Evolution of the Sun, Stars,

and Habitable Zones

fs

The fraction of suitable stars N = N* fs fp nh fl fi fc L/T

Hertzsprung-Russell Diagram

Parts of the H-R Diagram

• Supergiants

• Giants

• Main Sequence (dwarfs)

• White Dwarfs

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

Hertzsprung-Russell Diagram

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

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.

Post-Main Sequence Timescales

Timescale τ ~ E/L L >> Lms τ << τms

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.

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)

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

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?

The Continuously Habitable Zone

Stellar Lifetimes

τ ~ M/L On the main sequence, L~M3 Therefore, τ~M-2 τ¤ = 1010 years

τ~1010/M2 years

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

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?

Other Considerations

•  Tidal Locking •  Stellar Flaring

Both work against M stars

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

So Far…

N*: 4x1011 stars fs: 0.2 N: 8x1010 fp nh fl fi fc L/T