Miras, Mass-Loss, and the Ultimate Fate of the Earth L. A. Willson & G. H. Bowen, Iowa State University. Fire and Ice:

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1 Miras, Mass-Loss, and the Ultimate Fate of the Earth L. A. Willson & G. H. Bowen, Iowa State University Fire and Ice: Some say the world will end in fire, Some say in ice. From what I've tasted of desire I hold with those who favor fire. But if it had to perish twice, I think I know enough of hate To know that for destruction ice Is also great And would suffice Robert Frost Whether the Earth ends in fire or ice depends how, when, and how fast the Sun sheds mass. Early or extended mass loss: Earth survives the red giant stages of the Sun and ends "in ice". Late, abrupt mass loss: Earth is engulfed in the bloated Sun near the end of its red giant evolution. 1

2 1. Stages of Solar Evolution years (=10 Gyr) of 4H He in the core, then 4H He around a core of He to maximum L~2000L now abrupt start to He to C and O core He to C and O at ~ 100L nowv Alternating H and He "burning" until the C+O core ~ 0.6 M Sun, when mass loss removes the rest. Main Sequence Red Giant Branch (RGB) Helium Core Flash Horizontal Branch Asymptotic Giant Branch (AGB) The post-main sequences stages leading up to "the end" take an additional 2x10 9 years. Mass loss 10,000 Post-AGB L/L now 10 Asymptotic Giant Branch Red Giant Branch Pre-main sequence 1 Main sequence Surface Temperature, Kelvins 2

3 Increasing Solar Power => increasing T for the planets Radiative equilibrium temperatures for the planets are approximately given by T RE = 290K (L/now) 1/4 / (distance in AU) 1/2 600 Mercury C 200 Mercury 400 T, Kelvins Venus Earth Mars log(luminosity) luminosity / luminosity now The evolution of planetary temperatures during the main sequence (now to about 5x10 9 years ahead) Habitable zone (approximate): 3

4 Extending this to the end of the AGB: Rocky planet vaporization zone Mercury 2000 Venus Mercury 1000 Earth Mars Jupiter Saturn Uranus Neptune 0 Habitable zone 0 1log(L/now) ,000 log(luminosity) L/now time-> RGB tip Now End of Main Sequence Horizontal Branch shell flashing starts Mass Loss ends the AGB The maximum temperature a planet achieves depends on its distance from the Sun and the maximum luminosity of the Sun - both of these, in turn, depend on the mass loss that ends the AGB. 4

5 Most astronomers have been using Reimers' Relation as a recipe for mass loss = -dm/dt = η 4x10-13 (L/L Sun ) (R/R Sun )/(M/M Sun ) M Sun /year where L Sun, R Sun, and M Sun refer to our present-day Sun. This relation was derived from a fit to observations of mass loss from red giants, with the adjustable parameter added later when it was found that the original relation killed stars too soon logm -6 η = loglr/m Sackmann, Boothroyd and Kraemer (1993, Ap. J. 418, 457) modeled future solar evolution using Reimers' Relation with η=0.6. 5

6 Evolutionary stages in the Sackmann, Boothroyd and Kraemer models: 10,000 shell flashing and mass loss 1000 Asymptotic Giant Branch 100 L/L Sun Horizontal Branch Red Giant Branch 10 1 Now Pre-main sequence Surface Temperature, Kelvins 6

7 Compared with the radius of Earth's orbit, the Sun is small until it reaches nearly the tip of the red giant or asymptotic giant branch: 10, R Sun AGB RGB R Sun R Sun L/L Sun 10 R Sun 10 3 R Sun Surface Temperature, Kelvins 7

8 In their models Earth escapes its fiery fate mainly because solar masses are removed on the first ascent of the red giant branch. Their RGB mass loss is entirely due to the Reimers' relation - there is no mass loss "event" associated with the helium core flash. 8

9 Given an evolutionary track of the form R = function (M, L, Z), any mass loss law (L, R, M, Z) may be expressed as (R, M, Z) Bowen Vassiliadis & Wood log, M Sun /yr -6-7 Reimers Earth's orbit now Earth's orbit if M Sun = Radius / current solar radius Evolution ends near dlogl/dt = -dlogm/dt - closer to this for steeper mass loss laws, but always close. This is indicated by the squares (0.7M Sun ) and dots (1M Sun ). 9

10 Using the Bowen model results, one finds that AGB evolution ends with a "cliff" logm = M core mass Chandrasekhar limit ,000 luminosity whose position depends on mass and metallicity logm Z/Z = core mass Chandrasekhar limit logl 10

11 How can the empirical relation (Reimers' relation) and the theoretical mass loss law (Bowen's results) be so very different? Is one of these wrong? A steep mass loss law => severe selection effects: -4-5 Reimers' Reln. for η=1 is shown as a dashed red line logm The cliff is the bold black line, with mass labels loglr/m Evolution follows the blue arrows Reimers' relation reinterpreted: It tells us which stars are losing mass, not how a star loses mass. (Analogous to: The main sequence is not an evolutionary track but the location of stars "burning" hydrogen in their cores.) 11

12 The "cliff" edge stars are the Miras: 4 logl "Cliff" edge stars log(period, days) The Sun will end up between the 0.7 and the 1 solar mass points in this plot, depending on how much mass it loses at the helium core flash. With a very steep mass loss relation, it is less likely than for the "Reimers' mass loss formula" case that the Sun will lose much mass on the first ascent of the red giant branch. The most likely cases are "all" or "nothing" with the possible exception of a finite M ejected at the core flash. 12

13 Averaged over the pulsation cycle, density The density is increasing with time; the green curve describes the density near the end of the AGB. rho(170) rho(180) rho(190) H distance (AU) Earth's orbit rho(170) rho(180) rho(190) H Mars's orbit density distance (AU) 13

14 Assuming the Sun starts the AGB with a mass about the same as it is today, we find: 1.5 R, AU 1.0 Mars Earth time-averaged density = 10 x gm/cm 3, x = The Sun's mass decreases, and Mars escapes max R = 228 x now Venus R=200xnow 0.5 R=150xnow L Sun time in millions of years At the crash: R Sun = 180 R now (varying from 173 to 188 with P = 313 days) L Sun = 2790 L now At the end: L Sun = 3950 is the maximum achieved. 14

15 Shell flashes modify L and R on a scale of years * : logl ~10 5 years t time (years) Radius/RSun F time (years) Radius/RSun ~1000 years F time (years) This will need to be included in future mass-loss calculations. * Models by S. Kawaler using ISUEVO, February

16 The final fates of the planets, their moons, and the asteroids: Object distance from Sun (now) peak T reached (L<4000K) Final fate Mercury *** Into the Sun, RGB Venus *** Into the Sun, early AGB Earth <2306> Into the Sun, late AGB, unless M RGB >0.2 M Sun and its Moon Crashes into Earth before Earth dies. Mars Escapes unless M RGB 0 asteroids Small ones (<<100km) spiral in to Sun after Earth dies. Jupiter Baked but not destroyed Saturn, Uranus, and Neptune Also baked but not destroyed 16

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