Chapter 11: Stars (cont’d)
HOMEWORK ASSIGNMENT 9 DUE MONDAY MARCH 16
03/11/09 Habbal Astro110-01 Lecture 21 1 Recall: Fundamental Properties of Stars
• Luminosity • Surface Temperature • Mass
03/11/09 Habbal Astro110-01 Lecture 21 2 Relationship between luminosity and apparent brightness
Luminosity Brightness = 4π (distance)2
This is the inverse square law for light.
Can use this to determine a star’s luminosity:
Luminosity = 4π (distance)2 x (Brightness)
The larger the radius (distance), the more luminous the star
03/11/09 Habbal Astro110-01 Lecture 21 3 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 3 4 π 2 4 π2 a 2 = 3 pp = a G + G (M(1M + M2)M ) 1 2 p = period a = average separation M , M = mass of the 2 stars Isaac Newton 1 2 We measure the binary’s period and separation to get the sum of the stellar masses. 03/11/09 Habbal Astro110-01 Lecture 21 4
Most massive stars:
100 MSun
Least massive stars:
0.08 MSun
(MSun is the mass of the Sun)
03/11/09 Habbal Astro110-01 Lecture 21 5
Why are some red (cool) stars much more luminous than others? Because they have larger radii.
A star’s luminosity depends both on its size and temperature.
Biggest red stars:
1000 Rsun
Smallest red stars:
0.1 RSun
03/11/09 Habbal Astro110-01 Lecture 21 6
Relative sizes of stars
Betelgeuse (supergiant star)
Sp. type = M2 3400 K
38,000 Lsun 500 solar radii
03/11/09 Habbal Astro110-01 Lecture 21 7
Relative sizesWhy are ofsome stars red stars so much more luminous than others? Because they have larger radii. Aldebaran Remember, a star’s luminosity (giant star) depends both on its size and temperature. Sp. type = K5 4500 K Biggest red stars: 350 Lsun 1000 Rsun 30 solar radii Smallest red stars:
0.1 RSun
03/11/09 Habbal Astro110-01 Lecture 21 8
Relative sizesWhy are ofsome stars redProcyon stars so B much more luminous than(white others? dwarf) Because they0.01 have solar larger radius radii.
Remember, a star’sEarth luminosity depends both (foron its comparison) size and temperature.
Sun Biggest red stars: (main sequence star) 1000 R Sp. type = G2 sun
5800 K, 1 Lsun 1 solar radius Smallest red stars: 0.1 RSun
03/11/09 Habbal Astro110-01 Lecture 21 9 Review of stellar properties Luminosity: from brightness and distance -4 6 10 LSun - 10 LSun (0.08 MSun) (100 MSun)
Temperature: from color and spectral type 3,000 K - 50,000 K (0.08 MSun) (100 MSun)
Mass: from period (p) and average separation (a) of binary-star orbit
0.08 MSun - 100 MSun
In fact, the luminosity and temperature are directly determined by the mass (and age) of the star. 03/11/09 Habbal Astro110-01 Lecture 21 10 How does a star’s mass determine its luminosity?
• A more massive star Radius = 1.5 Rsun Radius = 1 Rsun needs more internal pressure to be in gravitational equilibrium. • This requires the core Lower core temperature & pressure, Higher core pressure to be higher. lower pressure, • Higher core luminosity. higher temperature boosts luminosity. the fusion rate, leading to a larger luminosity.
03/11/09 Habbal Astro110-01 Lecture 21 11 Main-sequence stars = fusing hydrogen into helium in their cores (like the Sun).
For these stars, color & luminosity are closely related: • Luminous M-S stars are hot (bluer). • Less luminous ones are cooler (yellow or red).
03/11/09 Habbal Astro110-01 Lecture 21 12 How does a star’s mass determine its lifetime?
Until core hydrogen Sun’s life expectancy: 10 billion years (10% of total) is used up
03/11/09 Habbal Astro110-01 Lecture 21 13 How does a star’s mass determine its lifetime?
Until core hydrogen Sun’s life expectancy: 10 billion years (10% of total) is used up
Life expectancy of 10 MSun star: 10 times as much fuel, uses it 104 times as fast Lifetime ~ Sun’s lifetime x Star’s mass / burning rate ~ 10 billion years x 10 / 104 ~ 10 million years
03/11/09 Habbal Astro110-01 Lecture 21 14 How does a star’s mass determine its lifetime?
Until core hydrogen Sun’s life expectancy: 10 billion years (10% of total) is used up
Life expectancy of 10 MSun star: 10 times as much fuel, uses it 104 times as fast Lifetime ~ Sun’s lifetime x Star’s mass / burning rate ~ 10 billion years x 10 / 104 ~ 10 million years
Life expectancy of 0.1 MSun star: 0.1 as much fuel, uses it 0.01 times as fast Lifetime ~ 10 billion years x 0.1 / 0.01 ~ 100 billion years 03/11/09 Habbal Astro110-01 Lecture 21 15 Classifying Stars
Learning goals • How do we classify stars? • Why is a star’s mass its most important property? • What is a Hertzsprung–Russell diagram?
03/11/09 Habbal Astro110-01 Lecture 21 16 How can we represent all this information about stellar properties?
• Hertzspring-Russell (H-R) diagram – A plot of stellar luminosity vs. temperature. – This is fundamental: the life history (evolution) of a star can be understood from this diagram. • Remember: a star’s luminosity depends on both its temperature and its radius. (e.g., cool red stars can span a wide range in sizes, and hence luminosity).
Generating the H-R diagram
03/11/09 Habbal Astro110-01 Lecture 21 17 The H-R diagram plots the luminosity versus the temperature of stars. Luminosity
03/11/09 Temperature Habbal Astro110-01(spectral Lecture type) 21 18 The positions of stars on the H-R diagram contains lots of information about their properties.
Luminosity - Temperature - Color - Spectral Type - Luminosity - Radius
03/11/09 Temperature Habbal Astro110-01(spectral Lecture type) 21 19 Stars with low surface temperature and high luminosity must have a large radius. Luminosity
03/11/09 Temperature Habbal Astro110-01(spectral Lecture type) 21 20 These diagonal lines show the positions of stars with the same
Luminosity radius.
03/11/09 Temperature Habbal Astro110-01(spectral Lecture type) 21 21 There are natural groupings of stars in different parts of the H-R diagram.
Luminosity These groups are related to evolutionary states (relative ages) of the stars.
03/11/09 Temperature Habbal Astro110-01(spectral Lecture type) 21 22 Normal (core Increasing hydrogen- stellar mass burning) stars reside on the main sequence. Increasing lifetime on the The relative main sequence positions on the main sequence Luminosity are directly related to the stellar masses, and hence the lifetimes (only true for main- sequence stars).
03/11/09 Temperature Habbal Astro110-01(spectral Lecture type) 21 23 Main-sequence star summary
• High mass stars – High luminosity – Short-lived – Large radii – High temperature (blue)
• Low mass stars – Low luminosity – Long-lived – Small radii – Low temperatures (red) 03/11/09 Habbal Astro110-01 Lecture 21 24 C B Which star is the hottest?
D
Luminosity A
03/11/09 Temperature Habbal Astro110-01 Lecture 21 25 C B Which star is the hottest?
D
Luminosity A
03/11/09 Temperature Habbal Astro110-01 Lecture 21 26 C B Which star is the most luminous? D
Luminosity A
03/11/09 Temperature Habbal Astro110-01 Lecture 21 27 C B Which star is the most luminous? D
Luminosity A
03/11/09 Temperature Habbal Astro110-01 Lecture 21 28 C B Which star is a main- sequence D star?
Luminosity A
03/11/09 Temperature Habbal Astro110-01 Lecture 21 29 C B Which star is a main- sequence D star?
Luminosity A
03/11/09 Temperature Habbal Astro110-01 Lecture 21 30 C B Which star has the largest radius? D
Luminosity A
03/11/09 Temperature Habbal Astro110-01 Lecture 21 31 C B Which star has the largest radius? D
Luminosity A
03/11/09 Temperature Habbal Astro110-01 Lecture 21 32 A Which star is most D like our Sun?
B Luminosity
C
03/11/09 Temperature Habbal Astro110-01 Lecture 21 33 A Which star is most D like our Sun?
B Luminosity
C
03/11/09 Temperature Habbal Astro110-01 Lecture 21 34 A Which of these stars will have D changed the least B 10 billion
Luminosity years from now? C
03/11/09 Temperature Habbal Astro110-01 Lecture 21 35 A Which of these stars will have D changed the least B 10 billion
Luminosity years from now? C
03/11/09 Temperature Habbal Astro110-01 Lecture 21 36 A Which of these stars can be no D more than 10 million B years old? Luminosity
C
03/11/09 Temperature Habbal Astro110-01 Lecture 21 37 A Which of these stars can be no D more than 10 million B years old? Luminosity
C
03/11/09 Temperature Habbal Astro110-01 Lecture 21 38