Reading and Announcements. Read Chapters 9.5, 9.6, and 11.4 Quiz #4, Thursday, March 7 Homework #5 due Tuesday, March 19

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1 Reading and Announcements Read Chapters 9.5, 9.6, and 11.4 Quiz #4, Thursday, March 7 Homework #5 due Tuesday, March 19

Henry David Thoreau (1849) Are Stars similar to our Sun?

2 Stars The stars are distant and unobtrusive, but bright and enduring as our fairest and most memorable experiences. Henry David Thoreau (1849) Are Stars similar to our Sun? How far away are they? Where did they come from? What do they do? Do they live forever?

3 Panorama view of the sky

6 What Properties of Stars Can We Measure? Position Apparent brightness Color Distance Luminosity Temperature Radius Mass Direct measurement Direct measurement Direct measurement Direct measurement Infer Infer Infer Infer Only luminosity, temperature, radius, and mass will help us understand how stars work.

7 The Four Basic Intrinsic Properties of Stars Luminosity Size Mass Surface Temperature To understand the physics of stars, we need to measure these four parameters.

8 Questions to be addressed How may a star s distance be measured? How may a star's luminosity be inferred? How may a star s temperature be inferred? How may a star's radius be inferred? How may a star's mass be inferred?

9 Luminosity Luminosity is the total amount of power given off by a star. -Since it s a power, Luminosity is measured in Watts, Lsun= 3.8x1026 Watt. -For convenience, we often refer to the luminosity of a star in terms of the luminosity of the Sun. -For example: - That star has a luminosity of 22LSun. - That galaxy has a luminosity of 2x1014LSun.

10 What makes stars appear different brightnesses? Intrinsic luminosity Temperature Radius Distance Intervening matter

11 However All one can measure is the FLUX. FLUX is the amount of energy that hits my detector. It is not the amount of energy that is emitted by the source. The inverse square law: Flux = L / 4 D2

13 Brightness, Distance, and Luminosity L=4 D B 2 luminosity distance B=L/(4 D2 ) apparent brightness or flux

14 Projection Stars at different distances.

15 How do we judge distances in everyday life? We know the real size and judge how big it looks. We know the real brightness and judge how bright it looks. We use stereoscopic vision, i.e. depth perception. A form of triangulation, i.e. trigonometry.

16 How do we measure distance? Parallax (a.k.a. triangulation) Using triangulation; requires 1. A baseline (distance over which observer moves). 2. Measurement of angles to the object from each end of the baseline. 3. Mathematical relationships between angles and lengths of sides of triangle. This is called trigonometry.

17 Stellar Parallax: Takes advantage of the fact that Earth orbits the Sun The measurements are taken six months apart. The baseline is the diameter of the Earth s orbit. What is seen What is seen Half of the angle between the current location and the 6month location is called the stellar parallax = P.

18 Parallax Distance 1 (AU) D (in Parsecs) = P (in arcseconds) P, the parallax angle, is measured in arcseconds 60 arcseconds = 1 arcminute 60 arcminutes = 1 degree There are 3600 arcseconds in a degree. Parsec = PARallax SECond

19 Remember the small angle formula: au angle (arcsec) = 206,265 size = 206,265 distance distance distance = 206,265 au angle (arcsec) 1 parsec = 206,265 au = 3.26 light years = 3.086x1016 meters The larger P, the smaller D The smaller P, the larger D

20 Parallax would be easier to measure if the stars were further away. Earth's orbit were larger. Earth moved backwards along its orbit. none of these.

21 Star A has a parallax angle that is twice that of Star B. What is the relationship between their distances? Star A is closer than Star B Star B is closer than Star A The stars are at the same distance Not enough information is given

22 There is a Big Range of Stellar Luminosities Out there! Star Sun Proxima Centauri Rigel (Orion) Deneb (Cygnus) Luminosity (in units of solar Luminosity) , ,000

23 Magnitudes and Distance Modulus Apparent magnitude: how bright it looks Absolute magnitude: magnitude at 10 pc M Msun = 4.75 Distance modulus: the larger the farther away m m M Example: m M = 5 magnitudes 5 mags = 100 times fainter = 10 times further away than 10 pc = 10 x 10 parsecs = 100 parsecs

How to measure the surface temperature of a star? 1. 2.

24 How to measure the surface temperature of a star? Overall spectral shape (the peak of the blackbody continuous spectrum), i.e. the color More accurately, use the spectral type.

25 Spectral Types For historical reasons, astronomers classify the temperatures of stars on a scale defined by spectral types, called O B A F G K M, ranging from the hottest (type O) to the coolest (type M) stars. Subdivided 0-9 The sun has a spectral type: G2

26 Stellar Size Stars are very spherical so we characterize a star s size by its radius. Stellar Radii vary in size R from ~1500RSun for a large Red Giant to 0.008RSun for a White Dwarf. How do we measure the radius of a star? Except for the Sun, we don t! We infer it!

27 The Size (Radius) of a Star We already know: flux increases with surface temperature (~ T4); hotter stars are brighter. But brightness also increases with size: If T is the same which is brighter? A Star B will be brighter than star A. B Absolute brightness is proportional to radius squared, L ~ R2 Quantitatively: L = 4 R2 T4 Surface area of the star Surface flux due to a blackbody spectrum

28 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 1002 = 10,000 times more than our sun s.

29 Putting it all together A star s luminosity, surface temperature, and size are all related by the Stefan-Boltzmann Law: Stefan-Boltzmann Law L=4πR2 σt4 Luminosity Stellar radius Surface temperature In terms of Solar quantities: L/LSun = (R/RSun)2 x (T/TSun)4 (R/RSun)2 = L/LSun / (T/TSun)4

30 L=4πR2 σt4 Two stars have the same surface temperature, but the radius of one is 10 times the radius of the other. The larger star is 10 times more luminous 100 times more luminous 1000 times more luminous 1/10th as luminous 1/100th as luminous

31 L=4πD2 B L=4πR2 σt4 Suppose two stars are at equal distance and have the same radius, but one has a temperature that is twice as great as the other. The apparent brightness of the hotter star is as the other. 1/2 as great 1/4 as great the same 4 times 16 times as great

5. A particular star has an angle of parallax of 0.2 arcsecond. What is the distance to this star? A) 50 pc B) 2 pc C) 5 pc D) 0.

5. A particular star has an angle of parallax of 0.2 arcsecond. What is the distance to this star? A) 50 pc B) 2 pc C) 5 pc D) 0. Name: Date: 1. How far away is the nearest star beyond the Sun, in parsecs? A) between 1 and 2 pc B) about 12 pc C) about 4 pc D) between 1/2 and 1 pc 2. Parallax of a nearby star is used to estimate its