B.S. Sathyaprakash School of Physics and Astronomy in collaboration with Kamaretsos, Hannam and Husa

Transcription

1 Black Holes Ain t Got No Hair But They Do Grin 46th Rencontres De Moriond Gravitational Waves and Experimental Gravity La Thuile, Aosta Valley, Italy March 20-27, 2011 B.S. Sathyaprakash School of Physics and Astronomy in collaboration with Kamaretsos, Hannam and Husa

2 Black Hole No-Hair Theorem

3 Black Hole No-Hair Theorem Perturbed black holes regain their quiescent state by emitting the energy in their deformation as gravitational radiation

4 Black Hole No-Hair Theorem Perturbed black holes regain their quiescent state by emitting the energy in their deformation as gravitational radiation These are called quasi-normal modes (QNM)

5 Black Hole No-Hair Theorem Perturbed black holes regain their quiescent state by emitting the energy in their deformation as gravitational radiation These are called quasi-normal modes (QNM) They are damped sinusoids with characteristic frequencies and decay times which depend on only the mass and spin of the black hole (below assume j=0)

6 Black Hole No-Hair Theorem Perturbed black holes regain their quiescent state by emitting the energy in their deformation as gravitational radiation These are called quasi-normal modes (QNM) They are damped sinusoids with characteristic frequencies and decay times which depend on only the mass and spin of the black hole (below assume j=0) There are infinitely large number of modes. For the dominant mode:

7 Black Hole No-Hair Theorem Perturbed black holes regain their quiescent state by emitting the energy in their deformation as gravitational radiation These are called quasi-normal modes (QNM) They are damped sinusoids with characteristic frequencies and decay times which depend on only the mass and spin of the black hole (below assume j=0) There are infinitely large number of modes. For the dominant mode: h(t) = A e -t/τ cos(ωt+ϕ)

8 Black Hole No-Hair Theorem Perturbed black holes regain their quiescent state by emitting the energy in their deformation as gravitational radiation These are called quasi-normal modes (QNM) They are damped sinusoids with characteristic frequencies and decay times which depend on only the mass and spin of the black hole (below assume j=0) There are infinitely large number of modes. For the dominant mode: h(t) = A e -t/τ cos(ωt+ϕ) f(m, j) = ω/(2π) = 1200 Hz (10 M /M) (2 khz for j=0.9)

9 Black Hole No-Hair Theorem Perturbed black holes regain their quiescent state by emitting the energy in their deformation as gravitational radiation These are called quasi-normal modes (QNM) They are damped sinusoids with characteristic frequencies and decay times which depend on only the mass and spin of the black hole (below assume j=0) There are infinitely large number of modes. For the dominant mode: h(t) = A e -t/τ cos(ωt+ϕ) f(m, j) = ω/(2π) = 1200 Hz (10 M /M) (2 khz for j=0.9) τ(m, j) = 0.55 ms (M/10 M )

10 Black Hole No-Hair Theorem Perturbed black holes regain their quiescent state by emitting the energy in their deformation as gravitational radiation These are called quasi-normal modes (QNM) They are damped sinusoids with characteristic frequencies and decay times which depend on only the mass and spin of the black hole (below assume j=0) There are infinitely large number of modes. For the dominant mode: h(t) = A e -t/τ cos(ωt+ϕ) f(m, j) = ω/(2π) = 1200 Hz (10 M /M) (2 khz for j=0.9) τ(m, j) = 0.55 ms (M/10 M ) Q = τω/2 ~ 2 (for j=0.9, Q=5)

11 Application of Black Hole No-Hair Theorem

12 Application of Black Hole No-Hair Theorem There are infinitely many quasi-normal modes enumerated by integers (l,m,n):

13 Application of Black Hole No-Hair Theorem There are infinitely many quasi-normal modes enumerated by integers (l,m,n): m = -l,..., l and overtones n=1,2,3,...

14 Application of Black Hole No-Hair Theorem There are infinitely many quasi-normal modes enumerated by integers (l,m,n): m = -l,..., l and overtones n=1,2,3,... In general relativity frequencies flmn and decay times τ lmn all depend only on the mass M and spin j of the black hole

15 Application of Black Hole No-Hair Theorem There are infinitely many quasi-normal modes enumerated by integers (l,m,n): m = -l,..., l and overtones n=1,2,3,... In general relativity frequencies flmn and decay times τ lmn all depend only on the mass M and spin j of the black hole All but the n=1 overtones are negligible (very small Q)

16 Application of Black Hole No-Hair Theorem There are infinitely many quasi-normal modes enumerated by integers (l,m,n): m = -l,..., l and overtones n=1,2,3,... In general relativity frequencies flmn and decay times τ lmn all depend only on the mass M and spin j of the black hole All but the n=1 overtones are negligible (very small Q) Measurement of a single mode could give the mass and spin of the black hole

17 Application of Black Hole No-Hair Theorem There are infinitely many quasi-normal modes enumerated by integers (l,m,n): m = -l,..., l and overtones n=1,2,3,... In general relativity frequencies flmn and decay times τ lmn all depend only on the mass M and spin j of the black hole All but the n=1 overtones are negligible (very small Q) Measurement of a single mode could give the mass and spin of the black hole Measuring two or modes would constrain General Relativity or provide smoking gun evidence of black holes

18 Application of Black Hole No-Hair Theorem There are infinitely many quasi-normal modes enumerated by integers (l,m,n): m = -l,..., l and overtones n=1,2,3,... In general relativity frequencies flmn and decay times τ lmn all depend only on the mass M and spin j of the black hole All but the n=1 overtones are negligible (very small Q) Measurement of a single mode could give the mass and spin of the black hole Measuring two or modes would constrain General Relativity or provide smoking gun evidence of black holes If modes depend on other parameters (e.g., the structure of the central object), then test of the consistency between different mode frequencies and damping times would fail

19 Application of Black Hole No-Hair Theorem There are infinitely many quasi-normal modes enumerated by integers (l,m,n): m = -l,..., l and overtones n=1,2,3,... In general relativity frequencies flmn and decay times τ lmn all depend only on the mass M and spin j of the black hole All but the n=1 overtones are negligible (very small Q) Measurement of a single mode could give the mass and spin of the black hole Measuring two or modes would constrain General Relativity or provide smoking gun evidence of black holes If modes depend on other parameters (e.g., the structure of the central object), then test of the consistency between different mode frequencies and damping times would fail Absence of quasi-normal modes after merger would reveal failure of GR

20 Frequency of quasi normal modes Berti, Cardoso and Will

21 Quality Factor of QNMs 2 Q lm = τ lm ω lm. Berti, Cardoso and Will

22 The Grin

23 The Grin No-hair theorem really doesn t apply to deformed BHs

24 The Grin No-hair theorem really doesn t apply to deformed BHs It should be possible to measure not just the mass and spin but also, for instance, the mass ratio of the progenitor binary

25 The Grin No-hair theorem really doesn t apply to deformed BHs It should be possible to measure not just the mass and spin but also, for instance, the mass ratio of the progenitor binary They key is that the amplitude of the modes cary additional information

26 The Grin No-hair theorem really doesn t apply to deformed BHs It should be possible to measure not just the mass and spin but also, for instance, the mass ratio of the progenitor binary They key is that the amplitude of the modes cary additional information They depend on the nature of the perturber

27 The Grin No-hair theorem really doesn t apply to deformed BHs It should be possible to measure not just the mass and spin but also, for instance, the mass ratio of the progenitor binary They key is that the amplitude of the modes cary additional information They depend on the nature of the perturber h(t) = A e -t/τ cos(ωt+ϕ)

28 The Grin No-hair theorem really doesn t apply to deformed BHs It should be possible to measure not just the mass and spin but also, for instance, the mass ratio of the progenitor binary They key is that the amplitude of the modes cary additional information They depend on the nature of the perturber h(t) = A e -t/τ cos(ωt+ϕ) A = A(perturbation) = A(mass ratio)

29 Luminosity in Modes from Numerical Simulations 10 0 L L 33 L 44 q=2 1 1 d relative luminosities L 21 r 33 r 44 r Mt 10 Te

30 Luminosity in Modes from Numerical Simulations 10 0 L L 33 L q=2 q= Absolute and relative luminosities L 21 r 33 r 44 r Mt q= Mt q= Mt Mt

31 Amplitudes of quasi-normal modes Kamaretsos, Hannam, Husa, Sathyaprakash, 2010

32 Amplitudes of quasi-normal modes Using numerical relativity simulations we extracted energy and relative amplitude of various quasi-normal modes Kamaretsos, Hannam, Husa, Sathyaprakash, 2010

33 Amplitudes of quasi-normal modes Using numerical relativity simulations we extracted energy and relative amplitude of various quasi-normal modes Table shows, for different mass ratios (q) the final spin of the black hole, energy in QNM and relative amplitudes of higher order modes 5M after peak luminosity Kamaretsos, Hannam, Husa, Sathyaprakash, 2010

34 Amplitudes of quasi-normal modes Using numerical relativity simulations we extracted energy and relative amplitude of various quasi-normal modes Table shows, for different mass ratios (q) the final spin of the black hole, energy in QNM and relative amplitudes of higher order modes 5M after peak luminosity q j % total energy A 21 /A 22 A 33 /A 22 A 44 /A Kamaretsos, Hannam, Husa, Sathyaprakash, 2010

35 Identifying the beginning of Ringdown

36 Identifying the beginning of Ringdown Plot shows the evolution of different mode frequencies

37 Identifying the beginning of Ringdown Plot shows the evolution of different mode frequencies Modes stabilize about 5-10 M after peak luminosity

38 Identifying the beginning of Ringdown Plot shows the evolution of different mode frequencies Modes stabilize about 5-10 M after peak luminosity Frequencies agree reasonably well with BH perturbation theory

39 Identifying the beginning of Ringdown Plot shows the evolution of different mode frequencies Modes stabilize about 5-10 M after peak luminosity Frequencies agree reasonably well with BH perturbation theory q=2 L 22 f 44 f 33 f 22 f Mt

40 Identifying the beginning of Ringdown Plot shows the evolution of different mode frequencies Modes stabilize about 5-10 M after peak luminosity Frequencies agree reasonably well with BH perturbation theory q=2 L 22 f 44 f 33 f 22 f Mt q j f 22 f 21 f 33 Fit NR Fit NR Fit NR

41 Waveform Models The waveform used in our study is given by h A (t) = l,m>0 B lm D L e t/τ lm cos (ω lm t + γ lm ) B lm = α lm (F A D + Y + ) 2 ( lm + F A Y L [ ] F γ lm = m φ + tan 1 A Y lm F+ A Y +. lm lm) 2, The amplitudes obtained with NR simulations α 22 (q) =0.25 e q/7.5. α 21 (q) =0.18 α 22 (q)(q 1) 1/3, α 33 (q) =0.13 α 22 (q)(q 1) 1/2, α 44 (q) =0.024 α 22 (q) q 3/4.

42 Quasi-Normal Modes in LISA 1.5 Depending on the mass of the black hole, one or more modes could be visible dρ 2 d f (5x10 5, 5x10 6 ) M h t Time s dρ 2 d f Frequency mhz (10 6, 10 7 )M Frequency mhz

43 Visibility of QNM in ET

44 Visibility of QNM in LISA

45 The Grin in ET

46 The Grin in LISA