1. Habitable Zones around Evolved Stars Lee Anne Willson Iowa State University April 30, 2014 STScI

2. 1 AU is in the habitable zone for our Sun, now. The planetary temperature scales as T planet /T Earth ≈ [(L*/a p 2 )(X A )] 1/4 where L* is in units of L sun, a p is in AU In the case of a planet without an atmosphere, X A = [(1-A)/ε] planet [(1-A)/ε] Earth

3. 6000 5000 4000 3000 Surface Temperature, Kelvins 10,000 1000 100 L / L Sun 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

4. Factors determining the location of the habitable zone in evolved stars L changes dramatically as a star evolves beyond the main sequence a p 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 X A.

5. Factors determining the location of the habitable zone in evolved stars L changes dramatically as a star evolves beyond the main sequence a p 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).

6. Factors determining the location of the habitable zone in evolved stars L changes dramatically as a star evolves beyond the main sequence a p 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).

7. Luminosity: MS through H & He burning 5 4 7 6 3 2 MSun Stars with M > 2 M sun spend < 1.5 Gyr on the MS at ≥ 20 L sun Red dots: AGB tip L from M i vs M f Source: Padova models See Bertelli, et al. 2008

8. L: Main Sequence -> RGB 1.7 1.4 2.0 1.2 1.0 0.9 0.8 0.7 MSun Source: Padova models See Bertelli, et al. 2008 Stars below about 2M sun have time on the MS to develop life He core flash

9. L: Main Sequence -> RGB 1.7 1.4 2.0 1.2 1.0 0.9 0.8 0.7 MSun Source: Padova models See Bertelli, et al. 2008 Stars below about 2M sun have time on the MS to develop life Still on the MS

10. L: Main Sequence -> RGB 1.7 1.4 2.0 1.2 1.0 0.9 0.8 0.7 MSun Source: Padova models See Bertelli, et al. 2008 Stars below about 2M sun have time on the MS to develop life Still on the MS

11. Maximum L and R on the RGB => habitable zone to ~ 50 AU, R*/Sun ~ 160 Source: Padova models See Bertelli, et al. 2008 logL max logR max He core flash

12. 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/10 4 ) 0.68 (1.175/M) 0.31S (Z/0.0001) 0.088 (l/H) -0.52 where S = 0 for M 1.175 *Different definition of mixing length; fits above models with Iben l/H ~ 0.9.

13. Comparing models – Figure 4 of Dell’Omodarme et al. 2012 Caption: Comparison at Z = 0.004, Y = 0.25 and α ml = 1.90 [matches Iben α ml ~0.9] among the different databases of Table 3. For the STEV database, we selected Y = 0.26 and α ml = 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.

14. Theoretical isochrones at t = 12.5 Gyr Dell’Omodarme et al, 2012

15. Theoretical isochrones at t = 12.5 Gyr 20% variation in mixing length Dell’Omodarme et al, 2012

16. From Dell’Omodarme et al 2012

17. Luminosity at the tip of the red giant branch => position of habitable zone at max L RGB (core flash) 53 50 47 Scaled Habitable Zone in AU

18. Important timescales At the He core flash, t ev approaches t dyn and is shorter than t KH On the AGB, t KH approaches t dyn and t Mdot decreases to <t ev

19. He Core Flash – MESA models capable of modeling fast changes Figure 1 from Acoustic Signatures of the Helium Core Flash Lars Bildsten et al. 2012 ApJ 744 L6 <- 2500L sun 60 L sun ->

20. 1.8 1.9 1.95 M ≤ 1.95 M sun spend >10 Myr in quiescent He burning with luminosities ~40-50 L sun Higher mass => lower L at this phase => longer time at nearly constant L. He core burning (HB or clump giant)

21. 1.8 1.9 1.95 M ≤ 1.95 M sun spend >10 Myr in quiescent He burning with luminosities ~40-50 L sun 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)

22. Near logL = 3 Time – Time(logL=3), years L ≈ L o e (t/t ev ) with t ev = (1/L dL/dt) -1 ~ 1-2x10 6 years (dashed lines ) Time axis shifted so all curves coincide where logL = 3. 43214321 t ev = 2 Myr t ev = 1 Myr

23. Mass loss in models PisaRGB models computed at constant mass; HB masses adjusted to allow for integrated RGB mass loss ranging from 0 to most of envelope. No AGB. BaSTIReimers (1975) with η = 0.4 and 0.2, RGB and AGB Dartmouthconstant mass to RGB tip Padova STEVmodels 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. 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 T eff.

24. Critical mass loss rate

25. - 10 -8 -6 -4 log M = 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

26. - 10 -8 -6 -4 log M = 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

27. Mass Loss terminates the AGB Two key parameters: – Where is the deathline L death (M, Z, etc)? – How big is dlogMdot/dlogL (along the evolutionary track) near the deathline?

28. LogLdeath vs Mass Reimers (top), Blöcker (bottom), and Vassiliadis & Wood (blue/green) Log(L death ) Less effective mass loss => higher L Death

29. Reimers (top), Blöcker (bottom), and Vassiliadis & Wood LogLdeath vs Mass With sample model results from 2012 Bowen/Wills on/Wang grid Log(L death )

30. 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’

31. Mass loss formulae At the deathline, -dM*/dt = a L b R c M -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.

32. Leaving the AGB LogT eff logM envelope 0.01 0.03 M sun left Small Big T eff (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)

33. Figure 1 from New Cooling Sequences for Old White Dwarfs Renedo 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.

34. 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

35. Conclusions (so far) Stable, slow stages of post-MS evolution for most stars: He core burning, White dwarf cooling L max on the RGB for low mass stars ≈ 2500 L Sun Mass-loss determines L max on the AGB – the Deathline

36. I oversimplified Before L = L death, 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

37. Shell flash luminosity variations

38. Pattern of mass loss during flashing

39. Together LogL ∆M

40. From Boothroyd & Sackmann 1988

41. Translate to P(Mdot) Log(Mdot o ) log(Mdot o )+0.8*b Where b = dlogMdot/dlogL ∆logMdot = 5 for VW formula

42. 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.

43. 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 L death (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

44. What about the distance a p ? Changing M* => changing distance – Slow mass loss (t >> orbit) => a p ~ 1/M* – Fast mass loss (t 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

45. Without pre-AGB mass loss For Earth to survive, mass loss before L = 2500 L sun ≈ L RGBtip is needed.

46. ©L. A. Willson 4/2004 The Sun must lose at least 0.2 M sun before L = 2500 for Earth to survive 2 1.5 1 0.5 Elapsed time, Myr 2000 4000 Mars Earth Venus -16 -14 -12 -10 log(density) =

47. Conclusions Stable, slow stages of post-MS evolution for most stars: He core burning, White dwarf cooling Mass-loss determines L max (AGB); uncertainties include the mass loss formula, shell flash effects and which stars become carbon stars At L max planets within about 1AU are engulfed (details depending on the mass loss formula)

48. Questions? Planet caught in the wind of a dying star