and Gabriella Agazie and Akash Anumarlapudi and Anne M. Archibald and Zaven Arzoumanian and Paul T. Baker and Paul R. Brook and H. Thankful Cromartie and Kathryn Crowter and Megan E. DeCesar and Paul B. Demorest and Timothy Dolch and Elizabeth C. Ferrara and William Fiore and Emmanuel Fonseca and Gabriel E. Freedman and Nate Garver-Daniels and Peter A. Gentile and Joseph Glaser and Deborah C. Good and Jeffrey S. Hazboun and Ross J. Jennings and Megan L. Jones and David L. Kaplan and Matthew Kerr and Duncan R. Lorimer and Jing Luo and Ryan S. Lynch and Alexander McEwen and Maura A. McLaughlin and Natasha McMann and Bradley W. Meyers and Cherry Ng and David J. Nice and Timothy T. Pennucci and Benetge B. P. Perera and Nihan S. Pol and Henri A. Radovan and Scott M. Ransom and Paul S. Ray and Ann Schmiedekamp and Carl Schmiedekamp and Brent J. Shapiro-Albert and Taylor Starkman and Ingrid H. Stairs and Kevin Stovall and Abhimanyu Susobhanan and Joseph K. Swiggum and Haley M. Wahl},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10431},
eprint = {2610.10431},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10431},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The NANOGrav 15 yr Dataset: Modified Functional Forms for Profile-Evolution Time Delays in Pulsar Timing Models
AU - Sofia V. Sosa Fiscella
AU - Michael T. Lam
AU - Olivia West
AU - Ruggero Valdata
AU - Gabriella Agazie
AU - Akash Anumarlapudi
AU - Anne M. Archibald
AU - Zaven Arzoumanian
AU - Paul T. Baker
AU - Paul R. Brook
AU - H. Thankful Cromartie
AU - Kathryn Crowter
AU - Megan E. DeCesar
AU - Paul B. Demorest
AU - Timothy Dolch
AU - Elizabeth C. Ferrara
AU - William Fiore
AU - Emmanuel Fonseca
AU - Gabriel E. Freedman
AU - Nate Garver-Daniels
AU - Peter A. Gentile
AU - Joseph Glaser
AU - Deborah C. Good
AU - Jeffrey S. Hazboun
AU - Ross J. Jennings
AU - Megan L. Jones
AU - David L. Kaplan
AU - Matthew Kerr
AU - Duncan R. Lorimer
AU - Jing Luo
AU - Ryan S. Lynch
AU - Alexander McEwen
AU - Maura A. McLaughlin
AU - Natasha McMann
AU - Bradley W. Meyers
AU - Cherry Ng
AU - David J. Nice
AU - Timothy T. Pennucci
AU - Benetge B. P. Perera
AU - Nihan S. Pol
AU - Henri A. Radovan
AU - Scott M. Ransom
AU - Paul S. Ray
AU - Ann Schmiedekamp
AU - Carl Schmiedekamp
AU - Brent J. Shapiro-Albert
AU - Taylor Starkman
AU - Ingrid H. Stairs
AU - Kevin Stovall
AU - Abhimanyu Susobhanan
AU - Joseph K. Swiggum
AU - Haley M. Wahl
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10431
UR - https://arxiv.org/abs/2610.10431
AB - Radio pulsars exhibit frequency-dependent variations in the shape of their pulse profiles that introduce systematic delays in the observed pulse times of arrival (TOA) across an observing band. The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) models these delays using a frequency-dependent (FD) log-polynomial function whose coefficients are fit to TOA measurements at different radio frequencies. However, FD parameters are prone to absorbing power from other chromatic effects, such as interstellar dispersion, leading to fitted FD values that overestimate profile evolution and vary significantly across datasets. To separate these effects, we introduce two new mathematical formulations of profile evolution: a monomial expansion (IFD) and a Legendre polynomial expansion (LIFD). We test these models on observations of 11 pulsars in the NANOGrav 15-year dataset and on simulated data, and also compare their performance to that of frequency-resolved pulse templates. We find that Legendre-based models generally predict timing delays that more closely replicate the true profile evolution, reducing the residual offset relative to FD by as much as 85% for the simulated data. Additionally, we find that the choice of profile evolution model can bias the fitted dispersion model, with FD-based models overestimating the injected DM by 0.013 pc cm^-3 compared to 0.0002 pc cm^-3 for LIFD. These results support the use of Legendre bases to mitigate covariances between chromatic effects, directly benefiting targeted timing studies of these effects and the development of advanced noise-modeling techniques for nanohertz gravitational-wave detection.
ER -