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
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 CentauriB. 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 = 0.0006 Lsun
Betelgeuse = 38,000 Lsun
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
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 - supergiantII - bright giantIII - giantIV - subgiantV - main sequence
Examples: Sun - G2 VSirius - A1 VProxima Centauri - M5.5 VBetelgeuse - 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
p2 = a3 4π2
G (M1 + M2)
Most massive stars:
100 MSun
Least massive stars:
0.08 MSun
(MSun is the mass of the Sun)
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
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 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
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
Lu
min
osi
tyAn 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
Lu
min
osi
ty
Which star is the most luminous?
A
BC
D
Temperature
Lu
min
osi
ty
Which star has the largest radius?
A
BC
D
Temperature
Lu
min
osi
ty
Which star is the main sequence star?
A
BC
D
Temperature
Lu
min
osi
ty
Which star is the hottest?
A
BC
D
Temperature
Lu
min
osi
ty
Which of these stars will have changed the least 10 billion years from now?
A
BC
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-sequenceturnoff
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