Radiation, CMDs,
and Spectral Classification
AST443, Lecture 12
Stanimir Metchev
Administrative
• Homework 2:
– problems 4.4, 5.1, 5.3, 5.4
– due in class Wed, Oct 21
• Midterm: Monday, Oct 26
– 1-hour review session, Wed, Oct 21
• Reading:
– chapters 8,10 of Bradt
2
Outline
• Statistics: overview
• Radiation and extinction: reprise
• Color-magnitude diagrams
– color-color diagrams
– extinction, reddening
• Spectral classification
3
Parametreic vs.
Non-Parametric Tests
• correlation
– parametric: bi-variate Gaussian, principal
component analysis
– non-parametric: Spearman rank test
• hypothesis testing:
– parametric: Student’s t test, F test
– non-parametric: χ2 test, K-S test
– one- vs. two-tailed tests
4
Correlation: Hubble Diagram
Hubble (1929)
5
Student’s t Distribution
k = d.o.f.
f (t, k)
t
source: wikipedia
6
χ2 Distribution
k = d.o.f.
f (χ2,k)
χ2
source: wikipedia
7
χ2 Distribution:
Hypothesis Testing
• probability that measured χ2 or higher
occurs by chance under H0
source: wikipedia
8
Outline
• Statistics: overview
• Radiation and extinction: reprise
• Color-magnitude diagrams
– color-color diagrams
– extinction, reddening
• Spectral classification
9
Radiation
•
specific intensity Iν
– dE = Iν dt dA dν dΩ
[erg s–1 cm–2 Hz–1 sterad–1] or [Jy sterad–1]
– 1 Jy = 10–23 erg s–1 cm–2 Hz–1 = 10–26 W m–2 Hz–1
– surface brightness of extended sources (independent of distance)
•
spectral flux density Sν
– Sν = ∫ Iν dΩ
[erg s–1 cm–2 Hz–1] or [Jy] or [W m–2 Hz–1]
– point sources, integrated light from extended sources
•
flux density F
– F = ∫ S ν dν
•
[erg s–1 cm–2] or [W m–2]
power P
– P = ∫ F dA = dE / dt
[erg s–1] or [W]
– received power: integrated over telescope area
– luminosity: integrated over area of star
•
conversion to photon counts
– energy of N photons: Nhν
10
Blackbody Radiation (Lecture 4)
2h" 3
1
I(" ,T) = 2 h" kT
c e
#1
• Planck law
– specific intensity
• 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
– power
– [erg s–1]
L* = 4 "R*2#Teff4
!
• Inverse-square law
L(r) = L* / r2
11
!
Blackbody Radiation (Lecture 4)
Teff, Sun = 5777 K
T λmax= 0.29 K cm
12
Magnitudes (Lecture 4)
• 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
13
Magnitudes and Colors
(Lecture 4)
• magnitude differences:
– relative brightness
V1 – V2 = –2.5 lg FV1/FV2
• ∆m = 5 mag approx. equivalent to F1/F2 = 100
– color
B – V = –2.5 (lg FB/FV – lg FB,Vega/FV,Vega)
14
Extinction and Optical Depth
(Lecture 4)
•
Light passing through a medium can be:
– transmitted, absorbed, scattered
•
•
extinction at frequency ν over distance s
dLν(s) = –κν ρ Lν ds = –L dτν
Lν = Lν,0e–τ = Lν,0e–κρs =Lν,0e–s/l
Aν = 2.5 lg (Fν,0/Fν) = 2.5 lg(e)τν = 0.43τν mag
– medium opacity κν [cm2 g–1], density ρ [g cm–3]
– optical depth τν = κν ρs [unitless]
– photon mean free path: lν = (κν ρ)–1 = s/τν [cm]
AV = mV – mV,0
reddening between two frequencies (ν1, ν2)
Eν1,ν2 = mν1 – mν2 – (mν1 – mν2)0
[mag]
– (mν1 – mν2)0 is the intrinsic color of the star
15
Interstellar Extinction Law
extinction is highest at ~100 nm = 0.1 µm
unimportant for >10 µm
16
Interstellar Extinction Law
•
AV / E(B–V) = 3.1
– AV / E(J–K) = 5.8
– AV / E(V–K) = 1.13
– Aλ / E(J–K) = 2.4 λ–1.75 (0.9 < λ < 6µm)
•
AV ≈ 0.6 r / (1000 ly) mag
– b < 2º (galactic latitude)
•
AV ≈ 0.18 / sin b mag
– b > 10º
•
NH / AV ≈ 1.8 x 1021 atoms cm–2 mag–1
– atoms of neutral hydrogen (H I)
17
Atmospheric Extinction
18
Photometric Bands: Visible
19
Photometric Bands: NearInfrared
20
Outline
• Statistics: overview
• Radiation and extinction: reprise
• Color-magnitude diagrams
– color-color diagrams
– extinction, reddening
• Spectral classification
21
Color-Magnitude Diagram
22
CMD at a Constant Age: M55
• visible
23
source: APoD, Mochejska et al.
CMD at a Constant Age: Pleiades
• near-IR
24
source: 2MASS
Color-Color Diagram
25
source: RAVE survey
Extinction and Reddening: CMD
•
Legend:
– arrow: AV = 5 mag
extinction
– solid line: main
sequence
– dotted line: substellar
models
– crosses: known
brown dwarfs
– solid points: brown
dwarf candidates
Metchev et al. (2003)
AV = 5 mag
26
Extinction and Reddening: CCD
•
Legend:
– arrow: AV = 5 mag
extinction
– solid line: main
sequence + giants
– dotted line: substellar
models
– crosses: known
brown dwarfs
– solid points: brown
dwarf candidates
Metchev et al. (2003)
AV = 5 mag
27
Outline
• Statistics: overview
• Radiation and extinction: reprise
• Color-magnitude diagrams
– color-color diagrams
– extinction, reddening
• Spectral classification
28
Astronomical Spectrograph
telescope focus
29
OBAFGKM + LT
higher
ionization
potential
species
30
Spectroscopic
Bestiary
31