Sound Waves Sound Waves:

Transcription

1 Sound Waves Sound Waves: 1

2 Sound Waves Sound Waves Linear Waves compression rarefaction 2

3 H H L L L Gravity Waves 3

4 Gravity Waves Gravity Waves 4

5 Gravity Waves Kayak Surfing on ocean gravity waves Oregon Coast 5

6 Waves: sea & ocean waves Phase & Group Velocity 6

7 7

8 Doppler Effect 8

9 Jeans Instability 9

10 Shock Waves 10

11 Shocks 1. Shocks are sudden transitions in flow properties such as density, velocity and pressure; 2. In shocks the kinetic energy of the flow is converted into heat, (pressure); 3. Shocks are inevitable if sound waves propagate over long distances; 4. Shocks always occur when a flow hits an obstacle supersonically 5. In shocks, the flow speed along the shock normal changes from supersonic to subsonic Wave Breaking High-pressure/density regions move faster u 2c s0 1 0 ( 1)/2 1 Shock must form c s0 11

12 12

13 Chelyabinsk Meteorite (Feb. 2013): Sonic Boom 13

14 Examples of Astrophysical shocks Cometary bow-shocks Earth s bow shock 14

15 Heliosphere 15

16 Supernova Remnant Cassiopeia A Supernova blast waves Tycho s Remnant (SN 1572AD) 16

17 Radio galaxy Cygnus A Radio picture Hot spots are shocks! X-ray picture Knots in jet of Galaxy M87 are shocks! 17

18 18

19 Summary : Shock Physics Across an infinitely thin steady shock you have, in the shock frame where the shock is at rest, the following Rankine-Hugoniot Jump conditions: Mass-flux conservation V V 1 n1 2 n2 Momentum-flux conservation 2 2 V P V P 1 n1 1 2 n2 2 V V t1 t2 Energy-flux conservation P V V P n1 2 n2 ( 1) 1 ( 1) 2 Summary: Rankine-Hugoniot relations (for normal shock) Fundamental parameter: Mach Number shock speed s sound speed V c 1 s1 R-H Jump Conditions relate the up- and downstream quantities at the shock: P2 P 2 1 s 1 2 s 2 2 s

20 From normal shock to oblique shocks: All relations remain the same if one makes the replacement: V V V cos, 1 n1 1 1 V / c cos S n n1 s1 S 1 is the angle between upstream velocity and normal on shock surface Tangential velocity along shock surface is unchanged V V sin V V sin t1 1 1 t2 2 2 Example from Jet/Rocket engines 20

21 21

22 Supernova Remnants 22

23 Kepler (1604) Tycho SNR (1572) SN1006 SNR (1006) Cas A Cas A (1680?) De Stella Nova 23

24 Cas A: Remnant Supernova (1680) Brightest Radio source on the sky 24

25 Cas A SNR flythrough 25

26 Theory of Supernova Blast Waves Supernovae: Type Ia Subsonic deflagration wave turning into a supersonic detonation wave in outer layers. Mechanism: explosive carbon burning in a mass-accreting white dwarf Type Ib-Ic & Type II Core collapse of massive star Core-Collapse SN 26

27 In the last stages of its life, high-mass star: - iron-rich core - surrounded by concentric shells, hosting the various thermonuclear reactions The sequence of thermonuclear reactions stops here: - formation of elements heavier than iron requires - input of energy rather than causing energy to be released 27

28 Supernova II Explosion: SN

29 Pulsars and Neutron Stars 29

30 Supernova 1987A 30

31 Thermonuclear SN (Supernova Ia) SN1006 Supernova SN1006: brightest stellar event recorded in history 31

32 SN1006 Supernova SN1006: - brightness: m = distance: d=2.2 kpc - recorded: China, Egypt, Iraq, Japan, Switzerland, North America Supernova SN1006: brightest stellar event recorded in history SN1006 Supernova SN1006: present-day Supernova Remnant - brightness: m = distance: d=2.2 kpc - recorded: China, Egypt, Iraq, Japan, Switzerland, North America Supernova SN1006: brightest stellar event recorded in history 32

33 Supernova Ia Explosion 33

34 Blast Waves Tsar Bomba Nuclear Explosion 34

35 Tsar Bomba Nuclear Explosion Tsar Bomba Nuclear Explosion 35

36 Hiroshima, the Shockwave Sedov-Taylor Expansion Law 36

37 Blast waves 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 37

38 Tsar Bomba Nuclear Explosion Radio map Cassiopeia A (VLA) 38

39 Remnant of Tycho s supernova of 1572 AD An old supernova remnant (age ~ 10,000 years) 39

40 Energy budget: Free-expansion phase E 3 grav 5 GM R c 2 c erg 99% into neutrino's 1% into mechanical energy Expansion speed: V 1/2-1/2 2Emech Emech M ej exp 3000 km/s 51 Mej 10 erg 10 M 40

41 Sedov-Taylor stage Expansion starts to decelerate due to swept-up mass - Interior of the bubble is reheated due to reverse shock - Hot bubble is preceded in ISM by strong blast wave V s 1/ 2 1/ 2 2E 1 1 V snr M ej 1 R/ Rd 1 R/ Rd 2/5 t R 3/2 t 41

42 Shock relations for strong (high-mach number) shocks: s s 2 1 P2 P V1 1V1 s cs1 P as s 2 s P2 1V1 1 42

43 2 2 P P V s 1 ism s Pressure behind strong shock (blast wave) P i SNR e 1 i 1 E 4 R 3 3 S Pressure in hot SNR interior At contact discontinuity: equal pressure on both sides! 2 1 ism V 1 2 SNR s 4 3 Rs E 3 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! 43

44 At contact discontinuity: equal pressure on both sides! 2 1 ism V 1 2 SNR s 4 3 Rs E 3 V s dr s snr 2 dt 3 1 ism 8 E 1/2 R 3/2 s Relation between velocity and radius gives expansion law! 1/2 3/2 8 E snr Rs drs dt ism Step 1: write the relation as difference equation 44

45 1/2 3/2 8 E snr Rs drs dt ism 2 5/2 8 E snr drs ism 1/2 dt Step 2: write as total differentials and 1/2 3/2 8 E snr Rs drs dt ism 2 5/2 8 E snr drs ism 1/2 dt integrate to find the Sedov Taylor solution 1/5 R t C E t snr 2/5 s( ), ism C 2/ /

46 Sedov & Taylor 46