Refractive index of humid air in the infrared: model fits

Abstract

The theory of summation of electromagnetic line transitions is used to tabulate the Taylor expansion of the refractive index of humid air over the basic independent parameters (temperature, pressure, humidity, wavelength) in five separate infrared regions from the H to the Q band at a fixed percentage of Carbon Dioxide. These are least-squares fits to raw, highly resolved spectra for a set of temperatures from 10 to 25 • C, a set of pressures from 500 to 1023 hPa, and a set of relative humidities from 5 to 60%. These choices reflect the prospective application to characterize ambient air at mountain altitudes of astronomical telescopes. The paper provides easy access to predictions of the refractive index of humid air at conditions that are typical in atmospheric physics, in support of ray tracing [5] and astronomical applications [4,16,47,50] until experimental coverage of the infrared wavelengths might render these obsolete. The approach is in continuation of earlier work [46] based on a more recent HITRAN database [60] plus more precise accounting of various electromagnetic effects for the dielectric response of dilute gases, as described below.The literature of optical, chemical and atmospheric physics on the subject of the refractive index of moist air falls into several categories, sorted with respect to decreasing relevance (if relevance is measured by the closeness to experimental data and the degree of independence to the formalism employed here):1. experiments on moist air in the visible [3,9,18,53 [42,61,79] and eventually in the static limit [24], the refractive index plotted as a function of wavelength is more and more structured by individual lines. Since we will not present these functions at high resolution but smooth fits within several bands in the infrared, their spiky appearance sets a natural limit to the far-IR wavelength regions that our approach may cover. II. DIELECTRIC MODEL A. MethodologyThe complex valued dielectric function n(ω) of air n = 1 +χ (1) is constructed from molecular dynamical polarizabilitiesN m are molecular number densities, S ml are the line intensities for the transitions enumerated by l. ω 0ml are the transition angular frequencies, Γ ml the full linewidths at half maximum. c is the velocity of light in vacuum, and i the imaginary unit. The line shape (2) adheres to the complex-conjugate symmetry χ m (ω) = χ * m (−ω), as required for functions which are real-valued in the time domain. The sign convention of Γ ml merely reflects a sign choice in the Fourier Transforms and carries no real significance; a sign in the Kramers-Kronig formulas is bound to it. The integrated imaginary part is [28] whereν = k/(2π) = ω/(2πc) = 1/λ is the wavenumber.

VLT/NACO astrometry of the HR 8799 planetary system

“…Next, we used the model fits for the refractive index of humid air in the infrared as computed by Mathar (2007) to estimate the amplitude of differential atmospheric refraction of HR 8799 and its exoplanets. We found that this effect caused a shift of ≈5−6 mas of the planet positions along the parallactic angle.…”

ARTS, the Atmospheric Radiative Transfer Simulator – version 2.2, the planetary toolbox edition

“…For Earth's atmosphere, commonly empirical parameterizations are applied that summarize the air, or at least its dry part, into one component scaled by the total pressure. Water vapor is often considered as a separate component due to its different reference refractivity and its strong variability in abundance (e.g., Thayer, 1974;Mathar, 2007). With N ref,i being specific to the gas species and varying notably between different species, it is obvious that further refined or generalized models are necessary when atmospheric composition is fundamentally different from Earth.…”

KIC 4150611: a rare multi-eclipsing quintuple with a hybrid pulsator

“…Finally, we applied corrections for the atmospheric refraction, using the method described in Hełminiak (2009), assuming monochromatic refraction at the effective wavelength of a given filter, and calculating the refractive index n with the method of Mathar (2004Mathar ( , 2007. For the atmospheric conditions (outside temperature, air pressure and humidity) we either used the values listed in the headers of files downloaded from KOA, or (for our own observations) we checked them in the KOA Ancillary Weather Data service 5 .…”