Habitable Zones around Evolved Stars Lee Anne Willson Iowa State University April 30, 2014 STScI.
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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 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)/] planet [(1-A)/] Earth Surface Temperature, Kelvins 10, 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 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. 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). 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). Luminosity: MS through H & He burning 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 L: Main Sequence -> RGB MSun Source: Padova models See Bertelli, et al Stars below about 2M sun have time on the MS to develop life He core flash L: Main Sequence -> RGB MSun Source: Padova models See Bertelli, et al Stars below about 2M sun have time on the MS to develop life Still on the MS L: Main Sequence -> RGB MSun Source: Padova models See Bertelli, et al Stars below about 2M sun 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 models See Bertelli, et al logL max logR max He core flash Online evolutionary tracks Pisa (DellOmodarme 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) (l/H) where S = 0 for M *Different definition of mixing length; fits above models with Iben l/H ~ 0.9. Comparing models Figure 4 of DellOmodarme et al Caption: Comparison at Z = 0.004, Y = 0.25 and ml = 1.90 [matches Iben ml ~0.9] among the different databases of Table 3. For the STEV database, we selected Y = 0.26 and 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. Theoretical isochrones at t = 12.5 Gyr DellOmodarme et al, 2012 Theoretical isochrones at t = 12.5 Gyr 20% variation in mixing length DellOmodarme et al, 2012 From DellOmodarme et al 2012 Luminosity at the tip of the red giant branch => position of habitable zone at max L RGB (core flash) Scaled Habitable Zone in AU 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 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) 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) 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 = t ev = 2 Myr t ev = 1 Myr 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 = 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 = 0.35 AGB: Bowen & Willson (1991) for C/O < 1, Wachter et al. (2002) for C/O > 1. Reimers relation: Mdot = -dM*/dt = 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. Critical mass loss rate log M = core mass Chandrasekhar limit logM logL Bowen and Willson 1991 Deathline log M = core mass Chandrasekhar limit logM 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 L death (M, Z, etc)? How big is dlogMdot/dlogL (along the evolutionary track) near the deathline? LogLdeath vs Mass Reimers (top), Blcker (bottom), and Vassiliadis & Wood (blue/green) Log(L death ) Less effective mass loss => higher L Death Reimers (top), Blcker (bottom), and Vassiliadis & Wood LogLdeath vs Mass With sample model results from 2012 Bowen/Wills on/Wang grid Log(L death ) 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 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) = P because pulsation period P has small uncertainty. Leaving the AGB LogT eff logM envelope 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) Figure 1 from New Cooling Sequences for Old White Dwarfs Renedo et al ApJ Including evolution to the white dwarf stage Figure 1. HertzsprungRussell diagram of our evolutionary sequences for Z = 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 ApJ Figure 7. Cooling curves at advanced stages in the white dwarf evolution for our sequences of masses M (upper left panel), M (upper right panel), M (bottom left panel), and M (bottom right panel). . The metallicity of progenitor stars is Z = Another slow evolutionary stage 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 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 Shell flash luminosity variations Pattern of mass loss during flashing Together LogL M From Boothroyd & Sackmann 1988 Translate to P(Mdot) Log(Mdot o ) log(Mdot o )+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 ApJ 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 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 Without pre-AGB mass loss For Earth to survive, mass loss before L = 2500 L sun L RGBtip is needed. L. A. Willson 4/2004 The Sun must lose at least 0.2 M sun before L = 2500 for Earth to survive Elapsed time, Myr Mars Earth Venus log(density) = 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) Questions? Planet caught in the wind of a dying star