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Slide 1 The Family of Stars Chapter 9
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Slide 2 Part 1: measuring and classifying the stars What we can measure directly: – Surface temperature and color – Spectrum – Apparent magnitude or intensity –Diameter of a few nearby stars – Distance to nearby stars What we usually cannot: – Distance to most stars – Luminosity (energy radiated per second) – Diameter and mass
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Slide 3 Surface temperature and color indices Color indices: B-V, U-B Color filters Differences in apparent magnitudes observed through different filters
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Slide 4 Spectral Classification of Stars Mnemonics to remember the spectral sequence: OhOhOhOhOnly BeBeBoy,Bad AAnAnAstronomers FineFForget Girl/GuyGradeGenerally KissKillsKnown MeMeMeMeMnemonics
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Slide 5 How to find distances to the stars? Parallax (only for stars within ~1500 ly) From stellar motions For moving clusters Using “standard candles” (model-dependent) Using mass-luminosity relation (for main- sequence stars) or period-luminosity relations (for binaries and variable stars; model- dependent)
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Slide 6 When d is too large, angles A and B become too close to 90 0 The larger the baseline, the longer distances we can measure
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Slide 7 Apparent shift in the position of the star: parallax effect The longest baseline on Earth is our orbit! Angular shift; we can measure it directly
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Slide 8 Effect is very small: shift is less than 1 arcsec even for closest stars Aristotle used the absence of observable parallax to discard heliocentric system Larger shift Smaller shift
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Slide 9 Half of the angular shift is called parallax angle p and used to define new unit of distance
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Slide 10 The parallax angle p Define 1 parsec as a distance to a star whose parallax is 1 arcsec d (in parsecs) = 1/p 1 pc = 206265 AU = 3.26 ly Small-angle formula:
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Slide 11 The Trigonometric Parallax Example: Nearest star, Centauri, has a parallax of p = 0.76 arc seconds d = 1/p = 1.3 pc = 4.3 LY With ground-based telescopes, we can measure parallaxes p ≥ 0.02 arc sec => d ≤ 50 pc With Hipparcos satellite: parallaxes up to 0.002 arcsec, i.e. d up to 500 pc. 118218 stars measured!
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Slide 12 Proper Motion In addition to the periodic back-and- forth motion related to the trigonometric parallax, nearby stars also show continuous motions across the sky. These are related to the actual motion of the stars throughout the Milky Way, and are called proper motion.
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Slide 13 Barnard’s star: highest proper motion 10 arcsec per year, or one lunar diameter per 173 yr Approaches us at 160 km/sec Fourth closest star
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Slide 14 Brightness and distance Apparent magnitude: tells us how bright a star looks to our eyes Intensity, or radiation flux received by the telescope: Energy of radiation coming through unit area of the mirror per second (J/m 2 /s)
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Slide 15 Brightness and Distance The flux received from the star is proportional to its intrinsic brightness or luminosity (L) and inversely proportional to the square of the distance (d): R d L
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Slide 16 d1d1 d2d2
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Slide 17 Intrinsic Brightness, or luminosity The flux received from the star is proportional to its intrinsic brightness or luminosity (L) and inversely proportional to the square of the distance (d): I = L __ 4d24d2 Star A Star B Earth Both stars may appear equally bright, although star A is intrinsically much brighter than star B.
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Slide 18 Brightness and Distance (SLIDESHOW MODE ONLY)
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Slide 19 Define the magnitude scale so that two objects that differ by 5 magnitudes have an intensity ratio of 100. Order of terms matters! Recall the definition of apparent magnitude:
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Slide 20 However, the apparent magnitude mixes up the intrinsic brightness of the star (or luminosity) and the effect of distance (which has nothing to do with the luminosity of the star). Inverse square law:
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Slide 22 Distance and Intrinsic Brightness Betelgeuse Rigel Example: App. Magn. m V = 0.41 Recall that: Magn. Diff. Intensity Ratio 12.512 22.512*2.512 = (2.512) 2 = 6.31 …… 5(2.512) 5 = 100 App. Magn. m V = 0.14 For a magnitude difference of 0.41 – 0.14 = 0.27, we find an intensity ratio of (2.512) 0.27 = 1.28
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Slide 23 Distance and Intrinsic Brightness (2) Betelgeuse Rigel Rigel is appears 1.28 times brighter than Betelgeuse, Thus, Rigel is actually (intrinsically) 1.28*(1.6) 2 = 3.3 times more luminous than Betelgeuse. But Rigel is 1.6 times further away than Betelgeuse
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Slide 24 A star that is very bright in our sky could be bright primarily because it is very close to us (the Sun, for example), or because it is rather distant but is intrinsically very bright (Rigel, for example). It is the "true" (intrinsic) brightness, with the distance dependence factored out, that is of most interest to us as astronomers. Therefore, it is useful to establish a convention whereby we can compare two stars on the same footing, without variations in brightness due to differing distances complicating the issue. Astronomers define the absolute magnitude M to be the apparent magnitude that a star would have if it were (in our imagination) placed at a distance of 10 parsecs (which is 32.6 light years) from the Earth. To determine the absolute magnitude M the distance to the star must also be known! Absolute Magnitude
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Slide 25 Absolute magnitude Recall that for two stars 1 and 2 Let star 1 be at a distance d pc and star 2 be the same star brought to the distance 10 pc. Then Inverse: m 2 = M
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Slide 26 The Distance Modulus If we know a star’s absolute magnitude, we can infer its distance by comparing absolute and apparent magnitudes: Distance Modulus = m V – M V = -5 + 5 log 10 (d [pc]) Distance in units of parsec Equivalent: d = 10 (m V – M V + 5)/5 pc
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Slide 27 Absolute magnitudes of two different stars 1 and 2: If two stars are at the same distance of 10 pc from the earth:
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Slide 28 Absolute Magnitude (2) Betelgeuse Rigel BetelgeuseRigel mVmV 0.410.14 MVMV -5.5-6.8 d152 pc244 pc Back to our example of Betelgeuse and Rigel: Difference in absolute magnitudes: 6.8 – 5.5 = 1.3 => Luminosity ratio = (2.512) 1.3 = 3.3
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Slide 29 Is there any correlation between stellar luminosities, radii, temperature, and masses??? We learned how to characterize stars with many different parameters Organizing the Family of Stars
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Slide 30 The Size (Radius) of a Star We already know: flux increases with surface temperature (~ T 4 ); hotter stars are brighter. But luminosity also increases with size: A B Star B will be brighter than star A. Luminosity is proportional to radius squared, L ~ R 2. Quantitatively: L = 4 R 2 T 4 Surface area of the star Surface flux due to a blackbody spectrum
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Slide 31 Example: Star Radii Polaris has just about the same spectral type (and thus surface temperature) as our sun, but it is 10,000 times brighter than our sun. Thus, Polaris is 100 times larger than the sun. This causes its luminosity to be 100 2 = 10,000 times more than our sun’s.
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Slide 32 However, star radius is not a convenient parameter to use for classification, because it is not directly measured. Surface temperature, or spectral class is more convenient!
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Slide 33 Organizing the Family of Stars: The Hertzsprung-Russell Diagram We know: Stars have different temperatures, different luminosities, and different sizes. To bring some order into that zoo of different types of stars: organize them in a diagram of Luminosity versus Temperature (or spectral type) Luminosity Temperature Spectral type: O B A F G K M Hertzsprung-Russell Diagram or Absolute mag.
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Slide 34 Hertzsprung-Russell Diagram 1911 1913 Absolute magnitude Color index, or spectral class Betelgeuse Rigel Sirius B
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Slide 37 Stars in the vicinity of the Sun
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Slide 38 Stars in the vicinity of the Sun
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Slide 39 90% of the stars are on the Main Sequence!
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Slide 40 Total radiated power (luminosity) L = T 4 4 R 2 J/s Check whether all stars are of the same radius:
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Slide 41 No, they are not of the same radius
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Slide 42 The Radii of Stars in the Hertzsprung-Russell Diagram 10,000 times the sun’s radius 100 times the sun’s radius As large as the sun Rigel Betelgeuse Sun Polaris
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Slide 43 Specific segments of the main sequence are occupied by stars of a specific mass Majority of stars are here
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Slide 44 The mass-luminosity relation for 192 stars in double-lined spectroscopic binary systems. L ~ M 3.5 much stronger than inferred from L ~ R 2 ~ M 2/3
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Slide 45 However, this M 3.5 dependence does not go forever: Cutoff at masses > 100 M and < 0.08 M
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Slide 46 All stars visible to the naked eye + all stars within 25 pc H-R diagram for nearby+bright stars:
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