1. Prof. dr. A. Achterberg, Astronomical Dept., IMAPP, Radboud Universiteit

2.  Shocks occur in supersonic flows;  Shocks are sudden jumps in velocity, density and pressure;  Shocks satisfy flux in = flux out principle for - mass flux - momentum flux - energy flux

3. Mass flux Momentum flux Energy flux Three equations for three unknowns: post-shock state (2) is uniquely determined by pre-shock state (1)! Three conservation laws means three fluxes for flux in = flux out!

5. 1D case: Shocks can only exist if M s >1 ! Weak shocks: M s =1+  with  << 1; Strong shocks: M s >> 1.

6. Compression ratio: density contrast Pressure jump Shocks all have  S > 1

10. Tangential velocity along shock surface is unchanged All relations remain the same if one makes the replacement: θ is the angle between upstream velocity and normal on shock surface

13. Bell X1 Rocket Plane

15. “Diamond” shocks in Jet Simulation

16. Fundamental parameter of shock physics: Mach Number Rankine-Hugoniot jump conditions: Strong shock limit

17. Trinity nuclear test explosion, New Mexico, 1945 Supernova remnant Cassiopeia A

18. Tycho’s Remnant (SN 1572AD)

19. Assumptions: 1.Explosion takes place in uniform medium with density ρ; 2. → spherical expanding fireball! 3.Total available energy: E. Point explosion + uniform medium: no EXTERNAL scale imposed on the problem!

20. Dimensional analysis: Sedov: fireball radius ~ Sedov radius R S

21. Steps: 1.Photo dissociation of Iron in hot nucleus star:  loss of (radiation) pressure! 2.Collapse of core under its own weight  formation of proto-neutron star when ρ ~ 10 14 g/cm 3 3.Gravitational binding energy becomes more negative:  positive amount of energy is lost from the system! 4. Core Bounce  shock formation and ejection envelope

22. Evolution of a massive star (25 solar masses) Collapse onset: photo-dissociation of iron Core collapse: t ~ 0.2 s (!)

23. Processes around collapsed core

25. Gravitational binding energy:

28. neutronization core:

29. Main properties: 1.Strong shock propagating through the Interstellar Medium; (or through the wind of the progenitor star) 2.Different expansion stages: - Free expansion stage (t < 1000 yr) R  t - Sedov-Taylor stage (1000 yr < t < 10,000 yr) R  t 2/5 - Pressure-driven snowplow (10,000 yr < t < 250,000 yr) R  t 3/10

31. Energy budget: Expansion speed:

32. - Expansion decelerates due to swept-up mass; - Interior of the bubble is reheated due to reverse shock; - Hot bubble is preceded in ISM by strong shock: - the supernova blast wave.

34. Shock relations for strong (high-Mach number) shocks:

35. Pressure behind strong shock (blast wave) Pressure in hot SNR interior

36. At contact discontinuity: equal pressure on both sides! This procedure is allowed because of high sound speeds in hot interior and in shell of hot, shocked ISM: No large pressure differences are possible!

37. At contact discontinuity: equal pressure on both sides! Relation between velocity and radius gives expansion law!

38. Step 1: write the relation as difference equation

39. Step 2: write as total differentials and………

40. ……integrate to find the Sedov-Taylor solution

41. Deceleration radius R d : shock speed = expansion speed

43. 1.Energy is put in gradually: E(t)=L wind t

44. 2. Dimensional analysis:

45. View from rest frame FW Shock for V w >> V S Towards Star

46. Sedov:Wind properties:

47. Sedov:Wind properties:

48. Ring Nebula

49. Eskimo Nebula Helix Nebula

50. Eta Carinae Hourglass Nebula