The Grand Power Law of turbulence in the Milky Way from in situ observations of Voyager 1

The electron density power spectrum with scales of 50m to 15au in the local interstellar medium is obtained from in situ observations of Voyager 1. By combining the in situ data with the earlier ground remote observations, we now have the turbulent spectrum extending from 50m to 100 light-years, over 16 orders of magnitude.
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The Grand Power Law of turbulence in the Milky Way from in situ observations of Voyager 1

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  The sun emits high-speed flows of protons and electrons, i.e., the solar wind, leading to the formation of heliosphere. As shown in Figure 1b, the heliopause separates the solar wind from the interstellar medium. The solar wind is supersonic inside the termination shock and subsonic outside the termination shock. The interstellar space refers to the huge gaps between stars, and the matter that fills in such space is the interstellar medium. The interstellar medium consists of mostly molecular, atomic and ionized hydrogen particles. Unlike neutral fluids in hydrodynamics (HD), the motion of charged particles is highly influenced by the magnetic field that resides in the interstellar space and the heliosphere. The study of the fluid dynamics of such magnetized and ionized matter is called magnetohydrodynamics (MHD).

Figure 1 (a) Frequency-time dynamic spectrum of electric field measured by Voyager 1 from 2012 to 2016. (b) An illustration of the heliosphere and the trajectories of Voyager 1 and Voyager 2. The heliopause separates the heliosphere and the interstellar medium.

  In 1941, Kolmogorov proposed the first hydrodynamic turbulence model and gave the well-known power law index, -11/3, of energy spectrum. On the other hand, the first MHD turbulence model was proposed by Iroshnikov (1963) and Kraichnan (1965) individually, while that proposed by Goldreich and Sridhar (1995) is the most widely discussed.

  In 1976, Lee and Jokipii first suggested that the interstellar turbulence at the length scale λ of 108m to 1018m (100 light-years) also has a Kolmogorov-like spectrum based on observations of radio wave scintillations and interstellar clouds. The scintillations of pulsar radio wave by interstellar turbulent electrons provide the turbulence power at the scale λ=108m, and the observations of interstellar clouds provide the turbulence power at λ=1018m. The slope of the line connecting the powers in logarithmic scale at λ=108m and at λ=1018m is about -11/3 (Figure 2a). Many later ground observations confirmed this speculation. Armstrong et al. (1995) constructed the composite spectrum extending from 106.4m to 1018m, a.k.a. the Big Power Law in the sky, based on several observational results (Figure 2b). Chepurnov and Lazarian (2010) obtained the spectrum at the scale of 1016m-1018m. So far the observational techniques for interstellar turbulence were all based on remote observations, such as measuring the scintillation of radio waves propagating through the interstellar medium. Also, the length scale of the spectrum obtained in these studies only covered the inertial range (106m-1018m).

Figure 2 Interstellar turbulence spectra: (a) the Kolmogorov spectrum suggested by Lee & Jokipii (1976), (b) the Big Power Law by Armstrong et al. (1995), (c) the in situ spectrum obtained from Voyager 1 by Lee & Lee (2018), and (d) The Grand Power Law from combination of the ground remote observations (Armstrong et al., 1995; Chepurnov and Lazarian, 2010) and satellite in situ observations (Lee & Lee, 2018).

  In 1977, two satellites named Voyager 1 & 2 were launched. The early objective was to study the solar wind, Jupiter and Saturn as well as other planets inside the heliosphere. Owing to the surprisingly good condition in the power supply and the scientific equipment of Voyagers, the mission was extended to the exploration of the interstellar medium. Voyager 1 entered the local interstellar medium in 2012 and traveled more than 23 astronomical units beyond the heliopause to date (Figure 1b). Recently, NASA announced that Voyager 2 crossed the outer edge of the heliosphere and entered the interstellar medium on 2018 November 5. Thanks to the Voyager science team, we can now use the data from in situ measurements in the local interstellar medium.

  Although the plasma density instrument onboard Voyager 1 was shut down in 2007, we can still use the plasma waves measured by the plasma wave instrument to infer the plasma density and construct the density profiles (Figure 1a). The density profiles are then used to determine the spectrum of the turbulent density fluctuations from 50m to 2.25x1012m (15 au) as shown in Figure 2c.

  For the length scale of 106m to 2.25x1012m, lying within the inertial range, our results (red, blue and green dots in Figure 2d) show great consistency with earlier remote observations. We can also obtain the turbulence spectrum at finer scales of ion and electron kinetic range (purple and part of green dots in Figure 2c), and the data show an interesting result with an enhanced spectral power (illustrated by the dashed orange curve in Figure 2c). Similar spectral bulge in the kinetic range has also been observed in the solar wind, and a few theoretical explanations were proposed, including the local ion wave instability and the kinetic Alfvén wave cascade, and may be related to the shocks of solar origin propagating in the local interstellar medium.

  By combining our in situ measured spectrum and the earlier remote observed data, we now obtain the composite spectrum, the Grand Power Law in the Milky Way, extending from 50m to 1018m (100 light-years), over 16 orders of magnitude in length scale. Yet the debate of theoretical models of the interstellar MHD turbulence is not settled. The observational results, especially in situ measurements, can provide a verification of theoretical models in the inertial and kinetic ranges. The results are published in Nature Astronomy (K. H. Lee and L. C. Lee, 2018 December 31).

Written by Kun-Han Lee and Lou-Chuang Lee.


Armstrong, J. W., Cordes, J. M., & Rickett, B. J., Nature 291, 561 (1981).
Chepurnov, A. & Lazarian, A., Astrophys. J. 710, 853 (2010).
Goldreich, P. & Sridhar, S., Astrophys. J. 438, 763 (1995).
Iroshnikov, P. S., Astronomicheskii Zhurnal 40, 742 (1963).
Kolmogorov, A. N., Dokl. Akad. Nauk SSSR 30 4, 299 (1941).
Kraichnan, R. H., Phys. Fluids 8, 1385 (1965).
Lee, L. C. & Jokipii, J. R., Astrophys. J. 206, 735 (1976).
Lee, K. H. & Lee, L. C., Nature Astronomy (2018)

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