The Stellar Ultrasound

Seminar given at CIERA, Northwestern (Chicago)

Transcript

1. The Stellar Ultrasound M.Cantiello (Kavli Institute for Theoretical Physics) J.Fuller, D. Stello, L. Bildsten, R. A. Garcia, T. Bedding, D. Huber, V. Silva Aguirre
2. Exciting times for Stellar Physics ! Transient surveys unraveling unpredicted variety of explosive stellar deaths (PTF, Pan-STARRS and soon LSST). We do not understand SN progenitors ! Exoplanetary science requires precise characterization of host stars properties ! We are entering the era of high precision stellar physics (Kepler, K2, GAIA, TESS, PLATO). Theory is lagging behind Motivation
3. How to probe the deep stellar interiors? “It would seem that the deep interiors of the Sun and stars is less accessible to investigation than any other region of the Universe” Sir Eddington, 1926 ! Rotation ! Magnetic Fields Motivation
4. Asteroseismology now allows to probe the deep interiors of stars and measure properties like radial differential rotation and internal magnetic fields! ! Rotation ! Magnetic Fields Take Away Message € ω
5. Stars are born rotating
6. Range of rotational velocity Fukuda 1982 “In practice all stars are rotating around their axis” - Maeder & Meynet
7. P ( VEq sin i ) P ( VEq ) 334 B Stars Dufton et al. 2013 Early type stars in 30 Doradus VLT-FLAMES Tarantula Survey
8. Long GRB Central Engine Collapsar Woosley 1993 Eacc ~ 0.01..1Msunc2~1052..54ergs Q: What sets the rotation rate of stellar cores?
9. (Spitkovski 2006) Erot ~ 3 1052 (P/ms)-2 (R/10km)2 ergs Millisecond Magnetar Usov 1992 Long GRB Central Engine Q: Strong B-fields: Where do they come from?
10. Final j-distribution 1D Stellar evolution calculations SN: no accretion disk during collapse / no rapidly rotating NS GRB (?): enough angular momentum in the core to make an accretion disk during collapse / create a rapidly rotating NS
11. Physics of Angular Momentum Transport
12. ! Hydrodynamics instabilities ! Rotationally induced circulations ! Magnetic torques ! Internal gravity waves Angular Momentum Transport Different classes of mechanisms have been proposed: e.g. Rogers et al. 2013 e.g Maeder & Meynet 2002 e.g. Spruit 2002 e.g. Heger et al. 2000 Convective Regions usually assumed rigidly rotating
13. ! Dynamical Shear Hydrodynamic Instabilities Dynamical shear instability occurs when the energy that can be gained from the shear flow becomes comparable to the work that has to be done against the gravitational potential for the adiabatic turnover of a mass element
14. The thermal flux through the surface of a (radiative) rotating star is proportional to the local effective gravity. Since this depends on the co-latitude, one expects a greater radiative flux at the poles than at the equator. Rotationally Induced Circulations Convective Core € ω Von Zeipel (1924) Von Zeipel Theorem
15. Interferometry of rotating stars Altair (A7IV-V Star): confirms Von Zeipel ‘gravity darkening’ even if with a slightly different exponent
16. Thermal imbalance drives circulations Core Meridional circulation
17. ! Eddington-Sweet Circulation ! Is a meridional circulation mixing the stellar interior ! Mixing process on tKH τES ∝τKH ωK ω ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 Rotationally Induced Circulations Maeder & Meynet 2002
18. ! Hydrodynamics instabilities ! Rotationally induced circulations ! Magnetic torques ! Internal gravity waves Angular Momentum Transport Different classes of mechanisms have been proposed: e.g. Rogers et al. 2013 e.g Maeder & Meynet 2002 e.g. Spruit 2002 e.g. Heger et al. 2000
19. Tayler-Spruit Dynamo ! Dynamo in a radiative layer ! Magnetic energy is generated from differential rotation ! Initially a seed magnetic field is stretched by the differential rotation, amplifying the toroidal component of the field ! An instability in the toroidal component of the field (Tayler instability) is used to close the dynamo loop Spruit 2002 Toroidal Poloidal
20. ! Tayler-Spruit Dynamo (Spruit 2002) ! Core - Envelope coupling 1.Differential rotation winds up toroidal component of B 2.Magnetic torques tend to restore rigid rotation Core If the envelope slows down angular momentum is also removed from the core Tayler-Spruit Dynamo
21. ! Hydrodynamics instabilities ! Rotationally induced circulations ! Magnetic torques ! Internal gravity waves Angular Momentum Transport Different classes of mechanisms have been proposed: e.g. Rogers et al. 2013 e.g Maeder & Meynet 2002 e.g. Spruit 2002 e.g. Heger et al. 2000 ! Rogers et al. 2013 ! Charbonnel & Talon 2005 ! Alvan et al. 2014 ! Fuller, MC et al. 2015 ! Fuller, Lecoanet, MC et al. 2014
22. Internal Gravity Waves Alvan et al. 2014 IGW: Excited by turbulent convection Spectrum: Not well understood. But likely Kolmogorov-like with a steep exponent Dissipation: Radiative dissipation usually dominates in stellar interiors They carry angular momentum See e.g.: Charbonnel & Talon 2005, Goldreich & Kumar 1990, Lecoanet & Quatert 2013, Mathis et al. 2014, Rogers et al. 2013
23. Tests of Angular Momentum Transport
24. !Surface abundances !Rotation of compact remnants !Asteroseismology Testing angular momentum transport mechanisms
25. 200 400 600 800 ModelNumber 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 M/M⊙ 1.5M⊙ , Z=0.02, MESA V. 5118 −1 0 1 2 3 4 5 6 Nueclear Energy generation, Log (erg/g/s) Evolution of a 1.5 MSun Core H-burning Convective Envelope H-Shell burning In Mass Coordinate
26. 2.96 2.98 3.00 3.02 3.04 3.06 3.08 3.10 3.12 t ×109 0 2 4 6 8 10 12 14 r/R⊙ 1.5M⊙ , Z=0.02, MESA V. 5118 −1 0 1 2 3 4 5 6 Nueclear Energy generation, Log (erg/g/s) Convective Envelope H-Shell burning In Radius Coordinate Evolution of a 1.5 MSun
27. Evolution of a 1.5 MSun Zoom In Radius Coordinate H-Shell burning
28. Evolution after H-exhaustion ! A dramatic change in the stellar structure ! Huge density contrast between core and envelope ! Assuming simple conservation of angular momentum, core spins up, envelope spins down ! As a star evolves past H-exhaustion angular momentum transport mechanisms determine the rotation rate of the core
29. Credit: BBSO/NJIT Solar-Like Oscillations n m l ! Turbulent convection causes stochastic excitation of (non-radial) pulsation ! Solar-like oscillations expected and observed in red giants as well (see e.g. Dupret et al. 2009)
30. Space-Based Photometry 27 cm diameter Launched December 2006 CoRoT Kepler 95 cm diameter Launched March 2009
31. Solar-Like Oscillations Huber et al. 2016 Pre CoRot/Kepler
32. Courtesy: Jim Fuller
33. evanescent zone g-mode cavity p-mode cavity νmax p-mode cavity (envelope) g-mode cavity (core) evanescent zone Courtesy: Dennis Stello Mixed Modes N2
34. Mixed Modes p-mode cavity (envelope) g-mode cavity (core) If the frequencies of the stochastically excited p-modes become comparable to the frequencies of the g-modes, a ‘cross-talk’ between core and envelope is possible (mixed modes). This happens in Red Giant stars due to the increased core density.
35. Courtesy: Jim Fuller
36. Mixed Modes p-mode cavity (envelope) g-mode cavity (core) Since a mixed mode lives both as a p-mode (in the envelope) and as a g-mode (in the core), if observed at the surface can give informations about conditions (e.g. rotation rate) in different regions of the star!
37. A test for the physics of rotation Beck et al. 2012 Stellar rotation lifts the degeneracy (in the azimuthal order ‘m’) of non radial modes, resulting in a multiplet of (2l+1) frequency peaks in the power spectrum for each mode. Observed splittings ~ 0.2 MicroHz l=1 l=0
38. Evolution of Core Rotation Mosser et al. 2012 Early RGB H-burning Clump Stars He-burning P~R2 P~R0.7
39. SLOW FAST 1.5MSun Vini=50 km/s Cantiello et al. (2014)
40. SLOW FAST 1.5MSun Vini=50 km/s Cantiello et al. (2014)
41. Other possible mechanisms? !Angular momentum transport from IGW during the Red Giant Phase !Magnetic coupling from fossil or convective dynamo generated magnetic fields Alvan et al. 2014 See also e.g. Charbonnel & Talon (2007) See e.g. Mader & Meynet (2014)
42. Internal Gravity Waves Alvan et al. 2014 IGW: Excited by turbulent convection Spectrum: Not well understood. But likely Kolmogorov-like with a steep exponent Dissipation: Radiative dissipation usually dominates in stellar interiors They carry angular momentum See e.g.: Charbonnel & Talon 2005, Goldreich & Kumar 1990, Lecoanet & Quatert 2013, Mathis et al. 2014, Rogers et al. 2013
43. IGW: Damping Length Zahn et al. (1997) Compositional Gradients inhibit the propagation Higher Frequency IGW propagate further
44. IGW: Wave Decoupling Fuller et al. (2014) Core: Decoupled Core: Coupled 0.9 1.0 1.1 1.2 1.3 1.4 1.5 2.0 2.5 Consistent with Tayar & Pinsonneault (2013) requiring decoupling of the low mass subgiant star “Otto”(Deheuvels et al. 2012) to occur at a stellar radius 1.5-1.9 RSun
45. IGW: Wave Decoupling Deheuvels et al. (2014)
46. IGW: Dissipation Length Decoupling of the core occurs due to 3 effects: 1. Evolution timescale decreases from 109 to 107 yr 2. Convection zone deepens, resulting in smaller turnover frequencies (hence smaller frequencies of the IGW) 3. As the core contracts the Brunt-Vasaila frequency N increases by more than an order of magnitude The inner core becomes optically thick to the waves, prohibiting efficient core-envelope coupling (due to IGW) Fuller et al. (2014)
47. !Thanks to space-based asteroseismology it is now possible to access the internal rotational profile of stars other than the Sun !Despite great progress in last few years, the nature of internal mixing of angular momentum is still an unsolved problem Conclusions (I) SLOW FAST Cantiello et al. 2014, Fuller et al. 2014 Credits: R. Townsend
48. A new puzzle!
49. Stars evolve this direction Depressed Depressed Stello, Cantiello, Fuller et al. (Nature 2016) Depressed Dipolar Modes
50. Stello, Cantiello, Fuller et al. (Nature 2016) Puzzle: Depressed Dipolar Modes Important fact: l=0 normal, l=1 depressed! Stars evolve this direction
51. Mode Visibility
52. Core Mode Visibility Not to Scale! In normal red giants with mixed modes, wave energy that tunnels into the core eventually tunnels back out to produce the observed oscillation mode
53. Excitation Damping Convective Envelope p-modes B Alfven Waves Magneto Gravity Waves Evanescent Region Core For depressed mixed modes let’s assume that all the energy leaking into the g-mode cavity never makes it back to the envelope At equilibrium, damping and excitation rate balance each other (Dupret et al. 2009)
54. Excitation Damping Convective Envelope p-modes B Alfven Waves Magneto Gravity Waves Evanescent Region Core Transmission through the evanescent region Envelope crossing time At equilibrium, damping and excitation rate balance each other (Dupret et al. 2009)
55. Convective Envelope p-modes B Alfven Waves Magneto Gravity Waves Evanescent Region Core One can write the ratio of visibility of suppressed/normal modes as: Envelope crossing Inverse of the envelope damping rate (typical value for RGB ~ 10d) norm e.g. Corsaro et al. 2015 r2 r1
56. Fuller + Cantiello et al. 2015 (Science) Conclusion: Depressed dipoles explained by a mechanism efficiently trapping wave energy in the core Stars evolve this direction Data: Mosser+2012, Garcia+2014
57. Magnetic Fields
58. In the presence of strong B-fields, magnetic tension forces can become comparable to buoyancy Critical Field Strength Lorentz Force ~ Buoyancy Force
59. Magnetic Greenhouse Effect Fuller + Cantiello et al. (Science 2015) Dipolar waves “scattered” to high harmonic degrees l Magnetic fields break spherical symmetry in the core High l waves trapped in the core Reese et al. 2004, Rincon & Rieutord 2003, Lee 2007,2010, Mathis & De Brye 2010,2012 Typical Critical B-field ~ 105 G
60. Courtesy: Jim Fuller
61. Augustson et al. 2016 ! Convective core dynamos on the MS: Beq~105 G ! Magnetic field topology is complex ! Flux conservation can easily lead to B~106-107 G on the RG ! Stable magnetic configurations of interlocked poloidal+toroidal fields exist in radiative regions Prendergast 1956, Kamchatnov 1982, Mestel 1984, Braithwaite & Nordlund 2006, Duez et al. 2010 Brun et al. 2005 2Msun
62. Stars evolve this direction Stello, MC, JF et al. (Nature 2016) Mass Dependence
63. Stello, Cantiello, Fuller et al. (Nature 2016) Fraction of stars with strong internal B-fields From a sample of 3000+ stars
64. Conclusions (II) ! Novel asteroseismic technique allows to reveal the presence of strong internal magnetic fields in thousand red giants ! Fields of roughly 105 G are very common in the core of intermediate mass stars ! These fields are likely dynamo generated in the star’s convective core during the main sequence Courtesy: Kyle Augustson