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# Evidence for three-dimensional spin–velocity alignment in a pulsar

## Abstract

More than 50 years after the discovery of pulsars1 and confirmation of their association with supernova explosions2,3,4, the origin of the initial spin and velocity of pulsars remains largely a mystery. The typical space velocities of several hundred km s−1 have been attributed to ‘kicks’ resulting from asymmetries either in the supernova ejecta or in the neutrino emission5,6,7. Observations have shown a strong tendency for alignment between the pulsar space velocity and the spin axis in young pulsars, but until now these comparisons have been restricted to two dimensions. Here, we report evidence for three-dimensional alignment between the spin and velocity vectors, largely based on observations made with the Five-hundred-meter Aperture Spherical Radio Telescope (FAST) of the pulsar PSR J0538+2817 and its associated supernova remnant S147. Analysis of these and related observations has enabled us to determine the location of the pulsar within the supernova remnant and hence its radial velocity. Current simulations of supernova explosions have difficulty producing such three-dimensional alignment7,8,9. Our results, which depend on the unprecedented sensitivity of the observations, add another dimension to the intriguing correlation between pulsar spin-axis and birth-kick directions, thereby deepening the mysteries surrounding the birth of neutron stars.

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## Data availability

The data used in this investigation are available at https://crafts.bao.ac.cn/pub/data/yjm/2021/PSR0538+2817DS.zip. The data that support the plots can be requested from the corresponding authors.

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## Acknowledgements

This work was supported by the National Natural Science Foundation of China (grant nos. 11988101, 11903049, 12041304, 12041303, 11873067, 11690024 and U1831104), the CAS-MPG LEGACY project and Strategic Priority Research Program of the Chinese Academy of Sciences (grant no. XDB23000000) and the national Square Kilometre Array program of China (grant no. 2020SKA0120200). J.Y. acknowledges support from the Chinese Academy of Sciences ‘Light of West China’ Program (grant no. 2017-XBQNXZ-B-022), the Tianchi Doctoral Program 2017 and the funding of a Future Academic Scholars in Teaching (FAST) fellowship. W.Z. was supported by the Chinese Academy of Science ‘Hundred Talents Program’ Pioneer Initiative. We thank H.-T. Janka and S. Dai for valuable comments on earlier versions of the manuscript.

## Author information

Authors

### Contributions

J.Y. led the project. W.Z., D.L., N.W., J.L. and D.R.S. were involved in discussing the proposal for these observations. P.W. and C.M. helped with data analysis and M.Y. made the two 3D plots. R.N.M., W.Z., W.A.C. and D.L. made major contributions to the preparation of the manuscript. D.R.S. commented on the ISS data analysis, and Y.F., W.Y. and M.K. helped with polarization calibrations. All authors reviewed, discussed and commented on the results and the manuscript.

### Corresponding authors

Correspondence to Jumei Yao, Weiwei Zhu or Di Li.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Astronomy thanks the anonymous reviewers for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 One-dimensional time-domain ACFs for dynamic spectra and the corresponding structure functions.

Left panels show the ACF and the structure function for MJD 58766. Right panels show the ACF and the structure function for MJD 58767. The best-fit parameters with 1-σ uncertainties are showed in four panels. To facilitate comparison of the linear parts of the structure functions for the two bands, the Dϕ axis for the 1,100 MHz structure function has been scaled by (1,100/1,400)2.

### Extended Data Fig. 2 Distribution of the summed arc power.

Left and right panel show the distribution of the summed arc power in the η direction and the γ direction, respectively. The vertical dashed lines delineate the η and γ ranges used for the two-dimensional fit to the power and the plotted points are from within these ranges. The red lines are cuts through the 2D Gaussian fit at the best-fit value of the other coordinate. The Gaussian fit results of η and γ are showed as best-fit value with 1-σ uncertainties.

### Extended Data Fig. 3 The adopted coordinate system for the SNR S147 - PSR J0538+2817 system.

The coordinate system is centred at the geometric centre of SNR S147 (O) with the +x axis in the direction of increasing right ascension (E), the +y axis toward north, and the +z axis away from the observer. We mark the current pulsar position as P (xp, yp, zp) and its projection on the x-y plane as K (xp, yp, 0), and the scattering screen as S (xs, ys, zs). The inclination of the pulsar velocity $$\overrightarrow{V}$$ to the line of sight is ζv, r is the distance of the scattering screen from the origin and the SNR shell radius is Rs.

### Extended Data Fig. 4 The value of η and γ and seven parameters derived from 1400 MHz observations at four observational epochs.

All quantities are listed as the best-fit value with 1-σ uncertainties.

### Extended Data Fig. 5 Simulated secondary spectra.

Isotropic (left); anisotropic aligned with V, as proposed for the observations (centre); anisotropic perpendicular to V (right), with a logarithmic (dB) colour scale. The axial ratio of the anisotropic cases is 3. Each has the same phase gradient, set equal to the value of γ inferred from the observations.

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Yao, J., Zhu, W., Manchester, R.N. et al. Evidence for three-dimensional spin–velocity alignment in a pulsar. Nat Astron 5, 788–795 (2021). https://doi.org/10.1038/s41550-021-01360-w

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• DOI: https://doi.org/10.1038/s41550-021-01360-w