chapter 11 surveying the stars the brightness of a star depends on both distance and luminosity how...
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Chapter 11Surveying the Stars
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The brightness of a star depends on both distance and luminosity
How luminous are stars?
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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)
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(not much) Thought Question
These two stars have about the same luminosity -- which one appears brighter?
A. Alpha CentauriB. The Sun
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Luminosity passing through each sphere is the same
Area of sphere:
4π (radius)2
Divide luminosity by area to get brightness
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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 = 0.0006 Lsun
Betelgeuse = 38,000 Lsun
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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 brightB. It would be only 1/6 as brightC. It would be only 1/9 as brightD. It would be three times brighter
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Parallax and distance.p = parallax angle in
arcseconds
d (in parsecs) = 1/p
1parsec= 3.26 light years
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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
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hotter brighter, cooler dimmer
hotter bluer, cooler redder
Laws of Thermal Radiation
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Hottest stars:
blue~50,000 K
Coolest stars:
Red~3,000 K
(Sun’s surface is 5,800 K)
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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.
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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
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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.
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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
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(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
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A star’s full classification includes spectral type (line identities) and luminosity class (line shapes, related to the size of the star):
I - supergiantII - bright giantIII - giantIV - subgiantV - main sequence
Examples: Sun - G2 VSirius - A1 VProxima Centauri - M5.5 VBetelgeuse - M2 I
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Star Types
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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
p2 = a3 4π2
G (M1 + M2)
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Most massive stars:
100 MSun
Least massive stars:
0.08 MSun
(MSun is the mass of the Sun)
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Stellar Properties Review Luminosity: from brightness and distance
10-4 LSun - 106 LSun
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 MSun - 100 MSun
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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
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Mass & Lifetime
Sun’s life expectancy: 10 billion years
Life expectancy of 10 MSun star:
10 times as much fuel, uses it 104 times as fast
10 million years ~ 10 billion years x 10 / 104
Life expectancy of 0.1 MSun 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
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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.
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Temperature
Lu
min
osi
tyAn H-R diagram plots the luminosity and temperature of stars
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Normal hydrogen-burning stars reside on the main sequence of the H-R diagram
Low-Mass Stars
High-Mass Stars
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H-R diagram depicts:
Temperature
Color
Spectral Type
Luminosity
Radius
*Mass
*Lifespan
*Age
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Temperature
Lu
min
osi
ty
Which star is the most luminous?
A
BC
D
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Temperature
Lu
min
osi
ty
Which star has the largest radius?
A
BC
D
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Temperature
Lu
min
osi
ty
Which star is the main sequence star?
A
BC
D
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Temperature
Lu
min
osi
ty
Which star is the hottest?
A
BC
D
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Temperature
Lu
min
osi
ty
Which of these stars will have changed the least 10 billion years from now?
A
BC
D
E
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Main-Sequence Star Summary
High Mass:
High Luminosity Short-Lived Large Radius Blue
Low Mass:
Low Luminosity Long-Lived Small Radius Red
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Open cluster: A few thousand loosely packed stars
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Globular cluster: Up to a million or more stars in a dense ball bound together by gravity
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How do we measure the age of a star cluster?
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Pleiades: no stars with life expectancy of less than 100 million years
Main-sequenceturnoff
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Main-sequence turnoff point of a cluster tells us its age
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Detailed modeling of the oldest globular clusters reveals that they are about 13 billion years old