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# Sub-second periodicity in a fast radio burst

## Abstract

Fast radio bursts (FRBs) are millisecond-duration flashes of radio waves that are visible at distances of billions of light years1. The nature of their progenitors and their emission mechanism remain open astrophysical questions2. Here we report the detection of the multicomponent FRB 20191221A and the identification of a periodic separation of 216.8(1) ms between its components, with a significance of 6.5σ. The long (roughly 3 s) duration and nine or more components forming the pulse profile make this source an outlier in the FRB population. Such short periodicity provides strong evidence for a neutron-star origin of the event. Moreover, our detection favours emission arising from the neutron-star magnetosphere3,4, as opposed to emission regions located further away from the star, as predicted by some models5.

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## Data availability

The data used in this paper are stored in Hierarchical Data Format 5 files available at https://doi.org/10.11570/22.0003.

## Code availability

The code used to model the signal from the sources presented in this publication, calculate their periodicities and plot the results is available at https://doi.org/10.11570/22.0003, together with the algorithms to calculate the $$\hat{S}$$ score and the Rayleigh statistic $${Z}_{1}^{2}$$ used to estimate the significance of the periodicities.

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## Acknowledgements

We acknowledge that CHIME is located on the traditional, ancestral and unceded territory of the Syilx/Okanagan people. We thank the Dominion Radio Astrophysical Observatory, operated by the National Research Council Canada, for gracious hospitality and expertise. CHIME is funded by a grant from the Canada Foundation for Innovation (CFI) 2012 Leading Edge Fund (Project 31170) and by contributions from the provinces of British Columbia, Québec and Ontario. The CHIME/FRB Project is funded by a grant from the CFI 2015 Innovation Fund (Project 33213) and by contributions from the provinces of British Columbia and Québec, and by the Dunlap Institute for Astronomy & Astrophysics at the University of Toronto. Further support was provided by the Canadian Institute for Advanced Research (CIFAR), McGill University and the McGill Space Institute through the Trottier Family Foundation, and the University of British Columbia. The Dunlap Institute is funded through an endowment established by the David Dunlap family and the University of Toronto. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. The National Radio Astronomy Observatory is a facility of the National Science Foundation (NSF) operated under cooperative agreement by Associated Universities, Inc. FRB research at UBC is supported by an NSERC Discovery Grant and by CIFAR. The CHIME/FRB baseband system is funded in part by a Canada Foundation for Innovation John R. Evans Leaders Fund award to I.S.

A.B.P. is a McGill Space Institute (MSI) Fellow and a Fonds de Recherche du Quebec – Nature et Technologies (FRQNT) postdoctoral fellow. A.O. is supported by the Dunlap Institute. A.S.H. is supported by an NSERC Discovery Grant. B.M.G. is supported by an NSERC Discovery Grant (RGPIN-2015-05948) and by the Canada Research Chairs (CRC) Program. C.L. was supported by the U.S. Department of Defense (DoD) through the National Defense Science and Engineering Graduate (NDSEG) Fellowship Program. D.C.G. is supported by the John I. Watters Research Fellowship. D.M. was a Banting Fellow. E.P. acknowledges funding from an NWO Veni Fellowship. J.M.-P. is a Kavli Fellow. K.B. is supported by an NSF grant (2006548). K.W.M. is supported by an NSF Grant (2008031). M.B. is supported by a FRQNT Doctoral Research Award. M.Dobbs is supported by a Killam Fellowship, Canada Research Chair, NSERC Discovery Grant, CIFAR and by the FRQNT Centre de Recherche en Astrophysique du Québec (CRAQ). M.M. is supported by an NSERC PGS-D award. P.C. is supported by a FRQNT Doctoral Research Award. P.Scholz is a Dunlap Fellow and an NSERC Postdoctoral Fellow. S.C. acknowledges support from the National Science Foundation (AAG 1815242). S.R. is a CIFAR Fellow and is supported by the NSF Physics Frontiers Center award 1430284. U.-L.P. receives the support of the Natural Sciences and Engineering Research Council of Canada (NSERC, funding reference numbers RGPIN-2019-067, CRD 523638-18 and 555585-20), Ontario Research Fund—Research Excellence Program (ORF-RE), CIFAR, Thoth Technology, Inc., Alexander von Humboldt Foundation and the Ministry of Science and Technology (MOST) of Taiwan (110-2112-M-001-071-MY3). V.M.K. holds the Lorne Trottier Chair in Astrophysics and Cosmology and a Distinguished James McGill Professorship and receives support from an NSERC Discovery Grant and Herzberg Award, from an R. Howard Webster Foundation Fellowship from CIFAR and from the FRQNT Centre de Recherche en Astrophysique du Quebec. Z.P. is a Dunlap Fellow.

## Author information

Authors

### Contributions

All authors from the CHIME/FRB collaboration played either leadership or significant supporting roles in one or more of: the management, development and construction of the CHIME telescope, the CHIME/FRB instrument and the CHIME/FRB software data pipeline, the commissioning and operations of the CHIME/FRB instrument, the data analysis and preparation of this manuscript. All authors from the CHIME collaboration played either leadership or significant supporting roles in the management, development and construction of the CHIME telescope.

### Corresponding author

Correspondence to D. Michilli.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Extended data figures and tables

### Extended Data Fig. 1 Radio signal from FRBs 20210206A and 20210213A.

a,b, Waterfall plots of the signal intensity (colour-coded) as a function of time and frequency. Frequency channels missing or masked owing to radio-frequency interference are replaced with off-burst median values and are indicated in red. Effects of dispersion have been removed and data have been plotted at the native frequency resolution of 390.625 kHz and at time resolutions of 0.16 and 0.32 ms, respectively. c,d, In black, the pulse profiles obtained by averaging the frequency channels of the waterfall plots in which signal is visible. Peak locations are highlighted by vertical lines. a,c, FRB 20210206A. b,d, FRB 20210213A.

### Extended Data Fig. 2 Periodicity analysis of FRBs 20210206A and 20210213A.

a,b, Power spectrum obtained with a discrete Fourier transform of the pulse profile. Vertical pink lines indicate the periods reported in Extended Data Table 1. c,d, Residuals of a timing analysis assuming that the peaks forming the FRB profile are separated by integer numbers times these periods, respectively. 1σ error bars are often smaller than the symbol sizes. Horizontal pink lines indicate a phase of zero around which residuals have been rotated. e,f, Study of the statistical significance of the measured periodicity by using the periodicity-sensitive score $$\hat{S}$$. The grey histograms have been obtained with an ensemble of simulations, whereas the value measured for each FRB is represented with a vertical pink line. The corresponding probability of obtaining such a periodicity by chance is indicated on the plots. a,c,e, FRB 20210206A. b,d,f, FRB 20210213A.

### Extended Data Fig. 3 Reduced chi-square test as a function of the number of components used to model the profile of FRB 20191221A.

The vertical line highlights the chosen number of components, whereas the horizontal line is placed at the $${\chi }_{{\rm{red}}}^{2}$$ value for nine components. The minimum $${\chi }_{{\rm{red}}}^{2}$$ variation that can be measured confidently with our data is estimated with equation (2) and plotted as en error bar for each number of peaks.

### Extended Data Fig. 4 ToAs of the components of FRB 20191221A as a function of their measured cycle.

The cycle is defined in equation (3). The periodicity appears clearly as the points fall nearly on the straight grey line, which highlights the trend expected for a period of 216.8 ms. Vertical lines mark gaps in which no pulse is observed within one period.

### Extended Data Fig. 5 Polarization profiles of FRB 20210206A.

a, The polarization angle (PA) values with 1σ error bars referenced to infinite frequency and rotated by an arbitrary angle. b, The total (I, black), linear (L, red) and circular (V, blue) intensities across the burst envelope.

### Extended Data Fig. 6 Parameters of a binary system producing a radio signal compatible with the FRBs presented here through gravitational lensing.

The system, located at 1 Gpc, contains a 1M pulsar emitting 1-Jy pulses that are lensed by its companion. The allowed parameter space is shown with brighter colours as a function of the minimum alignment angle (colour-coded), companion mass and separation of the binary system.

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The CHIME/FRB Collaboration., Andersen, B.C., Bandura, K. et al. Sub-second periodicity in a fast radio burst. Nature 607, 256–259 (2022). https://doi.org/10.1038/s41586-022-04841-8

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