The Sun and Earth in the
(K-P Schröder & R C Smith,
distant future MNRAS, submitted)
Will the Sun look like this?
Outline:
 Introduction
 Evolution of the Sun
 Fate of the planets (and us)
 The end-game
3-D simulation of a pulsating red giant
(http://www.lcse.umn.edu/research/RedGiant/)
The Sun and Earth in the distant future
Introduction
 Global warming
 The
climate change
Sun’s luminosity is slowly increasing – what will that do to
us?
 On ZAMS, Lsun ~ 70% Lsun(now) – but geological evidence
suggests Tearth ~ constant for last 3-4 billion years
 Can the feedback mechanism that kept the temperature
constant in the past also do so in the future, and for how long?
The Sun and Earth in the distant future
What happened in the past?
 Early atmosphere was rich in CO2 – kept Earth warm by strong
greenhouse effect
 Clouds may also matter – some evidence that CR encourage
cloud cover at low altitudes, leading to higher reflection and lower
temperature; strong early solar wind may have excluded galactic
CR, leading to lower cloud cover and higher temperature
 CO2 gradually locked up in carbonates and plants (limestone
deposits contain about 70 atmospheres of it!) – so greenhouse
effect decreased as solar irradiation increased (the Gaia effect)
 Current climate models suggest that including biospheric (Gaiatype) effects may actually increase CO2 production as vegetation
dies back – so feedback probably won’t help in future.
The Sun and Earth in the distant future
Expansion up Asymptotic Giant Branch
He flash
Core He
burning
Evolution of
the Sun
(schematic)
Sun expands up red giant branch
Core H
exhausted
The Sun
now
Detailed
calculations
made by Peter
Schröder,
using modified
Eggleton code
The Sun and Earth in the distant future
Evolution of the Sun: No mass loss
Log Rsun and Log Dplanets (Units: Rsun(now)).
2.8
2.6
Mars
2.4
Earth
2.2
Venus
2
Mercury
1.8
All planets swallowed
at RGB or AGB stage
1.6
1.4
Sun
1.2
Age/10^6 yrs
12,300
12,275
12,250
12,225
12,200
12,175
12,150
12,125
12,100
1
The Sun and Earth in the distant future
Evolution of the Sun: With mass loss
 Solar wind mass-loss is negligible (~10-14 Msun/year).
 Mass loss is much greater at RGB and AGB stages. We
use a new semi-empirical formula, calibrated from globular
cluster giants and nearby galactic giants (Schröder & Cuntz,
ApJ, 630, L73, 2005 and A&A, 465, 593, 2007):
3.5
g sun 
L* R*  Teff  
M 


 1 
M *  4000 K   4300 g* 
where  = 810-14 solar masses/year. This leads to a loss
of 0.332 Msun by the tip RGB.
The Sun and Earth in the distant future
Evolution of the Sun: With mass loss
 Mass
loss  weaker gravitational pull – so the Sun
expands a bit more, but also the planetary orbits expand.
 If angular momentum is conserved, then:
rE   / M sun (t )
2
E
where rE is the radius of the Earth’s orbit at time t and
E is the (constant) orbital angular momentum.
 At the tip RGB, the Sun reaches a radius of 1.2 AU,
but the Earth’s orbit has moved out to 1.5 AU.
 By the time it gets to the AGB, the Sun has lost so
much mass from its envelope that it expands less far,
only to 0.7 AU, so the Earth escapes:
The Sun and Earth in the distant future
Evolution of the Sun: With mass loss
Earth’s orbit
Sun: RGB
AGB
The Sun and Earth in the distant future
Fate of the planets
 So – it appears that Mercury and Venus get swallowed,
but the other planets escape.
 Is that the whole story?
 No – orbital angular momentum is NOT conserved: tidal
interaction and dynamical friction act to decrease it.
 Assuming the Sun is non-rotating on the RGB
(conservation of its AM), the orbital motion of the Earth
raises a tidal bulge on the Sun that pulls the Earth back
in its orbit.
 In addition, the Earth is orbiting through the extended
chromosphere of the Sun, giving rise to drag.
 Detailed computations give:
The Sun and Earth in the distant future
Fate of the Earth – doomsday!
Effect of mass loss
Earth’s orbit
Sun’s radius
Effect
of tides
and drag
The Sun and Earth in the distant future
What happens to life, and when?
 The Earth is swallowed ~0.5 million years before the RGB tip, or
about 7.59 Gy in the future
 But increased solar irradiation acts much faster – even without
increased CO2, the rise in temperature will cause evaporation of the
oceans to start – and water vapour is another greenhouse gas
 A moist greenhouse effect will continue until the oceans have
boiled dry (Laughlin, Sky & Telescope, June 2007, p.32)
 Solar UV will then dissociate the water molecules, and the
hydrogen will escape, leaving the Earth a lifeless dust-bowl
 The subsequent dry greenhouse effect will raise the temperature
further until the Earth is essentially a molten ball
 Timescale is ~1 Gy – so life will disappear long before the Earth
does
The Sun and Earth in the distant future
Can we postpone the extinction of life?
 Options: terra-forming Mars? Space stations drifting
out through the solar system? Colonise the Galaxy? None
would save more than a tiny fraction of life on Earth
 Move the Earth itself outwards?!
 Serious proposal (Korycansky et al, Ap&SpSci, 275, 349, 2001)
to use Kuiper Belt objects in close fly-by to nudge the
Earth every 6000 years so that it moves out at just the
right rate
 Energetically possible, and could be technically possible
in the near future (a few centuries)
 Very dangerous! But could extend habitability of Earth
for whole MS lifetime of Sun (~6 Gy) – a big gain
The Sun and Earth in the distant future
What happens to the Sun?
 Textbooks say: Sun ends as white dwarf after ejecting
planetary nebula (PN)
 Our calculations show mass loss on AGB is relatively low
(0.116 Msun) because most of envelope lost on RGB
 PN usually emitted by superwind as part of last thermal
pulse on AGB – but our calculations show only 0.0075 Msun
is lost in final pulse – much less than a normal PN mass. So
any PN would be very tenuous and faint
 A final thermal pulse after leaving the AGB causes final
mass loss, and the expected final WD mass is 0.5405 Msun
The Sun and Earth in the distant future
Conclusions
 The Earth is lost eventually: engulfed by Sun 7.59 Gy in
the future
 Life might hang on for ~6 Gy*, but the ultimate future
of the human race (if it survives) would need to be
elsewhere
* If the Kuiper Belt Object nudging scheme worked – and then in fact the
Earth itself might avoid engulfment
The Sun and Earth in the distant future
Might the Earth be saved after all?
A planet
with initial
orbital
radius 1.15
AU or more
will escape
engulfment
The Sun and Earth in the distant future
Conclusions
 The Earth is lost eventually: engulfed by Sun 7.59 Gy in
the future (probably: certainly true in absence of human
intervention)
 Life might hang on for ~6 Gy, but the ultimate future of
the human race (if it survives) would need to be elsewhere
 The Sun doesn’t even produce a proper planetary nebula!