ATMOSPHERIC SPECTRAL DISPERSION

1. ATMOSPHERIC SPECTRAL DISPERSION Dr. Wayne Bailey - Coordinator Lunar Topographic Studies/Selected Areas Program wayne.bailey@alpo-astronomy.org Dr. Anthony Cook - Coordinator Lunar Transient Phenomena atc@aber.ac.uk

2. What is Atmospheric Dispersion? • The difference between atmospheric refraction for various wavelengths of light • Refraction of light passing at an angle through the atmosphere raises the image - Index of refraction changes with wavelength (λ) therefore, angle of refraction changes with λ (Snell’s law) i.e. image position changes with λ - Angle of refraction changes with zenith angle (z) therefore, image is distorted • Contrast: Chromatic aberration changes size of image with λ

3. Characteristics For atmosphere that depends only on height - dispersion is vertical - Size of dispersion depends on atmospheric properties (T, P, ρ, H2O) Horizontal differences in atmosphere - modify direction and/or amount of dispersion - direction of density gradient determines effect horizontal gradient rotates direction of dispersion vertical gradient changes amplitude of dispersion

4. Atmospheric Refraction R (arcsec) = R0tan(z) [z ≦ 80º] = R0{2.06/[0.0589+(π/2-z)]-3.71} [z > 80º] λ (nm) R0(arcsec) 400 61.46 450 60.97 500 60.64 550 60.39 600 60.20 650 60.06 700 59.94 800 59.77 900 59.67 1000 59.58 Dispersion = R(λ1) – R(λ2) Both dispersion & rate of change of dispersion is greater for short λ than for long. Where T0=273.15 K P0=1013.25x102 Pa For other T,P Multiply R0 by (PT0)/P0T Cox, Arthur N. ed. Allen’s Astrophysical Quantities, 4th Ed. Springer-Verlag (AIP Press), New York, 2000. (ISBN 0-387-98746-0)

5. Direction of Dispersion Basic dispersion direction is vertical Vertical is direction toward zenith What direction is vertical in image? Ephemeris provides position angle of lunar pole = angle between lunar axis and direction to north pole But still need position angle of zenith Position angle of zenith depends on: - Hour angle & declination of moon - Observer’s latitude

6. Position Angle of Zenith sin(p) = cos(φ) sin(h) / sin(z) cos(p) = [sin (φ) – cos(z) sin(δ)] / [sin(z) cos (δ)] cos(z) = sin (φ) sin(δ) + cos(φ) cos (δ) cos(h) h = LST - α where: p = position angle of zenith (+ from N toward E) φ = observer latitude α,δ = right ascension, declination h = hour angle (+ W of meridian) LST = observer’s local sidereal time = right ascension on the meridian

7. Example: Zenith Position Angle from: http://www.noao.edu/kpno/manuals/l2mspect/node17.html

8. Spectral Dispersion in Our Atmosphere In the 1970’s Lawrence Fitton, of the BAA Lunar Section, proposed that you could also get atmospheric spectral dispersion, not just along the perpendicular to the horizon, but also when there was a pressure gradient from a pressure system moving across the line of sight. It was speculated too that inversion layers in our atmosphere could also induce spectral dispersion. So, if this is the case, then it might be possible to have summation of spectral dispersion effects, in different directions – here is a simulation below.... Note we cannot make presumptions about the amount of spectral dispersion from these Fitton effects, nor how many spectra dispersions will be mixed, or their angles, it all depends upon which layers in the atmosphere are causing the dispersion

9. Example: Star from: http://www.paquettefamily.ca/astro/star_study/

10. Simulation: Spectral Dispersion Fitton in the 1970’s proposed that many coloured TLP were just due to spectral dispersion and that spectral dispersion could occur in non-vertical directions (wrt horizon) from differential pressure due to pressure systems moving across the observing site Sheenan and Dobbins (1990’s) in their sky and telescope article revised this theory by suggesting that Rayleigh scattering towards the blue end of the spectrum makes blue glows more difficult to see due to lower image contrast in the blue, hence why we sometimes see red but no corresponding blue 2004 Sep 02 UT 23:21 Plato image by Shaw - in the centre Surrounding images are with spectral dispersion in different directions

11. Effects of Gradients Spectral dispersion, although producing strong colour fringes on light/dark edges, can also produce subtle hints of colour on brightness gradients too. Note that this will not work if there is a uniform grey scale, only if there is a brightness gradient e.g. Towards the terminator on a mare region. Also the gradient must be in the same direction as the spectral dispersion, else it won’t work! Spectral dispersion in one direction – subtle blue tinge Monochrome image with brightness gradient Spectral dispersion in other direction – subtle red tinge