Class 4 : Basic Properties Of Stars

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Class 4 :Basic properties of stars Distance to stars Parallax method for determining distanceDefinition of the “parsec” Flux, luminosity, magnitude and color HR diagramsI : The distance to the stars The distance to any astronomical object is themost basic parameter we want to know Require knowledge of distance in order to calculatejust about any other property of the objectDistance is often difficult to determine!Most direct method for measure distances to“nearby” stars uses an effect called parallax As Earth orbits Sun, we view a star along a slightlydifferent line of sightThis causes the star to appear to move slightly withrespect to much more distant starsWe can currently use this technique to measurestellar distances out to 3000 light years from Earth1

If star displays parallax of θ 1arcsec, then distance D isgiven by This distance is called a parsec and is a commonly usedunit of distance in astronomyIn general, if a star displays a parallax of θ, then itsdistance is 2

II : Flux and luminosity Definition : The observed flux of a star is the energyreceived from the star per unit time per unit area. The area under consideration must be oriented face-on to lineof-sight to the starIn principle, this definition works for any kind of energyemitted by the star most commonly, we mean e/m radiationSometimes, it is useful to consider the observed flux in arestricted range of e/m wavelengths (e.g., the “optical flux” or“X-ray flux”, or “500-600nm flux”)Definition : The luminosity of a star is the energy per unittime (i.e. power) emitted by the star Again, this can apply to any kind of energy but we will usuallymean e/m radiationAgain, it is sometimes useful to consider the luminosity in arestricted range of e/m wavelengths3

Suppose a star emits equally in alldirections (ie the emission is isotropic)and is steady in time. Then, if D is thedistance to the star, observed flux Fand luminosity L and related accordingto:Inverse squarelaw for fluxIII : Stellar magnitudes 2000 years ago, Hipparcus ranked theapparent brightness of stars according to“magnitudes” 1st magnitude - brightest stars in sky2nd magnitude - bright but not brightest 6th magnitude - faintest stars visible to human eyeThis system is based on visual perception(which is a logarithmic system) mag 1 is factor of f brighter than mag 2mag 2 is factor of f brighter than mag 3THUS, mag 1 is factor of f2 brighter than mag 34

Modern definition: If two stars have fluxes F1and F2, then their apparent magnitudes m1and m2 are given by Notes The star Vega is defined to have an apparentmagnitude of zero! This allows one to talk aboutthe apparent magnitude of a given star rather thanjust differences in apparent magnitudesValue of constant k setby reference to Vega Higher apparent magnitudes, are fainter stars!A difference of 5 magnitudes corresponds to a factorof 100 in fluxBrightest star (Sirius) has m -1.44Faintest stars visible to human eye have m 6.5Sun has m -26.7Full Moon has m -12.6Venus at its brightest m -4.7Pluto has m 13.65Faintest object visible by Hubble Space Telescope ism 305

Definition : The absolute magnitude (M) ofa star is its apparent magnitude if it wereplaced at a distance of 10pc. If star is at distance D, we get The quantity m-M is called the distance modulusAll of this sounds complicated but just keepin mind that: Apparent magnitude fluxAbsolute magnitude luminosityDistance modulus distance6

IV : Colors “Traditional” astronomers often observe using filtersthat only allow a certain range fo wavelengths through.Common “bands” are UBVRK-ultravioletbluevisualrednear infraredSo we can measure the apparent magnitude of a givestar in different filters mB, mV, mR etc. We then define color indices by taking differences of themagnitudes measured in the different filters U-B mU-mB,B-V mB-mV etc.Confused?Color index stellar temperatureQuestion : Is B-V 0 a blue or red star, and what is thereference point? How does this change with distance?V : Spectral types Stellar spectra possess much more informationthan simple color the presence/strengths ofthe absorption lines characterize the nature ofthe outer layers of the star In 1901, Annie Cannon showed that stars can beclassified into seven groups (spectral-type) accordingto strengths of absorption lines: O B A F G K MEach spectral-type is subdivided into 10 subclasses:A0,A1,A2,A3, ,A9Sun is a G2 starIn 1921, Cecilia Payne showed that all stars arecomposed mostly of H and He; spectral differencesreflect differences of temperature, not composition7

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VI : Patterns in the properties of stars Consider the following experiment Find a star cluster so that you know that all stars are atapproximately the same distance from EarthMeasure apparent magnitude and colors of the starsPlot these two quantities against each otherThis is a Hertzsprung-Russell diagramWhat would you expect?Despite all of the potential complexities, most stars lieon a single line in this diagram! The rest inhabit veryspecific lines/regions. What underlies this surprising simplicity?All stars have basically the same composition 75% H, 24%He, 1% everything elseOnce born, stars “forget” environment they were born inSo only mass and age matter.9

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1 Class 4 : Basic properties of stars Distance to stars Parallax method for determining distance Definition of the “parsec” Flux, luminosity, magnitude and color HR diagrams I : The distance to the stars The distance to any astronomical object is the most basic parameter we want to

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