Gravity Waves Gravity Waves

Transcription

1 Gravity Waves Gravity Waves 1

2 Gravity Waves Gravity Waves

3 Kayak Surfing on ocean gravity waves Oregon Coast Waves: sea & ocean waves 3

4 Sound Waves Sound Waves: 4

5 Sound Waves Sound Waves Linear Waves compression rarefaction 5

6 H H L L L Phase & Group Velocity 6

7 Doppler Effect 7

8 Shock Waves 8

9 Shocks 1. Shocks are sudden transitions in flow properties such as density, velocity and pressure;. 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 9

10 10 Wave Breaking High-pressure/density regions move faster ( 1)/ s s c u c Shock must form

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12 Chelyabinsk Meteorite (Feb. 013): Sonic Boom Examples of Astrophysical shocks Cometary bow-shocks 1

13 Earth s bow shock Heliosphere 13

14 Supernova Remnant Cassiopeia A Supernova blast waves 14

15 Tycho s Remnant (SN 157AD) Tsar Bomba Nuclear Explosion 15

16 Tsar Bomba Nuclear Explosion Tsar Bomba Nuclear Explosion 16

17 Hiroshima, the Shockwave Radio galaxy Cygnus A Radio picture Hot spots are shocks! X-ray picture 17

18 Knots in jet of Galaxy M87 are shocks! 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 n Momentum-flux conservation V P V P 1 n1 1 n V V t1 t Energy-flux conservation P V V P n1 n ( 1) 1 ( 1) 19

20 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: P P 1 s 1 s s 1 1 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 t 0

21 Example from Jet/Rocket engines 1

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23 Supernova Remnants Kepler (1604) Tycho SNR (157) SN1006 SNR (1006) Cas Cas A (1680?) 3

24 Cas A SNR flythrough 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 4

25 Supernova II Explosion: SN1054 5

26 Supernova Ia Explosion Blast waves Main properties: 1. Strong shock propagating through the Interstellar Medium, or through the wind of the progenitor star;. Different expansion stages: - Free expansion stage (t < 1000 yr) R t - Sedov-Taylor stage (1000 yr < t < 10,000 yr) R t /5 - Pressure-driven snowplow (10,000 yr < t < 50,000 yr) R t 3/10 6

27 Tsar Bomba Nuclear Explosion Sedov-Taylor Expansion Law 7

28 Blast waves Main properties: 1. Strong shock propagating through the Interstellar Medium, or through the wind of the progenitor star;. Different expansion stages: - Free expansion stage (t < 1000 yr) R t - Sedov-Taylor stage (1000 yr < t < 10,000 yr) R t /5 - Pressure-driven snowplow (10,000 yr < t < 50,000 yr) R t 3/10 8

29 Radio map Cassiopeia A (VLA) Remnant of Tycho s supernova of 157 AD 9

30 An old supernova remnant (age ~ 10,000 years) 30

31 Energy budget: Free-expansion phase E 3 grav 5 GM R c c erg 99% into neutrino's 1% into mechanical energy Expansion speed: V 1/ -1/ Emech Emech M ej exp 3000 km/s 51 Mej 10 erg 10 M 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 31

32 V s 1/ 1/ E 1 1 snr V M ej 1 R/ Rd 1 R/ Rd /5 t R 3/ t 3

33 Shock relations for strong (high-mach number) shocks: 1 s 1 1 1s 1 P P 1 V1 1V1 s cs1 P1 1 as s s 1 +1 P 1V1 1 P P V 1 1 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 33

34 At contact discontinuity: equal pressure on both sides! 1 ism V 1 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! At contact discontinuity: equal pressure on both sides! 1 ism V 1 SNR s 4 3 Rs E 3 V s dr s snr dt 3 1 ism 8 E 1/ R 3/ s Relation between velocity and radius gives expansion law! 34

35 1/ 3/ 8 E snr Rs drs dt 3 1 ism Step 1: write the relation as difference equation 1/ 3/ 8 E snr Rs drs dt 3 1 ism 5/ 8 E snr drs ism 1/ dt Step : write as total differentials and 35

36 1/ 3/ 8 E snr Rs drs dt 3 1 ism 5/ 8 E snr drs ism 1/ dt integrate to find the Sedov Taylor solution 1/5 R t C E t snr /5 s( ), ism C / / Sedov & Taylor 36