AST 443 / PHY 517 The Atmosphere Atmospheric Refrac;on. I • Light refracts as it passes through a medium with a varying index of refrac;on n. • In air, n decreases with height from 1.000297 (STP) to 1.000 (vacuum) – – – – Let y (horizontal) and z (ver;cal) axes have origin on the Earth's surface. An incoming photon is detected at a zenith angle α. The curvature of the photon's path K = cos(α) dα/dz Solve using Fermat’s Principle (least 'me) – see Schroeder’s Astronomical Op;cs, chapter 3 Z n=1.00000 n=1.000297 Y Fermat’s Principle • Op;cal path length (OPL) = ct • d(OPL) = c dt =(c/v) vdt = nds • OPL = c∫dt = ∫nds • n: index of refrac;on (≡c/v) • To trace the path of a light ray, minimize OPL Atmospheric Refrac;on. II • Fermat’s principle: cos(α)dn/dy -­‐ sin(α)dn/dz -­‐n cos(α) dα/dz =0 • Since cos(α) dα/dz = K, nK = cos(α)dn/dy -­‐ sin(α)dn/dz – If dn = 0, K=0 and there is no curvature. – In a plane-­‐parallel atmosphere, dn/dy = 0 and n=n(z) • nK = n cos(α) dα/dz = -­‐ sin(α) dn/dz -­‐> n dα/dz = -­‐ tan(α) dn/dz – dn is small, α is almost constant, so integra;ng over dz -­‐> dα = -­‐tan(α0) dn. – For dn>0, dα<0. The ray is bent towards the zenith (the star appears higher in the sky than it actually is). – For <α0 = 45o, dα = -­‐0.00029 rad, or about 1 arcmin. • n is wavelength dependent, increasing from 1.0002890 at 1 micron to 1.0003049 at 3200 Angstroms. This leads to differen;al refrac;on. – At 2 airmasses (α0 = 60o) the 3200A image appears 6" above the 5400A image. – The shic is 2.5" at 45o and 13" at 75o. • If using a slit spectrograph in the blue, do not guide on the red image while at high airmass, or make sure that the slit is aligned along the parallac;c angle! Seeing. I • Ideal performance requires parallel wavefronts. • Varia;ons in n distort wavefronts • Varia;ons in n are caused by temperature differences or turbulence. • Under adiaba;c condi;ons, dn ∝ 2dT P/T2 – P: atmospheric pressure – T: atmospheric temperature • The changes in n lead to speckles, or defocussing of the image. Seeing. II • Coherence length r0: the distance over which the wavefront remains coherent (the change in phase is < one radian). • r0 ∼ λ1.2(cos(z))0.6 – z: zenith distance. – A telescope with an aperture smaller than r0 will be diffrac;on limited. • At a good sight (laminar airflow), such as a mountaintop in the middle of the ocean, r0 ∼10 cm at 5500 Angstroms. • The atmosphere acts as a series of incoherent lenses of aperture r0: λ/r0 is ~ the diameter of the seeing disk. – The ra;o of the seeing disk to the Rayleigh criterion at zenith is D/24 (5500A/
λ)1.2 cm. – An op;cal telescope smaller than about 25 cm is diffrac;on limited; larger telescopes are seeing-­‐limited. – In the 2.2 μm K band), telescopes are diffrac;on-­‐limited up to about 3 m diameter. – In the near-­‐IR, much of the seeing can be compensated for by using ac;ve or adap;ve op;cs, permiong diffrac;on-­‐limited imaging in the 8m VLT and 10m Keck telescopes. • Telescopes in space (above 25 km al;tude) are never seeing-­‐limited. Seeing. III • Images from SMARTS 1.3m/Andicam. • V band • 0.369″pixels • Upper image: σ=8.1″FWHM=9.5″ • Lower image: σ=0.8″FWHM=1.0″ Seeing. IV • Seeing at K: – 0.7 sec integra;ons – a= 3.1 arc. – The slow dric is poor tracking • Shiced and co-­‐added image: