Transcript Document
OUR UNIVERSE Lectures 7 - 9 The Physics of Radiation & Spectroscopy The windows to Our Universe & the keys to our knowledge & understanding. The Physics in Astrophysics. Light is electromagnetic radiation Oscillating Electric & Magnetic fields E c speed B wavelength frequency c =c/ To produce electromagnetic radiation we must accelerate electric charge e - Oscillation back-and-forth Oscillating currents (e-) • in antennae (radio, TV, radar, microwaves, etc) • in atoms (IR, visible light, X-rays, etc) To produce electromagnetic radiation Radio Gamma rays we must accelerate electric charge Low High energy -14 km 10 m + e - electron Deflected by a nucleus - Bending in magnetic field: synchrotron radiation e also sometimes called magnetic We can picture a diatomic molecule as a dumbell + + - C = O CO Carbon Monoxide To produce electromagnetic radiation we must accelerate electric charge C O Typically 1-100 µm Infrared (IR FIR) Vibrations of a diatomic molecule To produce electromagnetic radiation we must accelerate electric charge C O Typically mm cm mm microwaves Rotation of a diatomic molecule ro-vibrational spectrum of CO ro-vibrational spectrum of CO ro-vibrational spectrum of CO The Electromagnetic Spectrum The Electromagnetic Spectrum from Radio Gamma Rays Gamma Rays X-rays Ultraviolet (UV) Visible Infrared (IR) mm waves Microwaves Radio Atmospheric Windows Transmission Radio Window Optical Window Atmosphere is transparent 100 nm 10 µm 1 µm 1mm 1cm 1 m 10 m 100 µm Visible: 400-700 nm Wavelength Interference of Waves A consequence of the wave-like nature of radiation is interference & Constructive Interference diffraction. Interference of Waves Destructive Interference Interference of Waves Young’s Experiment: 2-slit interference Interference of Waves Diffraction through a single slit. D Diffraction peak Angular wi dth D 1.2 D D Diffraction through a circular aperture, diameter D. Diffraction through a telescope of Diameter D: the diffraction-limited angular resolution is: 1.2 D in radians 0.25 10 6 D in arcsec Images merge as 2 sources moved together to below the angular resolution What is the diffraction limit for a 2.4m telescope for light with =600 nm? 0.25 10 6 in arcsec D 600 10 = 0.25 10 2.4 9 6 = 0.063 arcsec Electromagnetic Radiation behaves in 2 complementary ways: • waves - frequency = c/ • particles (photons) - energy E = h Atoms & molecules emit and absorb radiation in discrete quanta of energy h • The frequencies are characteristic of atomic & molecular structure. (The photons are their “fingerprints” or “DNA”) The Rutherford model of the atom. classical e- (electron) orbits Quantum Mechanics gives discrete “orbits” for the e in a Hydrogen atom. In each orbit the discrete energy: 1 En = 13.6 eV 2 n e has a n = 1, 2, 3, 4,. .. H atom: Allowed orbits for the e- Ground state n=1 1st Excited state n=2 3rd 2nd Excited state n=3 Excited state n = 4 Emission & Absorption of Radiation • In each orbit the e- has a 1 En ∝- 2 n unique quantised energy: • In falling down from orbit m n a photon of energy h = Em - En is emitted. • In jumping up from orbit n m a photon of energy h = Em - En is absorbed. Absorption & emission of an H photon by Hydrogen = 656 nm Absorption & emission of an H photon by Hydrogen = 656 nm Emission & Absorption of Radiation • In each orbit the e- has a unique quantised energy: • Transitions down (emission) & up (absorption) from level n give rise to unique, identifiable spectral lines. • Therefore Spectral lines provide powerful methods for: (a) identifying different elements (b) discovery physical conditions in space Hydrogen atom Spectral Series L L etc H H etc P P Hydrogen atom Spectral Series Emission Spectra for rarefied gases & vapours of the elements. Emission Spectra for rarefied vapours of the elements. This example is the Omega nebula, M17 M17 H =656 nm The typical reddish pink glow of Hydrogen excited by young stars in the galaxy NGC 2363 (in the constellation Camelopardis) NGC 2363 H =656 nm Hydrogen H =656 nm Hydrogen NGC 3310: z = 0.0033 v = 1000 km/s Markarian 609: z = 0.034 v = 10,000 km/s z = 6.58, 97%c Spectra of the 2 galaxies 500 550 600 650 Wavelength Intensity nm 500 550 600 650 Wavelength Intensity H H Laboratory wavelengths 0 nm Emission Spectra for rarefied gases & vapours are line spectra, unique for each element; but we also often see an underlying continuum. What causes the continuous spectrum? Kirchoff’s Laws of spectroscopy. 1) A low density hot gas emits discrete lines - emission lines. 2) A hot solid, liquid or dense enough gas emits a continuous spectrum. 3) A cool gas absorbs radiation at the same frequencies as it emits when hot - this produces dark absorption lines. Kirchoff’s Laws of spectroscopy. 1) A low density hot gas emits discrete lines - emission lines. These lines are a unique signature of the atoms in the gas. A low density hot H gas: discrete emission lines. Kirchoff’s Laws of spectroscopy. 2) A hot solid, liquid or dense enough gas emits a continuous spectrum. The spectrum is independent of the constitution of the solid, but depends only on its Temperature, T This is the Black Body Spectrum or Planck Spectrum A hot solid emits a continuous spectrum. A boy and his dog are much cooler than the Sun. They emit radiation in the infrared (IR). They are NOT in thermodynamic equilibrium. A continuous Spectrum Incandescent solid IR UV The Black Body Spectrum or the Planck Spectrum is produced by a body in thermodynamic equilibrium. Spectrum only depends on T A Furnace and its contents emit a Planck Spectrum The Black Body Spectrum or the Planck Spectrum is produced by a body in thermodynamic 4 equilibrium. Ene rgy ∝T Spectrum only depends and on T pe ak ∝T -1 The Black Body Spectrum Here plotted against wavelength log The Black Body Spectrum Here plotted against log frequency, log log The Black Body Spectrum Here plotted against log for different T The Sun’s continuous spectrum can be well approximated by a Black Body Spectrum or Planck Spectrum at 5800 K RADIATION Specific Intensity -1 -2 -1 I = Js m ste r Hz solid angle integrate over frequency Intensity -1 -2 I= Js m ste r integrate over solid angle Flux -1 -1 F= Js m -2 -1 BLACK BODY RADIATION Emitted by a body, at temperature T in thermodynamic equilibrium 3 Planck’s Law 2h I = 2 h /kT c e -1 -1 -2 -1 -1 = Js m ste r Hz Stefan-Boltzmann Law F= T 4 -1 Js m -2 = 5.6710-8 W m-2 K-4 Stefan-Boltzmann constant BLACK BODY RADIATION Planck’s I = 2 h 2 h c e Law 3 / kT -2 -1 -1 W m ste r Hz -1 At the peak: h M AX = 2 M AX = .82 k T J 5. 88× 10 2. 9 × 10 M AX = T Wien’s Law 10 M AX ∝T T Hz -3 m 1 M AX ∝ T APPLICATIONS OF BLACK BODY LAWS Wien’s Law 2 . 9 × 10 M AX = T SUN T = 5800 K therefore MAX = 500 nm -3 m APPLICATIONS OF BLACK BODY LAWS F= For a Star: T 4 Wm -2 • radius R* • Temperature T • Total energy output/sec Luminosity L* Watts L st ar = 4 π R st ar 2 T 4 The Star Sirius has a surface temperature 2 .of 9 × 10 Wien’s Law = M AX 10000K T Sirius T = 10000 K therefore MAX = 290 nm -3 m What is the relative Flux of Sirius compared with the Sun? F= F sirius = F S un T 4 T sirius = 4 T S un 4 Wm -2 4 10000 = 8.8 4 5800 THE END OF LECTURE 8 OUR UNIVERSE Lecture No. 9 An application of Black Body law: The Earth is heated by the Sun. What is the equilibrium temperature of the Earth? Sun’s R radiation reaching Earth covers a circular area R2 • Solar flux at earth’s distance d F = L⊙/4d2 = 1387 W m-2 Energy reaching Earth: R2 F • • Solar flux at earth’s distance d F = L⊙/4d2 = 1387 W m-2 Energy reaching Earth: R2 F • But the Earth reflects back into space a fraction A A = 0.29 is the Earth’s albedo • • Solar flux at earth’s distance d F = L⊙/4d2 = 1387 W m-2 Energy reaching Earth: R2 F • But the Earth reflects back into space a fraction A A = 0.29 is the Earth’s albedo • Therefore the power retained by Earth is R2 F (1-A) Watts • The power retained by Earth is R2 F (1-A) Watts • The Earth at temperature T emits into space as a Black Body, losing energy at a rate Area T4 = 4R2 T4 • The power retained by Earth is R2 F (1-A) Watts • The Earth at temperature T emits into space as a Black Body, losing energy at a rate Area T4 = 4R2 T4 • In equilibrium, loss = gain, 4 R2 T4 = R2 F (1-A) • The power retained by Earth is R2 F (1-A) Watts • The Earth at temperature T emits into space as a Black Body, losing energy at a rate Area T4 = 4R2 T4 • In equilibrium, loss = gain, 4 R2 T4 = R2 F (1-A) • The power retained by Earth is R2 F (1-A) Watts • The Earth at temperature T emits into space as a Black Body, losing energy at a rate Area T4 = 4R2 T4 • In equilibrium, loss = gain, 4T4 = F (1-A) In equilibrium, loss = gain 4T = F (1 A) 4 F (1 A _) T = 4 4 For the Earth: 1387 0.71 T = 8 4 5.7 10 T = 256 K i.e. T = -16.6oC 1 4 F (1 A _) T = 4 4 In equilibrium loss = gain Earth Actual surface T = 288K T = 256 K +15 C Mars Actual surface T = 223K T = 217 K -50 C Venus Actual surface T = 732K T = 227 K 459 C In equilibrium, loss = gain Earth Discrepancy T = 32K Mars Discrepancy T = 6K Venus Discrepancy T = 505K WHY In equilibrium, loss = gain Explanation: Greenhouse effect huge for Venus mild but significant for Earth almost none for Mars. Planck spectrum: & therefore the colours of stars only depend on T Peak T 1 Peak T 1 The colours of stars tell us their temperatures. Note the different colours of stars in the following picture. The interaction between galaxies has triggered star formation: the hot young stars are blue. Hot young O-B stars Betelgeuse Cool Red Giant M Orion Visible Rigel B8 Orion IR Examples for a variety of cosmic objects showing their Black Body Spectrum / Planck Spectrum • Rho Ophiuchi at 60 K (mm waves) • Young IR star in Orion 600 K (IR) • Sun, 5800 K • Omega Centauri star cluster very hot young stars around 60,000 K Black Body Spectra Rho Ophiuchi at 60 K (mm) Young IR star in Orion 600 K (IR) Sun, 5800 K Omega Centauri star cluster Hot young stars 60,000 K The entire Universe glows with a perfect Black Body Spectrum or Planck Spectrum Isotropic & Homogeneous to 1 part in 105 The entire Universe glows with a perfect Black Body Spectrum or Planck Spectrum at 2.725 K Isotropic & Homogeneous to 1 part in 105 COBE 1992 What produced the Universe’s Planck spectrum? The hot dense early universe. The radiation has been cooling down ever since as the universe expands. The Sun’s Spectrum A continuous spectrum The Sun’s continuous spectrum is well approximated by a Black Body or Planck Spectrum at 5800 K Our success in fitting the Sun’s continuous spectrum with a Black Body (Planck) Spectrum tells us that it is a dense sphere at 5800 K. But what about the absorption lines? Kirchoff’s Laws of spectroscopy. 1) A low density hot gas emits discrete lines - emission lines. 2) A hot solid, liquid or dense enough gas emits a continuous spectrum. 3) A cool gas absorbs radiation at the same frequencies as it emits when hot - this produces dark absorption lines. Kirchoff’s Laws of spectroscopy. 3.) A cool gas absorbs radiation at the same frequencies as it emits when hot: this produces dark absorption lines. Dense Hot Black Body Cooler gas cloud Absorption line spectrum Emission & Absorption of Radiation Absorption & emission of an H photon by Hydrogen = 656 nm Absorption Absorption Spectra for cool rarefied gases emission absorption Sodium vapour All Kirchoff’s Laws I n action. 1.) A low density hot gas emits discrete lines - emission lines. 2.) A hot solid, liquid or dense enough gas emits a continuous spectrum. 3.) A cool gas absorbs radiation at the same frequencies as it emits when hot - this produces dark absorption lines. Interpreting the Sun’s spectrum: (2) The line spectrum is an absorption spectrum We know this is produced by a rarefied gas cooler than the Sun’s photosphere. (Kirchoff’s 3rd law) Therefore we infer…... The Sun is a dense sphere emitting a Black Body (Planck) Spectrum at 5800 K with a cool rarefied gas atmosphere. Dense photosphere emitting Planck spectrum at 5800 K SUN Cooler rarefied atmosphere absorbing in spectral lines characteristic of the elemental composition The spectral lines tell us what elements are present in the Sun’s atmosphere (and for other stars too). Their strength tells us how much there is. The spectral lines tell us what elements are present Iron (Fe) in the Sun. A small part of the Sun’s spectrum Laboratory spectrum of Fe (incandescent vapour!) Hydrogen Balmer lines in spectrum of the star HD 193182 around 20 Balmer lines from H13 to H40 are seen here. (H to H12 are present, but not shown here.) Balmer limit =364.6 nm Stellar spectra for temperatures 3500K to 35,000K Element abundances (by number). Determined from Solar spectra & meteorites. Also found to be typical of most stars. H He C, N, O Fe A Reminder: The Black Body Spectrum is a continuous spectrum Spectrum only depends on T Black Body Spectrum or Planck Spectrum How is a continuous spectrum produced by a dense collection of atoms if each atom only produces a line spectrum? The Doppler shift. v The Red shift. • Speed of source is v, the red shift is z • the rest wavelength is 0 • the observed wavelength is 0 1 vc z= = 1 1 vc v z≈ c For v/c << 1 A spectral line from a hot gas has a width which increases with the temperature of the gas. kT v h kT v h FWHM Light-emitting atoms moving randomly in the hot gas produce broadened spectral lines. A spectral line is the sum of the Doppler shifts of billions of light-emitting atoms. Black Body Radiation In a solid the interactions and collisions between the atoms increase the range of velocities so much, that the broadened lines overlap and merge into a continuum. Spectral information from starlight • Peak or : • Presence of Line: • Line intensity: • Line width : • Doppler shift: T = Temperature Composition & T Composition & T T, density, rotation, outflows, jets,….. Line-of-sight velocity Broadening of lines due to stellar rotation enables us to measure rotation speed. An Example: Broadening of lines due to circumstellar outflow IRC+10216 at 15 km/s IRC+10216 outflow Telescope (JCMT) 1000 AU THE END OF LECTURE 9