Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

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.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

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.

Similar content being viewed by others

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.

References

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

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

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  Google Scholar 

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

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

Download references

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 and Affiliations

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.

Additional information

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

Supplementary information

Supplementary Information

Supplementary Figures 1–5, Supplementary references.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41550-018-0650-6

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing