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arXiv · 2608.09781

Pulsar Timing Array Sensitivity to Anisotropy: Empirical Sensitivity Curves, Scaling Relations, and the Multi-Resolution Pixel Basis

Taha T. Moursy·Nihan S. Pol·Gabriella Agazie·Nikita Agarwal·Akash Anumarlapudi·Anne M. Archibald·Zaven Arzoumanian·Anjana Ashok·Jeremy G. Baier·Paul T. Baker·Bence Bécsy·Laura Blecha·Adam Brazier·Paul R. Brook·Sarah Burke-Spolaor·Rand Burnette·Robin Case·J. Andrew Casey-Clyde·Maria Charisi·Shami Chatterjee·Tyler Cohen·James M. Cordes·Neil J. Cornish·Fronefield Crawford·H. Thankful Cromartie·Kathryn Crowter·Megan E. DeCesar·Paul B. Demorest·Heling Deng·Lankeswar Dey·Timothy Dolch·Graham M. Doskoch·Elizabeth C. Ferrara·William Fiore·Emmanuel Fonseca·Gabriel E. Freedman·Emiko C. Gardiner·Nate Garver-Daniels·Peter A. Gentile·Kyle A. Gersbach·Joseph Glaser·Deborah C. Good·Kayhan Gültekin·Aiden Gundersen·C. J. Harris·Jeffrey S. Hazboun·Ross J. Jennings·Aaron D. Johnson·Megan L. Jones·David L. Kaplan·Anala K. Sreekumar·Luke Zoltan Kelley·Matthew Kerr·Joey S. Key·Nima Laal·Michael T. Lam·William G. Lamb·Bjorn Larsen·T. Joseph W. Lazio·Natalia Lewandowska·Tingting Liu·Duncan R. Lorimer·Jing Luo·Ryan S. Lynch·Chung-Pei Ma·Dustin R. Madison·Ashley Martsen·Cayenne Matt·Alexander McEwen·James W. McKee·Maura A. McLaughlin·Natasha McMann·Bradley W. Meyers·Patrick M. Meyers·Matthew T. Miles·Chiara M. F. Mingarelli·Andrea Mitridate·Cherry Ng·David J. Nice·Shania A. Nichols·Stella Koch Ocker·Daniel J. Oliver·Ken D. Olum·Timothy T. Pennucci·Benetge B. P. Perera·Polina Petrov·Henri A. Radovan·Scott M. Ransom·Paul S. Ray·Joseph D. Romano·Jessie C. Runnoe·Alexander Saffer·Shashwat C. Sardesai·Ann Schmiedekamp·Carl Schmiedekamp·Kai Schmitz·Levi Schult·Brent J. Shapiro-Albert·Xavier Siemens·Joseph Simon
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Abstract

We quantify pulsar timing array (PTA) sensitivity to anisotropy in the gravitational wave 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 $N_\mathrm{psr}$ in the array, the error $\delta t$ on the times of arrival, the frequency $f_\mathrm{GW}$ of the gravitational waves, and the angular scale $\Delta\Omega$ of the anisotropy. The sensitivity scales approximately as $N_\mathrm{psr}^{0.8}$, $\delta t^{-0.08}$, and $\Delta\Omega^{1.6}-\Delta\Omega^{2.1}$ (depending on the ranges of $\ell$ and $m$ under consideration). In addition, we use realistic simulations to project the NANOGrav PTA sensitivity to a 30-year baseline and quantify the growth in sensitivity at several timeslices. 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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Taha T. Moursy, Nihan S. Pol, Gabriella Agazie, Nikita Agarwal, Akash Anumarlapudi, Anne M. Archibald, Zaven Arzoumanian, Anjana Ashok, Jeremy G. Baier, Paul T. Baker, Bence Bécsy, Laura Blecha, Adam Brazier, Paul R. Brook, Sarah Burke-Spolaor, Rand Burnette, Robin Case, J. Andrew Casey-Clyde, Maria Charisi, Shami Chatterjee, Tyler Cohen, James M. Cordes, Neil J. Cornish, Fronefield Crawford, H. Thankful Cromartie, Kathryn Crowter, Megan E. DeCesar, Paul B. Demorest, Heling Deng, Lankeswar Dey, Timothy Dolch, Graham M. Doskoch, Elizabeth C. Ferrara, William Fiore, Emmanuel Fonseca, Gabriel E. Freedman, Emiko C. Gardiner, Nate Garver-Daniels, Peter A. Gentile, Kyle A. Gersbach, Joseph Glaser, Deborah C. Good, Kayhan Gültekin, Aiden Gundersen, C. J. Harris, Jeffrey S. Hazboun, Ross J. Jennings, Aaron D. Johnson, Megan L. Jones, David L. Kaplan, Anala K. Sreekumar, Luke Zoltan Kelley, Matthew Kerr, Joey S. Key, Nima Laal, Michael T. Lam, William G. Lamb, Bjorn Larsen, T. Joseph W. Lazio, Natalia Lewandowska, Tingting Liu, Duncan R. Lorimer, Jing Luo, Ryan S. Lynch, Chung-Pei Ma, Dustin R. Madison, Ashley Martsen, Cayenne Matt, Alexander McEwen, James W. McKee, Maura A. McLaughlin, Natasha McMann, Bradley W. Meyers, Patrick M. Meyers, Matthew T. Miles, Chiara M. F. Mingarelli, Andrea Mitridate, Cherry Ng, David J. Nice, Shania A. Nichols, Stella Koch Ocker, Daniel J. Oliver, Ken D. Olum, Timothy T. Pennucci, Benetge B. P. Perera, Polina Petrov, Henri A. Radovan, Scott M. Ransom, Paul S. Ray, Joseph D. Romano, Jessie C. Runnoe, Alexander Saffer, Shashwat C. Sardesai, Ann Schmiedekamp, Carl Schmiedekamp, Kai Schmitz, Levi Schult, Brent J. Shapiro-Albert, Xavier Siemens, Joseph Simon. 2026-08-10. Pulsar Timing Array Sensitivity to Anisotropy: Empirical Sensitivity Curves, Scaling Relations, and the Multi-Resolution Pixel Basis. https://arxiv.org/abs/2608.09781

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