08 Radiation.pdf

Radiation Radiation Electromagnetic radiation (i.e., light) is both – a particle (i.e., geometrical optics, photon); and – a wave (i.e., perturbation of electromagnetic fields). Radiation is the only way we have to study the Universe … until fairly recently....

Radiation Radiation Electromagnetic radiation (i.e., light) is both – a particle (i.e., geometrical optics, photon); and – a wave (i.e., perturbation of electromagnetic fields). Radiation is the only way we have to study the Universe … until fairly recently. 1/30 Wave terminology time time period 1/ν tic (frequency ν) is νλ er = ct c ra y cit a ch lo ve e as ph perturbed space quantity space perturbed wavelength λ quantity 2/30 Wave phenomena Diffraction Interference both have implications for telescope operation 3/30 Speed of light Ole Rømer: Earth’s velocity causes the distance to Jupiter, and hence the interval between consecutive observations of Io entering Jupiter’s shadow, to vary (similar to the classical Doppler effect) 4/30 Speed of light n directio n io ct actual ire td en par ap telescope velocity James Bradley: stellar aberration is due to Earth’s velocity (apparent direction is actual direction minus telescope velocity) 5/30 Inverse-square law of radiation F: flux (unit: J s−1 m−2 ) F = L/(4πd ) 2 d: luminosity distance L: luminosity (unit: J s−1 ) 6/30 PointSolutions What is the ratio of the solar flux received by Jupiter (orbital semimajor axis ≈ 5.2038 AU) to that received by Earth? 1. ≈ 0.036 928 2. ≈ 0.192 17 3. ≈ 1.0000 4. ≈ 5.2038 5. ≈ 27.080 Photon E: photon energy (unit: eV) ν: frequency (unit: Hz) E = hν = hc/λ λ: wavelength (unit: m or Å) h: Planck’s constant c: speed of light 7/30 Redshift observational definition of redshift (similarly for blueshift) λ − λ0 λ: observed wavelength z≡ ≥0 λ0 λ0 : emitted wavelength redshift and blueshift in special relativity (Doppler effect) gravitational redshift in general relativity cosmological redshift 8/30 Doppler effect in special relativity for any v: change in frequency – bunching up of wavefronts (classical effect) ̂n – time-dilation of emitter v (relativistic effect) for v ∦ ̂n: change in angle (relativistic stellar aberration) 9/30 Doppler effect in special relativity for v ∥ ̂n: λ 1 + β 1/2 v = βc: velocity =( ) λ0 1−β (|β| < 1; β > 0 if ≈1+β if |β| ≪ 1 moving away) Astronomers are really good at measuring radial motion… and really bad at measuring proper (i.e., transverse) motion. 10/30 Cosmological redshift (and Lyman alpha forest) YouTube 6Bn7Ka0Tjjw 11/30 PointSolutions A source moves with a velocity 0.1 c away from an observer. A spectral line emitted at 1000 nm is observed at: 1. ≈ 818 nm 2. ≈ 905 nm 3. ≈ 1100 nm 4. ≈ 1106 nm 5. ≈ 1222 nm Electromagnetic spectrum Wavelength (m) 103 102 101 100 10-1 10-2 10-3 10-4 10-5 10-6 10-7 10-8 10-9 10-10 10-11 10-12 Wikimedia Commons/© User:DrSciComm/ Approximate Scale of Wavelength Buildings Humans Butterflies Needle Point Cells Molecules Atoms Atomic Nuclei Visible Radiation Type Radio waves Infrared Ultraviolet ‘Hard’ X-rays Microwaves ‘Soft’ X-rays Gamma rays Frequency (Hz) 105 106 107 108 109 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 slightly off CC BY-SA 4.0 Sources AM Radio Microwave Radar Humans Fluorescence X-ray Radioactive oven bulbs machines Elements Non Ionizing Ionizing Energy (eV) 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101 102 103 104 105 106 optical (i.e. visible) range is ∼ 700 nm to 400 nm (red to blue) 12/30 Electromagnetic spectrum: Corrected m 103 102 101 100 10−1 10−2 10−3 10−4 10−5 10−6 10−7 10−8 10−9 10−10 10−11 10−12 Hz 106 107 108 109 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 eV 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100 101 102 103 104 105 106 K 10−5 10−4 10−3 10−2 10−1 100 101 102 103 104 105 106 107 108 109 1010 1 eV ≈ hc/(1 µm) ≈ h × 1014.5 Hz ≈ kB × 104 K compare Wien’s displacement law 13/30 PointSolutions What is the energy of a green (∼ 550 nm) photon? 1. ∼ 1 eV 2. ∼ 2 eV 3. ∼ 3 eV 4. ∼ 4 eV 5. ∼ 5 eV Is it any coincidence that electronic transitions of atoms also have energies ∼ eV? Photometry map from filter to pseudocolor NASA, ESA, CSA, STScI 14/30 Photometric filters optical r g i u z SDSS-III SDSS-III 15/30 Spectroscopy emission absorption continuum Ho (2008) ARA&A, 46, 475 16/30 Photometry and spectroscopy What are the relative strengths of photometry and spectroscopy? 17/30 Continuum emission special case of continuum emission: black-body an entity that absorbs all incoming light an entity that emits thermal radiation (i.e., radiation that is in thermal equilibrium at temperature T ) Why is this “special case” important? Are there other kinds of continuum emission? 18/30 Black-body spectrum log(λBλ ) increasing T log λ emission is nonzero for all λ emission increases with T for all λ assuming the same emitting area λ of peak emission decreases with T 19/30 PointSolutions The effective temperatures of the Sun and Betelguese are ≈ 5772 K and ≈ 3600 K, respectively. Therefore, in terms of the luminosity per unit surface area, how does Betelguese compare with the Sun? 1. as bright in the infrared and ultraviolet 2. dimmer in the infrared and ultraviolet 3. brighter in the infrared and ultraviolet 4. dimmer in the infrared and brighter in the ultraviolet 5. brighter in the infrared and dimmer in the ultraviolet PointSolutions The effective temperatures of the Sun and Betelguese are ≈ 5772 K and ≈ 3600 K, respectively. Therefore, in terms of the fraction of the total luminosity emitted in each waveband, how does Betelguese compare with the Sun? 1. as bright in the infrared and ultraviolet 2. dimmer in the infrared and ultraviolet 3. brighter in the infrared and ultraviolet 4. dimmer in the infrared and brighter in the ultraviolet 5. brighter in the infrared and dimmer in the ultraviolet  PointSolutions In absolute terms Relative to bolometric log(λBλ ) log(λBλ /B) Sun Sun Betelguese Betelguese log λ log λ ultraviolet infrared ultraviolet infrared Stefan–Boltzmann law L: bolometric black-body luminosity σSB : Stefan–Boltzmann constant L = σSB T 4 A T: black-body temperature (unit: K) A: emitting area often: A = 4πr 2 r: black-body radius 20/30 Wien’s displacement law max{ Bλ } ∝ 1/T max{ Bν } ∝ T λ ν max{λBλ } ∝ 1/T max{νBν } ∝ T λ ν specifically: kB : Boltzmann constant hc/ max{λBλ } ≈ 4kB T T : black-body temperature (unit: K) λ i.e., as a black body heats up, it glows red then white then blue 21/30 Wien’s displacement law Why does a black body not glow green? Without using a calculator, determine the wavelength at which the Sun, with an effective photospheric temperature of ≈ 5772 K, puts out most of its energy. 22/30  Annie Jump Cannon, Cecilia Payne-Gaposchkin, Stellar spectra and other Harvard “computers” spectral line stellar Harvard spectral classification: class hotter/bluer cooler/redder O B A F G K M hotter stars happen to be brighter, cooler stars dimmer 23/30 Stellar spectra Why are there only absorption lines? Why is temperature correlated with absorption line strength? Why are emission lines relatively uncommon? 24/30 Atomic spectroscopy Joseph von Fraunhofer (1787–1826): (re)discovered a set of absorption lines in the optical spectrum of the Sun Robert Bunsen (1811–1899): invented a gas burner with a hot and clean flame that is useful for flame spectroscopy Gustav Kirchhoff (1824–1887), Bunsen: matched several Fraunhofer lines with emission lines of heated chemical elements KH Gf e F b E D C B A h g d h c h 4-1 3-1 a 390 450 550 650 750 400 500 600 700 wavelength in nm Wikimedia Commons/User:Cepheiden/PD 25/30 Bohr model of the hydrogen atom the electron must be at discrete energy levels: En = (−1/n2 ) Ry n ∈ {1, 2, 3, …} 1 Ry ≈ 13.6 eV 1 2 3 4 5 electrons do not buzz around the nucleus because accelerating electrons radiate and lose their energy rapidly 26/30 Emission and absorption emission 0.0 eV −1.5 eV absorption −3.4 eV continuum ⋯ n ⋯ m ⋯ −13.6 eV line hν = |1/n − 1/m | Ry 2 2 27/30 Hydrogen series nm Lyman series 94 nm 95 nm Lyα, Lyβ, Lyγ, …, LyC 97 n=?→1 3 nm nm 10 122 656 nm486 nm 434 nm n=1 410 nm Balmer series 187 n=2 5 nm Baα, Baβ, Baγ, … or 128 2n m Hα, Hβ, Hγ, … n=3 10 94 n=?→2 nm Paschen series n=4 n=5 n=6 Paα, Paβ, Paγ, … n=?→3 Wikimedia Commons/© User:OrangeDog/CC BY 2.5 How do wavelength, frequency, and energy vary within a series? Why are the bold transitions important in astronomy? 28/30 Emission and absorption Kirchhoff’s law of thermal radiation: Gas are as good in emitting as they are in absorbing. Atoms in thermal equilibrium with radiation emit and absorb radiation constantly, in equal amounts. Therefore, they do not produce lines. Absorption lines are produced when an optically thin (read: transparent), cold gas is in front of a hot continuum source. Emission lines are produced when an optically thin, hot or otherwise excited gas is in front of a cold continuum source. Einstein coefficients: Stimulated emission happens when another photon of the same energy is present. 29/30 Absorption line formation hotter cooler black body of background foreground log(λBλ ) hotter gas gas gas black body of cooler gas log λ 30/30