Radiation and TelescopesAST443, Lecture 4Stanimir Metchev2Administrative• Tonight’s lecture/lab– ESS 437A (back of coffee lounge)– Keys to ESS 437A• see Owen Evans (ESS 255, 2-8061)• $25 refundable deposit• Astronomy accounts• Homework 1:– Bradt, problems 3.22, 3.32, 4.22, 4.53– new due date: in class, Monday, Sep 143Outline• Electromagnetic radiation• Detection of light:– telescopes4Blackbody Radiation• Planck law– specific intensity– [erg s–1 cm–2 Hz–1 sterad–1] or [Jy sterad–1]– 1 Jy = 10–23 erg s–1 cm–2 Hz–1• Wien displacement law T λmax= 0.29 K cm• Stefan-Boltzmann law F = σ T 4– energy flux density– [erg s–1 cm–2]• Stellar luminosity– [erg s–1]• Inverse-square law L(r) = L* / r2! "=2#5k415c2h3= 5.67 $10%5erg cm–2 s–1 K–4! L*= 4"R*2#Teff4! I(",T) =2h"3c21eh"kT#15Blackbody RadiationTeff, Sun = 5777 K6Magnitudes• Stefan-Boltzmann Law: F = σ T 4[erg s–1 cm–2]• apparent magnitude: m = –2.5 lg F/F0– m increases for fainter objects!– m = 0 for Vega; m ~ 6 mag for faintest naked-eye stars– faintest galaxies seen with Hubble: m ≈ 30 mag• 109.5 times fainter than faintest naked-eye stars– dependent on observing wavelength• mV, mB, mJ, or simply V (550 nm), B (445 nm), J (1220 nm), etc• bolometric magnitude (or luminosity): mbol (or Lbol)– normalized over all wavelengths7Magnitudes and Colors• magnitude differences:– relative brightness of two objects at the same wavelengthV1 – V2 = –2.5 lg FV1/FV2• ∆m = 5 mag approx. equivalent to F1/F2 = 100– relative brightness of the same object at different wavelengths(color)B – V = –2.5 (lg FB/FV – lg FB,Vega/FV,Vega)– by definition Vega has a color of 0 mag at all wavelengths, i.e.(B – V)Vega = 0 mag8Magnitudes and Colors(Zuckerman & Becklin 1988)J H K2MASS1.2, 1.6, 2.2 µmcolor compositewhite/brown dwarf pairGD 165 A/B~10,000 K~2,200 K9Color of Blackbody Radiation10Extinction and Optical Depth• Light passing through a medium can be:– transmitted, absorbed, scattered• dLν(s) = –κν ρ Lν ds = –L dτν– medium opacity κν [cm2 g–1]– optical depth τν = κν ρs [unitless]• Lν = Lν,0e–τ = Lν,0e–κρs =Lν,0e–s/l– photon mean free path: lν = (κν ρ)–1 = s/τν [cm]• If there is extinction along the line of sight, apparent magnitudemν is attenuated by Aν = 2.5 lg (Fν,0/Fν) = 2.5 lg(e)τν = 0.43τν mag– reddening between two frequencies (ν1, ν2) or wavelengths isdefined asEν1,ν2 = mν1 – mν2 – (mν1 – mν2)0 [mag]– (mν1 – mν2)0 is the intrinsic color of the starAV / E(B–V) ≈ 3.011Interstellar Extinction Lawextinction is highest at ~100 nm = 0.1 µ munimportant for >10 µm12Interstellar Extinction: Dustvisible(0.5 micron)mid-infrared (~20 micron)13Atmospheric Extinction14source: Kitt Peak National Observatory15Photometric Bands: Visible16PhotometricSystems• UBVRI(ZY) (visible)– Johnson, Bessel, Cousins,Kron, etc• ugriz (visible)– Thuan-Gunn, Strömgren,Sloan Digital Sky Survey(SDSS), etc• JHKLM(NQ) (infrared)– Johnson, 2-micron All-SkySurvey (2MASS), MaunaKea Observatory (MKO), etc17Photometric Bands: Near-Infrared18Atmospheric Refractionn (3200 Å) = 1.0003049n (5400 Å) = 1.0002929n (10,000 Å) = 1.0002890differential atmosphericrefraction D between3200 Å and 5400 Å1920Outline• Electromagnetic radiation• Detection of light:– telescopes21Focusing• focal length (fL), focal plane• object size (α, s) in the focal planes = fL tan α ≈ fLα• plate/pixel scaleP = α/s = 1/fL– Lick observatory 3m• fL = 15.2m, P = 14″/mm22Energy and Focal Ratio• Specific intensity:– Planck law– [erg s–1 cm–2 Hz–1 sterad–1] or [Jy sterad–1]• Integrated apparent brightnessEp ∝ (d / fL)2 : energy per unit detector area• focal ratio: ℜ ≡ fL / d– “fast” (< f/3) vs. “slow” optics (>f/10)– fast data collection vs. larger magnificationmagnification = fL / fcamera! I(",T) =2h"3c21eh"kT#123Optical Telescope ArchitecturesAlso:• Schmidt-Cassegrain• spherical primary (sph. aberration), corrector plate; cheap for large FOV• no coma or astigmatism; severe field distortion• Ritchey-Chrétien• modified Cassegrain with hyperbolic primary and hyperbolic convex secondary• no coma; but astigmatism, some field distortion24Fraunhofer (Far-Field) Diffraction• constructive interference from plane-parallelwave-fronts diffracted by telescope apertures– Figure 5.6 in Bradt• spatial profile of intensity is FT of aperture– from Fraunhofer diffraction theory– intensity I on detector is square of amplitude of EMvector25Fraunhofer DiffractionCircular Aperture• Airy disk• Airy nulls at 1.220, 2.233,3.238, … λ/d• angular resolution–θmin ~ 1.22 λ/d• Rayleigh criterion• gives 74% drop in intensitybetween peaks– can do as little as ~80% of that• 3% drop in intensity betweenpeaks (Dawes criterion)! I(") =#r2J1(2m)m$ % & ' ( ) 2m =#r sin"*26Point Spread Function (PSF)27Imaging through a TurbulentAtmosphere: Seeing• FWHM of seeing disk–θseeing <1.0″ at a good site• r0: Fried parameter–θseeing = 1.2 λ/r0– r0 ∝ λ6/5 (cos z)3/5–θseeing ∝ λ–1/5• t0: coherence time– t0 = r0 / vwind– vwind ~ several m/s– t0 is tens of milli-sec28Walter et al. (2003)series of 0.7s integrations of3.1″ double star HD 28867A/Bafter shifting and co-adding:can see 1st Airy ringImaging through a TurbulentAtmosphere: Seeing29Adaptive Optics30Adaptive Optics31Adaptive
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