Recovering Pulsar Periodicity from Time-of-arrival Data by Finding the Shortest Vector in a Lattice
The strict periodicity of pulsars is one of the primary ways through which their nature and environment can be studied, and it has also enabled precision tests of general relativity and studies of nanohertz gravitational waves using pulsar timing arrays (PTAs). Identifying such a periodicity from a...
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2025-01-01
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| Online Access: | https://doi.org/10.3847/1538-4357/ad9449 |
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| author | Dotan Gazith Aaron B. Pearlman Barak Zackay |
| author_facet | Dotan Gazith Aaron B. Pearlman Barak Zackay |
| author_sort | Dotan Gazith |
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| description | The strict periodicity of pulsars is one of the primary ways through which their nature and environment can be studied, and it has also enabled precision tests of general relativity and studies of nanohertz gravitational waves using pulsar timing arrays (PTAs). Identifying such a periodicity from a discrete set of arrival times is a difficult algorithmic problem, In particular when the pulsar is in a binary system. This challenge is especially acute in γ -ray pulsar astronomy, as there are hundreds of unassociated Fermi-LAT sources that may be produced by γ -ray emission from unknown pulsars. Recovering their timing solutions will help reveal their properties and may allow them to be added to PTAs. The same issue arises when attempting to recover a strict periodicity for repeating fast radio bursts (FRBs). Such a detection would be a major breakthrough, providing us with the FRB source’s age, magnetic field, and binary orbit. The problem of recovering a timing solution from sparse time-of-arrival data is currently unsolvable for pulsars in unknown binary systems, and incredibly hard even for isolated pulsars. In this paper, we frame the timing recovery problem as the problem of finding a short vector in a lattice and obtain the solution using off-the-shelf lattice reduction and sieving techniques. As a proof of concept, we solve PSR J0318+0253, a millisecond γ -ray pulsar discovered by FAST in a γ -ray-directed search, in a few CPU minutes. We discuss the assumptions of the standard lattice techniques and quantify their performance and limitations. |
| format | Article |
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| institution | Kabale University |
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| language | English |
| publishDate | 2025-01-01 |
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| spelling | doaj-art-33d293b8e7f14f1a9402c6abf20c638d2025-01-17T13:29:04ZengIOP PublishingThe Astrophysical Journal1538-43572025-01-0197914810.3847/1538-4357/ad9449Recovering Pulsar Periodicity from Time-of-arrival Data by Finding the Shortest Vector in a LatticeDotan Gazith0https://orcid.org/0000-0001-6698-3693Aaron B. Pearlman1https://orcid.org/0000-0002-8912-0732Barak Zackay2https://orcid.org/0000-0001-5162-9501Department of Particle Physics and Astrophysics, Weizmann Institute of Science , 76100 Rehovot, Israel ; dotan.gazith@weizmann.ac.il, barak.zackay@weizmann.ac.ilDepartment of Physics, McGill University , 3600 rue University, Montréal, QC H3A 2T8, Canada ; aaron.b.pearlman@physics.mcgill.ca; Trottier Space Institute, McGill University , 3550 rue University, Montréal, QC H3A 2A7, Canada; Division of Physics, Mathematics, and Astronomy, California Institute of Technology , Pasadena, CA 91125, USADepartment of Particle Physics and Astrophysics, Weizmann Institute of Science , 76100 Rehovot, Israel ; dotan.gazith@weizmann.ac.il, barak.zackay@weizmann.ac.ilThe strict periodicity of pulsars is one of the primary ways through which their nature and environment can be studied, and it has also enabled precision tests of general relativity and studies of nanohertz gravitational waves using pulsar timing arrays (PTAs). Identifying such a periodicity from a discrete set of arrival times is a difficult algorithmic problem, In particular when the pulsar is in a binary system. This challenge is especially acute in γ -ray pulsar astronomy, as there are hundreds of unassociated Fermi-LAT sources that may be produced by γ -ray emission from unknown pulsars. Recovering their timing solutions will help reveal their properties and may allow them to be added to PTAs. The same issue arises when attempting to recover a strict periodicity for repeating fast radio bursts (FRBs). Such a detection would be a major breakthrough, providing us with the FRB source’s age, magnetic field, and binary orbit. The problem of recovering a timing solution from sparse time-of-arrival data is currently unsolvable for pulsars in unknown binary systems, and incredibly hard even for isolated pulsars. In this paper, we frame the timing recovery problem as the problem of finding a short vector in a lattice and obtain the solution using off-the-shelf lattice reduction and sieving techniques. As a proof of concept, we solve PSR J0318+0253, a millisecond γ -ray pulsar discovered by FAST in a γ -ray-directed search, in a few CPU minutes. We discuss the assumptions of the standard lattice techniques and quantify their performance and limitations.https://doi.org/10.3847/1538-4357/ad9449PulsarsAstronomy data analysisGamma-ray astronomyComputational methods |
| spellingShingle | Dotan Gazith Aaron B. Pearlman Barak Zackay Recovering Pulsar Periodicity from Time-of-arrival Data by Finding the Shortest Vector in a Lattice The Astrophysical Journal Pulsars Astronomy data analysis Gamma-ray astronomy Computational methods |
| title | Recovering Pulsar Periodicity from Time-of-arrival Data by Finding the Shortest Vector in a Lattice |
| title_full | Recovering Pulsar Periodicity from Time-of-arrival Data by Finding the Shortest Vector in a Lattice |
| title_fullStr | Recovering Pulsar Periodicity from Time-of-arrival Data by Finding the Shortest Vector in a Lattice |
| title_full_unstemmed | Recovering Pulsar Periodicity from Time-of-arrival Data by Finding the Shortest Vector in a Lattice |
| title_short | Recovering Pulsar Periodicity from Time-of-arrival Data by Finding the Shortest Vector in a Lattice |
| title_sort | recovering pulsar periodicity from time of arrival data by finding the shortest vector in a lattice |
| topic | Pulsars Astronomy data analysis Gamma-ray astronomy Computational methods |
| url | https://doi.org/10.3847/1538-4357/ad9449 |
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