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Tphysicsletters/6698/10/1490/987680tpl/Measurement of the scaling slope of compressible magnetohydrodynamic turbulence by synchrotron radiation statistics
Thursday, June 29, 2023 at 1:30:00 PM UTC
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Measurement of the scaling slope of compressible magnetohydrodynamic turbulence by synchrotron radiation statistics
Xue-Wen Zhang,1
Jian-Fu Zhang,1,2★
Ru-Yue Wang 1
Fu-Yuan Xiang1,2†
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1Department of Physics, Xiangtan University, Xiangtan 411105, China,
2Key Laboratory of Stars and Interstellar Medium, Xiangtan University, Xiangtan 411105, China
ACKNOWLEDGMENTS
We thank the anonymous referee for valuable comments that significantly improved the quality of the paper. J.F.Z. thanks to the support from the National Natural Science Foundation of China (grant Nos. 11973035), the Hunan Province Innovation Platform and Talent Plan-HuXiang Youth Talent Project (No. 2020RC3045), and the Hunan Natural Science Foundation for Distinguished Young Scholars (No. 2023JJ10039). F.Y.X. acknowledges the support from the Joint Research Funds in Astronomy U2031114 under a cooperative agreement between the National Natural Science Foundation of China and the Chinese Academy of Sciences.
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ABSTRACT
Based on magnetohydrodynamic turbulence simulations, we generate synthetic synchrotron observations to explore the scaling slope of the underlying MHD turbulence. We propose the new 𝑄-𝑈 cross intensity 𝑋 and cross-correlation intensity 𝑌 to measure the spectral properties of magnetic turbulence, together with statistics of the traditional synchrotron 𝐼 and polarization 𝑃𝐼 intensities. By exploring the statistical behaviour of these diagnostics, we find that the new statistics 𝑋 and 𝑌 can extend the inertial range of turbulence to improve measurement reliability. When focusing on different Alfvénic and sonic turbulence regimes, our results show that the diagnostics proposed in this paper not only reveal the spectral properties of the magnetic turbulence but also gain insight into the individual plasma modes of compressible MHD turbulence. The synergy of multiple statistical methods can extract more reliable turbulence information from the huge amount of observation data from the Low- Frequency Array for Radio astronomy and the Square Kilometer Array.
INTRODUCTION
The magnetized turbulent fluids in astrophysical environments can be usually described by magnetohydrodynamic (MHD) turbulence theory, which plays a critical role in many astrophysical processes such as star formation (Mac Low & Klessen 2004), heat conduction (Narayan & Medvedev 2001), magnetic reconnection (Beresnyak 2017), and acceleration of cosmic rays (Yan & Lazarian 2008; Zhang & Xiang 2021; Zhang et al. 2023). Therefore, studying the properties of MHD turbulence helps to advance the theory of MHD turbulence and to understand astrophysical processes associated with MHD turbulence. Here, we briefly describe three significant advances made in earlier research on turbulence. The first is about incompressible nonmagnetized turbulence. By using a self-similarity assumption of the turbulence cascade, Kolmogorov (1941, henceforth K41) derived a power-law relation of 𝐸(𝑘) ∼ 𝑘−5/3 in the inertial range, which is called a classic Kolmogorov spectrum. The second is about incompressible magnetized turbulence. Iroshnikov & Kraichnan (1963; 1965, henceforth IK65) obtained the power-law scaling of 𝐸(𝑘) ∼ 𝑘−3/2 in the inertial range by introducing nonlinear energy cascade. Although IK65 advanced the K41 theory by considering the effect of magnetic fields, it ignored a critical issue that the turbulence should be anisotropic in the magnetized fluids (Montgomery & Turner 1981). The third is still about incompressible magnetized turbulence but focuses on the anisotropy of MHD turbulence due to turbulent magnetic fields. Focused on the nonlinear energy cascade of incompressible strongMHDturbulence, Goldreich&Sridhar power-law scaling and anisotropic relationship, as described in moredetail in Section 2.1. At present, many numerical simulations have significantly increased our knowledge on the scaling, anisotropy and compressibility of MHD turbulence (e.g., Cho & Lazarian 2002; see textbook by Beresnyak & Lazarian 2019; and a recent review by Beresnyak 2019 ). The properties obtained by the simulation ofMHDturbulence can understand the acceleration and propagation of cosmic rays (Yan & Lazarian 2002). In particular, the turbulent reconnection model proposed in Lazarian & Vishniac (1999, hereafter LV99), which provides a new interpretation for GS95 theory from the perspective of eddies, has been applied to various astrophysical environments such as gamma-ray bursts (Lazarian et al. 2003; Zhang & Yan 2011), microquasars (de Gouveia dal Pino & Lazarian 2005), active galactic nuclei (Kadowaki et al. 2015) and radio galaxies (Brunetti & Lazarian 2016). Due to the large scale of astrophysical system with a high Reynolds number 𝑅e > 1010, it is challenging to simulate a realistic astrophysical environment by direct numerical simulation. The currently available 3D MHD simulations can achieve the case of the Reynolds number 𝑅e ≃ 105 (e.g., Beresnyak & Lazarian 2019). A distinctive feature is that the realistic inertial range in astrophysical turbulence is much greater than that revealed by numerical simulations. It is more effective to move away from direct numerical simulations and develop statistical techniques using observational data, to explore the properties of MHD turbulence.
CONCLUSION
In this paper, we proposed two new synchrotron diagnostics: the cross intensity 𝑋 and cross-correlation intensity𝑌 to reveal theMHD turbulence properties. Using their PS and SF together with traditional diagnostics 𝑃𝐼 and 𝐼, we have well understood the spectral properties of the underlying compressible MHD turbulence. We focused on exploring how Mach numbers, noise, Faraday depolarization, and numerical resolution affect the spectral measurement of magnetic turbulence. The main results are summarized as follows.
• The SF of statistics 𝑋, 𝑌, 𝑃𝐼, and 𝐼 can determine the scaling slope of MHD turbulence in sub-Alfvénic regimes. Interestingly,new statistics 𝑌 could better measure the scaling slope compared with other statistics 𝑋, 𝑃𝐼, and 𝐼 in the different Alfvénic regimes.
• The noise does not impede the recovery of the scaling index of MHD turbulence, and the inertial range of PS measured by 𝑋 is wider than that by 𝑃𝐼 and 𝑌 at the same noise level.
• In the case of moderate Faraday depolarization, they still improve the scaling slope measurements since the statistics 𝑋 and 𝑌 extend the inertial range. The influence of numerical resolution does not change our conclusions.
• The change of angle between the mean magnetic field and the LOS does not affect the measurement of the scaling index, but the inertial range and amplitude.
• Using the synchrotron radiation diagnostics (𝑋, 𝑌 and 𝑃𝐼) can measure the spectral properties of Alfvén, slow and fast modes.
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