Chapter 15 Surveying the Stars. Properties of Stars. Parallax and Distance. Distances Luminosities Temperatures Radii Masses

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1 hapter 15 Surveying the Stars Properties of Stars istances Luminosities s Radii Masses istance Use radar in Solar System, but stars are so far we use parallax: apparent shift of a nearby object against a background of more distant objects Parallax and istance Nearest star: lpha entauri at 1.3 parsecs Works well out to 200 parsecs (pc) The local 10 pc neighborhood (dric Riedel, GSU): Power radiated by star = surface area x rate/unit area = 4 R 2 x T 4 where R = radius T = temperature = Stefan-oltzmann constant pparent brightness: mount of starlight that reaches Earth 1

2 With increasing distance, luminosity is spread over a larger area rea of sphere = 4 (distance) 2 ivide luminosity by area to get brightness Inverse-Square Law: brightness proportional to 1/distance 2 Thought Question How would the apparent brightness of lpha entauri change if it were three times farther away?. It would be only 1/3 as bright. It would be only 1/6 as bright. It would be only 1/9 as bright. It would be three times brighter Magnitude Scale Magnitude Scale Given apparent magnitude m and distance d, we can find absolute magnitude M = apparent magnitude if moved to d = 10 pc Sun: M = 5 m M = 5 log d 5 Recall: log 1 = 0, log 10 = 1, log 100 = 2, Suppose star has absolute mag M = 5, d = 1000: What is apparent mag m? : Thermal Radiation 1. Hotter objects emit more light per unit area at all frequencies. 2. Hotter objects emit photons with a higher average energy. m = 5 + 5x3 5 = 5 2

3 The color of a star is indicative of its temperature (compare blue and visual (yellow) V magnitudes) 106 K 105 K Red stars are relatively cool, while blue ones are hotter. 104 K Ionized Gas (Plasma) 103 K Neutral Gas 102 K Molecules 10 K Solid Level of ionization seen in spectral absorption lines; spectral classification and Spectral lassification Pioneers of Spectral lassification nnie Jump annon and the calculators at Harvard laid the foundation of modern stellar classification Stellar spectra are much more informative than the blackbody curves. There are seven (ten) general categories corresponding to different temperatures. From highest to lowest, those categories are: O F G K M (L T Y) Oh, e Fine Girl/Guy, Kiss Me Radii ngular radius and distance give radius. Most stars are pin-points, but we are starting to measure their sizes using interferometry; GSU HR rray at Mt Wilson Regulus arcsec 3

4 Stellar Radii from Eclipsing inary Stars uration of light dips related to size (radius) Mass Many stars are in binary pairs; measurement of their orbital motion allows determination of the masses of the stars. Kepler s Third Law: (M1 + M2) P2 = a3 where M1 and M2 are the masses (MSUN), P is the period (years), and a is the separation or semimajor axis (U) Mass from Visual inaries Types of inary Star Systems Orbital motion can be measured directly Visual inary Eclipsing inary Spectroscopic inary bout half of all stars are in binary systems Kruger 60 4

5 Mass from Spectroscopic inaries: Motion detected by oppler shifts Masses from Eclipsing inaries ombine light curve and oppler shift curve: + radii, temperatures, system inclination, masses Hertzsprung- Russell diagram plots the luminosity and temperature of stars Positions of stars in the HR Most stars occupy the main sequence where stars create energy by H fusion (like the Sun). Higher mass stars have larger luminosities and shorter lives. Large radius For given T, stars with higher L have larger radii: giants and supergiants. Older stars where core H fusion done. 5

6 Small radius For given T, stars with lower L have lower radii: white dwarfs. Very old stars, all nuclear fusion complete. Full spectral classification includes spectral type and luminosity class: I - supergiant II - bright giant III - giant IV - subgiant V - main sequence Examples: Sun - G2 V Sirius - 1 V Proxima entauri - M5.5 V etelgeuse - M2 I Extending the osmic istance Scale Extending the osmic istance Scale istance from spectroscopic parallax We can estimate a star s luminosity if we know its spectral type and luminosity class 1. Measure the star s apparent magnitude m and spectral classification 2. Use spectral classification to estimate luminosity (absolute magnitude M) from HR 3. pply inverse-square law to find distance Magnitude version: m M = 5 log d - 5 Extending the osmic istance Scale Spectroscopic parallax can extend the cosmic distance scale to several thousand parsecs: H-R diagram depicts: olor Spectral Type Radius 6

7 Which star is the hottest? Which star is the most luminous? Which star is a main-sequence star? Which star has the largest radius? Stellar Properties Review : from brightness and distance 10-4 L Sun L Sun : from color and spectral type Stellar Properties Review : from brightness and distance (0.08 M 10-4 L Sun Sun ) L Sun (100 M Sun ) : from color and spectral type 3,000 K - 50,000 K (0.08 M Sun ) 3,000 K - 50,000 K (100 M Sun ) Mass: from period (p) and average separation (a) of binary-star orbit Mass: from period (p) and average separation (a) of binary-star orbit 0.08 M Sun M Sun 0.08 M Sun M Sun 7

8 Lifetime Main-Sequence Star Summary High Mass: Until core hydrogen (10% of total) is used up Sun s life expectancy: 10 billion years High Short-Lived Large Radius lue Life expectancy of 10 MSun star: 10 times as much fuel, uses it 104 times as fast 10 billion years x 10 / 104 ~ 10 million years Low Mass: Life expectancy of 0.1 MSun star: Low Long-Lived Small Radius Red 0.1 times as much fuel, uses it 0.01 times as fast 10 billion years x 0.1 / 0.01 ~ 100 billion years Which star is most like our Sun? Which of these stars will have changed the least 10 billion years from now? Which of these stars can be no more than 10 million years old? Star clusters: groups of same age stars 8

9 Open cluster: few thousand loosely packed stars (Pleiades) Globular cluster: Up to a million or more stars in a dense ball (M80) Massive blue stars die first, followed by lower mass stars (white, yellow, orange, and red) In HR, stars die away first at the top end (massive stars) of main sequence. Find cluster age by determining the turn-off point, the most massive stars still on main sequence. Oldest globular clusters are 13 billion years old 9