Download Habitable Zones around Evolved Stars

Habitable Zones around
Evolved Stars
Lee Anne Willson
Iowa State University
April 30, 2014
STScI
1 AU is in the habitable zone for our
Sun, now.
The planetary temperature scales as
Tplanet/TEarth ≈ [(L*/ap2)(XA)]1/4
where L* is in units of Lsun, ap is in AU
In the case of a planet without an atmosphere,
XA = [(1-A)/ε]planet
[(1-A)/ε]Earth
10,000
The evolution
of the Sun
shell flashing
and mass loss
1000
100
Asymptotic Giant
Branch
Horizontal
Branch or
clump
Red Giant
Branch
L / LSun
10
Pre-main
sequence
From Sackmann, Boothroyd,
and Kramer 1993, Ap. J. 418, 457
Now
1
6000
5000
4000
3000
Surface Temperature, Kelvins
Factors determining the location of the
habitable zone in evolved stars
• L changes dramatically as a star evolves
beyond the main sequence
• ap is altered by changing M*
or in extreme cases by tidal or gas drag
• Detailed properties of the star and the planet
are hiding in XA.
Factors determining the location of the
habitable zone in evolved stars
• L changes dramatically as a star evolves
beyond the main sequence
• ap is altered by changing M*
or in extreme cases by tidal or gas drag
• The albedoratio depends on planetary
atmosphere, surface properties, => and the
stellar spectral energy distribution (SED).
.
Factors determining the location of the
habitable zone in evolved stars
• L changes dramatically as a star evolves
beyond the main sequence
• ap is altered by changing M*
or in extreme cases by tidal or gas drag
• The albedoratio depends on planetary
atmosphere, surface properties, => and the
stellar spectral energy distribution (SED).
.
Luminosity: MS through H & He burning
Stars with
M > 2 Msun
spend
< 1.5 Gyr
on the MS
at
≥ 20 Lsun
Red dots:
AGB tip L
from
Mi vs Mf
Source: Padova models
See Bertelli, et al. 2008
7 6
5 4
3
2 MSun
L: Main Sequence -> RGB
Stars
below
about
2Msun have
time on
the MS to
develop
life
1.7 1.4
2.0
1.2 1.0
Source: Padova models
See Bertelli, et al. 2008
0.9
0.8
0.7 MSun
He core
flash
L: Main Sequence -> RGB
Stars
below
about
2Msun have
time on
the MS to
develop
life
1.7 1.4
2.0
1.2 1.0
Source: Padova models
See Bertelli, et al. 2008
0.9
0.8
0.7 MSun
Still
on
the
MS
L: Main Sequence -> RGB
Stars
below
about
2Msun have
time on
the MS to
develop
life
1.7 1.4
2.0
1.2 1.0
Source: Padova models
See Bertelli, et al. 2008
0.9
0.8
0.7 MSun
Still
on
the
MS
Maximum
L and R on
the RGB =>
habitable
zone to
~ 50 AU,
R*/Sun
~ 160
Source: Padova models
See Bertelli, et al. 2008
logLmax
He core
flash
logRmax
Online evolutionary tracks
•
•
•
•
Pisa (Dell’Omodarme et al, 2012)
BaSTI (Pietrinferni et al. 2004, 2006)
Dartmouth (Dotter et al. 2007, 2008)
Padova STEV (Bertelli et al. 2008, 2009)
Approximate formula for AGB (Iben 1984*)
R = 312 (L/104)0.68(1.175/M)0.31S(Z/0.0001)0.088 (l/H)-0.52
where S = 0 for M<1.175 and S=1 for M>1.175
*Different definition of mixing length;
fits above models with Iben l/H ~ 0.9.
Comparing models – Figure 4 of
Dell’Omodarme et al. 2012
Caption: Comparison at Z = 0.004, Y = 0.25 and
αml = 1.90 [matches Iben αml~0.9] among the
different databases of Table 3. For the STEV
database, we selected Y = 0.26 and αml = 1.68 as
the values among those available that are
closest to those of the other databases. The
tracks of the Dartmouth databases were
interpolated in Z, see text.
Theoretical isochrones at t = 12.5 Gyr
Dell’Omodarme et al, 2012
Theoretical isochrones at t = 12.5 Gyr
20%
variation in
mixing
length
Dell’Omodarme et al, 2012
From Dell’Omodarme et al 2012
Luminosity at the tip of the red giant branch =>
position of habitable zone at max LRGB (core flash)
Scaled
Habitable
Zone in AU
53
50
47
Important timescales
At the He core flash, tev approaches tdyn and is shorter than tKH
On the AGB, tKH approaches tdyn and tMdot decreases to <tev
He Core Flash – MESA models capable
of modeling fast changes
<- 2500Lsun
60 Lsun ->
Figure 1 from Acoustic Signatures of the Helium Core Flash
Lars Bildsten et al. 2012 ApJ 744 L6
He core burning (HB or clump giant)
M ≤ 1.95 Msun
spend
>10 Myr in
quiescent He
burning with
luminosities
~40-50 Lsun
Higher mass =>
lower L at this
phase => longer
time at nearly
constant L.
1.8 1.9 1.95
He core burning (HB or clump giant)
M ≤ 1.95 Msun
spend
>10 Myr in
quiescent He
burning with
luminosities
~40-50 Lsun
Higher mass =>
lower L at this
phase => longer
time at nearly
constant L.
1.8 1.9 1.95
3 AU
2.5 AU
Near logL = 3
4
L ≈ Loe(t/tev)
with
tev = (1/L dL/dt)-1
~ 1-2x106 years
(dashed lines )
Time axis shifted
so all curves
coincide where
logL = 3.
tev = 1 Myr
3
tev = 2 Myr
2
1
Time – Time(logL=3), years
Mass loss in models
BaSTI
RGB models computed at constant mass;
HB masses adjusted to allow for integrated RGB mass loss ranging from 0 to
most of envelope. No AGB.
Reimers (1975) with η = 0.4 and 0.2, RGB and AGB
Dartmouth
constant mass to RGB tip
Padova STEV
models evolve to RGB tip at constant mass; isochrones adjusted for Reimers’
mass loss with η = 0.35
AGB: Bowen & Willson (1991) for C/O < 1,
Wachter et al. (2002) for C/O > 1.
Pisa
Reimers’ relation: Mdot = -dM*/dt = η 4e-13 LR/M solar masses/year from fitting observations
– it is, however, strongly affected by selection bias.
The Padova “Bowen & Willson (1991)” formula is not the same as our current formula
(derived from later models with different selection criteria).
Wachter et al. (2002) is based on carbon star models and formulated in terms of Teff.
Critical mass loss rate
Luminosity evolves on time scale tev = 1-2x106 yr
=> dlogM/dt = dlogL/dt
Mdot = -dM*/dt = M*/tev
= (0.5 to 1) 10-6 M* solar masses/year
defines the
Deathline
logM= -10 -8
-6
4
-4
0.6
2.8
logM
2
0.4
Chandrasekhar
limit
1.4
0.2
0.0
1
0.7
core mass
-0.2
3.0
4.8
3.2
3.4
3.6
3.8
4.0
4.2
4.4
4.6
logL
Bowen and Willson 1991
Evolution at constant mass to the deathline,
then at constant core mass to its final state
logM= -10 -8
-6
4
-4
0.6
2.8
logM
2
0.4
Chandrasekhar
limit
1.4
0.2
0.0
1
0.7
core mass
-0.2
3.0
4.8
3.2
3.4
3.6
3.8
4.0
4.2
4.4
4.6
logL
Bowen and Willson 1991
Mass Loss terminates the AGB
• Two key parameters:
– Where is the deathline Ldeath(M, Z, etc)?
– How big is dlogMdot/dlogL (along the
evolutionary track) near the deathline?
LogLdeath vs
Mass
Reimers (top),
Blöcker
(bottom),
Log(Ldeath)
and
Vassiliadis &
Wood
(blue/green)
Less effective
mass loss =>
higher LDeath
Reimers (top),
Blöcker (bottom), and
Vassiliadis & Wood
LogLdeath vs Mass
With sample
model results
from 2012
Bowen/Wills
Log(Ldeath)
on/Wang grid
Reimers’ relation vs. Deathline
• Red arrows:
dlogMdot/dlog(LR/M)
>>1 (e.g. VW formula)
L, R and M are
uncertain => strong
selection bias =>
empirical relations
(e.g. Reimers’) greatly
underestimate the
exponents
Reimers’
Mass loss formulae
• At the deathline, -dM*/dt = a LbRcM-d with
large b, c, and d =>
– Small errors in L, R, M => empirical relations
underestimate b, c, d
– Empirical relations tell us which stars are losing
mass (the Deathline) not how a star loses mass
(dlogMdot/dlogL along an evolutionary track)
An exception is the Vassiliadis & Wood relation
log(-dM*/dt) = -11.4 + 0.0123 P
because pulsation period P has small uncertainty.
Leaving the AGB
Small
Teff (or radius, as L≈ constant)
depends on envelope mass.
Envelope mass decreases
because
nuclear processing
(H->He -> C, O)
Mass loss
LogTeff
0.01 0.03 Msun left
Big
logMenvelope
Curves from Wood models
fitted by Frankowski (2003)
approximating
L = constant after the
deathline (red, black dots)
Including evolution to the white dwarf stage
Figure 1. Hertzsprung–Russell
diagram of our evolutionary
sequences for Z = 0.01.
From bottom to top:
evolution of the
1.0 M☉, 1.5 M☉,
1.75 M☉, 2.0 M☉,
2.25 M☉, 2.5 M☉,
3.0 M☉, 3.5 M☉,
4.0 M☉, and 5.0 M☉
model stars.
Figure 1 from New Cooling Sequences for Old White Dwarfs
Renedo et al. 2010 ApJ 717 183
Another slow evolutionary stage
Figure 7. Cooling curves at
advanced stages in the white
dwarf evolution for our
sequences of masses
0.525 M☉ (upper left panel),
0.570 M☉ (upper right panel),
0.609 M☉ (bottom left panel),
and 0.877 M☉ (bottom right
panel). …. The metallicity of
progenitor stars is Z = 0.01.
Figure 7 from Renedo et
al. 2010 ApJ 717 183
Conclusions (so far)
• Stable, slow stages of post-MS evolution for
most stars:
He core burning,
White dwarf cooling
• Lmax on the RGB for low mass stars ≈ 2500 LSun
• Mass-loss determines Lmax on the AGB – the
Deathline
I oversimplified
• Before L = Ldeath, He shell flashing begins
• Varying L and R => varying Mdot
• How big an effect this has depends on
– dlogMdot/dlogL
– Nonlinear effects during rapid changes in L
Shell flash luminosity variations
Pattern of mass loss during flashing
Together
∆M
LogL
From Boothroyd & Sackmann 1988
Translate to P(Mdot)
∆logMdot = 5 for VW formula
Log(Mdoto)
log(Mdoto)+0.8*b
Where b = dlogMdot/dlogL
I oversimplified II
• Some of the AGB stars become carbon stars,
with C abundance > O abundance
• This changes the opacity, the radius, the
spectrum, the character of the dust, and the
mass loss rate.
• When there is deep dredge-up, the final core
mass becomes less dependent on the mass
loss process.
Effects of variation in metallicity
lower metallicity
=> smaller radius at a given L
=> lower –dM/dt at a given L
=> higher Ldeath(M)
However, shell-flashing occurs at
about the same range of L, and
conversion to C/O>1 increases
the radius and the mass loss
rate.
Figure 9 from Evolution,
Nucleosynthesis, and Yields of LowMass Asymptotic Giant Branch Stars
at Different Metallicities S. Cristallo
et al. 2009 ApJ 696 797
What about the distance ap?
• Changing M* => changing distance
See
– Slow mass loss (t >> orbit) => ap ~ 1/M*
Mustill
– Fast mass loss (t < orbit) => Elliptical orbit poster
– Both -> destabilization of the planetary system
A: Small dlogMdot/dlogL (e.g. Reimers’ formula)
– Planets migrate outward before star reaches max L
B: Large dlogMdot/dlog (e.g. VW, BW)
– Star will engulf more of its planets
Without pre-AGB mass loss
For Earth
to survive,
mass loss
before
L=
2500 Lsun
≈ LRGBtip
is needed.
The Sun
must lose
at least
0.2 Msun
before
L = 2500
for
Earth to
survive
2
Mars
log(density) = -16
1.5
-14
Earth
-12
1
-10
Venus
0.5
2000
4000
Elapsed time, Myr
©L. A. Willson 4/2004
Conclusions
• Stable, slow stages of post-MS evolution for
most stars: He core burning, White dwarf
cooling
• Mass-loss determines Lmax(AGB); uncertainties
include the mass loss formula, shell flash
effects and which stars become carbon stars
• At Lmax planets within about 1AU are engulfed
(details depending on the mass loss formula)
Questions?
Planet caught in the wind of a dying star