Evolution of the Sun, Stars, and Habitable Zones*/D2)0.25 The habitable zone is the region where the...
Transcript of Evolution of the Sun, Stars, and Habitable Zones*/D2)0.25 The habitable zone is the region where the...
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Evolution of the Sun, Stars,
and Habitable Zones
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fs
The fraction of suitable stars N = N* fs fp nh fl fi fc L/T
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Hertzsprung-Russell Diagram
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Parts of the H-R Diagram
• Supergiants
• Giants
• Main Sequence (dwarfs)
• White Dwarfs
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Making Sense of the H-R Diagram
• The Main Sequence is a sequence in mass
• Stars on the main sequence undergo stable H fusion
• All other stars are evolved
• Evolved stars have used up all their core H
• Main sequence → Giants → Supergiants
• Subsequent evolution depends on mass
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Hertzsprung-Russell Diagram
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Evolutionary Timescales
Pre-main sequence: Set by gravitational contraction • The gravitational potential energy E is ~GM2/R • The luminosity is L • The timescale is ~E/L We know L, M, R from observations For the Sun, L ~ 30 million years
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Evolutionary Timescales Main sequence: • Energy source: nuclear reactions, at ~10-5 erg/reaction • Luminosity: 4x1033 erg/s This requires 4x1038 reactions/second Each reaction converts 4 H → He The solar core contains 0.1 M¤, or ~1056 H atoms
1056 atoms / 4x1038 reactions/second -> 3x1017 sec, or 1010 years. This is the nuclear timescale.
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Post-Main Sequence Timescales
Timescale τ ~ E/L L >> Lms τ << τms
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Habitable Zones
Refer back to our discussion of the Greenhouse Effect. Tp ~ (L*/D2)0.25
The habitable zone is the region where the temperature is between 0 and 100 C (273 and 373 K), where liquid water can exist. All stars have habitable zones. Tp depends on both • the stellar luminosity L* • the distance D. D does not change, but L* does, as the star evolves.
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The Habitable Zone in the Solar System
Location depends on assumptions about atmospheric composition and albedo • Inner edge: • 0.84 – 0.95 AU
• Outer edge: • 1.37 – 1.67 AU ____________ 0.9 – 1.5 AU Kasting, J.F., Whitmire, D.P., & Reynolds, R.T. Science, 101, 108 (1993)
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Why do stars brighten with time?
• Sun is in hydrostatic balance – Pressure is proportional to nT – n is density of particles – Pressure depends on total mass
• Nuclear fusion reduces the number of particles in the core – 4 protons + 4 electrons -> 1 He nucleus + 2
electrons – As n decreases, T increases – Reaction rates increase, and Luminosity goes up
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Bright Old Sun Problem
The Sun is brightening with time. In about 109 years, the mean temperature on Earth will exceed 100 C.
Why is this a problem?
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The Continuously Habitable Zone
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Stellar Lifetimes
τ ~ M/L On the main sequence, L~M3 Therefore, τ~M-2 τ¤ = 1010 years
τ~1010/M2 years
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Other Stars • All stars have habitable zones • Width ~ √(L)
– More massive stars have wider HZs – Less massive stars have narrower HZs
• Implications for probability of planets in HZ
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Appropriate Stars
Massive stars (M >≈ 1.5 M¤): • Lifetimes are short • Habitable zones are wide • Many habitable planets? Low Mass stars (M <≈ 0.5 M¤): • Lifetimes are long • Habitable zones are narrow • Few habitable planets?
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Other Considerations
• Tidal Locking • Stellar Flaring
Both work against M stars
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Appropriate Stars
For nuclear timescale to exceed 109 years, then O,B,A stars must be excluded. For a wide-enough habitable zone to include at least one planet (for a system like the Solar System), exclude the M stars. Late-F, G, and K main sequence stars comprise about 20% of the stars in the Galaxy
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So Far…
N*: 4x1011 stars fs: 0.2 N: 8x1010 fp nh fl fi fc L/T