Astronomy 162:
Introduction to Stars, Galaxies, & the Universe
Prof. Richard Pogge, MTWThF 9:30

Lecture 40: The Once and Future Sun

Key Ideas

Solar Evolution: The Sun is a middle-aged, low-mass, main-sequence star; Its future evolution can be computed using stellar models
The Main Stages of the Sun's Life: Main-Sequence Star; Red Giant Star; Horizontal Branch Star; Asymptotic Giant Star & Unstable Pulsations; Planetary Nebula Phase; White Dwarf

The Fate of the Sun

Question: How will the Sun evolve?

To answer this question, astronomers have made detailed calculations including:

State-of-the-Art Stellar Evolution codes
Detailed Solar Structure Model
Inclusion of realistic mass-loss processes

The goal is to produce a self-consistent model of the Sun that will trace its evolution from the time it reached the Main Sequence until its emergence as a hot white dwarf.

In preparing this lecture, I have drawn on two relatively recent calculations of detailed Solar Evolution models:

Sackmann, Boothroyd, & Kraemer (1993), Astrophysical Journal (Vol. 418, 457)
Bahcall, Pinsonneault & Basu (2001), Astrophysical Journal, (Vol. 555, 990)

The Sun Today

The Sun is currently a middle-aged, low-mass star on the Main Sequence.

Properties:

Age = 4.55 Gyr
Mass = 1 M_sun = 1.99x10³³ g
Radius = 1 R_sun = 700,000 km
Luminosity = 1 L_sun = 3.83x10²⁶ Watts
Temperature = 5779 K
~50% of its core Hydrogen has been fused into Helium

The Sun at this time is in a state of Hydrostatic and Thermal Equilibrium.

Note: This and subsequent pictures show the inner solar system with the Sun drawn to scale with respect to the orbits of the planets. The scale is also the same between each solar system graph, so you can see how much the planets move outward as mass loss proceeds.

"Quiet Adulthood"

The Sun took about 50 Myr to form from a molecular cloud core.

It reached the Main Sequence about 4.50 Gyr ago. When the Sun first alighted onto the Zero-Age Main Sequence it was

A little fainter: 0.70 L_sun
A little smaller: 0.897 R_sun
A little cooler: 5586 K

than we see today.

The Sun can maintain itself in Hydrostatic and Thermal Equilibrium as long as it can stably burn Hydrogen into Helium in its core.

As the Sun consumes its core Hydrogen, it slowly grows brighter with age. We see a brighter, hotter, and slighly bigger Sun today than when it formed. This trend will continue so long as the Sun is on the Main Sequence.

Mid-Life Crisis for the Earth

The steady brightening trend will spell trouble for the Earth in the distant future.

5.6 Gyr (1.1 Gyr from today):

Sun 10% brighter: ~1.1 L_sun
The extra sunlight triggers a Moist Greenhouse Effect.

A "Moist Greenhouse Effect" is one in which most of the water in the atmosphere is driven off into space. This will likely mean the end of large surface life on Earth, though some types of marine life and simpler lifeforms might survive in the deep oceans or underground.

Venus on Earth

The warming trend will continue through the Sun's Main Sequence phase.

9 Gyr (3.5 Gyr from today):

Sun 40% brighter: ~1.4 L_sun
Extra solar energy triggers a Runaway Greenhouse Effect

The oceans will totally evaporate into space, releasing all of the Carbon Dioxide (CO₂) currently locked up in marine sediments into the atmosphere. The result will be to turn the Earth's moist, light, warm atmosphere today into a hot, heavy, bone-dry CO₂ atmosphere like that on Venus today.

Hydrogen Core Exhaustion

11 Gyr (5.5 Gyr from today):

The Sun's core runs out of Hydrogen, most of the volume of the core having been replaced by inert Helium "ash".

The Inert He core starts to contract and heat up
H burning moves out into a shell
T = 5517 K
R = 1.575 R_sun
L = 2.21 L_sun

The Sun leaves the Main-Sequence and becomes a Sub-Giant star.

"Lively Old Age"

The Next 0.7 Gyr:

Sun expands a near-constant Luminosity of about 2.2 L_sun towards the base of the Red Giant Branch.
Sun swells in size from 1.58 R_sun to 2.3 R_sun
Surface layers cool from 5517 K to 4902 K

This growth is accompanyied by the start of slow mass loss in a stellar wind:

The wind steadily picks up as the Sun approaches the base of the Red Giant Branch

Climbing the Red Giant Branch

It will take the Sun about 0.6 Gyr to climb up the Red Giant Branch.

During this time, the Sun will lose up to 28% of its total mass in a strong stellar wind.

This mass-loss causes the planets to move outwards a little:
Venus moves out to about 1 AU (where Earth is now)
Earth moves out to abou 1.4 AU (about where Mars is now)
The other planets also move out similarly.

All the mass-loss occurs from the outer envelope.

At the Tip of the Red Giant Branch, the outwards appearance of the Sun is as follows:

T = 3107 K (M0 III Star)
L = 2350 L_sun
R = 166 R_sun (0.775 AU)

The Sun's swelling red-giant envelope will swallow Mercury!

The Helium Flash

When the Sun reaches the Tip of the Red Giant Branch:

Helium Burning to C & O ignites rapidly in a Helium Flash.
Extra energy stablizes the core against collapse.
Commences Hydrogen Burning in a thin shell outside the He burning core.

The Sun descends quickly onto the Horizontal Branch in about 1 Myr as it rearranges its internal structure to accomodate this new source of energy.

The Sun becomes a Horizontal Branch star

The Horizontal Branch

With a new source of energy (He fusion), the Sun settles onto the Horizontal Branch for a brief "retirement" period of Hydrostatic and Thermal Equilibrium:

Radius: R=9.5 R_sun
Temperature: T = 4724 K
Luminosity: L = 41 L_sun

However, because He fusion is about 100-times less efficient at producing energy per reaction than H fusion, the Sun can only keep this up for about 100 Myr...

An All-Too-Brief Retirement

After 100Myr, the Sun runs out of core Helium, and slips out of Equilibrium again:

C-O "ash" core begins to contract and heat up
Remaining He is displaced into an He-burning shell, surrounded by a thin H-burning shell.

The Sun starts to swell up & get brighter:

R = 18 R_sun
T = 4450 K
L = 110 L_sun

Helium Core Exhaustion

Driven out of Hydrostatic and Thermal Equilibrium by exhaustion of He in the core, the Sun now begins to climb the Asymptotic Giant Branch.

This process is rapid, taking only about 20 Myr:

The C-O core steadily contracts and heats up.
Fusion is moved out into a He burning shell
A thin H burning shell sits outside the He-burning shell.

During this time, the Sun swells up rapidly, getting cooler & brighter:

R = 180 R_sun (0.84 AU)
T = 3160 K
L = 3000 L_sun

Note that this is brighter than when it climbed the Red Giant Branch before, and it happens much faster than before (20 Myr compared to 0.6 Gyr).

The Sun climbs the Asymptotic Red Giant Branch

AGB Phase Mass Loss

The Sun's ascent of the Asymptotic Giant Branch is also accompanied by mass loss in the form of a strong stellar wind:

The Sun's mass is reduced to about 0.6 M_sun

The surviving planets (Mercury was engulfed during the Red Giant phase) move further outward:

Venus moves out to 1.22 AU
Earth moves out to 1.69 AU
The others move out proportionally...

Near the tip of the AGB, thermal pulsations in the envelope begin.

The Tremors of Old Age

As the Sun nears the tip of the Asymptotic Giant Branch, unstable thermal pulsations begin in the He-burning shell:

Models predict 4 pulses at roughly 100,000 year intervals.
Each pulse puffs the Sun up to 213 R_sun (about 1 AU!)
The largest is pulse #4, with L = 5200 L_sun!

These pulsations will progressively eject most of the remaining envelope of the Sun.

Each episode of pulsational mass-loss causes the surviving planets to move further away from the Sun.

A Final Flowering

The last of the thermal pulses blows off what is left of the envelope over the course of a few thousand years.

As the last of the envelope comes off, the hot C-O core of the Sun is unveiled. As seen from the outside:

T goes from 4000K (envelope) to 120,000K (bare core)
L stays constant at ~3500 L_sun
The bare core rapidly traverses the H-R diagram

UV photons from the core ionize the ejected envelope gas, forming a Planetary Nebula

The Sun puffs off its envelope as a Planetary Nebula

Actually, there is some controversy about this. The minimum stellar mass needed to get a planetary nebula stage is not known, mostly because of uncertainty about how much mass is lost during the stellar wind phases, and how that effects the evolution of the bare core plus expanding envelope. There are two possiblities: One is the scenario above where the Sun briefly flowers as a Planetary Nebula, the other where the envelope dissipates before the core gets hot enough to ionize it and light up the nebula. There is currently no concensus.

The Final Configuration

The bare core, now with a Mass of about 0.54 M_sun, evolves into a slowly cooling White Dwarf with a radius a little smaller than the Radius of the Earth.

With mass loss now ended, and the final mass of the white dwarf fixed, the surviving planets settle into their essentially final orbits:

Venus is at 1.34 AU
Earth is at 1.85 AU
Mars is at 2.8 AU
and so forth...

The planets will continue orbiting the remnant white dwarf in this configuration unless a passing star happens to come close enough to disrupt their orbits.

The Final Configuration of the Solar System

The white dwarf that was the Sun now begins a long, slow cooling phase that will last for nearly a Trillion years as it fades away into a long night.

The Seven Ages of the Sun

1 M_sun Main-Sequence Star: 11 Gyr
Red Giant Star: 1.3 Gyr
Horizontal Branch Star: 100 Myr
Asymptotic Giant Branch Star: 20 Myr
Thermal Pulsation Phase: 400,000 yrs
Planetary Nebula Phase: ~10,000 yrs
0.54 M_sun White Dwarf as the final state.

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