9. Properties of Stars

Transcription

1 Astronomy 110: SURVEY OF ASTRONOMY 9. Properties of Stars 1. Distances & other parameters 2. The Hertzsprung-Russell diagram 3. Star clusters & stellar evolution

2 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.

3 1. DISTANCES & OTHER PARAMETERS a. The Scale of the Solar System b. How Far to the Stars? c. Luminosity and Brightness

4 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 Venus S Earth Mars Jupiter Saturn To find the value of one AU, a measurement of the actual distance (in km) to any planet would suffice.

5 Parallax Method: Theory Observe P from points 1, 2 separated by baseline, b. 1 D 2 b θ θ P 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.

6 Parallax Method: Theory How many triangles? 360 N = θ D Circumference C of big circle? b θ θ P C 360 C b θ Radius of big circle? D 1 2π 360 b θ That s the distance to P!

7 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: DMars km 1 AU km

8 Measuring the AU 1. Transits of Venus: 1761, 1769, 1874, 1882 inconclusive due to effects of atmosphere 2. Observations of Mars: AU = km 3. Observations of Eros: AU = km 4. Radar measurements: 1958 and since 1 AU = km

9 How Far to the Stars? We need a much larger baseline to measure stellar distances! The Dec June Earth s orbit gives a baseline of b = 2 AU

10 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

11 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.

12 Parallax Calculations The parallax angle p is half the total shift: D 1 2π 360 AU p Dec 2p June Stars are far away, so D p is measured in arcsec (1 = 1 /3600). Define a new distance p AU unit, the parsec (pc): 1 pc = AU = km 2π D p 1 pc

13 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.

14 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.

15 Nearest Known Stars Most too dim 3.50 pc = 11.4 ly to see without a telescope! 3.50 pc = 11.4 ly 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

16 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 = 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.

17 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%.

18 Luminosity and Brightness Absolute Luminosity (L) is the energy a star radiates per unit time. L = watt Apparent Brightness (B) is the energy received per unit time and unit area. B = 1366 watt / m 2

19 Brightness: Inverse-Square Law Energy conservation implies that the same luminosity passes through each sphere. Sphere of radius D has area A = 4πD 2 Thus, brightness is inversely proportional to (distance) 2 : B = L A L = 4πD 2

20 The Sun and αcen Compared αcen appears much fainter: Bα = watt / m 2 B = 1366 watt / m 2 αcen is much further away: Dα = 1.32 pc = m D = 1 AU = m What about their luminosities? Lα = Bα (4πDα 2 ) = watt L = B (4πD 2 ) = watt αcen is about 50% more luminous than the Sun!

21 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.

22 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: From (L ) To (L ) Number of Stars Examples Vega: 50 L αcen: 1.5 L τcet: 0.46 L

23 DISTANCES & OTHER PARAMETERS: REVIEW 1. Parallax equation: (a) number of triangles, (b) circumference of circle, (c) radius of circle. D D 1 2π 360 b θ b θ P 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.

24 2. THE HERTZSPRUNG-RUSSELL DIAGRAM a. Interpreting Stellar Spectra b. The Main Sequence c. Beyond the Main Sequence

25 Stars have different luminosities and colors. luminous stars may be red or blue dim stars are generally red SWEEPS ACS/WFC Color Composite

26 Types of Spectra: Review Black Body Spectrum

27 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

28 Properties of Thermal Radiation Higher temperature more light at all wavelengths Higher temperature peak shifts towards blue

29 Types of Spectra: Review Black Body Spectrum Emission Spectrum Black Body + Absorption Spectrum

30 Spectral Lines: Review n = 13.6 ev Each electron orbit has a n = ev definite energy level. n = ev n = ev In hydrogen, orbit n has energy ( 1 ) En = ev n 2 n = ev 2.6 ev 434 nm 12.1 ev where an ev is an energy unit. 1.9 ev 486 nm To jump from orbit to orbit takes a photon with exactly 656 nm the right amount of energy. n = ev

31 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

32 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.

33 Spectral Types Hydrogen T > K T ~ K T ~ 9000 K T ~ 6800 K T ~ 5500 K T ~ 4200 K T < 3500 K Old Bread And Fruit Get Kinda Moldy Ionized Calcium Titanium Oxide Sodium Titanium Oxide

34 Spectral Types Hydrogen T > K T ~ K T ~ 9000 K Most H atoms are ionized. Most H atoms at n = 2 level. T ~ 6800 K T ~ 5500 K T ~ 4200 K Most H atoms at n = 1 level. T < 3500 K Ionized Calcium Titanium Oxide Sodium Titanium Oxide

35 Plotting the HR Diagram The HR diagram shows surface temperature on the horizontal axis and luminosity on the vertical axis.

36 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.

37 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. A star s place along the main sequence is fixed by its mass.

38 Measuring Stellar Masses: Review For any two masses M and m orbiting each other, Newton s version of Kepler s Law III states: P 2 4π 2 a 3 = G(M + m) m M Wikipedia: Kepler s Laws This provides a way of weighing stars we observe a pair of stars orbiting each other (a double-star) and solve this equation to get their masses.

39 Stellar Lifetimes Along the Main Sequence The main sequence is also a sequence of lifetimes. High-mass stars must have hotter cores to balance gravity, so they use up hydrogen faster.

40 The Main Sequence: Summary Mass is the key property of a main-sequence star: other basic properties are all determined by mass. Low Mass High Mass low luminosity high luminosity low temperature high temperature long lifetime short lifetime

41 Giants and Supergiants Some stars are not part of the main sequence; they are relatively cool but very luminous. These stars must have enormous radii to give off so much energy.

42 White Dwarfs Other stars are hot but very dim. These stars must have tiny radii to give off so little energy.

43 Stellar Radii

44 THE H-R DIAGRAM: SUMMARY a. Interpreting Stellar Spectra spectra differ mostly because of temperature. b. The Main Sequence on the main sequence, stars are arranged by mass. c. Beyond the Main Sequence giants and dwarfs have very different radii.

45 Main Sequence Lifetimes 1 M star: L = L lifetime: T yr 10 M star: L 10 4 L 10 fuel; use at 10 4 rate T (10/10 4 ) T 10 7 yr 0.1 M star: L L 0.1 fuel; use at rate T (0.1/0.003) T yr

46 3. STAR CLUSTERS & STELLAR EVOLUTION a. Nature of Star Clusters b. Cluster HR Diagrams c. Cluster Distances

47 Nature of Star Clusters Open clusters Globular clusters

48 Two Types of Clusters 1. Globular Clusters old, metal -poor stars contain 10 5 to 10 6 stars found in halo of Milky Way 2. Open Clusters young, metal -rich stars contain 100 to 10 4 stars found in disk of Milky Way

49 Cluster Formation Star clusters form in massive interstellar gas clouds. cloud well-mixed stars have similar composition rapid formation stars have similar ages Star Cluster R136 Bursts Out

50 Star Cluster Dynamics Clusters are held together by mutual gravity of stars. Simulated Star Cluster High-mass cluster stars tend to form pairs and eject smaller stars. This eventually disrupts open clusters.

51 Cluster HR Diagrams All the stars in a cluster The Pleiades (M45) have the same age, so HR diagrams for cluster stars tell us about: cluster ages stellar evolution cluster distances

52 Evolution of HR Diagrams High-mass stars burn out first; low-mass stars die later. So as a cluster ages, the main sequence burns down in order. lifetime: 10 7 yr lifetime: 10 8 yr lifetime: 10 9 yr lifetime: yr (Note: this animation also shows stars after they leave the main sequence.) Using the H-R Diagram to Determine the Age of a Star Cluster

53 Evolution of HR Diagrams High-mass stars burn out first; low-mass stars die later. So as a cluster ages, the main sequence burns down in order. Instead of plotting stars, we represent them with a line of constant age. Using the H-R Diagram to Determine the Age of a Star Cluster

54 The Pleiades: A Young Cluster Using the H-R Diagram to Determine the Age of a Star Cluster Pleiades and Stardust

55 M67: An Older Cluster Using the H-R Diagram to Determine the Age of a Star Cluster Star Cluster Messier 67

56 Cluster HR Diagrams Compared Globular Cluster M4 Clusters have a range of ages; giant and dwarf stars appear at different stages of cluster aging process.

57 Cluster Distances All stars in a cluster are at the same distance Pleiades Hyades Plot apparent brightness instead of luminosity. Main seq. in Hyades appears ~9 brighter than in Pleiades; why? apparent brightness Pleiades are ~3 more 10-5 distant than Hyades! surface temperature 3000

58 A Cluster Distance Scale 1. Parallax measurements at two (or more) points on Earth s orbit yield distances to nearby stars. 2. Nearby stars are used to measure luminosity of main sequence. 3. Main sequence luminosity is used to get distance to Hyades & Pleiades (also checked by parallax). 4. Improved main sequence luminosities yield distances to other clusters throughout galaxy (and beyond!). At each step, known distances are used to find unknown distances.