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9. Properties of Stars Astronomy 110: SURVEY OF ASTRONOMY 9. Properties of Stars 1. Distances & other parameters 2. The Hertzsprung-Russell diagram 3. Star clusters & stellar evolution Distance measurements are critical to understanding stellar properties. Stars span an enormous range of luminosity, temperature, and size, and these parameters are profoundly related to each other. Studying clusters of stars born at the same time provides clues to the lives of stars. 1. DISTANCES & OTHER PARAMETERS a. The Scale of the Solar System b. How Far to the Stars? c. Luminosity and Brightness The Scale of the Solar System Kepler and later astronomers made good scale models of the Solar System, but they didn’t know its true size. Planet a (AU) P (yr) Mercury 0.387 0.241 S Venus 0.723 0.615 Earth 1.000 1.000 Mars 1.524 1.881 Jupiter 5.203 11.857 Saturn 9.537 29.424 To find the value of one AU, a measurement of the actual distance (in km) to any planet would suffice. Parallax Method: Theory Observe P from points 1, 2 separated by baseline, b. D 1 b θ P 2 θ to distant star Suppose that from point 1 the planet lines up with a distant star, while from point 2 the angle between the planet and star is θ. Parallax Method: Theory How many triangles? 360° N = θ D b θ C Circumference P C of big circle? θ 360° C ≃ b θ Radius of big circle? 1 360° D ≃ b That’s the distance to P! 2π θ The Distance to Mars On October 1, 1672, Mars lined up with a bright star: Paris (Europe) Cayenne (South America) Wikipedia: Giovanni Cassini Mars was then 0.43 AU from Earth. Cassini used the known distance between the two observing points and the measured parallax angle to find this distance in km: 7 8 DMars ≃ 6.0×10 km ⇒ 1 AU ≃ 1.38×10 km Measuring the AU 1. Transits of Venus: 1761, 1769, 1874, 1882 — inconclusive due to effects of atmosphere 2. Observations of Mars: 1877 1 AU = 1.49×108 km 3. Observations of Eros: 1930 1 AU = 1.4960×108 km 4. Radar measurements: 1958 and since 1 AU = 1.49597871×108 km How Far to the Stars? We need a much larger baseline to measure Dec June stellar distances! The Earth’s orbit gives a baseline of b = 2 AU Stellar Parallax Over the course of a year, nearby stars seem to move in small ovals as a result of Earth’s motion about the Sun. Parallax of a Nearby Star Stellar Parallax Over the course of a year, nearby stars seem to move in small ovals as a result of Earth’s motion about the Sun. Parallax Calculations The parallax angle p is half the total shift: 1 360° 2p D ≃ Dec June 2π p AU Stars are far away, so D p is measured in arc- sec (1˝ = 1°/3600). p Define a new distance AU unit, the parsec (pc): 360 × 3600 1˝ 1 pc = AU = 3.09×1013 km ⇒ D ≃ 2π p pc 1. Suppose star B is twice as far away as star A. A. Star B has 4 times the parallax angle of star A. B. Star B has 2 times the parallax angle of star A. C. Both stars have the same parallax angle. D. Star A has 2 times the parallax angle of star B. E. Star A has 4 times the parallax angle of star B. 2. If we could measure stellar parallaxes from Mars instead of Earth, would nearby stars move in ovals which are A. the same size as seen from Earth, because the stars are just about as far from Mars. B. larger than seen from Earth, because Mars has a larger orbit. C. smaller than seen from Earth, because Mars is a smaller planet. Nearest Known Stars Most too dim 3.50 pc = 11.4 ly to see without 3.50 pc = 11.4 ly a telescope! 3.22 pc = 10.5 ly 3.65 pc = 11.9 ly 2.63 pc = 8.6 ly 1.32 pc = 4.3 ly 3.62 pc = 11.8 ly Wikipedia: Nearest stars A Stellar Distance Scale 1. Distances on Earth are determined by surveying techniques. 2. Parallax measurements at two points on Earth yield distances to other planets (now checked by radar). 3. These distances set the scale for the Solar System, and fix our distance to the Sun: 1 AU = 1.496×108 km. 4. Parallax measurements at two (or more) points on Earth’s orbit yield distances to nearby stars. At each step, known distances are used to find unknown distances. 3. Suppose we found an error in our calculation of the AU, and the correct value was 10% larger. How would this change our values for stellar distances? A. Stellar distances would be unchanged. B. Stellar distances would increase by 10%. C. Stellar distances would decrease by 10%. Luminosity and Brightness Absolute Luminosity (L) is the energy a star radiates per unit time. 26 L⊙ = 3.8×10 watt Apparent Brightness (B) is the energy received per unit time and unit area. 2 B⊙ = 1366 watt / m Brightness: Inverse-Square Law Energy conservation implies that the same luminosity passes through each sphere. Sphere of radius D has area A = 4πD2 Thus, brightness is inversely proportional to (distance)2: L L B = = A 4πD2 The Sun and αCen Compared αCen appears much fainter: αCen is much further away: -8 2 16 Bα = 2.8×10 watt / m Dα = 1.32 pc = 4.1×10 m 2 11 B⊙ = 1366 watt / m D⊙ = 1 AU = 1.49×10 m What about their luminosities? 2 26 Lα = Bα (4πDα ) = 5.9×10 watt 2 26 L⊙ = B⊙ (4πD⊙ ) = 3.8×10 watt αCen is about 50% more luminous than the Sun! 4. How would αCen’s apparent brightness change if it was 3 times further away? A. It would be 1/3 as bright. B. It would be 1/6 as bright. C. It would be 1/9 as bright. D. It would appear the same. E. It would be 3 times as bright. Neighbors of the Sun A few nearby stars are more luminous than the Sun, but most are much less luminous; of the 150 nearest stars: Number From (L⊙) To (L⊙) Examples of Stars 10 100 4 Vega: 50 L⊙ 1 10 14 αCen: 1.5 L⊙ 0.1 1 25 τCet: 0.46 L⊙ 0.01 0.1 21 0.001 0.01 57 0.0001 0.001 29 DISTANCES & OTHER PARAMETERS: REVIEW 1. Parallax equation: (a) number of triangles, (b) circumference of circle, (c) radius of circle. D b θ 1 360° P D ≃ b 2π θ 2. Brightness and luminosity: — brightness is what we observe; it has units of energy per unit time per unit area. — luminosity is what a star puts out; it has units of energy per unit time. 2. THE HERTZSPRUNG-RUSSELL DIAGRAM a. Interpreting Stellar Spectra b. The Main Sequence c. Beyond the Main Sequence Stars have different luminosities and colors. — luminous stars may be red or blue — dim stars are generally red SWEEPS ACS/WFC Color Composite Types of Spectra: Review Black Body Spectrum Black-Body (Thermal) Radiation Any opaque object (black body) with a temperature T > 0 K emits light (radiation). As the temperature goes up, this light gets brighter and bluer. Relationship Between Temperature and Luminosity Properties of Thermal Radiation • Higher temperature ⇒ more light at all wavelengths • Higher temperature ⇒ peak shifts towards blue Types of Spectra: Review Black Body Spectrum Emission Spectrum Black Body + Absorption Spectrum Spectral Lines: Review n = ∞ 13.6 eV Each electron orbit has a n = 6 13.2 eV n = 5 13.1 eV definite energy level. n = 4 12.8 eV In hydrogen, orbit n has energy n = 3 12.1 eV 1 2.9 eV En = ( 1 - 2 ) × 13.6 eV n 2.6 eV 434 nm 1.9 eV where an eV is an energy unit. 486 nm To jump from orbit to orbit 656 nm takes a photon with exactly the right amount of energy. n = 2 10.2 eV Stellar Spectra In stars, the lower photosphere produces a black-body spectrum, while cooler gas above creates dark lines. Black Body + Absorption Spectrum Text Stars exhibit a tremendous variety of spectra — why? Stellar Spectra Interpreting Stellar Spectra Stars have different spectra almost entirely because they have different surface temperatures! Stellar Spectra and Temperatures Composition plays a minor role — almost all stars are mostly hydrogen and helium, just like the Sun. Spectral Types Hydrogen T > 30000 K OOld T ~ 20000 K BBread T ~ 9000 K AAnd T ~ 6800 K FFruit T ~ 5500 K GGet T ~ 4200 K KKinda T < 3500 K MMoldy Ionized Titanium Sodium Titanium Calcium Oxide Oxide Spectral Types Hydrogen T > 30000 K Most H atoms are ionized. T ~ 20000 K Most H atoms T ~ 9000 K at n = 2 level. T ~ 6800 K T ~ 5500 K Most H atoms at n = 1 level. T ~ 4200 K T < 3500 K Ionized Titanium Sodium Titanium Calcium Oxide Oxide Plotting the HR Diagram The HR diagram shows surface temperature on the horizontal axis and luminosity on the vertical axis. The Main Sequence Most stars in the Sun’s neighborhood fall along a roughly diagonal line on an HR diagram. This line is called the main sequence. Nature of the Main Sequence All main-sequence stars produce energy in the same way as the Sun, by fusing hydrogen to form helium in their cores.
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