Gravitational Waves. Masaru Shibata U. Tokyo

Transcription

1 Gravitational Waves Masaru Shibata U. Tokyo 1. Gravitational wave theory briefly 2. Sources of gravitational waves 2A: High frequency (f > 10 Hz) 2B: Low frequency (f < 10 Hz) (talk 2B only in the case I have time)

2 I Gravitational wave theory Dynamical (nonstationary), nonspherical massive objects emit gravitational waves (GWs); Specifically, GWs are emitted when tracefree-part of quadrupole moment of the system changes

3 Amplitude by Quadrupole formula TF TF G I&& ij Iij = tracefree-part of quadrupole hij 4 c D D = distance to source Displacement ΔL h L: L L=effective length of detector ij ~ several 100 km for Grand-based

4 Order estimate 2 TF MR 2 I&& ij ~ ε ~ Mv ε 2 T Mpc M v hij 2 10 D 3M 0.4c M : Mass, R: Characteristic radius, v T : Characteristic speed, : Characteristic dynamical time ε: Nonsphericity 1 for binary, ~ 0.1 for SN ( ) This is amplitude at an instantaneous time. Not the amplitude measured. 2 ε

5 Effective amplitude 1 In detection, amplitude is integrated by N, where N is number of cycle. N is approximately given by N = f max(obs. time T obs, emission time τ ) f is frequency of GWs. Emission time is < ~ E/(dE/dt)GW c 1 0.4c τ ~ N ~ 2 v fε v where quadrupole formula v GM R 2 and virial relation ~ / is used. ε 2

6 Effective amplitude 2 h = h N eff Mpc M v D 3M 0.4c for T > τ ij obs 100 Mpc M v D 3M 0.4c for T < τ 22 obs 1/2 2 ε ft obs High velocity is not always important for a source longterm integration is done

7 Maximum emission timescale 8/3 5/3 6 f M 2 τ ~2 10 sec 1Hz M For τ < T = 1 yrs, f crit obs M ~ 0.3Hz M 5/8 ε 3/4 ε Low f (low v/c) source is weak emitter emission timescale is longer.

8 Frequency f 1/2 R GM, π f 3 π v R v M v f 4kHz πgm M 0.4c Mass of sources of GWs: M > ~ M Velocity must be < c. Frequency of GWs should be < ~ 10kHz. But no limit for low-frequency region.

9 Upper limit of GW amplitude Strict constraint! h = h N eff 100 Mpc M v D 3M 0.4c for T > τ ij obs 22 10Gpc obs 1/ Mpc M v ε D 3M 0.4c for T < τ D=100Mpc ft obs Integration Time = 1yrs

10 Nature of GW sources High mass Near periodic (longterm emitter) Small distance (frequent event) (high velocity is not very important) Lower frequency is better region. Discuss sources specifying frequency

11 2A Sources of ground detectors Almost no sensitivity for f < 10 Hz due to seismic noise 10 Hz < f < 10 khz f 1 3 M v 4kHz M 0.4c 3 3 v M v c M 0.4c M = 2 M : v/ c 0.07, mildly relativistic M = 20 M : v/ c 0.15, relativistic Compact stars: Neutron star, black hole

12 1st LIGO Current level Frequency (Hz) Advanced LIGO LCGT

13 Sources (< ~200, 300Msun) Coalescence of neutron star (NS) and black hole (BH): NS/NS, BH/NS, BH/BH Supernova Oscillation of neutron stars Primary sources

14 Merger rate of NS-NS 1 per ~10^4 yrs in our Galaxy 1 per yrs in ~ Mpc (<< 4 Gpc) Not rare in the whole universe V. Kalogera et al. 04

15 Merger rate predicted by population synthesis Rate per galaxy ~ NS-NS NOT SMALL because of high M Kalogera et al. Astroph

16 Last ~ 10 minutes of coalescing binary r 2R << r Adiabatic Inspiral r >> R, Temission >> P Orbital separation gradually decreases due to GW emission BH or NS Merger

17 Inspiral waveform T Sec Determined only by mass & spin of NSs, BHs

18 1st LIGO Current level BH=10Msun NS=1.4Msun Frequency (Hz) Advanced LIGO LCGT

19 Primary goal of LIGO/LCGT Detection of GWs Detection of inspiral waveforms Distribution of mass & spin of NS/BH Detection of quasi-normal mode of black hole Prove BH exists and observe highly curved spacetime directly Determining the central engine of short gamma-ray bursts

20 Simulation by Pretorius: Lapse BH-BH merger From his homepage

21 Gravitational waves from BBH merger Inspiral waveform QNM BH ringing By F. Pretorius

22 Fourier spectrum (15+15Msun) Buonanno Cook Pretorius (2006) f^{-2/3} merger f^{-7/6} inspiral e^{ αω} damp

23 1st LIGO Larger mass Current level =h(f) f BH=10 Msun NS=1.4 Msun Frequency (Hz) Advanced LIGO LCGT

24 Signal-to-Noise ratio at 100Mpc For LIGO Buonanno et al (2006) Inspiral QNM BH ringing

25 GRB duration distribution Short Bursts Long Bursts 2 sec Duration

26 ? Clarifying sources is one of the Central issues in astrophysics Long

27 Next targets NS-NS merger waveform Physics of high-density matter Supernova Mechanism

28 Stiff EOS leads to formation of HMNS

29 Gravitational waveforms From HMNS + mode f Inspiral waveform 3/2 r M = 1.18 khz 30 km 2.8 M b r 2R EOS (i.e. NS radius determines frequency of the last waves 1/2

30 GW signal 1st LIGO For r < 50Mpc Detectable! Advanced LIGO Frequency (Hz) Detection = HMNS exists Stiff EOS Constrain EOS

31 Mass R-M relation of NSs Lower limit of max. mass Lattimer & Prakash Science 304, 2004 Quark star Radius

32 GW from supernovae No one knows mechanism for explosion GWs may carry information on the mechanism as well as on the EOS, rotation rate,

33 Gravitational waves at bounce Ott et al. (2006)

34 Gravitational waves spectrum ~khz Ott et al. (2006)

35 Standing Accretion Shock Instability Longterm simulation (Burrows et al. 2006)

36 GWs from SASI

37 Fourier 10kpc ~ khz

38 For this next step, Interesting sources for ~1kHz ~3kHz However, A-LIGO and LCGT are not high sensitive enough for detection Improve the sensitivity in the highfrequency region using, e.g., resonant side-band extraction technique.

39 RSE Hz

40 B Space interferometer For detecting GWs of f < 10Hz, detectors in space are necessary v M v f 4 mhz 10 6 πgm M 0.4 c Massive object, like SMBH, can be detected. Furthermore, amplitude is large h eff 1/ Gpc M v 2 10 for T 6 obs > D 3 10 M 04. c Gpc M v 6 D 3 10 M 0.4c 2 ε ft obs obs τ for T < τ

41 Mildly relativistic objects are also sources v M v f 1 Hz πgm 4 M 0.04 c And, if T > τ, h eff obs v 3 10 D 4M 0. 04c Gpc M c 1/2 0.4c Hz where τ ~ = 10 sec v f v f

42 Why is the amplitude large? Mass is large A large number of wave cycles can be accumulated near periodic (stationary) objects can be the sources GW corresp. EM khz Burst-like sources γ-ray X-ray <Hz Stationary & Burst Optical IR GW astronomy starts from γ-ray band, but it is natural to develop optical band.

43 Sources for mhz Hz band Coalescence of supermassive-bh binaries Coalescence of intermediate-mass BH binaries (if they really exist) Merger of SMBH and stellar mass BH/NS/white dwarf Stellar mass BH-BH, BH-NS, NS-NS are also potential sources for f ~ 1 Hz.

44 LISA 5M km f ~ mhz

45 Hierarchical clustering scenario

46 GW from SMBH binary

47 Detection rate of GWs from MBH binaries Sesena et al. (2005)

48 BBO, DECIGO Merger h(f) [Hz -1/2 ] yrs before merger DECIGO* Merger Inflation f [Hz] Correlation by 2 detectors

49 Study for theory of gravity Relativity: lowest order = quadrupole emission Scalar tensor theory: lowest order = dipole emission P& 192π μ GM Ω = 5 M c orb 3 M : Total mass, μ: Reduced mass 1/3 GM Ω v Ω : Orbital angular velocity, 3 = c c σ : Difference of scalar charge ~ 0.1 (BH-NS) ω : Brans-Dicke parameter 5/3 μ GM Ω 4π 3 M c 2 σ ω + 2

50 Ratio Scalar 5 GMΩ = c 2/3 2 σ 3 GW 48 ω + 2 2/3 2/ M f σ ω = M 0.2 Hz yrs integration at f = 0.2 Hz 6 10 cycles 1 phase difference by scalar-waves emission If 1 phase difference can be measured (S/N = 10), 7 ω is constrainted as ω 10.

51

52 Summary Step 0: Detection (< 2015) Step 1: Study of stellar-mass BHs and NSs using grand-based detectors (~ 15) Step 1.5: Study of details of NSs and nuclear matter using khz band (~ 20) Step 2: Observation of low frequency GWs using space-detectors (2020 ~?): Sources = SMBHs, evolution of galaxies, theory of gravity, Step??: Detect GW background (2048?)

53 By M. Ando GWBs of inflationary origins (Ω gw =10-14 ) f -3/2

54 Contours of electron fraction (Sekiguchi 07) ms ms ms ms ms ms Unstable to convection energy transport

55 Gravitational waveforms (Sekiguchi 07) A I&& I&& 2 zz xx A2 2 h = sin θ D 10 kpc A 10 sin D 3 m Advance LIGO θ