The Error Estimation of Transverse Coronal Loop Oscillation Parameters Based on Least Chi-squares Fitting

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Abstract
Transverse oscillations of coronal loops not only influence coronal dynamics, but also provide a new perspective for coronal detection. To enhance their exploitation and utilization, accurately estimating the oscillation parameters is crucial. The least chi-squares fitting is a widely employed method for this estimation. However, due to the highly nonlinear nature of the fitting process, there is no established theory to provide the exact error of the fitted parameters. In this study, we systematically investigated the accuracy and precision of the fitted parameters of transverse coronal oscillations through a series of forward simulations. Our investigation indicates that the accuracy and precision of fitted oscillation parameters are influenced not only by the standard deviation of the measurement error, but also by the temporal resolution and the characteristics of the signal itself. Based on these findings, we conducted additional forward simulations to estimate the influences on the real observation examples. The results clearly show that (1) the fitted damping timescale should be overestimated in a significant number of transverse coronal loop oscillations, and (2) errors estimated by the general method may be biased. In response, we have developed a forward simulation-based schema to achieve a self-consistent error estimation for the fitted oscillation parameters. These contributions not only offer valuable insights into the error estimation of fitted transverse coronal oscillation parameters, but also establish a robust foundation for obtaining accurate and precise transverse oscillation parameters of the corona.
Funding Information
  • The Project of Central Plains Science and Technology Innovation Leading Talents of Henan Province (244200510012)
  • National Scientific Foundation of China (42104158)
  • National Scientific Foundation of China (12203020)
  • National Scientific Foundation of China (42174202)
  • National Scientific Foundation of China (42474211)
  • Natural Science Foundation of Henan Province (242300420260)
  • Scientific Research Project in Universities of Henan Province (25IRTSTHN014)

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