BH SAIDA Hiromi (Daido University, Japan) BH source W 0 earth W 1 BH at, Subaru seminar at Hawaii, Typeset by FoilTEX 1

Size: px

Start display at page:

Download "BH SAIDA Hiromi (Daido University, Japan) BH source W 0 earth W 1 BH at, Subaru seminar at Hawaii, Typeset by FoilTEX 1"

艮鼓粉胡
4 years ago
Views:

1 BH SAIDA Hiromi (Daido University, Japan) BH source W 0 earth W 1 BH at, Subaru seminar at Hawaii, Typeset by FoilTEX 1

2 Plan of Talk 1. Introduction : Basic idea for direct BH detection 2. Proposal : A principle of direct BH detection method for one telescope 3. Under calculation : Short review of the aim of my current calculation 4. Summary Typeset by FoilTEX 2

3 1. Introduction : basic idea 1.1 From candidate to itself Best observational knowledge of BH at present BH candidates by Newtonian gravity Large Gap in Physics!! BH is a general relativistic (GR) object The only way to find BH itself is a direct detection of GR effect caused by BH. What is it? How can we do it? Typeset by FoilTEX 3

4 1.2 BH detection in GR context Theoretical (mathematical) fact in GR Uniqueness (or No Hair) Theorem BH is uniquely specified by 3 parameters (under physically suitable conditions in math. cal.): M : mass J : spin angular momentum Q : electric charge (No other parameter (hair) is assigned to BH.) Typeset by FoilTEX 4

5 BH detection in GR context is as follows: Qualitative meaning is ( BH is a GR object) to recognize the existence of BH Uniqueness Thm by detecting GR effect. Quantitative meaning of BH detection To measure the parameters M and J by detecting GR effect. Note: Q = 0 is expected in real situations. Typeset by FoilTEX 5

6 1.3 GR effect of BH as our target Target : Strong Gravitational Lensing effect An ideal situation we want to observe: Clear environment around BH except the source Burst-like and spherical emission seen from the source BH source W 1 W 0 earth W 0 : 0th ray (direct ray) W 1 : 1st ray (secondary ray) Typeset by FoilTEX 6

7 our basic idea is simple! Basic idea of a direct BH detection: From two observational quantities : Time delay t obs E obs = E 1 : Amp. ratio of W 0 and W 1, E 0 Obtaine two BH parameters M and J. Method to observe ( t obs, E obs ) should be realizable by one telescope. Typeset by FoilTEX 7

8 2. Principle of direct BH obs. Making use of time series data of one telescope 2.1 Ex. of time series data on one ideal tele. Suppose: The emission of source is Gaussian in time. Suppose: The telescope detects the time-variation of electric field (or its intensity) at all wave length. Then Typeset by FoilTEX 8

9 Gaussian emission waveform changes! E 0 W oscillation of observed wave at ONE telescope E 1 Hilbert Trans. of W E t obs t obs t obs t obs E 1 W source W BH 10 W 1 20 earth Ref: Zenginoglu &Galley PRD86(2012)064030, YouTube Typeset by FoilTEX 9

10 Gouy Phase Shift : General phenomenon of wave The phase of oscillation shifts unexpectedly, when the wave passes a caustic. (when some rays cross there.) Caustic BH = Crossing points of rays caustic ex. non-rotating BH Math.: Wave opt. approx. breaks down. Higher order approx. reveals this effect. Typeset by FoilTEX 10

11 When some rays of wave cross at a caustic, Positive freq. Fourier component: Phase shifts by π 2 [rad] Negative freq. Fourier component: Phase shifts by + π 2 [rad] Note: Spectrum remains unchanged. Math.: This is expressed by Hilbert trans. a wave f(t) Hilbert H[f](t) Re dz f(z) t z Typeset by FoilTEX 11

12 2.2 Ex. of time series data with line emission Suppose: An exact line emission by the source E Oscillation of observed wave at ONE telescope Τ 0 Τ 1 E obs W 0 W 1 t obs t obs { T 0 T 1 due to kinematic Doppler effect. Gouy phase shift H[sin](ωt) = cos(ωt) Typeset by FoilTEX 12

13 2.3 Ex. of an observation with a band width Waveform in time series data is a Beat ω = 2π Ex. W 0 = sin[ (ω + n δω) t ], δω = 2π n=0,±1,±2 30 E obs main peak W0 subpeaks Hilbert trans. W 1 main peak sub-peaks Waveform-change may be apparent in beating. E 1 E 0 t obs Typeset by FoilTEX 13

14 2.4 Time Delay Self-correlation (TDS) method Step1: Data copy (A, B) Step2: Modulation of B Hilbert trans. of B B Constant (E obs ) Doppler correction on B Step 3: Correlation search between A and B W 0 and W 1 are found, E original data (A) W 0 W 1 t obs strong corelation W 0 W t obs modulated data (B) and t obs, E obs, T 1 /T 0 are obtained. Typeset by FoilTEX 14

15 An actual case: W 0 and W 1 are covered with background noise. The background noise is a random oscillation. Background noise vanishes in Correlation Integral. dτ N(t)N(t + τ) = 0 for a random noise N(t) Non-random signals, W 0 and W 1, are to be obtained by Step 3. Typeset by FoilTEX 15

16 3. Under calculation (theory) 3.1 Correspondence ( obs, E obs ) (M, J) Suppose the values: source position : ( t s, r s, θ s, φ s ) at emission source velocity : ( u t, u s r, u s θ, u s φ ) at emission s emission spectrum : I s (ν s ) seen from the source inclination angle : θ obs observation frequency : ν obs Typeset by FoilTEX 16

17 1 ε o under calculation with General Relativity a ε o (a,m) t o (a,m) a = M t o by definition : ε o < 1, 0 < t o, a < M M This diagram enables us to read (M, J) from observational data ( t obs, E obs ) Typeset by FoilTEX 17

18 W 0 W 1 BH source W 1 W 0 earth { BH Typeset by FoilTEX 18

19 (1) one mesh (4) observed? source BH (3) absorbed? (2) impact para. obs. (1) (2) (k r ) 2 + V eff = 0 (3) BH (4) Typeset by FoilTEX 19

20 PC CPU 2.6GHz, 16GB 1 W 0 W 1 2 Shooting 3 Typeset by FoilTEX 20

21 Shooting (1) (2) BH (3) r obs (4) r obs source BH (5) r obs Typeset by FoilTEX 21

22 2 Shooting Typeset by FoilTEX 22

23 3.2 TDS with Light Curve? I obs E 2 (E : Amplitude) I obs (t obs ) Ex. Gaussian emission W 0 W 1 Under consideration: Mathematical transformation t obs between W 0 s curve and W 1 s curve. With this, the step 2 is extended to light curve. Typeset by FoilTEX 23

24 4. Summary Direct BH detection is to measure M and J via a direct observation of GR effect. For Strong Gravitational Lensing by BH, TDS method may realize the direct BH detection by one telescope. Correspondence diagram (M, J) ( t obs, E obs ) is under construction with GR. Extension of TDS to light curve, a construction of light curve trans. is also under consideration. Typeset by FoilTEX 24

投影片 1

投影片 1 Coherence ( ) Temporal Coherence Michelson Interferometer Spatial Coherence Young s Interference Spatiotemporal Coherence 參料 [1] Eugene Hecht, Optics, Addison Wesley Co., New York 2001 [2] W. Lauterborn,