Numerical trial for cleaning of gravitational wave foreground by neutron star binaries in DECIGO

Transcription

1 Numerical trial for cleaning of gravitational wave foreground by neutron star binaries in DECIGO Mitsuru Tokuda, Nobuyuki Kanda Osaka City University

2 Olbers Paradox Heinrich Wilhelm Matthäus Olbers ( ) x10-18 x x10-18 x x10-18 x x x x x x10-18 x x x10-3 x x x10-3 x10-3

3 Problem on DECIGO/BBO : NS-NS foreground Many neutron star binaries are exist. Roughly 10 4 ~10 6 binary mergers will appear on DECIGO for year(s) of observation. These signals called as NS-NS foreground DECIGO instrumental noise spectrum simulated signal : noise NS-NS binaries* * 0-10 years before merge It appear as confusion noise around 0.1Hz Hz

4 Foreground? Background? DECIGO/BBO would like to see Stochastic background GW from early universe, Inspiral GW from massive BH binaries or compact binaries, etc... However, huge numbers of NS-NS foreground will make difficult to see other GWs. (Even they have a many informations : NS-NS population, mass distribution, somthing about star formation...) Also POP-III burst GWs might contaminate the signals... -> We must clean up (identify and subtract) binary signals!

5 Difficulty of cleaning Known powerful tool to identify binary inspiral waveform is Matched filtering... Quite huge number of templates will be need.! 10 30~36 templates!! (Culter & Harms, Phys.Rev. D , for BBO) Thus, identification is hard work. Inaccurate wave subtraction will stuck up the errors. (=contamination!) Very acculate waveform parameters must be determined.!!m/m < ~10-7 % (in our estimation)

6 Our issues and works 1. Numerical simulation of signals NS-NS signals DECIGO noises 2. Idea of tagging NS-NS signal Let s see the signal on time-frequency domain. 3. Trial of cleaning the foreground Clean up current data with future 3 years data.

7 1. Numerical simulation Design sensitivity Sh(f) Gaussian noise time series data noise generator DECIGO simulation NS-NS foreground GW generator options uniform distribution z distribution mass region etc... options calibration, and any systematic simulated data s obs (t) = n(t) + h F G (t) + h BG (t) Cleaning: foreground subtraction Search & Identification of NS-NS signals Idea of tagging a priori identification + error on parameters evaluation, test analysis i.e. correlation of two DECIGO detectors s clean,1 (t) s clean,2 (t τ) dt s clean (t) = s(t) h F G (t)

8 1. Numerical simulation : Toy model of NS-NS signals 2PN, time series signal h +, = 2Gmν c 2 R ( Gmω c 3 H (0) + = (1 + c 2 i ) cos 2ψ, 10 5 binaries assumptions: merge within 10 years 1-3 Msolar ) 2/3 { } H (0) +, + x 1/2 H (1/2) +, + xh (1) +, + x 3/2 H (3/2) +, + x 2 H (2) +, + x 5/2 H (5/2) +, H (0) = 2c i sin 2ψ uniform placed within 1 Gpc (=uniform direction, inclination of orbit)

9 DECIGO antenna response F + (t) F (t) = 1 2 (1 + cos2 θ) cos(2φ(t)) cos(2ψ(t)) cos θ sin(2φ(t)) sin(2ψ(t)) = 1 2 (1 + cos2 θ) cos(2φ(t)) sin(2ψ(t)) + cos θ sin(2φ(t)) cos(2ψ(t)) h obs (t) = [h + (t) cos 2ϕ + h (t) sin 2ϕ]F + (t) + [ h + (t) sin 2ϕ + h (t) cos 2ϕ]F (t)

10 Example of generated signals strain frequency spectrum DECIGO instrumental noise spectrum simulated signal : noise NS-NS binaries* * 0-10 years before merge time series consists of 10 5 binaries! [1/rHz] Hz

11 2. Idea of tagging NS-NS signal f f = 3 5 f = 53/8 8π See signal in time-frequency domain. ( c 3 5G ( ) c 3 5/8 M 5/8 (t coal t) 3/8 G ) 5/3 M 5/3 f 8/5 M = (m 1 m 2 ) 3/5 (m 1 + m 2 ) 1/5 It will be possible to tag when the binary will merge. Frequency of GW Hz Frequency of Chirp signal time sec

12 2. Idea of tagging NS-NS signal f f = 3 5 f = 53/8 8π See signal in time-frequency domain. ( c 3 5G ( ) c 3 5/8 M 5/8 (t coal t) 3/8 G ) 5/3 M 5/3 f 8/5 M = (m 1 m 2 ) 3/5 (m 1 + m 2 ) 1/5 It will be possible to tag when the binary will merge. Frequency of GW Hz Frequency of Chirp signal time sec

13 Short FFT sonogram (Time-Frequency domain) time[sec] Typically, within 700Mpc events can be tagged easy. (Using DECIGO 5Hz-20Hz band, the detection range SNR>10 for optimal orientation reached 1Gpc.) Once tagged, the signal can be determined using matched filtering of past long duration data.

14 Parameter accuracy depend on S/N ratio. Accuracy of NS-NS waveform m m % 107 [sec] T 10 SNR 1!10-3 1!10-4 T:1!10 3 [sec] T:5!10 3 [sec] T:1!10 4 [sec] 1!10-4 1!10-5 SNR:2 SNR:4 SNR:6 SNR:8 1!10-5 1!10-6!m 1!10-6 1!10-7!m 1!10-7 1!10-8 1! SNR 1!10-8 1!10-9 1!10 2 1!10 3 1!10 4 1!10 5 1!10 6 1!10 7 T[sec]

15 3.Trial of cleaning the foreground Clean up the data using tagged information for following 3 (or 10) years. extrapolate and subtruct! useable data tagged (identified) merges in following 3 years

16 Requirement of binary parameter accuracy Requirement: m m 10 7 % " 1.4 years integration for SNR=2!" #$$!" #$'!" #$&!" #$% /012345/67896:8/;<8=>9?@ / /; AB; /CB8DA98/=E86FGF:H / ; =E86F //<AI89/;<8=>9?@ //!@J@/K/!" #% /L //!@J@/K/!" #( /L //!@J@/K/!" #) /L $ ' & % ( ) * + ",! $ ' & % ( ) * +! -.

17 cleaned spectrum Since whole matched filter calculus for 10 5 binaries is very hard, we assume a priori tagged data. use oriented within 700 Mpc (all = 1Gpc) For comparison, we also test for within 900 Mpc, and for all. use merge during 3 years ( all = 10 years) give 1x10-7 % mass error (p.d.f. is gaussian.) We subtract waveform of binaries as abobe in time domain signal.

18 Cleaning result h (@6[Hz]) Using 3years data, the cleaning band is >0.2 Hz. 700Mpc cleaning only remove 30% of spectrum. (900Mpc -> 60%)

19 Remarks & More study plan We propose the idea of tagging. Numerical demonstration was done with DECIGO noise with toy model with a priori tagging of NS-NS binary signals Cleaning may possible for 0.1Hz-10Hz band. Difficulty is cleaning for so far binaries. We must study more for/with more realistic model of binary distribution include other sources (i.e. POP-III) realizing tagging process