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.
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
Lee, L. C. & Jokipii, J. R. Strong scintillations in astrophysics. III. The fluctuations in intensity. Astrophys. J. 202, 439–453 (1975).
Lee, L. C. & Jokipii, J. R. The irregularity spectrum in interstellar space. Astrophys. J. 206, 735–743 (1976).
Armstrong, J. W., Cordes, J. M. & Rickett, B. J. Density power spectrum in the local interstellar medium. Nature 291, 561–564 (1981).
Armstrong, J. W., Rickett, B. J. & Spangler, S. R. Electron density power spectrum in the local interstellar medium. Astrophys. J. 443, 209–221 (1995).
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).
Scarf, F. L. & Gurnett, D. A. A plasma wave investigation for the Voyager mission. Space Sci. Rev. 21, 289–308 (1977).
Gurnett, D. A. et al. Precursors to interstellar shocks of solar origin. Astrophys. J. 809, 121 (2015).
Marple, S. L. in Digital Spectral Analysis Ch. 7 (Prentice-Hall, Upper Saddle River, 1987).
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).
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).
Huang, N. E. et al. On instantaneous frequency. Adv. Adapt. Data Anal. 1, 177–229 (2009).
Lomb, N. R. Least-squares frequency analysis of unequally spaced data. Astrophys. Space Sci. 39, 447–462 (1976).
Tatarski, V. I. in Wave Propagation in a Turbulent Medium 17 (McGraw-Hill, New York, 1961).
Larson, R. B. Stellar kinematics and interstellar turbulence. Mon. Not. R. Astron. Soc. 186, 479–490 (1979).
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).
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).
Burlaga, L. F., Florinski, V. & Ness, N. F. In situ observations of magnetic turbulence in the local interstellar medium. Astrophys. J. 804, L31 (2015).
Sridhar, S. & Goldreich, P. Toward a theory of interstellar turbulence. 1: weak Alfvénic turbulence. Astrophys. J. 432, 612–621 (1994).
Goldreich, P. & Sridhar, S. Toward a theory of interstellar turbulence. 2: strong Alfvénic turbulence. Astrophys. J. 438, 763–775 (1995).
Neugebauer, M. The enhancement of solar wind fluctuations at the proton thermal gyroradius. J. Geophys. Res. 80, 998–1002 (1975).
Kellogg, P. J. & Horbury, T. S. Rapid density fluctuations in the solar wind. Ann. Geophys. 23, 3765–3773 (2005).
Alexandrova, O., Carbone, V., Veltri, P. & Sorriso-Valvo, L. Small-scale energy cascade of the solar wind turbulence. Astrophys. J. 674, 1153–1157 (2008).
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).
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).
Šafránková, J. et al. Solar wind density spectra around the ion spectral break. Astrophys. J. 803, 107 (2015).
Neugebauer, M., Wu, C. S. & Huba, J. D. Plasma fluctuations in the solar wind. J. Geophys. Res. 83, 1027–1034 (1978).
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).
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).
Tsurutani, B. T. et al. Lion roars and nonoscillatory drift mirror waves in the magnetosheath. J. Geophys. Res. 87, 6060–6072 (1982).
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).
Claerbout, J. F. in Fundamentals of Geophysics Data Processing Ch. 7.2 (McGraw-Hill, New York, 1976).
Marple, S. L. Frequency resolution of Fourier and maximum entropy spectral estimates. Geophysics 47, 1303–1307 (1982).
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).
Stoica, P. & Moses, R. in Spectral Analysis of Signals Ch. 3 (Prentice-Hall, Upper Saddle River, 2005).
Munteanu, C., Negrea, C., Echim, M. & Mursula, K. Effect of data gaps: comparison of different spectral analysis methods. Ann. Geophys. 34, 437–449 (2016).
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).
Strutz, T. Data Fitting and Uncertainty: A Practical Introduction to Weighted Least Squares and Beyond (Springer Vieweg, Weisbaden, 2016).
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
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
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
About this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41550-018-0650-6
- Springer Nature Limited
This article is cited by
-
Turbulence in the Outer Heliosphere
Space Science Reviews (2022)
-
Persistent plasma waves in interstellar space detected by Voyager 1
Nature Astronomy (2021)
-
Fluid and kinetic aspects of magnetic reconnection and some related magnetospheric phenomena
Reviews of Modern Plasma Physics (2020)