Peer-reviewedCC BYThe Astrophysical Journal
Pulsar Timing Array Sensitivity to Anisotropy: Empirical Sensitivity Curves, Scaling Relations, and the Multi-resolution Pixel Basis
Abstract
We quantify pulsar timing array (PTA) sensitivity to anisotropy in the gravitational-wave (GW) background using the cross-correlation-based Fisher information matrix in the pixel and spherical harmonic bases. We use a set of simulations to empirically determine scaling relations of a PTA’s sensitivity to anisotropy with the number of pulsars N psr in the array, the error δt on the times of arrival, the frequency f GW of the GWs, and the angular scale ΔΩ of the anisotropy. The sensitivity scales approximately as N psr 0.8 , δt −0.08 , and ΔΩ 1.6 − ΔΩ 2.1 (depending on the ranges of ℓ and m under consideration). In addition, we use realistic simulations to project the NANOGrav PTA sensitivity to a 30 yr baseline and quantify the growth in sensitivity at several time slices. Except at the lowest frequencies, we find negligible effect on sensitivity through increasing the observation duration only. Finally, we introduce a multi-resolution pixel basis motivated by the large dependence of the sensitivity on sky location, and demonstrate the operation of the basis through a set of injections and recoveries.
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BibTeX
@article{moursy2026pulsar,
title = {{Pulsar Timing Array Sensitivity to Anisotropy: Empirical Sensitivity Curves, Scaling Relations, and the Multi-resolution Pixel Basis}},
author = {Taha Moursy and Nihan Pol and Gabriella Agazie and Nikita Agarwal and Akash Anumarlapudi and Anne Archibald and Zaven Arzoumanian and Anjana Ashok and Jeremy Baier and Paul Baker and Bence Bécsy and Laura Blecha and Adam Brazier and Paul Brook and Sarah Burke-Spolaor and Rand Burnette and Robin Case and J. Andrew Casey-Clyde and Maria Charisi and Shami Chatterjee and Tyler Cohen and James Cordes and Neil Cornish and Fronefield Crawford and H. Thankful Cromartie and Kathryn Crowter and Megan Decesar and Paul Demorest and Heling Deng and Lankeswar Dey and Timothy Dolch and Graham Doskoch and Elizabeth Ferrara and William Fiore and Emmanuel Fonseca and Gabriel Freedman and Emiko Gardiner and Nate Garver-Daniels and Peter Gentile and Kyle Gersbach and Joseph Glaser and Deborah Good and Kayhan Gültekin and Aiden Gundersen and C. Harris and Jeffrey Hazboun and Ross Jennings and Aaron Johnson and Megan Jones and David Kaplan and Anala Sreekumar and Luke Zoltan Kelley and Matthew Kerr and Joey Key and Nima Laal and Michael Lam and William Lamb and Bjorn Larsen and T. Joseph W. Lazio and Natalia Lewandowska},
journal = {The Astrophysical Journal},
year = {2026},
month = sep,
doi = {10.3847/1538-4357/ae9759},
eprint = {2608.09781},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05842599v1},
note = {CC BY},
}
RIS
TY - JOUR
TI - Pulsar Timing Array Sensitivity to Anisotropy: Empirical Sensitivity Curves, Scaling Relations, and the Multi-resolution Pixel Basis
AU - Taha Moursy
AU - Nihan Pol
AU - Gabriella Agazie
AU - Nikita Agarwal
AU - Akash Anumarlapudi
AU - Anne Archibald
AU - Zaven Arzoumanian
AU - Anjana Ashok
AU - Jeremy Baier
AU - Paul Baker
AU - Bence Bécsy
AU - Laura Blecha
AU - Adam Brazier
AU - Paul Brook
AU - Sarah Burke-Spolaor
AU - Rand Burnette
AU - Robin Case
AU - J. Andrew Casey-Clyde
AU - Maria Charisi
AU - Shami Chatterjee
AU - Tyler Cohen
AU - James Cordes
AU - Neil Cornish
AU - Fronefield Crawford
AU - H. Thankful Cromartie
AU - Kathryn Crowter
AU - Megan Decesar
AU - Paul Demorest
AU - Heling Deng
AU - Lankeswar Dey
AU - Timothy Dolch
AU - Graham Doskoch
AU - Elizabeth Ferrara
AU - William Fiore
AU - Emmanuel Fonseca
AU - Gabriel Freedman
AU - Emiko Gardiner
AU - Nate Garver-Daniels
AU - Peter Gentile
AU - Kyle Gersbach
AU - Joseph Glaser
AU - Deborah Good
AU - Kayhan Gültekin
AU - Aiden Gundersen
AU - C. Harris
AU - Jeffrey Hazboun
AU - Ross Jennings
AU - Aaron Johnson
AU - Megan Jones
AU - David Kaplan
AU - Anala Sreekumar
AU - Luke Zoltan Kelley
AU - Matthew Kerr
AU - Joey Key
AU - Nima Laal
AU - Michael Lam
AU - William Lamb
AU - Bjorn Larsen
AU - T. Joseph W. Lazio
AU - Natalia Lewandowska
PY - 2026
DA - 2026/09/04
JO - The Astrophysical Journal
DO - 10.3847/1538-4357/ae9759
UR - https://hal.science/hal-05842599v1
AB - We quantify pulsar timing array (PTA) sensitivity to anisotropy in the gravitational-wave (GW) background using the cross-correlation-based Fisher information matrix in the pixel and spherical harmonic bases. We use a set of simulations to empirically determine scaling relations of a PTA’s sensitivity to anisotropy with the number of pulsars N psr in the array, the error δt on the times of arrival, the frequency f GW of the GWs, and the angular scale ΔΩ of the anisotropy. The sensitivity scales approximately as N psr 0.8 , δt −0.08 , and ΔΩ 1.6 − ΔΩ 2.1 (depending on the ranges of ℓ and m under consideration). In addition, we use realistic simulations to project the NANOGrav PTA sensitivity to a 30 yr baseline and quantify the growth in sensitivity at several time slices. Except at the lowest frequencies, we find negligible effect on sensitivity through increasing the observation duration only. Finally, we introduce a multi-resolution pixel basis motivated by the large dependence of the sensitivity on sky location, and demonstrate the operation of the basis through a set of injections and recoveries.
SN - 0004-637X
SN - 1538-4357
ER -