Habitable Zones around Evolved Stars

Lee Anne WillsonIowa State University

April 30, 2014STScI

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

6000 5000 4000 3000Surface Temperature, Kelvins

10,000

1000

100

L / LSun

10

1

Pre-main sequence

Red Giant Branch

Horizontal Branch or clump

Asymptotic Giant Branch

shell flashing and mass loss

Now

The evolution of the Sun

From Sackmann, Boothroyd, and Kramer 1993, Ap. J. 418, 457

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).Scaled habitable zone: Take into account only changes in L and ap.

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).Scaled habitable zone: Take into account only changes in L and ap.

Luminosity: MS through H & He burning

5 4

7 6

3

2 MSun

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

L: Main Sequence -> RGB 1.7 1.42.0 1.2 1.0 0.9 0.8 0.7 MSun

Source: Padova modelsSee Bertelli, et al. 2008

Stars below about 2Msun have time on the MS to develop life

He core flash

L: Main Sequence -> RGB 1.7 1.42.0 1.2 1.0 0.9 0.8 0.7 MSun

Source: Padova modelsSee Bertelli, et al. 2008

Stars below about 2Msun have time on the MS to develop life

Still on the MS

L: Main Sequence -> RGB 1.7 1.42.0 1.2 1.0 0.9 0.8 0.7 MSun

Source: Padova modelsSee Bertelli, et al. 2008

Stars below about 2Msun have time on the MS to develop life

Still on the MS

Maximum L and R on

the RGB => habitable zone to ~ 50 AU, R*/Sun

~ 160

Source: Padova modelsSee Bertelli, et al. 2008

logLmax

logRmax

He core flash

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)

53

50

47

Scaled Habitable Zone in AU

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

Figure 1 from Acoustic Signatures of the Helium Core FlashLars Bildsten et al. 2012 ApJ 744 L6

<- 2500Lsun

60 Lsun ->

1.8 1.9 1.95

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.

He core burning (HB or clump giant)

1.8 1.9 1.95

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.

3 AU

2.5 AU

He core burning (HB or clump giant)

Near logL = 3

Time – Time(logL=3), years

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.

4

3

2

1

tev = 2 Myr

tev = 1 Myr

Mass loss in modelsPisa 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.

BaSTI 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 = 0.35AGB: Bowen & Willson (1991) for C/O < 1, Wachter et al. (2002) for C/O > 1.

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/yeardefines the

Deathline

-10 -8 -6-4

logM=

0.7

1

1.4

2

2.8

4

core mass

Chandrasekhar limit

0.6

0.4

0.2

0.0

-0.2

logM

3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 logL

Bowen and Willson 1991

Deathline

-10 -8 -6-4

logM=

0.7

1

1.4

2

2.8

4

core mass

Chandrasekhar limit

0.6

0.4

0.2

0.0

-0.2

logM

3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 logL

Bowen and Willson 1991

Evolution at constant mass to the deathline, then at constant core mass to its final state

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), and Vassiliadis & Wood (blue/green)

Log(Ldeath)

Less effective mass loss => higher LDeath

Reimers (top), Blöcker (bottom), and Vassiliadis & Wood LogLdeath vs Mass

With sample model results from 2012 Bowen/Willson/Wang gridLog(Ldeath)

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

LogTeff

logMenvelope

0.01 0.03 Msun left

Small

Big

Teff (or radius, as L≈ constant)depends on envelope mass.

Envelope mass decreases because

nuclear processing (H->He ->

C, O)Mass loss

Curves from Wood models fitted by Frankowski (2003) approximating L = constant after the deathline (red, black dots)

Figure 1 from New Cooling Sequences for Old White DwarfsRenedo et al. 2010 ApJ 717 183

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 7 from Renedo et al. 2010 ApJ 717 183

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.

Another slow evolutionary stage

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

LogL∆M

From Boothroyd & Sackmann 1988

Translate to P(Mdot)

Log(Mdoto) log(Mdoto)+0.8*b Where b = dlogMdot/dlogL

∆logMdot = 5 for VW formula

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.

Figure 9 from Evolution, Nucleosynthesis, and Yields of Low-Mass Asymptotic Giant Branch Stars at Different Metallicities S. Cristallo et al. 2009 ApJ 696 797

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.

Effects of variation in metallicity

What about the distance ap?

• Changing M* => changing distance– Slow mass loss (t >> orbit) => ap ~ 1/M*– Fast mass loss (t < orbit) => Elliptical orbit– 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

See Mustill poster

Without pre-AGB mass loss

For Earth to survive, mass loss before L = 2500 Lsun

≈ LRGBtip

is needed.

©L. A. Willson 4/2004

The Sun must lose at

least 0.2 Msun before

L = 2500for

Earth to survive

2

1.5

1

0.5

Elapsed time, Myr

2000 4000

Mars

Earth

Venus

-16

-14

-12 -10

log(density) =

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