Radiation, CMDs,and Spectral Classification

AST443, Lecture 12Stanimir Metchev

2

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

3

Outline

• Statistics: overview

• Radiation and extinction: reprise

• Color-magnitude diagrams– color-color diagrams– extinction, reddening

• Spectral classification

4

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

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Correlation: Hubble Diagram

Hubble (1929)

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Student’s t Distribution

k = d.o.f.

source: wikipedia

t

f (t, k)

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χ2 Distribution

source: wikipedia

k = d.o.f.

χ2

f (χ2,k)

8

χ2 Distribution:Hypothesis Testing

• probability that measured χ2 or higheroccurs by chance under H0

source: wikipedia

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Outline

• Statistics: overview

• Radiation and extinction: reprise

• Color-magnitude diagrams– color-color diagrams– extinction, reddening

• Spectral classification

10

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 = ∫ Sν 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

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Blackbody Radiation (Lecture 4)• Planck law

– specific intensity

• 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– power– [erg s–1]

• Inverse-square law L(r) = L* / r2!

" =2# 5

k4

15c 2h

3= 5.67 $10%5erg cm–2 s–1 K–4

!

L*

= 4"R*

2#Teff

4

!

I(",T) =2h" 3

c2

1

eh" kT

#1

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Blackbody Radiation (Lecture 4)

Teff, Sun = 5777 KT λmax= 0.29 K cm

13

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

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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)

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Extinction and Optical Depth(Lecture 4)

• Light passing through a medium can be:– transmitted, absorbed, scattered

• extinction at frequency ν over distance sdLν(s) = –κν ρ Lν ds = –L dτνLν = 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

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Interstellar Extinction Law

extinction is highest at ~100 nm = 0.1 µmunimportant for >10 µm

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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)

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Atmospheric Extinction

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Photometric Bands: Visible

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Photometric Bands: Near-Infrared

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Outline

• Statistics: overview

• Radiation and extinction: reprise

• Color-magnitude diagrams– color-color diagrams– extinction, reddening

• Spectral classification

22

Color-Magnitude Diagram

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CMD at a Constant Age: M55

• visible

source: APoD, Mochejska et al.

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CMD at a Constant Age: Pleiades

• near-IR

source: 2MASS

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Color-Color Diagram

source: RAVE survey

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Extinction and Reddening: CMD• Legend:

– arrow: AV = 5 magextinction

– solid line: mainsequence

– dotted line: substellarmodels

– crosses: knownbrown dwarfs

– solid points: browndwarf candidates

AV = 5 mag

Metchev et al. (2003)

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Extinction and Reddening: CCD• Legend:

– arrow: AV = 5 magextinction

– solid line: mainsequence + giants

– dotted line: substellarmodels

– crosses: knownbrown dwarfs

– solid points: browndwarf candidates

AV = 5 mag

Metchev et al. (2003)

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Outline

• Statistics: overview

• Radiation and extinction: reprise

• Color-magnitude diagrams– color-color diagrams– extinction, reddening

• Spectral classification

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Astronomical Spectrograph

telescope focus

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OBAFGKM + LT

higherionizationpotentialspecies

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SpectroscopicBestiary