Bolometric night sky temperature and subcooling of telescope structures

¹ European Southern Observatory (ESO), Karl-Schwarzschild-Str. 2, 85748 Garching, Germany
e-mail: rholzloe@eso.org
² Institut für Astro- und Teilchenphysik, Leopold–Franzens Universität Innsbruck, Technikerstr. 25, 6020 Innsbruck, Austria
³ Instituto de Astronomía, Universidad Católica del Norte, Av. Angamos 0610, Antofagasta, Chile
⁴ Institut für Physik, Universität Augsburg, Universitätsstraße 1, Augsburg 86159, Germany
⁵ Deutsches Fernerkundungsdatenzentrum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), Münchener Straße 20, Weßling-Oberpfaffenhofen 82234, Germany

Received: 6 July 2020
Accepted: 2 October 2020

Abstract

Context. The term sky temperature is used in the literature to refer to different phenomena in different contexts which often leads to confusion. In this work, we study T_sky, the effective bolometric sky temperature at which a hemispherical black body would radiate the same power onto a flat horizontal structure on the ground as the night sky, integrated over the entire thermal wavelength range of 1–100 μm. We then analyze the thermal physics of radiative cooling with special focus on telescopes and discuss mitigation strategies.

Aims. The quantity T_sky is useful to quantify the subcooling in telescopes which can deteriorate the image quality by introducing an optical path difference (OPD) and induce thermal stress and mechanical deflections on structures.

Methods. We employ the Cerro Paranal Sky Model of the European Southern Observatory to derive a simple formula of T_sky as a function of atmospheric parameters. The structural subcooling and the induced OPD are then expressed as a function of surface emissivity, sky view factor, local air speed, and structure dimensions.

Results. At Cerro Paranal (2600m) and Cerro Armazones (3060m) in the Atacama desert, T_sky towards the zenith mostly lies 25–50 Kelvin below the ambient temperature near the ground, depending to a great extent on the precipitable water vapor column in the atmosphere. The temperature difference can decrease by several Kelvin for higher zenith distances. The subcooling OPD scales linearly to quadratically with the telescope diameter and is inversely proportional to the local air speed near the telescope structure.