Using chromatic covariance to correct for scintillation noise in ground-based spectrophotometry

TL;DR

Atmospheric scintillation is the dominant, largely achromatic noise source in ground-based high-precision spectrophotometry of bright stars, limiting the achievable precision. The authors derive analytic expressions for the chromatic covariance of scintillation across two wavelengths on a large telescope, incorporating a turbulence profile $C_n^2(z)$, wind speed $w(z)$, wind direction $\theta(z)$, exposure time $\tau$, and airmass, for both short- and long-exposure regimes. They demonstrate a practical, data-driven pipeline to identify and remove scintillation using this covariance in a simulated exoplanet transit spectroscopy scenario, showing that scintillation can be suppressed below Poisson noise and biases across wavelength can be mitigated. The work provides a pathway to routinely achieve Poisson-limit precision for bright targets and outlines on-sky validation with the Henrietta spectrograph, with potential extensions such as time-varying covariance modeling and Gaussian Process methods to further improve robustness.

Abstract

Atmospheric scintillation is one of the largest sources of error in ground-based spectrophotometry, reducing the precision of astrophysical signals extracted from the time-series of bright objects to that of much fainter objects. Relative to the fundamental Poisson noise, scintillation is not effectively reduced by observing with larger telescopes, and alternative solutions are needed to maximize the spectrophotometric precision of large telescopes. If the chromatic covariance of the scintillation is known, it can be used to reduce the scintillation noise in spectrophotometry. This paper derives analytical solutions for the chromatic covariance of stellar scintillation on a large telescope for a given atmospheric turbulence profile, wind speed, wind direction, and airmass at optical/near-infrared wavelengths. To demonstrate how scintillation noise is isolated, scintillation-limited exoplanet transit spectroscopy is simulated. Then, a procedure is developed to remove scintillation noise and produce Poisson-noise limited light curves. The efficacy and limits of this technique will be tested with on sky observations of a new, high spectrophotometric precision, low resolution spectrograph.

Figures (10)

• Figure 1: Illustration of a ground-based (spectro)photometric noise budget. As a general rule, scintillation dominates the (spectro)photometric noise budgets in ground-based observations. Since it averages down slower than the photon noise ($D^{-2/3}$ vs. $D^{-1}$), scintillation will always prevent large telescopes from acting as true 'light buckets.'
• Figure 2: Illustration of dispersed wavefronts passing through layers of atmospheric turbulence. At the top of the atmosphere, all chromatic starlight enters undispersed. On the way from the top of the atmosphere to the telescope, chromatic wavefronts are dispersed and travel through layers of atmospheric turbulence. The direction of atmospheric dispersion (here, left to right on the page) introduces a preferential direction for the wind speed. When the wind blows in the direction of atmospheric dispersion, all wavefronts see nearly the exact same turbulence. However, when the wind blows perpendicular to the direction of atmospheric dispersion (cross-dispersed direction, here in/out of the page), there are always portions of each wavefront that are exposed to different regions of turbulence. This leads to the wavelength correlation of scintillation depending on the direction of the wind speed relative to the direction of atmospheric dispersion.
• Figure 3: How the covariance changes with exposure time and wind speed. For $w\tau < D$, the wind-direction does not influence the correlation between two wavefronts. This is because, when averaged over the telescope area, the area of turbulence that is common/normal to each wavefronts is the same. As $w \tau$ approaches and surpasses the telescope diameter, that the wind direction begins to play a role in the correlation coefficient. For completely perpendicular winds, the disjoint area grows as $\approx \rho w \tau$ whereas for parallel winds, the area is constant with exposure time.
• Figure 4: Comparing the parallel/perpendicular wind covariance weighting functions as a function of exposure time. The first $n=4$ terms of covariant weighting function, Equation \ref{['equation:longexposure_covariantweightingfunction_final']} are shown. The covariant weighting function is found by summing all terms together. The red curves represent the subtracted terms, and the blue curve represents the additive term. The covariant weighting function for perpendicular winds has a long-exposure slope equal to the variance/$n=0$ weighting function long-exposure slope. For parallel winds, the long-exposure covariance has a stronger slope leading to a larger covariance as the exposure time increases.
• Figure 5: Injected transmission spectra along with the recovered spectra prior to scintillation correction. Since scintillation is a nearly achromatic stochastic noise source, this adds the same bias to each spectrophotometric light curve, leading to a bias in the recovered transit spectra. This also causes the recovered radius ratio errors to appear inflated, since each light curve is fit independently without any knowledge of the covariance.