Overview of Astronomical Concepts
I. Radiation, Magnitudes, Distances
PHY 688, Lecture 3
Stanimir Metchev
Outline
• Radiation
– blackbody radiation, luminosity
– magnitudes, colors
– extinction, optical depth
• Detection and Measurement of Light
– Earth’s atmosphere, photometric bands
– detectors
• Astronomical yardsticks
– parallax
– absolute magnitude, distance modulus
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Blackbody Radiation
• Planck’s 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
• Stefan-Boltzmann law
T λmax= 0.29 K cm
F = σ T4
– energy flux density
– [erg s–1 cm–2]
• Stellar luminosity
2# 5 k 4
"=
15c 2 h 3
L* = 4 "R*2#Teff4
!
– [erg s–1]
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!
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Blackbody Radiation
Teff, Sun = 5777 K
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The Dreaded Magnitudes
• Stefan-Boltzmann Law:
• apparent magnitude:
F = σ T4
[erg s–1 cm–2]
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
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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
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Magnitudes and Colors
2MASS
GD 165 A/B
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J
H
K
PHY 688,
Lecture
3
(Zuckerman
& Becklin
1988)
1.2, 1.6, 2.2 µm
color composite
~10,000 K
~2,200 K
7
Color of Blackbody Radiation
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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
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Interstellar Extinction Law
extinction is highest at ~100 nm = 0.1 µm
unimportant for >10 µm
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Interstellar Extinction: Dust
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Atmospheric Transmission
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Outline
• Radiation
– blackbody radiation, luminosity
– magnitudes, colors
– extinction, optical depth
• Detection and Measurement of Light
– Earth’s atmosphere, photometric bands
– detectors
• Astronomical yardsticks
– parallax
– absolute magnitude, distance modulus
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Photometric Bands: Near-Infrared
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Photometric Bands: Visible
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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
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Detection of Light
Quantum efficiencies of the 4 CCD chips
on the Hubble WFPC2 camera
A charge-coupled
device (CCD)
converts photons to
electrons
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Detection of Light:
The Sloan Digital Sky Survey (SDSS)
SDSS 2.5 m telescope at Apache Point, NM
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Ritchey-Chretien design
(Cassegrain-like)
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Detection of Light:
The Sloan Digital Sky Survey (SDSS)
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Detection of Light:
The Sloan Digital Sky Survey (SDSS)
u
g
r
i
z
(ansgtroms)
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Proxima Cen
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Outline
• Radiation
– blackbody radiation, luminosity
– magnitudes, colors
– extinction, optical depth
• Detection and Measurement of Light
– Earth’s atmosphere, photometric bands
– detectors
• Astronomical yardsticks
– parallax
– absolute magnitude, distance modulus
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Measuring Distance:
The Trigonometric Parallax
•
•
•
distance to nearby star is 1 parsec (pc) when angle p = 1 arc second (1")
1 pc = 3.26 light years (ly) = 2.06x105 AU = 3.09x1018 cm
Proxima Cen is at 1.3 pc ~ 4.3 ly
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Absolute Magnitude and
Distance Modulus
• The apparent magnitude of a star at 10 pc
– used to compare absolute brightnesses of different stars
M = m + 2.5 lg F(r) / F(10 pc)
• Distance modulus (DM)
– a proxy for distance
m – M = 5 lg (r / 10 pc)
– DM = 0 mag for object at 10 pc
– DM = –4.4 mag for Proxima Cen
– DM = 14.5 mag to Galactic center
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