On the properties of turbulence in the remnant of Tycho supernova

We investigate the turbulent structures in the Tycho supernova remnant (SNR) by applying two-point autocorrelation and power spectral analyses to high-resolution X-ray and radio images. Using cleaned Chandra and VLA data, we derive two-dimensional (2D) and one-dimensional (1D) autocorrelation functions and power spectra, revealing that the fluctuations in both X-ray brightness (approximately tracing plasma density) and radio brightness (tracing magnetic field strength) follow the power-law distributions consistent with Kolmogorov-type turbulence. Specifically, power spectra exhibit a slope $8/3$ in 2D and $5/3$ in 1D analyses, indicating fully developed turbulence across a broad range of spatial scales. The structure functions and spectral slopes remain robust with and without correction for line-of-sight integration effects, suggesting the presence of Kolmogorov-like turbulence locally throughout the remnant's volume. Anisotropies in the 2D autocorrelation function are aligned with known density and magnetic field gradients. Analysis of the 1D radial properties of turbulence confirms Kolmogorov scaling and indicates that modes in the power spectra may be related either to periodicity in the fluctuations or to the physical sizes of bright or dim features in the surface brightness. Our results demonstrate that the Tycho SNR hosts a spatially and temporally developed turbulent cascade, providing insight into the physics of turbulence in SNRs.