Effects of earth’s atmosphere

1.     Limited wavelength ranges

·        Transparent (relatively) in optical, radio (and some infrared)

          =atmospheric “windows”

                    a.  Optical window : 300 nm to ~1.4 mm

b.     Radio window : 8 mm to ~15m

·    In addition to photons, atmosphere also stops energetic charged particles from space (“cosmic rays”)

Mainly P⁺ , e^-  ÞE ~ 10¹⁰~10²⁰ eV

     Atmosphere » 1 meter of lead

          If  v­­  , Þ v >    ( n = refractive index )

       Þ Čerenkov radiation

·        Even beyond earth’s atmosphere, there is absorption.

[ dust + gas ] in the solar system, in the interstellar medium,

in circum stellar medium.

a.      dust → strong absorption  in visual and UV

b.     gas  → strong absorption in EUV and soft X-ray                   

2.     Extinction (消光)

·        Absorption―photons are “destroyed”.

·        Scattering ―photon energy and direction redistributed

                                      ÞEffective absorption in the direction to the

                                          source.

         Why is the sky blue?

               Size of particles ≈ a

    (1) 2πa << λ (radio) Þ scattering ↔ λ

          I_scattering   λ^-4  ( Rayleigh scattering )

         ∴ Blue sky

    (2) 2πa >> λ  Þ scattering ≠ λ

         ∴ Gray sky in a cloudy day!

    (3) 2πa ≈ λ (dust, optical) Þ I_scattering   λ^-1

                                     Þ Interstellar reddening (紅化)

3.     Refraction

Sun/moon at zenith distance = 90∘(refraction ≈ 35’), but their sizes ≈ 30’, so when we seen center at horizon, they in fact are below the horizon.

4.     Curvature

          Curvature and refraction can be ignored if zenith distance ≦ 45∘

          If we ignore curvature and refraction,

          Atmosphere = a series of plane parallax layers, with thickness dz at

                                  height z.

          where κ= κ(z,λ)  : absorption coefficient

          If F₀ = flux outside atmosphere, then integrating z, we obtain flux at

          ground level (z=0)

           At the zenith (ζ=0)

          (Since )

           m_λ: observed from ground

          m₀ : would have observed outside atmosphere

           Δm₀ : absorption in terms of magnitude at zenith

           (cf. y = b + ax )

           So, m₀ and Δm₀  can be estimated by measuring m_λ(observable) at 

           different ζ(known).

           For ζ≧60∘, refraction and curvature have to be considered.

           Define similarly,

           For small ζ, M (ζ) ≈ secζ

           Otherwise → determine empirically Þlook-up table

           But air is not static Þ Try to observe as close to zenith as possible.

5.     Atmospheric turbulences also causes a stellar image to

―Blink (scintillation) ― variation of air mass along line of sight

―Move around (‘seeing’) ― variation of refractive index along

                                                line of sight

·        “seeing” (視相寧靜度) → a point source, after long exposures, is smeared into a ‘seeing’ disk.

     Typically, seeing (disk) ~ a few arcsec across

     Extended sources are not affected as much (∵averaged out)

     e.g. Planets θ~ 10”–30” would appear ‘steady’ but stars   

     (point sources) ‘twinkle’.

     Usually optical telescopes are seeing-limited.

·        At radio λ_s , with very small-scale turbulences, seeing/scintillation are not important.

     Radio telescopes are diffraction-limited.

     i.e. limited by the optics, rather than by atmosphere

·        Radio λ_s are affected by interplanetary and ISM scintillation.

     To overcome rapid scintillation

     ÞFast (high-time-resolutions) observations

·        Radio λ_sÞ Hewish in 1960s tried to study IS scintillation

                     Þ Discovered pulsars

     Optical λ_sÞ ‘speckle’ imaging