How To Make A Gw Antenna

Transcription

1 Data analysis of continuous GW using the Phase-II TOBA data Kazunari Eda University of Tokyo, RESCEU (RESearch Center for the Early Universe) Collaborators: A.Shoda, Y.Kuwahara, Y.Itoh & M.Ando 2015/08/07 Bi-monthly meeting 1

2 Contents 1. Introduction 2. Experiments 3. Data analysis of continuous GW 4. Conclusion 2

3 1. Introduction 3

4 Motivation Recently, we have developed the torsion-bar antenna (TOBA) based on PRD 90, We operated the TOBA for 24 hours from Dec.10 to Dec.11 in The sensitivity reached Hz -1/2 at around 1 Hz. Continuous GWs in low-frequency regime have yet to be investigated so far. We search for continuous GWs from an isolated neutron star. We put a constraint on the GW amplitude. 4

5 What is a TOBA? TOrsion-bar Antenna (TOBA) (Ando et al. PRL 105, (2010)) Low-frequency GW antenna which measures rotations of bars TOBA is formed by two bar-shaped orthogonal test masses sensitive to low-frequency ( f=0.1-1 Hz ) GWs even on the ground thanks to its resonant frequency f res < 1mHz. Main Targets Compact binary coalescence Stochastic GW background 10m-TOBA 5

6 Multi-output configuration Multi-output TOBA Eda, Shoda, Itoh & Ando PRD 90, (2014) Originally, only the bar rotation on the xy plane has been considered. We incorporate the additional outputs by measuring the rotation of the bars on the yz and xz planes. Merits Event detection rate is improved by a factor of 1.7. Waveform parameters can be measured with a single antenna even for short-duration signals. 6

7 Ando et al. PRL 105, (2010) Phase-I TOBA Single 20-cm bar Single output Single antenna History Ishidoshiro, PhD thesis 2. Network of two Phase-I TOBAs Single 20-cm bar Single output Two-antenna Tokyo and Kyoto Shoda, M thesis Laser Phase-II TOBA Two 24-cm bars Multi-output Single antenna Active & passive vibration system Shoda, PhD thesis Bar Bar PD 7

8 2. Experiments 8

9 Design Overview Basic design for the Phase-II TOBA Two 24-cm bars (0.61kg) Multi-output system Active + passive vibration isolation system 9

10 Measured strain sensitivity Sensitivity curve of the Phase-II TOBA Limited by seismic noise Strain sensitivity [Hz -1/2 ] Bar rotations on vertical planes Bar rotations on horizontal plane Limited by noise caused by the optical fiber Frequency [Hz] 10

11 Measured strain sensitivity Sensitivity curve of the Phase-II TOBA Limited by seismic noise In our analysis, we neglect the Φ 1 and Φ 2 signals Strain sensitivity [Hz -1/2 ] Bar rotations on vertical planes Bar rotations on horizontal plane Limited by noise caused by the optical fiber Frequency [Hz] 11

12 Statistical properties of the data Gaussian check Short Fourier Transform The distribution of bin power for each SFT and for every frequency bin. If the data is Gaussian, the power distribution is expected to follow χ 2 with 2 dof. Almost Gaussian noise 12

13 3. Data analysis of continuous GWs 13

14 Known isolated NS search GW from a rapidly rotating neutron star GW is generated by the non-axisymmetry around its spin axis Duration of the signal >> Observation time The non-axisymmetry is characterized by an ellipticity ε. Known NS search NSs known by EM observations Spin Spin axis Line of sight EM obs. => information about Sky position (α, δ) Spin frequency f 0 Spin evolution Neutron star 14

15 GW signals GW signal from a known pulsar GW signal in a detector 4 unknown parameters {h 0,Ψ,ι, Φ 0 } Antenna pattern functions : F +,F x Laser interferometer measures horizontal displacement of mirrors. TOBA measures rotation of bars 15

16 Search for GWs from PSR B PSR B Our target is the pulsar, PSR B Known isolated pulsar We can put constraint on the ellipticity of the targeted pulsar. Target NS Sky position and spin frequency are already known by EM obs. f GW = 2f 0 = [Hz]. ft 2 obs<< 1, so we don t have to care about the spin down effect. f-shift due to the spin evolution << f resolution 16

17 Flow chart of the search pipeline Input h(t) data Make 9000-sec SFTs List of candidates Yes Compute F-statistic 2F > 2F* No Set an upper limit on h 0 17

18 Flow chart of the search pipeline Input h(t) data Make 9000-sec SFTs List of candidates Yes Compute F-statistic 2F > 2F* No Set an upper limit on h 0 18

19 LAL LAL LSC Algorithm Library A library of routines for GW data analysis Written in C language GWF format We need to convert our data into the GWF format. Gravitational-wave frame (GWF) A GWF file contains information about the detector TOBA_data.txt TOBA_data.gwf 19

20 Flow chart of the search pipeline Input h(t) data Make 9000-sec SFTs List of candidates Yes Compute F-statistic 2F > 2F* No Set an upper limit on h 0 20

21 Short Fourier transform SFTs Frequency shifts induced by the Earth s spin Non-stationary noise MakeSFTs.c = 24 hours Make small segments... Fourier Transform... = 9000 sec Choice of T SFT f shift during T SFT < f resolution 21

22 SFTs Short Fourier transform Frequency shifts induced by the Earth s spin... Fourier Transform... MakeSFTs.c We Non-stationary can take longer noise SFT segments compared to higher frequency = 24 hours But, longer SFT segments lead to more significant Make small segments non-stationary noise T SFT = 9000 seconds Choice of T SFT f shift during T SFT < f resolution = 9000 sec 22

23 Flow chart of the search pipeline Input h(t) data Make 9000-sec SFTs List of candidates Yes Compute F-statistic 2F > 2F* No Set an upper limit on h 0 23

24 F-statistic Computation of F-statistic ComputeFstatistic_v2.c F-statistic is based on the method of maximum likelihood. If 2F > 2F th, we regard that the signal is detected. We use F-statistic to discriminate whether or not GW signals exist in the antenna. 24 Threshold of F-statistic If we choose the threshold as S/N=8, then 2F th =68. If 2F < 2F th, we proceed to place an upper limit on h 0. 24

25 Measured PDF of 2F over a 1Hz band for the TOBA data Almost all of our data are dominated by the Gaussian 2f 0 =

26 Flow chart of the search pipeline Input h(t) data Make 9000-sec SFTs List of candidates Yes Compute F-statistic 2F > 2F* No Set an upper limit on h 0 26

27 Setting an upper limit on h 0 How to set an upper limit on h 0 If 2F < 2F th, we place an upper limit h 0 (C) with confidence C. The upper limit with confidence level C ComputeMCUpperlimit.c Expected upper limit on h 0 1 % false alarm rate 10 % false dismissal rate PRD 69, (2004) 27

28 Observed upper limit on h 0 T obs = 24 hours Confidence level C=0.95, P FD =0.05 The observed value of UL is consistent with the expected value. Observed upper limit on ε Ellipticity = (Height of the mountain on NS) / (NS radius) Mountain on NS 100 billion km mountain on 10 km radius NS! NS 28

29 Summary The Phase-II TOBA was constructed based on PRD 90, We operated the Phase-II TOBA during Dec.10 to Dec.11. The sensitivity reached Hz -1/2 at around 1 Hz. We searched for the GW from PSR B We set an upper limit on h 0 as 8.7x10-13 with 95% confidence level using the 24-hour TOBA data. The search pipeline we used is basically applicable for the data analysis in ikagra. Thank you! 29