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# Interstellar turbulence spectrum from in situ observations of Voyager 1

## Abstract

Interstellar scintillation of radio waves from pulsars reveals that the interstellar turbulence spectrum of electron density approximates the Kolmogorov power law from wavenumber $$q = 10^{ - 18}\,{\rm{m}}^{ - 1}$$ to $$10^{ - 6.5}\,{\mathrm{m}}^{ - 1}$$ (refs. 1,2,3,4,5). Here we obtain the interstellar turbulence spectrum of electron density from in situ observations of Voyager 1. The observed spectrum extends from $$\lambda = 15\,{\mathrm{au}} \approx {\mathrm{2}}{\mathrm{.25}} \times {\mathrm{10}}^{12}\,{\mathrm{m}}$$ ($$q = 4.4 \times 10^{ - 13}\,{\mathrm{m}}^{ - 1}$$) to $$\lambda = q^{ - 1}$$ = 50 m ($$q = {\mathrm{2}} \times {\mathrm{10}}^{ - 2}\,{\mathrm{m}}^{ - 1}$$), close to the Debye length. The measured spectrum covers part ($$q = 4.4 \times 10^{ - 13}\,{\mathrm{m}}^{ - 1}\,{\mathrm{to}}\,1 \times 10^{ - 6}\,{\mathrm{m}}^{ - 1}$$) of the Kolmogorov inertial range, as well as ion and electron kinetic scales ($$q = 10^{ - 6}\,{\mathrm{m}}^{ - 1} \,{\mathrm{to }}\, {\mathrm{2}} \times {\mathrm{10}}^{ - 2}\,{\mathrm{m}}^{ - 1}$$). The observed Kolmogorov inertial range shows good agreement with earlier studies by Lee and Jokipii2 and Armstrong et al.3,4. Around the kinetic scales, a bulge of spectral intensity higher than the Kolmogorov spectrum is found.

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## Data availability

The Voyager 1 data that support the findings of this study are available from the Planetary Plasma Interactions Node of the Planetary Data System archives: https://pds-ppi.igpp.ucla.edu/index.jsp.

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## Acknowledgements

The research was supported by the Ministry of Science and Technology in Taiwan (MOST 106-2111-M-001-012 and 107-2111-M-002-015) and Science and Technology Development Fund of Macao (0035/2018/AFJ). We thank the PWS team of the Voyager mission for the plasma wave data. The Voyager data are downloaded from https://pds-ppi.igpp.ucla.edu/.

## Author information

Authors

### Contributions

L.C.L. conceived the idea and supervised the project. K.H.L. analysed the data. Both authors contributed to writing the manuscript.

### Corresponding authors

Correspondence to K. H. Lee or L. C. Lee.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Supplementary information

### Supplementary Information

Supplementary Figures 1–5, Supplementary references.

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Reprints and Permissions

Lee, K.H., Lee, L.C. Interstellar turbulence spectrum from in situ observations of Voyager 1. Nat Astron 3, 154–159 (2019). https://doi.org/10.1038/s41550-018-0650-6

• Accepted:

• Published:

• Issue Date:

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