Hydrodynamics in Astrophysics

1. Hydrodynamics in Astrophysics • LAPP/LAPTH - June 24 2011 M. Popov

2. Outline of the talk • Introduction: astrophysical phenomena • Fundamental equations in hydrodynamics • Supernova model • Supernova observations

3. Outline of the talk • Introduction: astrophysical phenomena • Fundamental equations in hydrodynamics • Supernova model • Supernova observation

4. Order of magnitudes

5. Stars are the buidling blocks of our Universe

6. Comparison of star sizes Antares Rigel Sirius A Sun

7. Nova Eridani 2009 8.4

8. Artist illustration of nova flash

9. Supernova Remnant E0102-72

10. Jet from active galactic nuclei Centaurus A

11. Black Hole Candidate Cygnus X-1

12. Formationofprotostellarcoresinmolecularclouds A. Kritsuk, S.D.Ustyugov,P.Padoan, R.Wagner,M.L.Norman

13. Schematic view of our Sun

14. Outline of the talk • Introduction: astrophysical phenomena • Fundamental equation in hydrodynamics • Supernova model • Supernova observations

15. Leonardo da Vinci : a precursor in hydrodynamics Il a compris aussi que la vitesse de l’eau est différente de la vitesse des ondes qui se déplacent à la surface libre : « La vitesse de propagation des ondulations (de surface) dépasse toujours de beaucoup celle de l’eau14... » Léonard de Vinci a surtout été le premier, après Héron, à formuler le principe de conservation de la masse, ou principe de continuité : « Une rivière à chaque endroit de son cours et au même moment donne passage à une même quantité d’eau, quelle que soit sa largeur, la profondeur, la pente, la rugosité, ou son caractère plus ou moins tortueux » ; ce qui n’est exact qu’en écoulement permanent, bien sûr. Ou encore : « Une rivière de profondeur constante aura un écoulement plus rapide dans un passage étroit que dans un passage plus large, dans la mesure de ce que la plus grande largeur excède la plus petite14. »

16. À Bâle, en Suisse, Daniel Bernoulli (1700-1782) et Leonhard Euler (1707-1783) furent les auteurs des premières traductions mathématiques des principes de la mécanique des fluides. À partir des principes de conservation de l’énergie appliquée aux corps solides par Huygens et Leibnitz, Bernoulli déduisit que dans un fluide la somme de l’énergie potentielle (représentée par la pression p et par l’altitude z) et de l’énergie cinétique doit rester constante

17. Equation of mass conservation Volume mass: Rate of mass change: Net flow through the control volume faces:

18. Euler equation Euler , écrivit les équations différentielles qui décrivent le mouvement d’un fluide, ainsi que l’équation de continuité qui exprime la conservation de la masse. Ce système est toujours connu aujourd’hui comme les équations d’Euler: principe de la dynamique appliqué au mouvement d’un fluide de vitesse V (de composantes notées u, v, w), sur lequel s’exerce, par unité de masse, une force F de composantes P, Q, R :

19. Navier-Stokes Equation

20. Equation of Energy conservation

21. Turbulence • Hydrodynamics equations are non linear • Transition from laminar regime to turbulent one (Osborne Reynolds) : • Andrei Nikolaevich Kolmogorov :

22. Turbulence

23. Instabilities • Kelvin-Helmholtz instability

24. Instabilities • Rayleigh–Taylor instability

25. Instabilities • Richtmyer-Meshkov instability

26. Outline of the talk • Introduction: astrophysical phenomena • Fundamental equations in hydrodynamics • Supernova model • Supernova observations

27. Piecewise Parabolic Method on a Local stencil Linear advection equation: Solution is constant along the characteristic

28. Piecewise Parabolic Method on a Local stencil similarly for a<0 characteristic comes from the zone i+1

29. Our code vs Athena: Rayleigh-Taylor instability test Our Athena hydrostatic equilibrium Unpub- lished material grid 300 x 900

30. Our code vs Athena: Bow shock A uniform supersonic x-velocity in all regions except for the overdense region and to the right of it. “The tails are not exactly symmetric about the x-axis even though the bow shock and flattened sphere maintain good symmetry. The reason for this behavior is currently unknown.” Jim Stone, Princeton Univ.

31. Our code vs Athena: Bow shock Unpublished material

32. Astrophysical bow shock Great Nebula in Orion (1500 light-years from Earth): bow shockaround the very young star LL Ori.

33. Presupernova initial configuration S. Woosley, A. Heger, T. Weaver "The evolution and explosion of massive stars", Rev. Mod. Phys., 74, 1015, 2002. Evolution of central temperature and density of 15 and 25 M stars.

34. Presupernova initial configuration

35. Presupernova initial configuration 25 M star parameters at helium burning stage:   Main source of energy is nuclear reactions: Energy generation is very sensitive to temperature: “Normal” helium burning time is 839 000 years

36. Asymmetric explosion model K. Maeda, T. Nakamura, K. Nomoto, P. Mazzali, F. Patat, I. Hachisu "Explosive Nucleosynthesis in Aspherical Hypernova Explosions and Late-Time Spectra of SN 1998bw", ApJ, 565, 405, 2002. Energy ergs was deposit below 0.17 R (contains 2 M )   Radiation pressure dominated: Cylindrical coordinate system Grid: 800 x 800 (1 quadrant) Energy distribution: 50% thermal, 50% kinetic Assymetric distribution of kinetic energy

37. Cylindrical coordinate system problems B. Fryxell, D. Arnett, E. Muller "Instabilities and clumping in SN 1987A. I - Early evolution in two dimensions", ApJ, 367, 619, 1991. S. Couch, D. Pooley, J. Wheeler, M. Milosavljevic "Aspherical Supernova Shock Breakout and the Observations of Supernova 2008D", Accepted to ApJ, Nov. 2010 • Numerical artifacts in the high-resolution simulations. • Artificially accelerated growth of instabilities near the axis. • Symmetry violation between the north and the south hemispheres.

38. Density Temperature Explosion dynamics (20 seconds of simulation)

39. Magnetic field influence Density Temperature

40. Magnetic field distribution

41. SN 1987 A

42. Initial composition S. Woosley, A. Heger, T. Weaver " The evolution and explosion of massive stars “, Rev. Mod. Phys., 74, 1015, 2002

43. Nuclides connected by all possible reactions with p and - particles, 30 nuclides in total. A simplified network of nuclear reactions

44. A Lagrangian component in an Eulerian grid code. • Tracers are massless - does not couple to the flow via gravity or inertia. • Advected by the flow, recording the history of conditions along their path. • Isotopic yield is calculated as a post-processing step over the recorded density and temperature. • Each tracer represents the same amount of mass. • 128 tracers per axis give the accuracy better than 2% for nuclides with mass fraction >10 -5 Tracer particles method S. Nagataki, M. Hashimoto,K. Sato, S. Yamada "Explosive Nucleosynthesis in Axisymmetrically Deformed Type II Supernovae", ApJ, 486, 1026, 1997.

45. 2 128 = 16384 tracers. Each tracer represents 0.001 M  Density reconstructed from tracers data Unpublished material

46. Explosive nucleosynthesis: detailed yields

47. Effect of initial composition

48. The distribution of main nuclides Unpublished material

49. Outline of the talk • Introduction: astrophysical phenomena • Fundamental equations in hydrodynamics • Supernova model • Supernova observations

50. Why nickel is important? • Explanation of supernova light curves, nickel decay defines the peak of the light emission when the expanding shell becomes optically thin. • p and heat and ionize the ejecta, the energy is reemitted in optical and infrared wavelengths. • Detailed description of the chemical and physical structure of the ejecta required for spectral synthesis calculations.