Chapter 11: Stars 1
Fundamental Properties of Stars Luminosity Surface Temperature Mass 2
The brightness of a star depends on both its distance and luminosity 3
Luminosity: Amount of power a star radiates. Expressed in units of energy per second (e.g. Watts) Apparent brightness: Amount of starlight that reaches Earth Expressed in energy per second per surface area (e.g. Watts/sq. meter). 4
Relationship between luminosity and apparent brightness Luminosity passing through each imaginary sphere is the same. Area of sphere = 2 4 π (radius) Divide luminosity by area to get brightness. 5
Relationship between luminosity and apparent brightness Brightness = Luminosity 2 4 π (distance) This is the inverse square law for light. Can use this to determine a star s luminosity: 2 Luminosity = 4 π (distance) x (Brightness) 6
QUESTION: How would the apparent brightness of Alpha Centauri change if it were three times farther away? A. It would be only 1/3 as bright B. It would be only 1/6 as bright C. It would be only 1/9 as bright D. It would be three times brighter 7
QUESTION: How would the apparent brightness of Alpha Centauri change if it were three times farther away? A. It would be only 1/3 as bright B. It would be only 1/6 as bright C. It would be only 1/9 as bright D. It would be three times brighter 8
We observe the apparent brightness of stars. To determine the luminosities (total energy output per second), we need to know the distances to stars. How do we measure the distances to stars? 9
Parallax = apparent motion of an object relative to the background due to change in viewing positions. More distant stars have smaller parallaxes. 03/09/09 10
Units of stellar distances d = 1/p (for very small angles p) 1 parsec is distance when parallax angle (p) is measured in arcseconds 1 parsec = 3.26 light years Example: a star with p = 1/10 arcsec, is d = 10 parsecs away, or 32.6 light years away. 03/09/09 11
Parallax Parallax is the apparent shift in position of a nearby object against a background of more distant objects. 03/09/09 12
Parallaxes of the nearest stars Apparent positions of the nearest stars shift by about an arcsecond as Earth orbits the Sun. 03/09/09 13
Parallax Angle as a Function of Distance Parallax angle is directly proportional to distance. More distant stars have smaller parallaxes. 03/09/09 14
Measuring Parallax Angle Parallax is measured by comparing snapshots taken at different times and measuring the shift in angle to star. 03/09/09 15
There is a large spread in stellar luminosities. Use the luminosity of the Sun L Sun as a reference Most luminous stars: ~10 6 L Sun Least luminous stars: ~10-4 L Sun (L sun = Sun s luminosity) Factor of 10 billion spread. 16
How hot are the stars? Every object emits thermal radiation: Hotter objects emit more light at shorter wavelengths (bluer colors). So by measuring the colors of stars, we can determine their surface temperature. 17
Measuring a star s surface T Astronomers measure the surface temperature because the interior temperature can only be inferred from models. Surface T is easier to measure than its luminosity because it does not depend on distance. 18
Two Properties of Thermal Radiation Hotter objects emit more light at all wavelengths per unit area. Hotter objects emit photons with a higher average energy (bluer). Relative intensity per unit area 19
Hottest stars: 50,000 K Coolest stars: 3,000 K The Sun: 5,800 K. (All these temperatures refer to the star s surface.) 20
Luminosity of an object depends both on its size and temperature An object of fixed size grows more luminous as temperature rises. An object of fixed temperature grows more luminous as it gets bigger. 21
The types of absorption lines in a star s spectrum also tell us about its temperature. (Hot interior emits a continuous spectrum, which is partly absorbed by the cool outer layers.) 22
10 6 K The level of ionization 10 5 K 10 4 K Ionized Gas (Plasma) depends on a star s surface temperature. 10 3 K 10 2 K 10 K Neutral Gas Molecules Solid Therefore, stars of different temperatures will show different absorption lines in their spectra. 23
Examples Spectral type = classification of stellar spectra based on the absorption lines (hence, another way of determining stellar temperature) Stars of Orion s Belt O 30,000 K Rigel Sirius Polaris Sun, Alpha Centauri A B A F G 20,000 K 10,000 K 7,000 K 6,000 K Arcturus Betelgeuse, Proxima Centauri K M 4,000 K 3,000 K 24
Remembering Spectral Types (Hottest) O B A F G K M (Coolest) = Oh, Be A Fine Girl, Kiss Me = Only Boys Accepting Feminism Get Kissed Meaningfully Spectral classes are further broken down into sub-classes, numbered from 0 to 9 (warmer to cooler). For example, the Sun is a G2 star, meaning it is warmer than a G5 star. 25
QUESTION: Which kind of star is hottest? A. M star B. F star C. A star D. K star 26
QUESTION: Which kind of star is hottest? A. M star B. F star C. A star D. K star Oh, Be A Fine Girl, Kiss Me 27
Pioneers of Stellar Classification Annie Jump Cannon and the calculators at Harvard laid the foundation of modern stellar classification. 28
Pioneers of Stellar Classification Williamina Fleming (1857-1911) classified stellar spectra according to the strength of their hydrogen lines: A strongest, B slightly weaker, and O for the weakest. She classified more than 10,000 stars, which Pickering published in 1890. Annie Jump Cannon joined Pickering s group in 1896. Building on the work of Fleming and Antonia Maury, she realized that the spectral classes fell into a natural order but not the alphabetical order determined by hydrogen lines alone. She also found that some of the original classes overlapped others and could be eliminated. She discovered that the natural sequence was OBAFGKM. She added subdivisions by number. Jump Cannon personally classified 400,000 stars. In 1925, Cecilia Payne-Gaposchkin showed that the differences in spectral lines from star to star reflected changes in the ionization of the emitting atom. She published her findings in her doctoral thesis. 29
How do we determine the masses of stars? Use binary stars (pairs of stars held together by gravity). About ~1/2 of all stars are binaries. Relative sky positions of Sirius A & B over 70 years 30
We measure mass using gravity (Newton s version of Kepler s Third Law). Direct mass measurements are possible only for stars in binary star systems p 2 4π 2 = a 3 G (M 1 + M 2 ) p2= 4π2 a 3 (M 1 +M 2 ) Isaac Newton p = period a = average separation M 1, M 2 = mass of the 2 stars We measure the binary s period and separation to get the sum of the stellar masses. 31
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