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Interstellar turbulence spectrum from in situ observations of Voyager 1


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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Fig. 1: Dynamic spectra observed in the local ISM by Voyager 1.
Fig. 2: Composite spectrum (red, blue, green and purple dots) obtained from in situ Voyager 1 data.

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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:


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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

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

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

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Lee, K.H., Lee, L.C. Interstellar turbulence spectrum from in situ observations of Voyager 1. Nat Astron 3, 154–159 (2019).

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