Whelan for LSC & ALLEGRO: prelim LIGO-ALLEGRO SB results LIGO-G060605-04-Z p.1 Preliminary Results of LIGO-ALLEGRO Stochastic Background Search John T. Whelan john.whelan@ligo.org on behalf of the LIGO Scientific Collaboration and the ALLEGRO Group 10th Gravitational Wave Data Analysis Workshop 2006 December 20 LIGO-G060605-04-Z
Whelan for LSC & ALLEGRO: prelim LIGO-ALLEGRO SB results LIGO-G060605-04-Z p.2 Outline I Background/Motivation for LLO-ALLEGRO Search • LLO-ALLEGRO Pair (proximity, overlap modulation) • Technical Considerations (sampling, heterodyning) II S4 Data Analysis • Data Volume by Orientation • Validation: Software & Hardware Injections • Preliminary Cross-Correlation Results • Statistical Interpretation: Upper Limit
Whelan for LSC & ALLEGRO: prelim LIGO-ALLEGRO SB results LIGO-G060605-04-Z p.3 Sensitivity to Stochastic GW Backgrounds • Optimally filtered CC statistic � s ∗ 1 ( f ) � Y = d f � Q ( f ) � s 2 ( f ) � �� � Y ( f ) Q ( f ) ∝ S gw( f ) γ 12 ( f ) • Optimal filter � P 1 ( f ) P 2 ( f ) (Initial analyses assume S gw ( f ) or Ω gw ( f ) ∝ f 3 S gw ( f ) constant across band) • Optimally filtered cross-correlation method has Ω gw sensitivity � � − 1 / 2 � d γ 2 f 12 ( f ) σ Ω ∝ T f 6 P 1 ( f ) P 2 ( f ) • Significant contributions when – detector noise power spectra P 1 ( f ), P 2 ( f ) small – overlap reduction function γ 12 ( f ) (geom correction) near ± 1
Whelan for LSC & ALLEGRO: prelim LIGO-ALLEGRO SB results LIGO-G060605-04-Z p.4 Overlap Reduction Function 1 0.8 0.6 LLO−LHO LLO−ALLEGRO (N72 ° E) "XARM" 0.4 LLO−ALLEGRO (E72 ° S) "YARM" 0.2 LLO−ALLEGRO (N27 ° E) "NULL" 0 −0.2 −0.4 −0.6 −0.8 −1 0 100 200 300 400 500 600 700 800 900 1000 Frequency (Hz) LLO-ALLEGRO only ∼ 40 km apart − → still sensitive @ 900 Hz Response different for XARM, YARM, NULL orientations ALLEGRO ran in all 3 orientations during LIGO S4 Run (2005 Feb 22-Mar 23)
Whelan for LSC & ALLEGRO: prelim LIGO-ALLEGRO SB results LIGO-G060605-04-Z p.5 LLO-ALLEGRO: Technical Considerations • LIGO data digitally downsampled 16384 Hz → 4096 Hz ALLEGRO data heterodyned at 904 Hz & sampled at 250 Hz • Heterodyning means CC stat complex: � f max s ∗ 1 ( f ) � Y = Q ( f ) � s 2 ( f ) d f � f min real part Gaussian-distributed about SGWB strength; imag part Gaussian-distributed about 0. • Differently-sampled data correlated in freq domain → Method written up in CQG 22 , S1087 (2005)
Whelan for LSC & ALLEGRO: prelim LIGO-ALLEGRO SB results LIGO-G060605-04-Z p.6 LLO-ALLEGRO data from LIGO S4 Run • ∼ 10% of data set aside as “playground”; co ¨ ınc Non-PG data surviving DQ vetoes divided into 60s segs; Incoherent stationarity cut applied to reject segs where sensitivity changing too rapidly (need stationarity for well-behaved optimal filter) • Non-playground data in 3 orientations: – “NULL” (0 . 023 < γ ( f ) < 0 . 029): 88 . 2 hr after cuts “off-source” data useful for data quality & cross-checks – “YARM” ( − 0 . 89 > γ ( f ) > − 0 . 91): 114 . 7 hr after cuts – “XARM” (0 . 95 < γ ( f ) < 0 . 96): 181 . 2 hr after cuts
Whelan for LSC & ALLEGRO: prelim LIGO-ALLEGRO SB results LIGO-G060605-04-Z p.7 Avg Calibrated ASD from S4 non−NULL non−PG −18 10 ALLEGRO ASD LLO ASD Spectrum for Ω gw (f)=1 −19 10 −20 10 Strain (Hz −1/2 ) −21 10 −22 10 −23 10 850 860 870 880 890 900 910 920 930 940 950 Frequency (Hz) Frequency band determined by ALLEGRO noise curve
Whelan for LSC & ALLEGRO: prelim LIGO-ALLEGRO SB results LIGO-G060605-04-Z p.8 Sensitivity Integrand from S4 non−playground data 2 1.8 1.6 Sensitivity Integrand (arb units) 1.4 1.2 1 0.8 0.6 0.4 0.2 0 850 860 870 880 890 900 910 920 930 940 950 Frequency (Hz) Most of sensitivity from 905–925 Hz
Whelan for LSC & ALLEGRO: prelim LIGO-ALLEGRO SB results LIGO-G060605-04-Z p.9 Software Injections into S4 Playground • Combined 90% error bars for all playground data ∼ 2 • Inject simulated signals of strength Ω R = 1 . 9, 3.9, 9.6, 19. • Note: individual jobs have error bars around 120. SW injections only detectable over time.
Whelan for LSC & ALLEGRO: prelim LIGO-ALLEGRO SB results LIGO-G060605-04-Z p.10 Stats w/ & w/o SW Inj (19 60-sec segs) no injection Re(Y/T) 400 Im(Y/T) 1−minute Ω R estimate 200 0 −200 −400 0 2 4 6 8 10 12 14 16 18 20 Segment Number Ω R =19.2901 injection Re(Y/T) 400 1−minute Ω R estimate Im(Y/T) 200 0 −200 −400 0 2 4 6 8 10 12 14 16 18 20 Segment Number Injecting Ω( f ) = 19 . 3 has negligible impact on minute-by-minute correlations
Whelan for LSC & ALLEGRO: prelim LIGO-ALLEGRO SB results LIGO-G060605-04-Z p.11 Stats w/ & w/o SW Inj (19 60-sec segs) no injection Re(Y/T) 400 Im(Y/T) 1−minute Ω R estimate 200 0 −200 −400 0 2 4 6 8 10 12 14 16 18 20 Segment Number Ω R =192.9012 injection Re(Y/T) 400 Im(Y/T) 1−minute Ω R estimate 200 0 −200 −400 0 2 4 6 8 10 12 14 16 18 20 Segment Number Compare Ω( f ) = 193 injection, which is visible minute-by-minute
Whelan for LSC & ALLEGRO: prelim LIGO-ALLEGRO SB results LIGO-G060605-04-Z p.12 ALLEGRO software injections (90% errorbars) 25 real imag 20 15 Ω detected 10 5 0 −5 −5 0 5 10 15 20 25 Ω injected Ω( f ) = 3 . 9, 9.6, 19 injections recovered from full PG (Ω( f ) = 1 . 9 just at threshold of detectability) Note: injected same random signals w/different amplitudes into same noise
Whelan for LSC & ALLEGRO: prelim LIGO-ALLEGRO SB results LIGO-G060605-04-Z p.13 S4 Hardware Injections • 1024-second simulated signals injected into LLO & ALLEGRO hardware a total of nine times. Simulated all three orientations. • One “round” of three injections had non-const Ω gw ( f ) • Other two rounds (“A” & “B”) injected const Ω gw ( f ) = 8100 − → Focus on those • Sensitivity of cross-correlation to injections simulating XARM (“plus”) and YARM (“minus”) is comparable • “null” injection less correlated b/c of simulated misalignment
Whelan for LSC & ALLEGRO: prelim LIGO-ALLEGRO SB results LIGO-G060605-04-Z p.14 Extraction of Hardware Injections A−minus A−plus A−null 8000 B−minus B−plus B−null injected 4000 Im(Point Estimate) 0 −4000 −8000 −4000 0 4000 8000 12000 16000 20000 24000 Re(Point Estimate) Circles: 90% statistical uncertainty (null measurements less sensitive) 90% dashed calib uncertainty “teardrop” around Ω R = 8100 HW injections recovered consistent w/cal uncertainty
Whelan for LSC & ALLEGRO: prelim LIGO-ALLEGRO SB results LIGO-G060605-04-Z p.15 Extraction of Hardware Injections A−minus A−plus A−null 8000 B−minus B−plus B−null injected 4000 Im(Point Estimate) 0 −4000 −8000 −4000 0 4000 8000 12000 16000 20000 24000 Re(Point Estimate) Circles: 90% statistical uncertainty (null measurements less sensitive) 90% dashed calib uncertainty “teardrop” around Ω R = 8100 HW injections recovered consistent w/cal uncertainty Zoom in on blue box . . .
Whelan for LSC & ALLEGRO: prelim LIGO-ALLEGRO SB results LIGO-G060605-04-Z p.16 Extraction of Hardware Injections 800 A−minus A−plus A−null B−minus B−plus 400 B−null injected Im(Point Estimate) 0 −400 −800 6800 7200 7600 8000 8400 8800 Re(Point Estimate) Circles: 90% statistical uncertainty 90% dashed calib uncertainty “teardrop” around Ω R = 8100 Systematic offset < cal uncertainty
Whelan for LSC & ALLEGRO: prelim LIGO-ALLEGRO SB results LIGO-G060605-04-Z p.17 S4 Preliminary Cross-Correlation Results Optimally filter looking for const Ω gw ( f ) ≡ Ω R Assume H 0 = 72 km / s / Mpc (so Ω R = h 2 72 Ω gw ( f )) Analyzed non-playground data w/overlapping 60-sec Hann windows: Ω R Type T eff (hrs) Point Estimate Error Bar XARM 181.2 0 . 61 + 0 . 25 i 0.56 YARM 114.7 − 0 . 47 + 0 . 47 i 0.90 non-NULL 295.8 0 . 31 + 0 . 31 i 0.48 NULL 88.2 10 . 96 − 43 . 89 i 28.62 all 384.1 0 . 31 + 0 . 30 i 0.48 No correlation observed − → Convert CC meas of 0 . 31 + 0 . 30 i & theor errorbar of 0.48 into upper limit . . .
Whelan for LSC & ALLEGRO: prelim LIGO-ALLEGRO SB results LIGO-G060605-04-Z p.18 Constructing Bayesian Posterior PDF • Formal prior on Ω gw (915 Hz) from Explorer-Nautilus: uniform on [0 , 115] • Marginalize likelihood fcn over calibration uncertainty: L1 5% amp, 2 ◦ phase; A1 10% amp, 3 ◦ phase. (Assume Gaussian prior in ln(amp) and phase.)
Whelan for LSC & ALLEGRO: prelim LIGO-ALLEGRO SB results LIGO-G060605-04-Z p.19 Posterior PDF & 90% conf band from all non−PG data 2.5 2 1.5 Posterior PDF 1 0.5 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Ω R � S gw (915 Hz) < 1 . 5 × 10 − 23 Hz − 1 / 2 prelim 90% CL UL: Ω R < 1 . 02 i.e., 100 × improvement on Ω gw (907 Hz) < 115 [ h 2 100 Ω gw (907 Hz) < 60] from NAUTILUS-EXPLORER [Astone et al., A & A 351 , 811 (1999)]
Recommend
More recommend
