Integral field spectroscopy supports atmospheric optics to reveal the finite outer scale of the turbulence

¹ Instituto de Astrofísica de Canarias, C/ Vía Láctea s/n, 38205 La Laguna, Tenerife, Spain
e-mail: begona.garcia@iac.es
² Departamento de Astrofísica, Universidad de La Laguna, 38200 La Laguna, Tenerife, Spain

Received: 23 October 2023
Accepted: 29 February 2024

Abstract

Context. The spatial coherence wavefront outer scale (ℒ₀) characterizes the size of the largest turbulence eddies in Earth’s atmosphere, determining low spatial frequency perturbations in the wavefront of the light captured by ground-based telescopes. Advances in adaptive optics (AO) techniques designed to compensate for atmospheric turbulence emphasize the crucial role of this parameter for the next generation of large telescopes.

Aims. The motivation of this work is to introduce a novel technique for estimating ℒ₀ from seeing-limited integral field spectroscopic (IFS) data. This approach is based on the impact of a finite ℒ₀ on the light collected by the pupil entrance of a ground-based telescope.

Methods. We take advantage of the homogeneity of IFS observations to generate band filter images spanning a wide wavelength range, enabling the assessment of image quality (IQ) at the telescope’s focal plane. Comparing the measured wavelength-dependent IQ variation with predictions derived from a first-order analytical approach based on turbulence statistics simplifications using the von Kármán model provides valuable insights into the prevailing ℒ₀ parameter during the observations. We applied the proposed technique to observations from the Multi-Unit Spectroscopic Explorer (MUSE) in the wide-field mode obtained at the Paranal Observatory.

Results. Our analysis successfully validates the first-order analytical expression, which combines the seeing (ε₀) and the ℒ₀ parameters, to predict the IQ variations with the wavelength in ground-based astronomical data. However, we observed some discrepancies between the measured and predictions of the IQ that are analyzed in terms of uncertainties in the estimated ε₀ and dome-induced turbulence contributions.

Conclusions. This work constitutes the empirical validation of the analytical expression for estimating IQ at the focal plane of ground-based telescopes under specific ε₀ and finite ℒ₀ conditions. Additionally, we provide a simple methodology to characterize the ℒ₀ and dome-seeing (ε_dome) as by-products of IFS observations routinely conducted at major ground-based astronomical observatories.