Overview of Astronomical ConceptsI. Radiation, Magnitudes, Distances

PHY 688, Lecture 3Stanimir Metchev

Jan 30, 2009 PHY 688, Lecture 3 2

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

Jan 30, 2009 PHY 688, Lecture 3 3

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 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] !

" =2# 5

k4

15c2h3

!

L*

= 4"R*

2#Teff

4

Jan 30, 2009 PHY 688, Lecture 3 4

Blackbody Radiation

Teff, Sun = 5777 K

Jan 30, 2009 PHY 688, Lecture 3 5

The Dreaded 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

Jan 30, 2009 PHY 688, Lecture 3 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

Jan 30, 2009 PHY 688, Lecture 3 7

Magnitudes and Colors

(Zuckerman & Becklin 1988)

J H K

2MASS

1.2, 1.6, 2.2 µmcolor composite

GD 165 A/B~10,000 K~2,200 K

Jan 30, 2009 PHY 688, Lecture 3 8

Color of Blackbody Radiation

Jan 30, 2009 PHY 688, Lecture 3 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 asEν1,ν2 = mν1 – mν2 – (mν1 – mν2)0 [mag]– (mν1 – mν2)0 is the intrinsic color of the starAV / E(B–V) ≈ 3.0

Jan 30, 2009 PHY 688, Lecture 3 10

Interstellar Extinction Law

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

Jan 30, 2009 PHY 688, Lecture 3 11

Interstellar Extinction: Dust

Jan 30, 2009 PHY 688, Lecture 3 12

Atmospheric Transmission

Jan 30, 2009 PHY 688, Lecture 3 13

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

Jan 30, 2009 PHY 688, Lecture 3 14

Photometric Bands: Near-Infrared

Jan 30, 2009 PHY 688, Lecture 3 15

Photometric Bands: Visible

Jan 30, 2009 PHY 688, Lecture 3 16

PhotometricSystems

• 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 KeaObservatory (MKO), etc

Jan 30, 2009 PHY 688, Lecture 3 17

Detection of LightQuantum efficiencies of the 4 CCD chips

on the Hubble WFPC2 camera

A charge-coupleddevice (CCD)converts photons toelectrons

Jan 30, 2009 PHY 688, Lecture 3 18

Detection of Light:The Sloan Digital Sky Survey (SDSS)

SDSS 2.5 m telescope at Apache Point, NMRitchey-Chretien design

(Cassegrain-like)

Jan 30, 2009 PHY 688, Lecture 3 19

Detection of Light:The Sloan Digital Sky Survey (SDSS)

Jan 30, 2009 PHY 688, Lecture 3 20

Detection of Light:The Sloan Digital Sky Survey (SDSS)

(ansgtroms)

u g r i z

Jan 30, 2009 PHY 688, Lecture 3 21

Proxima Cen

Jan 30, 2009 PHY 688, Lecture 3 22

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

Jan 30, 2009 PHY 688, Lecture 3 23

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

Jan 30, 2009 PHY 688, Lecture 3 24

Absolute Magnitude andDistance 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 distancem – 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