Radiation and Telescopes
AST443, Lecture 4
Stanimir Metchev
Administrative
• 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 14
2
Outline
• Electromagnetic radiation
• Detection of light:
– telescopes
3
Blackbody Radiation
2h" 3
1
I(" ,T) = 2 h" kT
c e
#1
• 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 T4
– energy flux density
– [erg s–1 cm–2]
2# 5 k 4
"=
= 5.67 $10%5 erg cm–2 s–1 K –4
2 3
15c h
• Stellar luminosity
L* = 4 "R*2#Teff4
– [erg s–1]
!
• Inverse-square law
L(r) = L* / r2
4
!
Blackbody Radiation
Teff, Sun = 5777 K
5
Magnitudes
• 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 wavelengths
6
Magnitudes and Colors
• magnitude differences:
– relative brightness of two objects at the same wavelength
V1 – 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 mag
7
Magnitudes and Colors
2MASS
white/brown dwarf pair
GD 165 A/B
J
H
K
(Zuckerman & Becklin 1988)
1.2, 1.6, 2.2 µm
color composite
~10,000 K
~2,200 K
8
Color of Blackbody Radiation
9
Extinction 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 magnitude
mν 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 is
defined as
Eν1,ν2 = mν1 – mν2 – (mν1 – mν2)0 [mag]
– (mν1 – mν2)0 is the intrinsic color of the star
AV / E(B–V) ≈ 3.0
10
Interstellar Extinction Law
extinction is highest at ~100 nm = 0.1 µm
unimportant for >10 µm
11
Interstellar Extinction: Dust
visible
(0.5 micron)
mid-infrared (~20 micron) 12
Atmospheric Extinction
13
source: Kitt Peak National Observatory
14
Photometric Bands: Visible
15
Photometric
Systems
• 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-Sky
Survey (2MASS), Mauna
Kea Observatory (MKO), etc
16
Photometric Bands: NearInfrared
17
Atmospheric Refraction
n (3200 Å) = 1.0003049
n (5400 Å) = 1.0002929
n (10,000 Å) = 1.0002890
differential atmospheric
refraction D between
3200 Å and 5400 Å
18
19
Outline
• Electromagnetic radiation
• Detection of light:
– telescopes
20
Focusing
• focal length (fL), focal plane
• object size (α, s) in the focal plane
s = fL tan α ≈ fLα
• plate/pixel scale
P = α/s = 1/fL
– Lick observatory 3m
• fL = 15.2m, P = 14″/mm
21
Energy and Focal Ratio
• Specific intensity:
2h" 3
1
I(" ,T) = 2 h" kT
c e
#1
– Planck law
– [erg s–1 cm–2 Hz–1 sterad–1] or [Jy sterad–1]
• Integrated apparent brightness
!
Ep ∝ (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 magnification
magnification = fL / fcamera
22
Optical Telescope Architectures
Also:
• 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 distortion
23
Fraunhofer (Far-Field) Diffraction
• constructive interference from plane-parallel
wave-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 EM
vector
24
Fraunhofer Diffraction
Circular Aperture
• Airy disk
• Airy nulls at 1.220, 2.233,
3.238, … λ/d
• angular resolution
$ #r 2 J1 (2m) ' 2
I(" ) = &
)
m
%
(
#r sin "
m=
*
– θmin ~ 1.22 λ/d
• Rayleigh criterion
!
• gives 74% drop in intensity
between peaks
– can do as little as ~80% of that
• 3% drop in intensity between
peaks (Dawes criterion)
25
Point Spread Function (PSF)
26
Imaging through a Turbulent
Atmosphere: 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-sec
27
Imaging through a Turbulent
Atmosphere: Seeing
series of 0.7s integrations of
3.1″ double star HD 28867A/B
after shifting and co-adding:
can see 1st Airy ring
Walter et al. (2003)
28
Adaptive Optics
29
Adaptive Optics
30
Adaptive Optics
31
Adaptive
Optics
32