Planets in the Wind of a Dying Star

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Planets in the Wind of a Dying Star

• Work by C. Struck, L. A. Willson, G. H. Bowen and
  B. Cohanim

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4 parts to this talk

• 1. Conditions in the atmospheres of dying stars
  (Miras) - the models.
• 2. Planet lt-gt star and planet lt-gt wind
  interactions
• 3. The fates of the planets in our own solar
  system.
• 4. Other systems and observability

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The evolution of the Sun
10,000 1000 100 L/LSun 10 1
shell flashing and mass loss
MIRAS
Asymptotic Giant Branch
Horizontal Branch
Red Giant Branch
Pre-main sequence
From Boothroyd, Sackmann, and Kramer 1993, Ap.
J. 418, 457
Now
6000 5000 4000
3000 Surface Temperature, Kelvins
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On the fate of the Sun the Earth
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1. Conditions in the atmospheres of dying stars
(Miras) - the models.

• Motions in and out
• Density vs. r
• Temperature vs r and t

..and some reasons for believing that the models
are right
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Water shell???
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R
photosphere
photosphere
phase ?
Bowen model
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Shocks form and propagate outward
Vesc
Jupiter
2 4 6 8 10
12 14 16
R/R
Bowen model
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-8 -10 -12 -14 -16
Note that the density is monotonic - it never
increases with increasing r
log ? gm/cm3
Bowen model
R/R
2 4 6
8 10 12
14
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Shock compression -gt heating -gt radiative losses
expansion between shocks -gt cooling and slower
radiative gains.
T/1000K
10 8 6 4 2
Almost nowhere in the atmosphere do you see
radiative equilibrium (the dotted line)!!
2 4 6 8 10 12
14 16 R
Bowen model
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Shock compression -gt heating -gt radiative losses
expansion between shocks -gt cooling and slower
radiative gains.
T/1000K
10 8 6 4 2
Jupiter
The gas temperature here depends on details of
the model, including non-LTE cooling and mass
outflow
2 4 6 8 10 12
14 16 R
Bowen model
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From 1 to 2 R 1 to 2 AU

• The material is propelled outward by shocks, then
  falls back until the next shock passes (with
  small net outward migration)
• The gas is NOT in radiative equilibrium - it is
  compressed/heated and expands/cools faster than
  it can reach equilibrium with the radiation field

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Some reasons for believing these models

• They fit and explain the Mira P-L relation
• They fit and explain empirical correlations of
  mass loss rates with stellar parameters

This part is also on the CD-ROM
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Models by Bowen (1995 grid) constraining
evolution to follow reasonable tracks
The dependence of mass loss rates on stellar
parameters along the AGB is VERY steep.
Sources see Willson 2000 ARAA Vol. 38.
Note Because R vs. L, M is given by the
evolutionary track, L serves as proxy for L, R,
and Teff, and the steep dependence on L in the
figure could be all R, all L, all Teff or (most
likely) a combination of these.
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Stars evolving up the AGB lose little mass until
they are close to the cliff where tmassloss
tnuclear
This is a lemming diagram
Bowen and Willson 1991
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Empirical relations result from selection effects
with very steep dependence of mass loss rates on
stellar parameters.
Reimers relation is a kind of main-sequence
for mass loss It tells us which stars are
losing mass, not how one star will lose mass.
x10
x0.1
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Individual stars do NOT follow Reimers relation
as they evolve.
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What are Mira variables?

• Late spectral types with emission lines some of
  the time
• Periods of hundreds of days
• Visual amplitudes 2.5 magnitudes in some cases
  up to 7 magnitudes or more.
• Mass loss rates 10-7 to 10-5MSun/year above
  10-5 OH-IR sources with opaque circumstellar
  shells.

These mass loss rates, and the emission lines,
and the large amplitude of visual variation gt
Miras have extended atmospheres.
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Miras are stars on or near the cliff
Miras
Bowen and Willson 1991
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Observations of Miras and OH-IR stars confirm
that Miras mark the location of the cliff
(K-L is a mass loss Rate indicator.)
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5 4 5 4 3
The cliff fits the observed Mira P-L relation
from the LMC very well. Hipparcos
distances to Miras show a lot of scatter.
logL
logL
4
2.8
2
1.4
0.7
1
2 2.2 2.4
2.6 2.8
logP
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From Wood 1998 triangles are supergiants
evolution is to the right.
Stars evolve through the Mira strip more massive
progenitors gt longer periods as Miras
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Figure from Wood 2000 based on MACHO data
Miras
Log(P in days)
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Planets interact with the star and the environment

• Interactions
• Radiative equilibrium with increasing LStar
• Gas drag in the wind
• Raising tides on the star

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Radiative equilibrium for planets

• (1-Avis) L pRp2/4pd2 4pR2 ? ltTp4gt (1-AIR)
• Avis need not be the same as AIR this produces a
  weak dependence on Teff.
• ltTp4gt is the temperature of the planet if the
  energy is redistributed over the entire surface
  before being radiated away.

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Simple estimate - now to the end of the main
sequence
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continued
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That assumed dconstant

• Gas drag could make d decrease
• Tides raised on the star could decrease
  d(assuming the star is rotating very slowly)
• Mass loss could make d increase

mvorbit d constant, vorbit ( v(GM/d) for m
ltlt M) decreases if M decreases,hence d
increases if M decreases.
This assumes slow mass loss (tMdot gtgt orbital
period)
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Effects of gas drag
Slow, laminar flow
Faster, turbulent flow
Drag coefficient
Drag D pr2 ?fluid vrel.
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Supersonic motion
The shock front increases the amount of fluid
whose velocity is altered by the planet gt it
increases the amount of drag
Magnetic fields complicate the picture further
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Structure of a bow shock Earths today
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Can we see the bow shock?
Shock ?v lt orbital speed 30 km/s _at_ 1AU
Pulsation shock ?v also 20-35 km/s
To get same power from the bow shock at the same
density, would need about the same area, pR2,
big!
Therefore Bow shock wont be obvious in
photometry but might give a few brightness
variation in an image
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Possible clues that it is a bow shock
Varies on an orbital time scale
Shows up as bright in Balmer and/or MgII emission
lines

Appropriate velocity variations
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-8 -10 -12 -14 -16
For reasonable estimates (0.1 D 10) Until
the planet gets into the exponential part of the
atmosphere, drag is unimportant for planet-sized
bodies (and Earths Moon)
log ? gm/cm3
E M J
Bowen model
R/R
2 4 6
8 10 12
14
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Tidal Torque
Slowly rotating star gt bulge lags behind
whizzing planet gt angular momentum is
transferred from the planet to the star
a
An approximate formula for the rate at which the
angular momentum is transferred from the planet
to the star by tidal torque is 106 (a/2R)8
(mJupiter/mplanet) years
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Effects of tidal interaction vs. drag
Timescale for action of tides (adapted from Soker
1998) 106 (a/2R)8 (mJupiter/mplanet) years
Gas drag depends on bow shock size (magnetic
field and/or planet size) and is large only when
a R, but then grows exponentially as a/R
decreases within the exp(-?r/H) part of the
atmosphere.
Drag time 105 yrs (?/10-11)-1
(m/mEarth)(Reff/Rearth)-2
Tidal torque is larger for larger m and is
important farther out (2R) for mmJupiter and
perhaps for Venus, Mercury but for Earth the
time scale is gt106 years for a gt R drag wins
over tides
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The fates of the planets

• Baked Alaska (radiative equilibrium temperatures)
• Eaten by the Sun Spiraling in from
• Effects of gas drag
• Effects of tides raised on the star

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What conditions will Earth encounter?
Where will Earth be?
What are the conditions (wind flux, wind speed)
at the position of Earth?
How bright is the Sun? (How hot is Earth?)
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If no mass is lost on the first ascent of the RGB
or at the core flash
Gas drag is important for Earth when it
encounters densities 10-11 gm/cm3
Bowen models
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To predict Earths fate one must know the mass
loss pattern
Gentle, prolonged mass loss (over a range of L,
R and Teff on the RGB and AGB) gt Earth gets
away
(for example, using Reimers Relation)
Mass loss occurring only after R1AU gt
Earth is engulfed.
( such as Bowens models suggest)
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The Mira ( mass loss) stage is the last few
100,000 years
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gt Earth will spiral in if the Sun grows to
nearly fill Earths orbit.
What IS the final radius of the Sun??? Theory

• How big are evolutionary models? Ans Depends
  on mixing length.
• B. Big shocks require big gravity gt relatively
  small R then pulsation mode models gt M/Rn, 2
  lt n 3. This suggests relatively small R
  (fundamental mode pulsation)

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gt Earth will spiral in if the Sun grows to
nearly fill Earths orbit.
What IS the final radius of the Sun???
Observations
Use observed L and Teff Teff is hard for these
stars - complex spectra formed in extended,
dynamical atmospheres

• Measure the angular diameters directly
• Interferometry is getting there, although the
  extended atmosphere, dust, and molecules make
  this hard too.

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Interferometry results(Example, from van Belle
data)
All these stars cant be pulsating in the same
mode with such different R(P)!
R/Rsun
cliff R vs. P
Note This version is different from - and
better than - the one on the CD-ROM.
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What does it take for the Earth to get away?
It needs to lose 0.2 solar masses before the AGB
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What do we know about ?M at the tip of the RGB?

• Clusters with pronounced blue horizontal branches
  RR Lyrae stars have ?MRGB0.1-0.2 MSun but do
  NOT have Miras.
• With a steep dependence of dM/dt on (L, R, T) it
  is difficult to lose just a little mass at the
  RG tip.
• Stars with higher masses typically have bluer RGB
  tracks (slightly) gt less mass loss at a given L
• The core flash event may lead to some mass loss
  (up to 0.1-0.2 Msun) but there is little
  evidence for ?MRGB for solar Z, solar mass stars.

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Map P -gt L -gtmass on the cliff
0.7 1.0 1.4 2
2.8
This is consistent with little or no mass loss
before the Mira stage.

200 400 600 days
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Does the heavy mass loss zone include the tip of
the RGB too?
MIRAS
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Which planets get eaten?
For most Miras, planets within about 1 to 1.5 AU
will spiral in. Details depend on the planets
mass, the mass of the star, the mass lost before
the AGB, and the character of the planet-wind
interaction, but all these effects give
uncertainties of less than a factor of 2.
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Observability?

• Hot flashes on Miras?
• Direct Imaging?
• Other?

The last two were addressed by Margarita Karovska
and Wes Traub this morning
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Can we observe the planet-wind interaction?
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Planets orbiting in Mira winds will produce wakes
and shocks these could give the impression of a
non-symmetric or a spotted star.
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TX Cam maser movie by Diamond et al.
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From Kemball Diamond 1997 TX Cam
snapshot and polarization
Interpretation Magnetic field or ??
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Tantalizing result

• De Laverny et al
• Rapid variations ( hours to days) mostly near
  minimum
• Some stars showed the same variation in two
  cycles at the same phase

Could this be due to planet-atmosphere
interactions?
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Hot Flashes on Miras??
Near minimum the visual flux of a Mira is about
the same as that of our Sun, or sometimes less.
Mira LC
Mira LC 1FV(Sun)
Mira LC 0.1FV(Sun)
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Model ingredients

• Smooth particle hydrodynamics(each particle
  represents a lot of gas)
• Planet/brown dwarf orbiting within 2 stellar
  radii where the material sometimes moves out,
  sometimes in, with the pulsation cycle.

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Movie, calculations courtesy of Curt Struck
Babak Cohanim
Yellow particles those whose velocity has
been changed by encounter with the planet
particles accreted by the planet reappear on
the inner boundary, creating a non-physical
ghost.
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Struck, Cohanim, Willson
Accreting onto a planet from a velocity field
that changes from inflow to outflow (with
respect to the star) suddenly, with an abrupt
jump in density Can this explain reports of
short time scale variability (hours to days) in
the light curves of Miras?
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10 vs 50 MJ
Accretion is periodic for lower mass companion
and flickering for higher masses
Angular momentum is flickering for lower mass
companion and periodic for higher masses
Low mass companion accretes directly the
increased post-shock density gives the periodic
signal.
High mass companion accretes by way of the wake
the wake is perturbed by the shock, changing the
direction of the accretion flow.
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Exoplanets as of the end of 2003
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Finding planets via hot flashes
For companions with masses 10-50 Mjupiter and up,
orbiting within about 2 R, we may see a flash
or flickering when the Mira is faint and at the
time that the shock passes the companion.
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Close AGB binary systems
MM a/R 2 Semi-detached binary system
mltltM a/R 1 Contact binary
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Given L, R, and m/M, what are the orbital
periods for amin to 2amin?
logL
Miras
Binaries with same R vs. L
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Figure from Wood 2000 based on MACHO data
Miras
Log(P in days)
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Figure from Wood 2000 based on MACHO data
Miras
Log(P in days)
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I have not seen the light curves, but Wood says
The fourth sequence contains red giants on the
first giant branch (FGB) or at the red end of the
core-helium burning loops of intermediate mass
stars (M gt2.25 MSun). The light curves of these
stars strongly suggest that they are contact
binaries, and they make up 0.5 of stars within
1 mag. of the FGB tip. Stars on the fifth
sequence show semi-regular, eclipse-like light
curves. The light curves and periods of these
stars suggest that they are in semi-detached
binaries, transferring mass to an invisible
companion via a stellar wind or Roche lobe
overflow. They make up 25 of AGB
stars. (Abstract of a paper for IAU 191)
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Note this complication

• Systems with main sequence mM and alt3R are
  likely to be classified as symbiotics, as are
  systems with white dwarf companions between a few
  R and several 10s of R.
• Example (long orbital period) R Aqr (Porbit44
  years, Pmira 387d)
• At 44 years with 0.9 lt M/Sun lt 1.9
• gt the WD orbit is between about 12 and 20 AU
• (Willson, Garnavich Mattei 1981)
• 1981IBVS.1961

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Ways to observe planets/companions

• Interaction of the atmosphere/wind with a planet
  or companion?
• Tidal distortion of primary in contact or
  semi-detached binary system explains the long P
  sequence in the Macho data (Wood, IAU Symposium
  191)
• Long period modulations of Mira light curves?
• About 25-30 of Miras show long secondary periods
  400-1500d

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Could planets/companions be responsible for
asymmetric PNe?
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Extreme cases most likely require the star to
have a relatively massive companion
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Spherical AGB Wind to bipolar PN

• Enough cases are now seen that it is possible
  this is the normal development
• What may happen (only) at the end of the AGB
  stage?

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Could Miras be distorted by rotation therefore
also perhaps have solar type magnetic activity?
R gt 100 RMS. I (Menvelope/2.4MSun)x 3x1059
gm-cm2. Very little of that is in the core for
reasonable Menvelope. Shape distortion and
wind modulaton depend on effective gravity,
geff g(1-(?r/vcirc)2). gt No distortion
as long as Menvelope is large (giving
?r/vcirc ltlt 1)
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Sudden onset of bipolar structure

• Spin-up the red giant?
• Possible for very low envelope mass and a common
  reservoir of angular momentum (core or planet)
• Planetary system modulates the flow?
• Planetary Nebulae could be well named after all!
• Still needs a low envelope mass
• Material collapsing from 1AU through Rms to RWD
  produces bipolar modulation of the flow?
• Still needs a very low envelope mass, ?1.

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Envelope mass for ?/?max0.1
Assuming we have about 1050 gm-cm2/s angular
momentum stored somewhere (core, Jupiter)
1050 (Menvelope/2.4MSun) 3x1059 vcirc/R
Mass Menv
With MgtMJ and an orbit 1 AU we could get
perhaps 10-3MSun spun up.
Mass stellar mass core mass with these small
enevelope masses.
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Not enough angular momentum to spin it up before
the very end.
Miras
OH-IR stars
Where rotation may matter
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Bipolarity through collapse

• Stellar radius at tip of AGB gt200 x main
  sequence radius
• Core (White Dwarf) radius lt1/100 x main
  sequence radius
• A small amount angular momentum in the envelope
  can lead to highly biased structure at lt
  10,000km, perhaps enough to shape the final
  outflow.
• Any coupling of planetary angular momentum to the
  envelope (such as eating planets near maximum
  stellar radius) could be greatly amplified this
  way.

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What else have we left out?
The details of convection are still not known
this affects everything, including tidal
spin-down times.
Shell flashes modulate L and R and also M on a
104 year cycle
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Helium Shell Flashes modulate L and R
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L and R variation gt M modulation
Quiescent H-burning
Post-flash He burning
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Shell flashes, drag tides
Double the radius Tidal drag increases by 28
256 Duration of flash lt 1 of the time
?atidal in flash ?atidal out of flash
Gas drag density for H/R ltlt 1, density may
increase many orders of magnitude when R
doubles ?agasdrag in flash may be gtgt ?agasdrag
out of flash
Shell flashes may make gas drag more important,
and could cause Earth to spiral into the Sun
sooner.
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Conclusions

• Mass loss rates increase steeply with increasing
  L and decreasing M - along an evolutionary track,
  LaM-b with a, b in the range 10-20!
• Asymmetric PNe emerge from symmetric (mostly) AGB
  winds when APN shaping event takes place when M
  Mremnant plus a little, but the mass loss
  process we understand is for M closer to the
  initial mass.
• Unless at least 0.2 solar masses is lost at the
  end of the RGB, the Earth ends up in the Sun
  shortly before it reaches its maximum L.

Truly a case of from dust to dust!
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The Fate of the Earth
I hold with those who favor fire
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Questions?