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Unformatted text preview: ‘ recitation will be on this Fri. and will I estimation. I _ to keep up with the reading! NASA, NOAO, ESAand The Hubble Herliage Team (STSCI/AURA) Radiation (Kulner, Ch. 2; see also Kamunen, Ch. 4; Shu, Ch. 2) AST 203 (Spring 2011) Properties of Stars - How we can measure various properties of stars? - What properties do you think that we can measure? AST 203 (Spring 2011) Units and Measurements - |n astrophysics, we use the cgs system of units — Unit of length: centimeter (cm) — Unit of mass: gram (g) — Unit of time: second (5) - Some derived units — Force is measured in dynes: g cm s'2 - Compare to Newtons: 1 N = 1 kg m s‘2 = 105 dyn — Energy is measured in ergs: g cm2 s'2 - Compare to Joules: 1 J =1 N m =1 kg m2 5'2 =107 erg — Power is measured in erg s'1 - Compare to Watts: 1 W: 107 erg s'1 AST 203 (Spring 2011) Fundamental Constants — Speed of light: c = 3.00 x 1010 cm s'1 — Gravitational constant: G = 6.67 x 10'8 g'1 cm3 s'2 — Planck's constant: h = 6.63 x 10'27 erg s — Electron charge: e = 4.80 x 10'10 esu (g“2 cm?"2 s") — Electron mass: me = 9.11 x10'28 g — Proton mass: mp = 1.67 x1024 g — Boltzmann's constant: k = 1.38 x 10'16 erg K'1 — Stefan-Boltzmann constant: a = 5.67 x 10'5 erg cm'2 s'1 K'4 Temperature is measured in Kelvin, K, but as we will see, it usually enters into equations as kT, which is measured in ergs. AST 203 (Spring 2011) Angles and Solid Angles For this course, it is often more convenient to work in radians. There are 27r radians in a circle: 271' rad : 360° lf 6 (measured in rad) is subtended by r‘ an arc, and r is the radius, arc length is l=7°0 Also useful are the small angle formulas. lf 6 << 1 then sin0m0; taanH How many degrees correspond to 1 radian? You should know how to sketch cos 6, sin6 AST 203 (Spring 2011) Angles and Solid Angles Solid angles describe a fraction of a sphere. If an emitting source covers an area A on a spherical surface of radius 7“, then the solid angle is Q:A/r2 Solid angles are measured in steradians How many steradians in a hemisphere? AST 203 (Spring 2011) Useful Formulas from Geometry You should be comfortable with computing the area and volume of objects. Circle 0 : 27w A : 71'7'2 S r h —l : 47rr2 4 3 7 371'?" Sphere ‘ / - T Cylinder I V : 7W2h What is the surface area of a cylinder? . l— AST 203 (Spran 2011) Astronomical Information - ln astronomy, we primarily get information in the form of electromagnetic radiation (I'll frequently use light to mean the entire electromagnetic spectrum). - To a lesser extent, we also get information from: — Meteorites — Neutrinos — Gravitational radiation (maybe someday...) — Cosmic rays AST 203 (Spring 2011) Mag n itudes - Look at the night sky: some stars are brighter than others - Greek astronomers created the magnitude system. — Stars assigned brightness on a scale of 1 to 6 - 1 = brightest, 6 = faintest. — Standardized: difference in 5 magnitudes = factor of 100 in brightness - Logarithmic scale—our eye's response to light is also logarithmic - By brightness, we really mean flux—energy/area/second AST 203 (Spring 2011) Equatorial Coordinate System p - Star chart gives the position of the stars in equatorial coordinates. - Right ascension, oz - analogous to longitude — measures distance vernal equinox in hours, minutes, seconds - Declination, 6 SCP — analogous to latitude — measures the angle in degrees north or south of the celestial equator. AsT 203 (Spl ing 2011) Mag nitudes Mathematically, we can relate the brightness or flux of two objects as E : 100(m2im1)/5 f2 remember—the brighter an object, the smaller the magnitude. Originally, the magnitude scale went from 1 to 6 6 is the “naked-eye limit" Today: Large telescopes can see down to magnitude 30 and below The brightest stars in the sky have negative magnitudes apparent magnitude refers to how bright something appears when viewed from earth. AST 203 (Spring 2011) ecliptic celestial equator Magnitudes Apparent Magnitudes of Known Celestial Objects App. Mag. Celestial Object 226 73 Sun —12 6 full Moon I—Q 5 Maximum brightness of an Iridium Flare| 74.7 Maximum brightness of Venus I—3 9 Faintest oblects observable during the day With naked eye 72 9 Maximum brightness of Mars I—2 8 Maximum brightness ofjubiter 7]. 9 Maximum brightness of Mercury I—l S Brightest star (except torthe sun! at Vlslble Wavelengths: Sirius 20.7 Second brightest star Canopus 0 The zero point by definition: This used to be Vega (see references for modern zero point) In 7 Maximum brightness of Saturn 3 Faintest stars Visible in an urban neighborhood With naked eye .4 6 Maximum brightness of Ganymede 5.5 Maximum brightness of Uranus '6 Faintest stars observable With naked eye .7 7 Maximum brightness of Neptune 12.6 Brightest quasar '13 Maximum brightness of Pluto 27 Faintest objects observable in visible light With Em ground-based telescopes '30 Faintest oblects observable in Visible light With Hubble Space Telescope I 38 Faintest objects observable in visible light With planned OWL E2020! Ilsee also List of brightest stars] (from Vlfikipedia) AST 203 (Spring 2011) Properties of Logarithms . lfN = apthen p = loga N — a is the base of the logarithm . loga MN = loga M + loga N . loga (MIN) = loga M — loga N . loga Mp = p loga M . We'll use “In” to mean loge, and “log” to mean log10 Properties of Exponents . ap aq = ap+q - a'p = 1/ap . (ap)q = apq AST 203 (Spring 2011) Magnitudes We can rewrite our magnitude equation f1 < e )/5 —:100m2 m1 f2 by taking the base-10 logarithm: m2 — m1 : 2.510g 2 What magnitude difference corresponds to a factor of 10 million in brightness? What brightness ratio corresponds to a 10 magnitude difference? The Sun is -26.73 and the faintest object visible in the HST is 30 —this corresponds to a brightness ratio of 5 x 1022! AST 203 (Spring 2011) Magnitudes (Kantunen el al.) Consider a binary star system consisting of a magnitude 1 star and a magnitude 2 star. What is the total magnitude of the binary system? AST 203 (Spring 2011) Light Astronomers primarily gain information about distant objects by looking at the light coming from them. Properties of light: / i in / fl \ \ / / my“ \ E *2???+‘*<i;i;i,ii2?ffhi:i? WE SupehManu/Wikipedia) Maxwell: light is an electromagnetic wave alternating electric and magnetic fields perpendicular to each other. Such a configuration can freely propagate through space. AST 203 (Spring 2011) Light EM waves have a number of properties associated with them: Wavelength: the distance between successive wave crests Polarization: the direction of oscillation of the electric field Direction of propagation: normal to the E and B fields Regardless of the wavelength or polarization, propagation speed of an EM wave is constant, and in vacuum has the value: C = 3.00 X 1010 cm (5—1 In addition to the wavelength,)\ , we can also consider frequency, 1/ ,—the number of oscillations per second. Auzc AST 203 (Spring 2011) Light Names assigned to different parts of the EM spectrum. é .. E E Our eyes are only sensitive to a g 3 small portion of this spectrum, 5 8 but astronomical objects can "” C” emit across the entire spectrum. 1000MHZ : Note, frequency is measured In 500MHz; units of Hz. ’ 50 MHz : AST 203 (Spring 2011) Light 3 Frequency (Hz) 1015_ 1D”, 1015_ 101a 1012_ 1D“_ \\101u_ \ 1093.. .. .. 1DE_ /. 1D7_ / 105_ Gamma—rays _ X-rays Ultraviolet Microwaves Rm: Radio TV A Vi Long-waves E. on 1: 2 m i: E 0.1 A _{1A 01nm — 1 nm / 400 rim / ,/ *1Dnm/ / / / 500nm 600nm 700 nm 710mm _{1000 pm 1mm — 1 cm — 10cm *1m — 10m —1DUm —1000m (\Mkipedia) Our atmosphere is not transparent across the whole EM 100% .9 a u 3 50% me spectrum nlnm Imn Iflnm 100nm Vlliflh uam MILI- mm. Mal lam Gamml um, Iva-y: IM unmiqu Llnm W by m- app-r mom-u lum loum 100w" 1mm 1cm mom Im 10m 1mm 1km (NASA/JPL; http:/Igallery.spitzer.callech.edullmagegallerylimage.php?image_name=bgOO5) Note the window at the visible spectrum—our eyes developed sensitivity to these wavelengths because of this window. AST 203 (Spring 2011) Light If we want to observe in the infrared, we need to get above the atmosphere. The James Webb Space Telescope (JWST) to be launched in 2013 (or later) will do just this. (NASA) AST 203 (Spring 2011) Light The Spitzer Space Telescope is in orbit now and returning all sorts of IR images—we'll see a lot of them in this class. Andromeda galaxy imaged in the IR by Spitzer (NASA/JPL-Caltecth. Gordon (University of Arizona» SOFIA will put a telescope in a 747 and fly high—above the water vapor in the atmosphere, to image in the IR. AST 203 (Spring 2011) Colors of Stars Some stars are different colors. Astronomers describe the color of a star by measuring the intensity of energy a star gives off over some wavelength interval, Cu, or frequency interval, 61,}. We call this the spectra of the star. (Mouser Williams) AST 203 (Spring 2011) Colors of Stars Spectra from normal stars MW over a range of masses. KSV Notice: smooth part, called the continuum + a number of Gav absorption lines—we'll talk M about those later. W Right now, we are interested in understanding the A“ continuum. Relative brightness 35V 05V 3500 4500 5500 0500 7500 8500 Wavelength f Angstroms (Jodrell Bank Observatory; based on Pickles 1988) AST 203 (Spring 2011) Intensity I(u)du = energy/unit time/unit surface area in the frequency range 1/ to V + dz/ being emitted into a cone of solid angle d9 Radiation moves through a small area dA into the cone described by d9 Energy moving through this area into the solid angle dB is dEzIV COSQdAdI/dfldt Intensity is measured in units of erg s"1 cm"2 Hz"1 ster'1 AST 203 (Spring 2011) Intensity (.059 {Actor [Vt lVl‘l‘eL/lsl‘ly ciefmd‘wh AST 203 (Spring 2011) Intensity In terms of wavelength, I(A)d)\ = energy/unit time/unit area in the wavelength range A to A + dA emitted into solid angle d9 Then dE : I,\ cos QdA dA d9 dt It is important to remember that intensity has a direction. Note—your book is a bit sloppy here. It leaves out the solid angle part. AsT 203 (spring 2011) Blackbody - We won't go deeply into what intensity means (AST 341 topic) — We'll use intensity to derive some important results. - Important concept: blackbody (thermal radiator) — Object in thermodynamic equilibrium — Emission = absorption — Emitted light has well-known intensity spectrum - Function ofT only - Isotropic, unpolarized. - Blackbody emission spectrum can be very different than that it absorbs — Only requirement is that the net energy gain is zero, is it is in equilibrium. AST 203 (Spring 2011) Blackbody A blackbody absorbs ALL incident radiation —> black. If emission ¢ absorption, then T would change —> no equilibrium. Stellar interior: atoms opaque to radiation—absorb and re-emit it. We see the stellar surface —> stars act as good blackbodies. (Fimoozwmema) AST 203 (Spring 2011) Thermal Radiation 1433.2? mm .123 .100 uflr Seeing in IR maritime 352-0 NA Elfin-"I P A C Ashttpwmnlopsmos.ipac.caltech .ed u/cosmic_kids/learn_ir/ind ex. html Blackbodies 10'5 infrared visibleUV Ximy Gammuiruy T the peak of the 10‘": emission moves to 3 higher frequencies 5— (shorter iO — : wavelengths) ? mo; 3 : Hotter objects ml appear bluer. 10710—— 10’”:— 105 10‘“ 10‘5 102” Notice that the higher temperature blackbody emits more radiation than the lower temperature blackbodies at all frequencies. AST 203 (Spring 2011) ...
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