Chapter 11 Surveying the Stars

The brightness of a star depends on both distance and luminosity How luminous are stars?

Luminosity: Amount of power a star radiates (energy per second=Watts) Apparent brightness: Amount of starlight that reaches Earth (energy per second per square meter)

(not much) Thought Question These two stars have about the same luminosity -- which one appears brighter? A. Alpha Centauri B. The Sun

Luminosity passing through each sphere is the same Area of sphere: 4π (radius) 2 Divide luminosity by area to get brightness

The relationship between apparent brightness and luminosity depends on distance: Luminosity Apparent Brightness = 4π (distance) 2 We can determine a star’s luminosity if we can measure its distance and apparent brightness: Luminosity = 4π (distance) 2 x (Brightness) Note that there is a huge range in stellar luminosities Proxima Centauri = L sun Betelgeuse = 38,000 L sun

Thought 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

Parallax and distance. p = parallax angle in arcseconds d (in parsecs) = 1/p 1parsec= 3.26 light years

Parallax and distance. Nearest Star: Alpha Centauri distance = 4.3 light years (since 1 parsec = 3.26 light years) Distance (d) in parsecs = 4.3/3.26 = 1.32 What is the parallax of this star? d=1/p hence p=1/d (in parsecs) p for nearest star is 0.76 arcseconds All other stars will have a parallax angle smaller than 0.76 arcseconds

hotter  brighter, cooler  dimmer hotter  bluer, cooler  redder Laws of Thermal Radiation

Hottest stars: blue~50,000 K Coolest stars: Red~3,000 K (Sun’s surface is 5,800 K)

An aside on “computers” In the old days an “Astronomical Computer” was not a machine, but a person….often a woman. These were the people who calculated positions and analyzed the photographic plates Women did most of the work in compiling these huge stellar catalogues.

An aside on “computers” What the “computers” did was sift through literally 100’s of thousands of stellar spectra. Established a classification scheme based on Hydrogen lines…. The types were alphabetical….letters were assigned in declining strength of the H-lines

Stellar Classification Like most early classification systems, they got it wrong initially Today we arrange spectral classes by temperature Wien’s Law: The hotter the object, the bluer the radiation it emits, and the more total energy is emitted.

Stellar Classification The hottest stars turned out to be (of course) the bluest. Also the level of heat determined what sorts elements would be prominent in the star’s spectrum For example only the hottest stars can ionize helium Only the coolest stars can have molecules

(Hottest) O B A F G K M (Coolest) Remembering Spectral Types Oh, Be A Fine Girl/Guy, Kiss Me Only Boys Accepting Feminism Get Kissed Meaningfully

A star’s full classification includes spectral type (line identities) and luminosity class (line shapes, related to the size of the star): I - supergiant II - bright giant III - giant IV - subgiant V - main sequence Examples:Sun - G2 V Sirius - A1 V Proxima Centauri - M5.5 V Betelgeuse - M2 I

Star Types

Now we know temperature, luminosity, and Distance……what about mass? Newton shows the way…… We measure mass using gravity Direct mass measurements are possible only for stars in binary star systems p = period a = average separation p 2 = a 3 4π 2 G (M 1 + M 2 )

Most massive stars: 100 M Sun Least massive stars: 0.08 M Sun (M Sun is the mass of the Sun)

Stellar Properties Review Luminosity: from brightness and distance L Sun L Sun Temperature: from color and spectral type 3,000 K - 50,000 K Mass: from period (p) and average separation (a) of binary-star orbit 0.08 M Sun M Sun

Core pressure and temperature of a higher- mass star need to be larger in order to balance gravity Higher core temperature boosts fusion rate, leading to larger luminosity

Mass & Lifetime Sun’s life expectancy: 10 billion years Life expectancy of 10 M Sun star: 10 times as much fuel, uses it 10 4 times as fast 10 million years ~ 10 billion years x 10 / 10 4 Life expectancy of 0.1 M Sun star: 0.1 times as much fuel, uses it 0.01 times as fast 100 billion years ~ 10 billion years x 0.1 / 0.01 Until core hydrogen (10% of total) is used up

Stellar Evolution Stars are like people in that they are born, grow up, mature, and die. A star’s mass determines what life path it will take. The Hertzsprung- Russel Diagram is a roadmap for following stellar evolution.

Temperature Luminosity An H-R diagram plots the luminosity and temperature of stars

Normal hydrogen- burning stars reside on the main sequence of the H-R diagram Low-Mass Stars High-Mass Stars

H-R diagram depicts: Temperature Color Spectral Type Luminosity Radius *Mass *Lifespan *Age

Temperature Luminosity Which star is the most luminous? A B C D

Temperature Luminosity Which star has the largest radius? A B C D

Temperature Luminosity Which star is the main sequence star? A B C D

Temperature Luminosity Which star is the hottest? A B C D

Temperature Luminosity Which of these stars will have changed the least 10 billion years from now? A B C D E

Main-Sequence Star Summary High Mass: High Luminosity Short-Lived Large Radius Blue Low Mass: Low Luminosity Long-Lived Small Radius Red

Open cluster: A few thousand loosely packed stars

Globular cluster: Up to a million or more stars in a dense ball bound together by gravity

How do we measure the age of a star cluster?

Pleiades: no stars with life expectancy of less than 100 million years Main-sequence turnoff

Main- sequence turnoff point of a cluster tells us its age

Detailed modeling of the oldest globular clusters reveals that they are about 13 billion years old