ATMOSPHERIC SPECTRAL DISPERSION

Dr. Wayne Bailey - CoordinatorLunar Topographic Studies/Selected Areas Program

wayne.bailey@alpo-astronomy.org

Dr. Anthony Cook - Coordinator Lunar Transient Phenomena

atc@aber.ac.uk

What is Atmospheric Dispersion?

• 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

• The difference between atmospheric refraction for various wavelengths of light

- Angle of refraction changes with zenith angle (z) therefore, image is distorted• Contrast:

Chromatic aberration changes size of image with λ

CharacteristicsFor 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

Atmospheric Refraction

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 59.671000 59.58

Where T0=273.15 K P0=1013.25x102 Pa

For other T,P Multiply R0 by (PT0)/P0T

R (arcsec) = R0tan(z) [z 80º]≦ = R0{2.06/[0.0589+(π/2-z)]-3.71} [z > 80º]

Dispersion = R(λ1) – R(λ2)

Both dispersion & rate of change of dispersion is greater for short λ than for long.

Cox, Arthur N. ed. Allen’s Astrophysical Quantities, 4th Ed. Springer-Verlag (AIP Press), New York, 2000. (ISBN 0-387-98746-0)

Direction of DispersionBasic dispersion direction is vertical Vertical is direction toward zenithWhat direction is vertical in image?Ephemeris provides position angle of lunar pole = angle between lunar axis and direction to north poleBut still need position angle of zenith

Position angle of zenith depends on: - Hour angle & declination of moon - Observer’s latitude

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 - αwhere:

p = position angle of zenith (+ from N toward E)φ = observer latitudeα,δ = right ascension, declinationh = hour angle (+ W of meridian)LST = observer’s local sidereal time = right ascension on the meridian

Example: Zenith Position Angle

from: http://www.noao.edu/kpno/manuals/l2mspect/node17.html

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

Spectral Dispersion in Our Atmosphere

Example: Star

from: http://www.paquettefamily.ca/astro/star_study/

Simulation: Spectral Dispersion

2004 Sep 02 UT 23:21 Plato image by Shaw - in the centre Surrounding images are with spectral dispersion in different directions

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

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! Monochrome

image with brightness gradient

Spectral dispersion in one direction – subtle blue tinge

Spectral dispersion in other direction – subtle red tinge

Effects of Gradients