Massive Stars: Rotation and Magnetic Fields

Lecture 2 given at the "Look & Listen" Astrophysics School, Playa del Carmen (Mexico), 2014. Topics: Massive Stars, stellar rotation and stellar magnetic fields

Transcript

1. Massive Stars: Rotation and B-fields Matteo Cantiello Kavli Institute for Theoretical Physics (University of California Santa Barbara)
2. Useful Resources:  Physics, Formation and Evolution of rotating stars (Maeder) Mexico 2014 Matteo Cantiello Look&Listen  Heger et al. 2000  Maeder & Meynet 2000  Woosley, Heger and Weaver 2002 (Review)  Langer 2012 (Review)
3. Range of rotational velocity NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Fukuda 1982 “In practice all stars are rotating around their axis” - Maeder & Meynet Mexico 2014 Matteo Cantiello Look&Listen
4. Galactic OB Stars NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Huang & Gies 2006 Mexico 2014 Matteo Cantiello Look&Listen
5. VLT-FLAMES Tarantula Survey (PI: Evans): ~ 900 OB stars observed spectroscopically in 30 Dor (LMC) region. Multi-epoch observations to separate binaries from single stars.  Nitrogen surface abundances  Rotational velocities  Binary fraction  A statistically significant sample of the most massive stars (see e.g. Crowther et al. 2010) (Evans et al. 2010) 30 Doradus (HST) VLT-Flames Tarantula Survey LCOGT 2012 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors IPMU 2012 Matteo Cantiello Long GRB Progenitors Mexico 2014 Matteo Cantiello Look&Listen
6. OB stars rotate rapidly Matteo Cantiello Pulsations and Magnetic Fields in Massive Stars IAU GA SpS13 – Beijing 2012 P ( VEq sin i ) P ( VEq ) 334 B Stars Dufton et al. 2013 Matteo Cantiello Pulsations, Turbulence and Magnetic Fields in Massive Stars NORDITA – Stockholm 2013 Mexico 2014 Matteo Cantiello Look&Listen
7. VFTS 102, fastest rotating star* NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Dufton et al. 2011 Mexico 2014 Matteo Cantiello Look&Listen
8. VFTS 102, fastest rotating star* NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Veq ~ 600 km/s Dufton et al. 2011 Mexico 2014 Matteo Cantiello Look&Listen
9. Rotation in compact remnants
10. Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors Central Engines: Spinning BHs Collapsar Woosley 1993 Eacc ~ 0.01..1Msunc2~1052..54ergs IPMU 2012 Matteo Cantiello Long GRB Progenitors Mexico 2014 Matteo Cantiello Look&Listen
11. Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors Central Engines: Spinning Magnetars Erot ~ 3 1052 (P/ms)-2 (R/10km)2 ergs Millisecond Magnetar Usov 1992 CfA 2012 Matteo Cantiello Long GRB Progenitors IPMU 2012 Matteo Cantiello Long GRB Progenitors Mexico 2014 Matteo Cantiello Look&Listen
12. Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors Central Engines: Spinning Magnetars (Spitkovski 2006) Erot ~ 3 1052 (P/ms)-2 (R/10km)2 ergs Millisecond Magnetar Usov 1992 CfA 2012 Matteo Cantiello Long GRB Progenitors IPMU 2012 Matteo Cantiello Long GRB Progenitors Mexico 2014 Matteo Cantiello Look&Listen
13. KITP 2013 Matteo Cantiello Differential Rotation in Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars Final J-distribution 1D MESA 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 IPMU 2012 Matteo Cantiello Long GRB Progenitors Mexico 2014 Matteo Cantiello Look&Listen
14. Effects of Rotation
15. Effects of rotation NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Rotation Mexico 2014 Matteo Cantiello Look&Listen
16. Effects of rotation NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Rotation Hydrostatic equilibrium Mexico 2014 Matteo Cantiello Look&Listen
17. Effects of rotation NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Rotation Radiative equilibrium Hydrostatic equilibrium Mexico 2014 Matteo Cantiello Look&Listen
18. Effects of rotation NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Rotation Radiative equilibrium Rotational Mixing Hydrostatic equilibrium Mexico 2014 Matteo Cantiello Look&Listen
19. Effects of rotation NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Rotation Mass loss Radiative equilibrium Rotational Mixing Hydrostatic equilibrium Mexico 2014 Matteo Cantiello Look&Listen
20. Hydrostatic Effects
21. The centrifugal term NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Georgy, Phd Thesis Mexico 2014 Matteo Cantiello Look&Listen The centrifugal force reduces the local gravity.The effect depends on the co-latitude, resulting in departures from spherical simmetry.
22. Departure from spherical structure NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Georgy, Phd Thesis In the Roche approximation the deformation of the star approaches the value Req/Rp=1.5 Mexico 2014 Matteo Cantiello Look&Listen The centrifugal force reduces the local gravity.The effect depends on the co-latitude, resulting in departures from spherical simmetry.
23. Interferometry of rotating stars NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Domiciano Da Souza et al.2003 Achernar (Be star) Star rotating at 96% of critical velocity (311 km/s) VLTI Observations show that: Req/Rp~1.5 Mexico 2014 Matteo Cantiello Look&Listen
24. Mass-loss
25. NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Ekstrom et al. 2008 N.B. Effects of radiation not included Critical Velocity Mexico 2014 Matteo Cantiello Look&Listen
26. NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Critical Velocity Gamma-Omega Limit Mexico 2014 Matteo Cantiello Look&Listen
27. Rotationally enhanced Mass-loss NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Theoretically one expects additional mass-loss as the star approaches critical rotation, as material becomes less and less bound to the stellar surface. Langer, 1998 See Georgy et al. 2011 for a more thorough discussion of rotationally enhanced mass-loss Mexico 2014 Matteo Cantiello Look&Listen
28. Effects of rotation NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Rotation Mass loss Hydrostatic equilibrium Mexico 2014 Matteo Cantiello Look&Listen
29. Effects of rotation NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Rotation Mass loss Radiative equilibrium Hydrostatic equilibrium Mexico 2014 Matteo Cantiello Look&Listen
30. Radiative Equilibrium
31. NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School 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. The Von Zeipel Theorem Convective Core € ω Von Zeipel (1924) Mexico 2014 Matteo Cantiello Look&Listen
32. NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School 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. The Von Zeipel Theorem Convective Core € ω Von Zeipel (1924) Mexico 2014 Matteo Cantiello Look&Listen
33. NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School In the case of solid body rotation: Both geff and Teff vary over the surface of a rotating star and influence the emergent spectrum. The equatorial regions are fainter and cooler than the polar ones, which are brighter and hotter (the differences of Teff may reach a factor of 2). This effect is called the gravity darkening. (Maeder, 1999, Maeder & Meynet 2012) The Von Zeipel Theorem Von Zeipel (1924) Mexico 2014 Matteo Cantiello Look&Listen
34. Interferometry of rotating stars NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Domiciano Da Souza et al.2005 Altair (A7IV-V Star) VLTI Observations Von Zeipel ‘gravity darkening’ Confirmed Mexico 2014 Matteo Cantiello Look&Listen
35. Interferometry of rotating stars NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Altair (A7IV-V Star): Von Zeipel ‘gravity darkening’ but with a different exponent Mexico 2014 Matteo Cantiello Look&Listen
36. Interferometry of rotating stars NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Mexico 2014 Matteo Cantiello Look&Listen
37. Modeling Rotating Stars
38. The computational Challenge NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors  Stars are rotating spheroids of hot plasma  They undergo a variety of instabilities  Large range of timescales  It would be ideal to perform fully (magneto) hydrodynamic calculations. But this is currently computationally impossible.  At this time 3D stellar evolution calculations can evolve a few hours of a star life.  How can we model rotation in a 1D, implicit code? UCSB 2012 Matteo Cantiello MESA School Mexico 2014 Matteo Cantiello Look&Listen
39. The Shellular Approximation NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School  Rotation and especially differential rotation generates turbulent motions. On Earth, we have the example of west winds and jet streams.  According to Zahn (1975), Chaboyer & Zahn (1992), and Zahn (1992), in a star anisotropic turbulence acts much stronger on isobars than in the perpendicular direction. This enforces a shellular rotation law (Meynet & Maeder 1997), and it sweeps out compositional differences on isobars. Therefore it can be assumed that matter on isobars is approximately chemically homogeneous and that angular momentum is quickly mixed along isobars. This allows to retain a one-dimensional approximation with mass shells corresponding to isobars instead of spherical shells. NORDITA 2013 Matteo Cantiello Differential Rotation in Red Giants KASC6, Sydney 2013 Matteo Cantiello Challenges with Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars The Shellular approximation allows to calculate 1D models of rotating stars Mexico 2014 Matteo Cantiello Look&Listen
40. ⌦ ! = !(r) The Shellular Approximation NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Mexico 2014 Matteo Cantiello Look&Listen r Composition is only function of the r coordinate, as each shell is assumed to be efficiently mixed Isobars
41. The structure equations of rotating stars NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School For a star in shellular rotation it is possible to modify the eqs of stellar structure to include the effect of the centrifugal force while keeping the form of the equations very close to that of the non- rotating case. Basically all quantities are redefined on isobars. Mass conservation Hydrostatic Eq. Energy transport ... Endal & Sofia 1978 Mexico 2014 Matteo Cantiello Look&Listen
42. Diffusion Equations NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Transport of chemical species: Transport of angular momentum: Mexico 2014 Matteo Cantiello Look&Listen
43. Advection- Diffusion Scheme NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School An alternative approach is to solve an advection-diffusion equation for the transport of angular momentum (e.g. in the GENEVA code or the ROSE code). However, as MESA adopts the diffusion approximation (like e.g. KEPLER and STERN), I will not discuss the advection-diffusion scheme here. Nevertheless I suggest you have a look at the relevant literature (e.g. Mader & Meynet 2000, 2012) A very interesting work comparing the different implementations has been published by Potter et al. 2012. While it has been claimed that the advection-diffusion scheme is mathematically more sound, a key result of Potter’s work is that is not yet possible to prefer one of the two implementations, given the available observational constraints. Mexico 2014 Matteo Cantiello Look&Listen
44. Effects of rotation NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Rotation Mass loss Radiative equilibrium Hydrostatic equilibrium Mexico 2014 Matteo Cantiello Look&Listen
45. Effects of rotation NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Rotation Mass loss Radiative equilibrium Rotational Mixing Hydrostatic equilibrium Mexico 2014 Matteo Cantiello Look&Listen
46. Rotational Instabilities
47. Differential rotation is expected to arise in stars because e.g. hydrostatic structural evolution and mass loss. As a consequence, stars are subject to a number of local hydrodynamic instabilities. These instabilities arise and cause diffusion of angular momentum (and chemicals) while they try to bring the star back to solid body rotation, its lowest energy state. The unstable interiors of rotating stars NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Mexico 2014 Matteo Cantiello Look&Listen Mexico 2014 Matteo Cantiello Look&Listen
48. Rotational Instabilities  Rotational “instabilities” mix rotating stars  Different timescales: secular/dynamical instabilities  Together with other processes (for example magnetic fields) they contribute to the internal transport of angular momentum and chemicals NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Mexico 2014 Matteo Cantiello Look&Listen Mexico 2014 Matteo Cantiello Look&Listen
49. KITP 2013 Matteo Cantiello Differential Rotation in Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars  Dynamical Shear Hydrodynamic Instabilities Mexico 2014 Matteo Cantiello Look&Listen
50. KITP 2013 Matteo Cantiello Differential Rotation in Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars  Secular Shear Hydrodynamic Instabilities  In the presence of a stabilizing thermal gradient, an eddy might have to wait for heat to diffuse out before an overturn is energetically favorable  Mixing process on t KH Thermal Timescale More Hydro instabilities: see e.g. Heger et al. 2000 Mexico 2014 Matteo Cantiello Look&Listen
51. NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School 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) NORDITA 2013 Matteo Cantiello Differential Rotation in Red Giants KASC6, Sydney 2013 Matteo Cantiello Challenges with Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars Von Zeipel Theorem Mexico 2014 Matteo Cantiello Look&Listen
52. NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Rotationally Induced Circulations NORDITA 2013 Matteo Cantiello Differential Rotation in Red Giants KASC6, Sydney 2013 Matteo Cantiello Challenges with Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars In the case of solid body rotation: Both geff and Teff vary over the surface of a rotating star and influence the emergent spectrum. The equatorial regions are fainter and cooler than the polar ones, which are brighter and hotter (the differences of Teff may reach a factor of 2). This effect is called gravity darkening.The von Zeipel theorem in a star with shellular rotation shows only minor differences (Maeder, 1999, Maeder & Meynet 2012) Von Zeipel (1924) Mexico 2014 Matteo Cantiello Look&Listen
53. Interferometry of rotating stars NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Altair (A7IV-V Star): confirms Von Zeipel ‘gravity darkening’ even if with a slightly different exponent NORDITA 2013 Matteo Cantiello Differential Rotation in Red Giants KASC6, Sydney 2013 Matteo Cantiello Challenges with Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars Mexico 2014 Matteo Cantiello Look&Listen
54. Thermal imbalance drives circulations NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School NORDITA 2013 Matteo Cantiello Differential Rotation in Red Giants KASC6, Sydney 2013 Matteo Cantiello Challenges with Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars Mexico 2014 Matteo Cantiello Look&Listen
55. Thermal imbalance drives circulations NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School NORDITA 2013 Matteo Cantiello Differential Rotation in Red Giants KASC6, Sydney 2013 Matteo Cantiello Challenges with Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars Mexico 2014 Matteo Cantiello Look&Listen
56. Thermal imbalance drives circulations NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors Core Meridional circulation UCSB 2012 Matteo Cantiello MESA School NORDITA 2013 Matteo Cantiello Differential Rotation in Red Giants KASC6, Sydney 2013 Matteo Cantiello Challenges with Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars Mexico 2014 Matteo Cantiello Look&Listen
57.  Eddington-Sweet Circulation  Is a meridional circulation mixing the stellar interior  Mixing process on t KH € ω NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors Core Meridional circulation UCSB 2012 Matteo Cantiello MESA School NORDITA 2013 Matteo Cantiello Differential Rotation in Red Giants KASC6, Sydney 2013 Matteo Cantiello Challenges with Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars Rotationally Induced Circulations Mexico 2014 Matteo Cantiello Look&Listen
58.  Eddington-Sweet Circulation  Is a meridional circulation mixing the stellar interior  Mixing process on t KH τES ∝τKH ωK ω ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 € ω NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors Core Meridional circulation UCSB 2012 Matteo Cantiello MESA School NORDITA 2013 Matteo Cantiello Differential Rotation in Red Giants KASC6, Sydney 2013 Matteo Cantiello Challenges with Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars Rotationally Induced Circulations Mexico 2014 Matteo Cantiello Look&Listen
59. NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Maeder & Meynet 2002 20 Msun Vini = 300 km/s τES ∝τKH ωK ω ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 NORDITA 2013 Matteo Cantiello Differential Rotation in Red Giants KASC6, Sydney 2013 Matteo Cantiello Challenges with Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars Rotationally Induced Circulations Mexico 2014 Matteo Cantiello Look&Listen
60. Other mixing mechanisms
61. KITP 2013 Matteo Cantiello Differential Rotation in Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars  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 Mexico 2014 Matteo Cantiello Look&Listen
62. Spruit-Tayler Dynamo NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School  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 NORDITA 2013 Matteo Cantiello Differential Rotation in Red Giants KASC6, Sydney 2013 Matteo Cantiello Challenges with Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars Toroidal Poloidal Mexico 2014 Matteo Cantiello Look&Listen
63.  Spruit-Tayler 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 NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School NORDITA 2013 Matteo Cantiello Differential Rotation in Red Giants KASC6, Sydney 2013 Matteo Cantiello Challenges with Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars Spruit-Tayler Dynamo Mexico 2014 Matteo Cantiello Look&Listen
64. 0 2 4 6 8 10 12 14 enclosed mass/M -2 0 2 4 6 8 10 log B (Gauss) 0 2 4 6 8 10 12 14 enclosed mass/M -2 0 2 4 6 8 10 log B (Gauss) -10 -8 -6 -4 -2 0 log angular velocity (rad/s) log j (1020 cm2/s) B r B ω j H Depletion φ KITP 2013 Matteo Cantiello Differential Rotation in Red Giants SkyHouse, Summer 2013 Matteo Cantiello MESA Overview Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars Spruit-Tayler Dynamo Core Torque ~ <Br Bphi> Paxton et al. 2013 Mexico 2014 Matteo Cantiello Look&Listen
65. Stockholm 2009 Matteo Cantiello Long GRB Progenitors Debate on the ST Dynamo Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School  The Spruit-Tayler (ST) dynamo is still under review  While the Tayler instability is sound, the loop proposed by Spruit has been criticized  Simulations of Zahn et al. 2007 could not find dynamo action  On the other hand simulations of Braithwaite et al. 2006 showed the Spruit-Tayler dynamo  The jury is still out, but it looks like a j-transport mechanism similar (or even more efficient) than the ST has to work in stars to reproduce some observations (e.g. spin rates of compact remnants, solar rotation profile) Suijs et al. 2008, Eggenberger et al. 2005 NORDITA 2013 Matteo Cantiello Differential Rotation in Red Giants KASC6, Sydney 2013 Matteo Cantiello Challenges with Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars Mexico 2014 Matteo Cantiello Look&Listen
66. KITP 2013 Matteo Cantiello Differential Rotation in Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars  Hydrodynamics instabilities  Rotationally induced circulations  Magnetic torques  Internal gravity waves Angular Momentum Transport Different classes of mechanisms have been proposed:  Rogers et al. 2013  Charbonnel & Talon 2005 Mexico 2014 Matteo Cantiello Look&Listen
67. KITP 2013 Matteo Cantiello Differential Rotation in Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars Internal Gravity Waves  Rogers et al. 2013  Cantiello et al. 2011 E(k) Mexico 2014 Matteo Cantiello Look&Listen
68. Tests of Transport Mechanisms
69. KITP 2013 Matteo Cantiello Differential Rotation in Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars Surface abundances Rotation of compact remnants Asteroseismology Testing transport mechanisms Mexico 2014 Matteo Cantiello Look&Listen
70. KITP 2013 Matteo Cantiello Differential Rotation in Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars Testing transport mechanisms Brott et al. 2011 Mexico 2014 Matteo Cantiello Look&Listen
71. KITP 2013 Matteo Cantiello Differential Rotation in Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars Surface abundances Rotation of compact remnants Asteroseismology Testing transport mechanisms Mexico 2014 Matteo Cantiello Look&Listen
72. KITP 2013 Matteo Cantiello Differential Rotation in Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars Testing transport mechanisms Langer 2012 Suijs et et. 2008 Mexico 2014 Matteo Cantiello Look&Listen
73. KITP 2013 Matteo Cantiello Differential Rotation in Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars Surface abundances Rotation of compact remnants Asteroseismology Testing transport mechanisms Mexico 2014 Matteo Cantiello Look&Listen
74. Credit: BBSO/NJIT KITP 2013 Matteo Cantiello Differential Rotation in Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars 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) Mexico 2014 Matteo Cantiello Look&Listen
75. KITP 2013 Matteo Cantiello Differential Rotation in Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars 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. Mexico 2014 Matteo Cantiello Look&Listen
76. KITP 2013 Matteo Cantiello Differential Rotation in Red Giants Caltech, 12/18/2013 Matteo Cantiello Angular Momentum Transport in Stars 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! Mexico 2014 Matteo Cantiello Look&Listen
77. Magnetic Fields in Massive Stars
78. B-fields in massive stars (direct evidence)  About 30+ magnetic OB stars found (e.g. MIMES, Donati, Hubrig, Neiner, Petit)  Detection through Zeeman spectral signature  Mostly dipolar, amplitude between 300 G and several kG  Bias toward strong, large scale fields  Origin unclear. Likely Fossil (Wade et al. 2010)  Similar to Ap/Bp stars ~ 5-15% ? Tau Sco Credits: Jardine & Donati Matteo Cantiello Pulsations and Magnetic Fields in Massive Stars IAU GA SpS13 – Beijing 2012 Matteo Cantiello Pulsations, Turbulence and Magnetic Fields in Massive Stars NORDITA – Stockholm 2013 Mexico 2014 Matteo Cantiello Look&Listen
79. ⌧Ohm ⇠ R2 ⌘ ⇠ ✓ R⇤ 1010cm ◆2 ✓ T 105K ◆3/2 107yr vAlfven = B p 4⇡⇢ ⌧Alfven ⇠ R vA ⇠ ✓ R⇤ R ◆ ✓ kG B ◆ ✓ ¯ ⇢ ¯ ⇢ ◆1/2 102yr Magnetic fields: Timescales NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Mexico 2014 Matteo Cantiello Look&Listen
80. Stable Configurations Matteo Cantiello Magnetic Fields & Massive Stars Evolution Santa Barbara – 06/17/2011 Matteo Cantiello Pulsations and Magnetic Fields in Massive Stars IAU GA SpS13 – Beijing 2012 Mexico 2014 Matteo Cantiello Look&Listen
81. Stable Configurations Matteo Cantiello Magnetic Fields & Massive Stars Evolution Santa Barbara – 06/17/2011  Purely poloidal fields are unstable Matteo Cantiello Pulsations and Magnetic Fields in Massive Stars IAU GA SpS13 – Beijing 2012 Mexico 2014 Matteo Cantiello Look&Listen
82. Stable Configurations Matteo Cantiello Magnetic Fields & Massive Stars Evolution Santa Barbara – 06/17/2011  Purely poloidal fields are unstable e.g. Flowers & Ruderman 1977 Matteo Cantiello Pulsations and Magnetic Fields in Massive Stars IAU GA SpS13 – Beijing 2012 Mexico 2014 Matteo Cantiello Look&Listen
83. Stable Configurations Matteo Cantiello Magnetic Fields & Massive Stars Evolution Santa Barbara – 06/17/2011  Purely poloidal fields are unstable  Purely toroidal fields are unstable e.g. Flowers & Ruderman 1977 Matteo Cantiello Pulsations and Magnetic Fields in Massive Stars IAU GA SpS13 – Beijing 2012 Mexico 2014 Matteo Cantiello Look&Listen
84. Stable Configurations Matteo Cantiello Magnetic Fields & Massive Stars Evolution Santa Barbara – 06/17/2011  Purely poloidal fields are unstable  Purely toroidal fields are unstable e.g. Spruit 1999 Tayler Instability e.g. Flowers & Ruderman 1977 Matteo Cantiello Pulsations and Magnetic Fields in Massive Stars IAU GA SpS13 – Beijing 2012 Mexico 2014 Matteo Cantiello Look&Listen
85. Stable Configurations Matteo Cantiello Magnetic Fields & Massive Stars Evolution Santa Barbara – 06/17/2011  Purely poloidal fields are unstable  Purely toroidal fields are unstable  Instability occurs on the Alfven timescale: the field rapidly becomes unobservable e.g. Spruit 1999 Tayler Instability e.g. Flowers & Ruderman 1977 Matteo Cantiello Pulsations and Magnetic Fields in Massive Stars IAU GA SpS13 – Beijing 2012 Mexico 2014 Matteo Cantiello Look&Listen
86. Stable Configurations Matteo Cantiello Magnetic Fields & Massive Stars Evolution Santa Barbara – 06/17/2011 Prendergast 1956, Kamchatnov 1982, Mestel 1984, Braithwaite & Nordlund 2006, Duez et al. 2010 Matteo Cantiello Pulsations and Magnetic Fields in Massive Stars IAU GA SpS13 – Beijing 2012 Mexico 2014 Matteo Cantiello Look&Listen
87. Origin of B-fields in massive stars Matteo Cantiello Magnetic Fields & Massive Stars Evolution Santa Barbara – 06/17/2011  Fossil Fields  B-field is produced/retained during star formation  Field arranged into a stable configuration (Braithwaite & Nordlund 2006, Duez et al. 2010)  Contemporary Dynamo Action  Configuration of the flow that transforms kinetic energy into magnetic energy. B-field maintained against Ohmic dissipation. Matteo Cantiello Pulsations and Magnetic Fields in Massive Stars IAU GA SpS13 – Beijing 2012 (Cantiello et al. 2010, Augustson et al. 2010) Matteo Cantiello Pulsations, Turbulence and Magnetic Fields in Massive Stars NORDITA – Stockholm 2013 Mexico 2014 Matteo Cantiello Look&Listen
88. Dynamo Action in OB stars e.g. Main Sequence 10 M Sun Dynamo in Convective Core (e.g. MacGregor & Cassinelli 2003, Augustson et al. 2010) Dynamo in Radiative Zone (e.g. Spruit 2002, implemented in stellar evolution codes) Dynamo in Iron Convection Zone (Cantiello et al. 2009,2010; Cantiello & Braithwaite 2011) Mexico 2014 Matteo Cantiello Look&Listen
89. Dynamo Action in OB stars e.g. Main Sequence 10 M Sun Dynamo in Convective Core (e.g. MacGregor & Cassinelli 2003, Augustson et al. 2010) Dynamo in Radiative Zone (e.g. Spruit 2002, implemented in stellar evolution codes) Dynamo in Iron Convection Zone (Cantiello et al. 2009,2010; Cantiello & Braithwaite 2011) B-Fields probably not observable, but potentially important for evolution and final stages Mexico 2014 Matteo Cantiello Look&Listen
90. Fossil Fields and Magnetic Braking  Magnetic fields can increase wind angular momentum loss (Weber & Davis 1967, ud-Doula & Owocki 2002)  Spin-down time measured in Sigma Ori matches theoretical predictions (Townsend et al. 2010)  Potentially important for stellar evolution models (e.g. Meynet et al. 2011) Tau Sco, Jardin & Donati UCSB 2012 Matteo Cantiello MESA School Mexico 2014 Matteo Cantiello Look&Listen
91.  Magnetic Flux Conservation? Origin of Magnetars fields NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Mexico 2014 Matteo Cantiello Look&Listen e.g. Spruit (2008)
92.  Magnetic Flux Conservation? MS = 4⇡R2 ⇤ B Origin of Magnetars fields NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Mexico 2014 Matteo Cantiello Look&Listen e.g. Spruit (2008)
93.  Magnetic Flux Conservation? MS = 4⇡R2 ⇤ B Origin of Magnetars fields NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Mexico 2014 Matteo Cantiello Look&Listen e.g. Spruit (2008) BMS BNS
94.  Magnetic Flux Conservation? MS = 4⇡R2 ⇤ B BNS = BMS ✓ RMS RNS ◆2 ⇠ 1015G Origin of Magnetars fields NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Mexico 2014 Matteo Cantiello Look&Listen e.g. Spruit (2008) BMS BNS
95.  Magnetic Flux Conservation? MS = 4⇡R2 ⇤ B BNS = BMS ✓ RMS RNS ◆2 ⇠ 1015G Origin of Magnetars fields NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Mexico 2014 Matteo Cantiello Look&Listen e.g. Spruit (2008) BMS BNS Thompson & Duncan (1993)  Convective Dynamo? Neutrino-Driven Convective Dynamo during PNS phase ?
96.  Magnetic Flux Conservation? MS = 4⇡R2 ⇤ B BNS = BMS ✓ RMS RNS ◆2 ⇠ 1015G B2 8⇡ ⇠ 1 2 ⇢v2 c Origin of Magnetars fields NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Mexico 2014 Matteo Cantiello Look&Listen e.g. Spruit (2008) BMS BNS Thompson & Duncan (1993)  Convective Dynamo? Neutrino-Driven Convective Dynamo during PNS phase ?
97.  Magnetic Flux Conservation? MS = 4⇡R2 ⇤ B BNS = BMS ✓ RMS RNS ◆2 ⇠ 1015G B2 8⇡ ⇠ 1 2 ⇢v2 c Origin of Magnetars fields NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Mexico 2014 Matteo Cantiello Look&Listen e.g. Spruit (2008) BMS BNS L⌫ ⇠ 1052erg/s ⇠ 1015G Thompson & Duncan (1993)  Convective Dynamo? Neutrino-Driven Convective Dynamo during PNS phase ?
98. BACKUP SLIDES
99. Barotropic Star NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School If Omega is constant (Solid body rotation) or has cilindric symmetry, the centrifugal acceleration can be derived from a potential (V). The eq. of Hydrostatic Equilibrium then implies that the star is Barotropic Mexico 2014 Matteo Cantiello Look&Listen
100. Barotropic Star NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School constant on equipotentials g Mexico 2014 Matteo Cantiello Look&Listen
101. Baroclinic Star NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School For different rotation laws (e.g. Shellular), the centrifugal acceleration can not be derived from a potential (V). In this case Isobars and Equipotentials DO NOT coincide. The star is Baroclinic Mexico 2014 Matteo Cantiello Look&Listen
102. Baroclinic Star NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School not constant on equipotentials g Mexico 2014 Matteo Cantiello Look&Listen
103. Baroclinicity leads to instabilities NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School g Isobar Isoentropic A B C Assumption: adiabatic displacement Mexico 2014 Matteo Cantiello Look&Listen
104. Baroclinicity leads to instabilities NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School g Isobar Isoentropic A B C Stable (higher density) Assumption: adiabatic displacement Mexico 2014 Matteo Cantiello Look&Listen
105. Baroclinicity leads to instabilities NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School g Isobar Isoentropic A B C Stable (higher density) Unstable (hotter) Assumption: adiabatic displacement Mexico 2014 Matteo Cantiello Look&Listen
106. Eddington - Sweet Circulation  Is a meridional circulation mixing the stellar interior  In massive stars is one of the most efficient processes  Mixing process on t KH € ω NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors Convective Core Meridional circulation UCSB 2012 Matteo Cantiello MESA School A diffusion coefficient D_ES enters the diffusion equations Mexico 2014 Matteo Cantiello Look&Listen Mexico 2014 Matteo Cantiello Look&Listen
107. Eddington - Sweet Circulation  Is a meridional circulation mixing the stellar interior  In massive stars is one of the most efficient processes  Mixing process on t KH τES ∝τKH ωK ω ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 € ω NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors Convective Core Meridional circulation UCSB 2012 Matteo Cantiello MESA School A diffusion coefficient D_ES enters the diffusion equations Mexico 2014 Matteo Cantiello Look&Listen Mexico 2014 Matteo Cantiello Look&Listen
108. Dynamical Shear NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Mexico 2014 Matteo Cantiello Look&Listen Mexico 2014 Matteo Cantiello Look&Listen
109. Dynamical Shear NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Jake Simon (JILA) Mexico 2014 Matteo Cantiello Look&Listen
110. Dynamical Shear NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School  Works very well on horizontal surfaces (isobars) and justifies (together with the baroclinic instabilities) the Shellular approximation  In the vertical direction it is strongly inhibited by density gradients. Can only work for large degree of differential rotation  Mixing process on t Dynamical  Results in a diffusion coefficient entering the diffusion equations = ... Mexico 2014 Matteo Cantiello Look&Listen
111. Dynamical Shear NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Mexico 2014 Matteo Cantiello Look&Listen
112. NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School  In the presence of a stabilizing thermal gradient, an eddy might have to wait for heat to diffuse out before an overturn is energetically favorable  Mixing process on t KH  Results in a diffusion coeff. entering the diffusion equations Secular Shear Thermal Timescale Mexico 2014 Matteo Cantiello Look&Listen
113. Solberg - Høiland NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School r Rayleigh Criterion for stability € ω Mexico 2014 Matteo Cantiello Look&Listen
114. Solberg - Høiland NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School r Including the effects of stratification etc. Solberg - Høiland Criterion for stability € ω Mexico 2014 Matteo Cantiello Look&Listen
115. Solberg - Høiland NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Heger et al. 2000  For no rotation (or constant j) we recover Ledoux  Can reduce size of convective regions (as j tends to increase outside, one has an extra restoring force)  Results in D_SH, entering the diffusion equations Mexico 2014 Matteo Cantiello Look&Listen
116. Goldreich-Schubert-Fricke NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School  Baroclinic instability  Two criteria: one is the secular analog of the SH, the other is an analog of the Taylor-Proudman theorem.  The second criteria is generally in contradiction with the shellular law. GSF would try to enforce uniform rotation. D_GSF entering the diffusion equations € ω Mexico 2014 Matteo Cantiello Look&Listen
117. Spruit-Tayler NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School  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 Convec Mexico 2014 Matteo Cantiello Look&Listen
118. Tayler Instability NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Spruit 1999 This is used to generate a poloidal component from the toroidal component of the field Mexico 2014 Matteo Cantiello Look&Listen
119. Magnetic fields  Spruit-Tayler Dynamo (Spruit 2002)  Core - Envelope coupling 1. Differential rotation winds up toroidal component of B 2. Magnetic torques tend to restore rigid rotation Convective Core If the envelope slows down angular momentum is also removed from the core NS & GRBs 2009 (ﺓةﻱيﺭرﺩدﻥنﻙكﺱسﺇإﻝلﺍا - Alexandria) Matteo Cantiello Long GRB Progenitors Fireworks 2009 (Bonn) Matteo Cantiello Long GRB Progenitors Leicester 2009 Matteo Cantiello Long GRB Progenitors Stockholm 2009 Matteo Cantiello Long GRB Progenitors Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School Mexico 2014 Matteo Cantiello Look&Listen
120. Stockholm 2009 Matteo Cantiello Long GRB Progenitors Debate on the ST Dynamo Sedgwick 2011 Matteo Cantiello Long GRB Progenitors CfA 2012 Matteo Cantiello Long GRB Progenitors UCSB 2012 Matteo Cantiello MESA School  The ST dynamo is still under review  While the Tayler instability is sound, the loop proposed by Spruit has been criticized  Simulations of Zahn et al. 2007 could not find a dynamo action  On the other hand simulations of Braithwaite et al. 2006 showed the Spruit-Tayler dynamo  The jury is still out, but it looks like a j-transport mechanism similar to the ST has to work in stars to reproduce some observations (e.g. asteroseismology and spin rates of compact remnants. g-waves could also play a role) Mexico 2014 Matteo Cantiello Look&Listen