Recovering turbulent velocity statistics from noisy integral-field spectroscopy
Turbulence plays a critical role in the evolution of H II regions, yet recovering its statistical properties from observations remains challenging, particularly when centroid velocities are affected by instrumental noise. We present a methodology for recovering the second-order velocity structure function from intermediate spectral-resolution integral-field spectroscopy and apply it to VLT MUSE observations of the Orion Nebula. The plane-of-sky velocity field is characterized by fitting a simple parametric model to the observed structure function, allowing the turbulent velocity variance, correlation length, power-law slope, and noise level to be estimated simultaneously. We investigate the trade-off between instrumental noise and spatial resolution through systematic spatial binning and validate the recovered turbulent parameters against previously analyzed high spectral-resolution KPNO echelle observations. We find that spatial binning improves the empirical structure function provided that the bin size remains below approximately $0.05 r_0$, while the fitted model recovers consistent turbulent parameters across all binning levels. The MUSE results agree closely with those from the KPNO data, demonstrating that intermediate-resolution integral-field spectroscopy can recover reliable turbulence statistics despite its relatively poor velocity resolution. We also identify modest but systematic differences in the turbulent properties traced by emission lines of different ionization potential, reflecting the geometric and ionization structure of the nebula. Our methodology provides a robust framework for extracting turbulent velocity statistics from noisy integral-field spectroscopic observations.