Letter | Published:

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.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

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.

Additional information

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


  1. 1.

    Lee, L. C. & Jokipii, J. R. Strong scintillations in astrophysics. III. The fluctuations in intensity. Astrophys. J. 202, 439–453 (1975).

  2. 2.

    Lee, L. C. & Jokipii, J. R. The irregularity spectrum in interstellar space. Astrophys. J. 206, 735–743 (1976).

  3. 3.

    Armstrong, J. W., Cordes, J. M. & Rickett, B. J. Density power spectrum in the local interstellar medium. Nature 291, 561–564 (1981).

  4. 4.

    Armstrong, J. W., Rickett, B. J. & Spangler, S. R. Electron density power spectrum in the local interstellar medium. Astrophys. J. 443, 209–221 (1995).

  5. 5.

    Cordes, J. M., Weisberg, J. M., Frail, D. A., Spangler, S. R. & Ryan, M. The galactic distribution of free electrons. Nature 354, 121–124 (1991).

  6. 6.

    Scarf, F. L. & Gurnett, D. A. A plasma wave investigation for the Voyager mission. Space Sci. Rev. 21, 289–308 (1977).

  7. 7.

    Gurnett, D. A. et al. Precursors to interstellar shocks of solar origin. Astrophys. J. 809, 121 (2015).

  8. 8.

    Marple, S. L. in Digital Spectral Analysis Ch. 7 (Prentice-Hall, Upper Saddle River, 1987).

  9. 9.

    Gurnett, D. A., Kurth, W. S., Burlaga, L. F. & Ness, N. F. In situ observations of interstellar plasma with Voyager 1. Science 341, 1489–1492 (2013).

  10. 10.

    Huang, N. E. et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. A 454, 903–995 (1998).

  11. 11.

    Huang, N. E. et al. On instantaneous frequency. Adv. Adapt. Data Anal. 1, 177–229 (2009).

  12. 12.

    Lomb, N. R. Least-squares frequency analysis of unequally spaced data. Astrophys. Space Sci. 39, 447–462 (1976).

  13. 13.

    Tatarski, V. I. in Wave Propagation in a Turbulent Medium 17 (McGraw-Hill, New York, 1961).

  14. 14.

    Larson, R. B. Stellar kinematics and interstellar turbulence. Mon. Not. R. Astron. Soc. 186, 479–490 (1979).

  15. 15.

    Simonetti, J. H., Cordes, J. M. & Spangler, S. R. Small-scale variations in the galactic magnetic field—the rotation measure structure function and birefringence in interstellar scintillations. Astrophys. J. 284, 126–134 (1984).

  16. 16.

    Chepurnov, A. & Lazarian, A. Extending the big power law in the sky with turbulence spectra from Wisconsin Hα mapper data. Astrophys. J. 710, 853–858 (2010).

  17. 17.

    Burlaga, L. F., Florinski, V. & Ness, N. F. In situ observations of magnetic turbulence in the local interstellar medium. Astrophys. J. 804, L31 (2015).

  18. 18.

    Sridhar, S. & Goldreich, P. Toward a theory of interstellar turbulence. 1: weak Alfvénic turbulence. Astrophys. J. 432, 612–621 (1994).

  19. 19.

    Goldreich, P. & Sridhar, S. Toward a theory of interstellar turbulence. 2: strong Alfvénic turbulence. Astrophys. J. 438, 763–775 (1995).

  20. 20.

    Neugebauer, M. The enhancement of solar wind fluctuations at the proton thermal gyroradius. J. Geophys. Res. 80, 998–1002 (1975).

  21. 21.

    Kellogg, P. J. & Horbury, T. S. Rapid density fluctuations in the solar wind. Ann. Geophys. 23, 3765–3773 (2005).

  22. 22.

    Alexandrova, O., Carbone, V., Veltri, P. & Sorriso-Valvo, L. Small-scale energy cascade of the solar wind turbulence. Astrophys. J. 674, 1153–1157 (2008).

  23. 23.

    Sahraoui, F., Goldstein, M. L., Robert, P. & Khotyaintsev, Y. V. Evidence of a cascade and dissipation of solar-wind turbulence at the electron gyroscale. Phys. Rev. Lett. 102, 231102 (2009).

  24. 24.

    Chen, C. H. K., Salem, C. S., Bonnell, J. W., Mozer, F. S. & Bale, S. D. Density fluctuation spectrum of solar wind turbulence between ion and electron scales. Phys. Rev. Lett. 109, 035001 (2012).

  25. 25.

    Šafránková, J. et al. Solar wind density spectra around the ion spectral break. Astrophys. J. 803, 107 (2015).

  26. 26.

    Neugebauer, M., Wu, C. S. & Huba, J. D. Plasma fluctuations in the solar wind. J. Geophys. Res. 83, 1027–1034 (1978).

  27. 27.

    Chandran, B. D. G., Quataert, E., Howes, G. G., Xia, Q. & Pongkitiwanichakul, P. Constraining low-frequency Alfvénic turbulence in the solar wind using density-fluctuation measurements. Astrophys. J. 707, 1668–1675 (2009).

  28. 28.

    Kim, T. K., Pogorelov, N. V. & Burlaga, L. F. Modeling shocks detected by Voyager 1 in the local interstellar medium. Astrophys. J. 843, L32 (2017).

  29. 29.

    Tsurutani, B. T. et al. Lion roars and nonoscillatory drift mirror waves in the magnetosheath. J. Geophys. Res. 87, 6060–6072 (1982).

  30. 30.

    Lee, K. H. Generation of parallel and quasi-perpendicular EMIC waves and mirror waves by fast magnetosonic shocks in the solar wind. J. Geophys. Res. 122, 7307–7322 (2017).

  31. 31.

    Claerbout, J. F. in Fundamentals of Geophysics Data Processing Ch. 7.2 (McGraw-Hill, New York, 1976).

  32. 32.

    Marple, S. L. Frequency resolution of Fourier and maximum entropy spectral estimates. Geophysics 47, 1303–1307 (1982).

  33. 33.

    Tary, J. B., Herrera, R. H., Han, J. & van der Baan, M. Spectral estimation—What is new? What is next? Rev. Geophys. 52, 723–749 (2014).

  34. 34.

    Stoica, P. & Moses, R. in Spectral Analysis of Signals Ch. 3 (Prentice-Hall, Upper Saddle River, 2005).

  35. 35.

    Munteanu, C., Negrea, C., Echim, M. & Mursula, K. Effect of data gaps: comparison of different spectral analysis methods. Ann. Geophys. 34, 437–449 (2016).

  36. 36.

    Friedman, V. A zero crossing algorithm for the estimation of the frequency of a single sinusoid in white noise. IEEE Trans. Signal Process. 42, 1565–1569 (1994).

  37. 37.

    Strutz, T. Data Fitting and Uncertainty: A Practical Introduction to Weighted Least Squares and Beyond (Springer Vieweg, Weisbaden, 2016).

Download references


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

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

Competing interests

The authors declare no competing interests.

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

Supplementary information

  1. Supplementary Information

    Supplementary Figures 1–5, Supplementary references.

Rights and permissions

To obtain permission to re-use content from this article visit RightsLink.

About this article

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.