Transcript Photometry
Photometry Measuring Energy • Photometry measures the energy from a source using a narrow range of wavelengths. – Visual wavelengths from 400-700 nm – Narrower slice of wavelengths • Spectroscopy measures energy over a wide range of wavelengths. – Visual spectrum – UV, IR spectra – Full EM spectra • Photometry uses filters to select wavelengths. • Spectroscopy requires instruments to get at each wavelength separately. – Interferometer Luminosity of Stars • Luminosity measures how much energy is produced. – Absolute brightness L • Relative luminosity is usually based on the Sun. • Astronomers measure luminosity relative to the Sun. – LSun = 1 L – LSirius = 23 L • Stars range from 0.0001 L to 1,000,000 L . Magnitude • The observed brightness is related to the energy received. m n 2.5 log( En / Em ) • The magnitude scale was originally 6 classes. – Effectively logarithmic For 1 unit of magnitude: En 101 2.5 2.512 Em • The magnitude (m) was made formal in 1856. – Lower numbers brighter – 6m at the limit of human vision Brightness Magnified • Images from a telescope must fit within the pupil. – Brightness proportional to the aperture squared – Ratio of observed to natural fe P D fo R • No increase for extended objects from magnification. – Eg. M31(> moon) – Light on more rods – Exclusion of other light Ltelescope Leye fo M fe 2 D M 1 P2 Point Source Magnified • Point sources are smaller than one pixel (or rod). – No increase in image size from magnification • The ratio of brightness increase is the light grasp G. – Pupil size 7 mm • The limiting magnitude comes from the aperture. – CCD 5 to 10 magnitudes better D2 G 2 P G 2 104 (m 2 ) D 2 mmin 16.8 5 log 10 D in meters 8” aperture is 13.3m Apparent Magnitude • The observed magnitude depends on the distance to the source. – Measured as apparent magnitude. • The scale is calibrated by stars within 2° of the north celestial pole. • Some bright stars (app. mag.): – Sun -26.7 – Sirius -1.4 – Alpha Centauri -0.3 – Capella 0.1 – Rigel 0.1 – Betelgeuse 0.5 – Aldebaran 0.9 • These are all brighter than first magnitude (m = 1.0) Distance Correction d M m 2.5 log 100 2 M m 5 5 log d M m 5 5 log d AD AD = 0.002 m/pc in galactic plane • Brightness falls off as the square of the distance d. • Absolute magnitude M recalculates the brightness as if the object was 10 pc away. – 1 pc = 3 x 1016 m = 3.26 ly • The absolute magnitude can be corrected for interstellar absorption AD. Absolute Magnitude • Distance is important to determine actual brightness. • Example: 2 identical stars A is 7 pc, B is 70 pc from Earth The apparent brightness of B is 1/100 that of A The magnitude of B is 5 larger. • Some bright stars (abs. mag.): – Sun 4.8 – Sirius 1.4 – Alpha Centauri 4.1 – Capella 0.4 – Rigel -7.1 – Betelgeuse -5.6 – Aldebaran -0.3 • These are quite different than their apparent magnitudes. Imaging • Photographic images used the width of an image to determine intensity. – Calibrate with known stars – Fit to curve D A B log 10 I • CCDs can directly integrate the photoelectrons to get the intensity. – Sum pixels covered by image – Subtract intensity of nearby dark sky • Data is corrected for reddening due to magnitude and zenith angle. Solar Facts • Radius: – R = 7 105 km = 109 RE • Mass : – M = 2 1030 kg – M = 333,000 ME • Density: – r = 1.4 g/cm3 – (water is 1.0 g/cm3, Earth is 5.6 g/cm3) • Composition: – Mostly H and He • Temperature: – Surface is 5,770 K – Core is 15,600,000 K • Power: – 4 1026 W Hydrogen Ionization ep = p2/2m • Particle equilibrium in a star is dominated by ionized hydrogen. • Equilibrium is a balance of chemical potentials. n=3 n=2 g H n nQp H n mH n c kT ln nH n 2 n=1 g p nQp p m p c kT ln n p g n e me c 2 kT ln e Qe ne 2 H n e p Saha Equation mH n c 2 mp c 2 mec 2 e n g ( H n ) g n ge g p 4n2 n( H n ) g n e n e ne n p nQe kT • The masses in H are related. – Small amount en for degeneracy • Protons and electrons each have half spin, gs = 2. – H has multiple states. • The concentration relation is the Saha equation. – Absorption lines Spectral Types • The types of spectra were originally classified only by hydrogen absorption, labeled A, B, C, …, P. • Understanding other elements’ lines allowed the spectra to be ordered by temperature. • O, B, A, F, G, K, M • Oh, Be A Fine Guy/Girl, Kiss Me • Our Brother Andy Found Green Killer Martians. • Type O B A F G K M • Temperature 35,000 K 20,000 K 10,000 K 7,000 K 6,000 K 4,000 K 3,000 K Spectral Classes • Some bright stars (class): – Sun G2 – Sirius A1 – Alpha Centauri G2 – Capella G8 – Rigel B8 – Betelgeuse M1 – Aldebaran K5 • Temperature and luminosity are not the same thing. • Detailed measurements of spectra permit detailed classes. • Each type is split into 10 classes from 0 (hot) to 9 (cool). Filters • Filters are used to select a restricted bandwidth. – Wide: Dl ~ 100 nm – Intermediate: Dl ~ 10 nm – Narrow: Dl < 1 nm • A standard set of optical filters dates to the 1950’s – U (ultraviolet – violet): lp = 365 nm, Dl = 70 nm – B (photographic): lp = 440 nm, Dl = 100 nm – V (visual): lp = 550 nm, Dl = 90 nm Filter Sets • Other filter sets are based on a specific telescope. – HST: 336, 439, 450, 555, 675, 814 nm – SDSS: 358, 490, 626, 767, 907 nm • The standard intermediate filter set is by Strömgren. – u, b, v, y, b – bw: lp =486 nm, Dl=15 nm • CCDs have are good in IR, so filter sets have moved into IR as well. – U, B, V, R, I, Z, J, H, K, L, M. – Example M : lp = 4750 nm, Dl = 460 nm Color Index • The Planck formula at relates the intensity to the temperature. – Approximate for T < 104 K • Two magnitude measurements at different temperatures can determine the temperature. – Standard with B and V filters – Good from 4,000 to 10,000 K Wl (l , T ) TB V 2c 2 h l5 e hc / lkT hc hc 0.65 10 4 K lB k lV k TB V B V 2.5 log 10 exp T T 7090 K ( B V ) 0.71 Stellar Relations • The luminosity of a star should be related to the temperature. – Blackbody formula – Depends on radius L 4R 2T 4 • Some bright stars: – Sun G2 4.8 – Sirius A1 1.4 – Alpha Centauri G2 4.1 – Capella G8 0.4 – Rigel B8 -7.1 – Betelgeuse M1 -5.6 – Aldebaran K5 -0.3 Luminosity vs. Temperature -20 -15 Abs. Magnitude -10 -5 0 Sun 5 10 15 20 O B A F G K M Spectral Type • Most stars show a relationship between temperature and luminosity. – Absolute magnitude can replace luminosity. – Spectral type/class can replace temperature. Hertzsprung-Russell Diagram • The chart of the stars’ luminosity vs. temperature is called the Hertzsprung-Russell diagram. • This is the H-R diagram for hundreds of nearby stars. – Temperature decreases to the right Main Sequence -20 • Most stars are on a line called the main sequence. -15 Abs. Magnitude -10 -5 0 Sirius 5 1 solar radius 10 15 20 O B A F G K M Spectral Type • The size is related to temperature and luminosity: – hot = large radius – medium = medium radius – cool = small radius Balmer Jump • The color indexes can be measured for other pairs of filters. • The U-B measurement brackets the Balmer line at 364 nm. – Opaque at shorter wavelength • This creates a discontinuity in energy measurement. – Greatest at type A – Drop off for B and G Michael Richmond, RIT Photometric Comparison • Stellar classification is aided by different response curves. Bolometric Magnitude BC mbol V BC M bol M V L 3 1028 W 100.4 M bol 2.5 108 W m 2 100.4 mbol • Bolometric magnitude measures the total energy emitted at all wavelengths. – Modeled from blackbody – Standard filter V – Zero for main sequence stars at 6500 K • Luminosity is directly related to absolute bolometric magnitude. – Flux to apparent bolometric magnitude