Transcript Document
The Dual Nature of Light • It’s a particle: photon with E (ergs) • It’s a wave: Wavelength , Frequency , velocity c Quic kTime™ and a GIF dec ompres s or are needed to s ee t his pic tur e. Radio: long , low , vel=c = c/ cm QuickTime™ and a GIF decompressor are needed to see this picture. 1 Å = 10-8cm E = h = hc/ ergs X-ray: short , high , vel=c LIGHT c/ E=h=hc/ ergs The wave is the electric and magnetic fields to each other E = Eosin[(2/) (x-ct)] IE2 Electromagnetic Spectrum: -ray MeV X-ray keV UV visible 500-3000Å 3900-7000Å 1 keV=12Å GRB, SN XRB, SN remnants 1Å=10-8cm IR µ radio cm-meter 1µ=10,000Å O, B stars Stars Brown dwarfs Molecular white dwarfs accretion disks planets clouds Half abs altitude (km) Wavelength (Å) Basic Properties of Light: • inverse square law: [E/4πd2 ergs/cm2] • reflection: angle of incidence to normal= angle of reflection [i=r] • refraction: light refracts (bends to normal) in material [n1sini = n2sinr] • dispersion: light disperses in prism or grating [spectrum] • diffraction: light passing through an aperture (telescope): [~/d(radians)=206265/d(arcsec)] x1.22 is resolution for a 10 cm telescope at =5000Å, = 1 arcsec • interference[max at dsin = m] gives location of lines in spectrograph - for a grating with 12000 slits/inch, d=21,000Å Basic Properties of Light: • inverse square law: [E/4πd2 ergs/cm2] Basic Properties of Light: • reflection: angle of incidence to normal = angle of reflection [i=r] Basic Properties of Light: • refraction: light refracts (bends to normal) in material [n1sini = n2sinr] Basic Properties of Light: • diffraction: light passing through an aperture (telescope) (radians) ~/d 1 radian=57.3 deg x 60 arcmin x 60 arcsec = 206265 arcsec resolution (arcsec) = 206265 (/d) x 1.22 (circular correction) for a 10 cm telescope at =5000Å(5x10-5cm), ~ 1 arcsec blue vs red telescope size Basic Properties of Light: • interference[max at dsin = m] gives location of lines in spectrograph - for a grating with 12000 slits/inch, d=21,000Å Basic Properties of Light: • dispersion: light disperses in prism or grating [spectrum] n() white light blue is bent more than red 3 types of spectra: continuous, absorption line and emission line Important points about Continuum radiation: • Planck Function (Black Body) E=2hc2/5[e(hc/kT)-1] ergs/cm2/s/Å • Stefan-Boltzmann Law E=T4 ergs/cm2/s • Luminosity L=4πR2T4 ergs/s • Wien’s Law (Å)=2.9x107/T(°K) Continuum radiation is approximated as a Black Body (black body is opaque and radiates as a function of its T); amount of energy from a BB is given by the Planck function: E=2hc2/5[e(hc/kT)-1] ergs/cm2/s/Å Note there is some E at all wavelengths even if its not visible 1000Å 4000Å 7000Å 10,000Å E=2hc2/5[e(hc/kT)-1] ergs/cm2/s/Å Eall = ∫ E () d = T4 ergs/cm2/s Stefan-Boltzmann law doubling T gives 16 X more energy from a star! 1000Å 4000Å 7000Å 10,000Å Stefan-Boltzmann is energy/s for each square cm on star Luminosity = total energy coming from star each sec = total emitting area (cm2) X T4 (ergs/cm2/s) = 4 R2 T4 ergs/s E=2hc2/5[e(hc/kT)-1] ergs/cm2/s/Å dE/()/d = 0 (Å) = 2.9 x 107/T (˚K) Wien’s law hot stars look blue, cool stars red, color gives T 1000Å 4000Å 7000Å 10,000Å Line emission is approximated by the Bohr model (Quantum physics tells the true story) E H n=1 n=2 n=3 p e • Each element has diff p, e-, n • Each element has diff E levels He n • e- sit at lowest E for gas T E=hc/ photon absorption line e- absorbs photon and moves to higher E level (n=2) emission line e- emits photon to move down to lower E level (n=1) Transitions to a given level are a series: 13.6eV 12.73eV 12.07eV 10.19eV 0 eV UV optical IR Line theory - Bohr model mvr=nh/2π mv2/r=(Ze)e/r2 E(n)=-2π2me4/h2n2 E=hc/ r= n2h2/4πme2Z 1/109678 [(1/m2)-(1/n2)] H (level 3 to 2) 1/109678 [(1/4)-(1/9)] so =6563Å Quantum theory: N, L, S, J, M quantum numbers Level Populations: - gas T determines E which determines level occupied - number of electrons in that level and abundance determines line strength Boltzman eqtn provides excitation: N2/N1=g2/g1 e[E1-E2/kT] Saha eqtn provides ionization : N+/No=A(kT)3/2/Nee[-o/kT] Lines are broadened by: • uncertainty principle: 1/t 0.05 mÅ • Doppler : rotational and thermal • pressure: collisions • magnetic field: Zeeman splitting Sun’s spectrum Spectra of stars like the Sun cool atm Normal Star: continuum + absorption lines WL Peculiar Star: disk of hot low density gas emission lines Planet: continua and absorption of sun + planet sun planet earth Typical CV spectra in DR1 Cyclotron humps Polar CVs in DR1 in Szkody et al. 2003, AJ, 126, 1499 Strong HeII Polar Strong continuum Shows WD ZZ Cet Strong lines Important Info from Spectra: 1. Composition (careful) 2. Temperature 3. Velocity Doppler Shift source moving to right source at rest red shift seen here blue shift seen here if v<< c / = v/c = observed shift, v=object velocity, = lab wavelength, c= 3x105 km/s if =1Å for H (4861Å), v= 62 km/s Uses of Doppler shift: 1) find motion of star or galaxy 2) find rotation of planet or star 3) determine if its a binary (star+star) or (star+planet) red shift no shift no shift only v component toward or away is measured! blue shift Useful info for telescopes: f-ratio = focal length/diameter = f/d [small f-ratio means brighter image] brightness increases as (diameter)2 resolution = 2.1x105/d x 1.22 arcsec magnification = focal length of objective/focal length of eyepiece plate scale s = 0.01745xf cm/deg = 4.85x10-6 f cm/arcsec Plate scale s: how the linear measure on your detector corresponds to angular measure on the sky s = 0.01745 x f in cm/deg s = 4.85x10-6 x f in cm/arcsec for an f/13 telescope of 60 cm diameter: f/d = 13 f = 780 cm s = 0.0037 cm/arcsec 1 cm on detector = 265 arcsec = 4.4 arcmin Our Nationally Funded Observatories: NSF (ground) • Kitt Peak National Obs (KPNO, Tucson) • Cerro Tololo Interamerican Obs (CTIO, Chile) • Gemini (Hawaii and Chile) • radio (VLA, New Mexico; Arecibo, Puerto Rico) NASA (space) + ground (space-related) • HST, Chandra, XMM, GALEX + others • Infrared Telescope Facility (IRTF, Hawaii) • Keck (Hawaii) US Optical Telescopes in the Next Decade • LSST - 8.4m in Chile, 10 yr imaging survey, $400 million, start 2018 • TMT - 30m on Mauna Kea, CA, Canada, Japan, India, China, $1 billion • GMT - 7x8.4m=24.5m in Chile, CA, Harvard, Texas, Arizona, Chicago, Australia, Korea QuickTime™ and a decompressor are needed to see this picture. Primary Instruments 1. Camera - Charge Coupled Device : CCD • time exposures, stars, clusters, galaxies • different filters (colors temps) • brightness, variability 2. Spectrograph - slit, lenses, CCD • composition • temperature • velocity CCDs - invented at Bell Labs about 1970 2D grid of picture elements (pixels) that are 7-30 microns across well capacity 10,000-60,000 e2048x2048 with 2 bytes/pxl = 8MB picture To use: take prior bias & flats then [prep, expose, read] Advantages: • linear over large range in brightness • good quantum efficiency (95% at 6000-9000Å) • dark current small at cold T (-100C) Disadvantages: • large pixel sizes compared to plates, overall small coverage • low blue response • long readout times for large arrays • cosmic rays add up