Physics of Gravitational Waves Valeria Ferrari SAPIENZA UNIVERSITÀ DI ROMA Invisibles17 Workshop Zürich 12-16 June 2017 1 September 15th, 2015: first Gravitational Waves detection first detection:GW150914 +3.7 m1 = 29.1 4.4 M − +5.2 +0.14 m2 = 36.2 3.8 M a1,a2 = 0.06 0.14 − − − +3.7 M = 62.3 3.1 M − final BH +0.05 a = J/M =0.68 0.06 − +150 +0.03 DL = 420 180Mpc z =0.09 0.04 − − 2 SNR=23.7 radiated EGW= 3M¤c week ending PRL 116, 241103 (2016) PHYSICAL REVIEW LETTERS 17 JUNE 2016 second detection:GW151226 +2.3 m1 =7.5 2.3 M − +8.3 +0.20 m2 = 14.2 3.7 M a1,a2 =0.21 0.10 − − +6.1 M = 20.8 1.7 M FIG. 1. The gravitational-wave event GW150914 observed by the LIGO Hanford (H1, left column panels) and Livingston (L1, − right column panels) detectors. Times are shown relative to September 14, 2015 at 09:50:45 UTC. For visualization, all time series +0.06 final BH are filtered with a 35–350 Hz band-pass filter to suppress large fluctuations outside the detectors’ most sensitive frequencya band,= andJ/M =0.74 0.06 band-reject filters to remove the strong instrumental spectral lines seen in the Fig. 3 spectra. Top row, left: H1 strain. Top row, right: L1 − +0.5 +180 +0.03 strain. GW150914 arrived first at L1 and 6.9 0.4 ms later at H1; for a visual comparison the H1 data are also shown, shifted in time − DL = 440 190Mpc z =0.09 0.04 by this amount and inverted (to account for the detectors’ relative orientations). Second row: Gravitational-wave strain projected onto − − each detector in the 35–350 Hz band. Solid lines show a numerical relativity waveform for a system with parameters consistent with those recovered from GW150914 [34, 35] confirmed by an independent calculation based on [11]. Shaded areas show 90% credible regions for two waveform reconstructions: one that models the signal as a set of sine-Gaussian wavelets [36, 37] and one that models 2 the signal using binary-black-hole template waveforms [38]. These reconstructions have a 95 % overlap, as shown in [38].SNR=13.0Third radiated EGW= 1M¤c row: Residuals after subtracting the filtered numerical relativity waveform from the filtered detector time series. Bottom row: A time- frequency decompositionfor both detections the significance is > 5 σ [39] of the signal power associated with GW150914. Both plots show a signal with frequency increasing over time. 2 planation for this evolution is the inspiral of two orbiting where f and f˙ are the observed frequency and its time masses, m1 and m2, due to gravitational-wave emission. derivative and G and c are the gravitational constant and At the lower frequencies, such evolution is characterized speed of light. Estimating f and f˙ from the data in Fig. 1 by the chirp mass [44] we obtain a chirp mass of 30 M , implying that the M '> total mass M = m1 + m2 is 70 M in the detector 3/5 3 3/5 frame. This bounds the sum of the⇠ Schwarzschild radii of (m1m2) c 5 8/3 11/3 FIG. 1. GW151226= observed= by the LIGO⇡− Hanfordf − (leftf˙ column), and Livingston (right column) detectors,2 > where times are relative to M (m + m )1/5 G 96 the binary components to 2GM/c 210 km. To reach December 26, 20151 at 03:38:53.6482 UTC. First row: Strain data from the two detectors, where the data⇠ are filtered with a 30–600-Hz bandpass filter to suppress large fluctuations outside this range and band-reject filters to remove strong instrumental spectral lines [46]. Also shown (black) is the best-match template from a nonprecessing7 spin waveform model reconstructed using a Bayesian analysis [21] with the same filtering applied. As a result, modulations in the waveform are present due to this conditioning and not due to precession effects. The thickness of the line indicates the 90% credible region. See Fig. 5 for a reconstruction of the best-match template with no filtering applied. Second row: The accumulated peak signal-to-noise ratio (SNRp) as a function of time when integrating from the start of the best-match template, corresponding to a gravitational-wave frequency of 30 Hz, up to its merger time. The total accumulated SNRp corresponds to the peak in the next row. Third row: Signal-to-noise ratio (SNR) time series produced by time shifting the best-match template waveform and computing the integrated SNR at each point in time. The peak of the SNR time series gives the merger time of the best-match template for which the highest overlap with the data is achieved. The single-detector SNRs in LIGO Hanford and Livingston are 10.5 and 7.9, respectively, primarily because of the detectors’ differing sensitivities. Fourth row: Time-frequency representation [47] of the strain data around the time of GW151226. In contrast to GW150914 [4], the signal is not easily visible. from 35 Hz to a peak amplitude at 450 Hz. The signal-to- Hanford and Livingston, respectively. The time-frequency noise ratio (SNR) accumulates equally in the early inspiral representation of the detector data shows that the signal is not (∼45 cycles from 35 to 100 Hz) and late inspiral to merger easily visible. The signal is more apparent in LIGO Hanford (∼10 cycles from 100 to 450 Hz). This is different from the where the SNR is larger. The SNR difference is predomi- more massive GW150914 binary for which only the last 10 nantly due to the different sensitivities of the detectors at the cycles, comprising inspiral and merger, dominated the time. Only with the accumulated SNR from matched filtering SNR. As a consequence, the parameters characterizing does the signal become apparent in both detectors. GW151226 have different precision than those of GW150914. The chirp mass [26,45], which controls the III. DETECTORS binary’s evolution during the early inspiral, is determined very precisely. The individual masses, which rely on The LIGO detectors measure gravitational-wave strain information from the late inspiral and merger, are measured using two modified Michelson interferometers located in far less precisely. Hanford, WA and Livingston, LA [2,3,46]. The two Figure 1 illustrates that the amplitude of the signal is less orthogonal arms of each interferometer are 4 km in length, than the level of the detector noise, where the maximum strain each with an optical cavity formed by two mirrors acting as 0.7 −22 0.8 −22 of the signal is 3.4−þ0.9 × 10 and 3.4−þ0.9 × 10 in LIGO test masses. A passing gravitational wave alters the 241103-2 week ending PRL 118, 221101 (2017) PHYSICAL REVIEW LETTERS 2 JUNE 2017 5 calibration uncertainties for strain data in both detectors for the times used in this analysis are better than 5% in third candidate: LVT151012 2σ 3σ 4σ 5σ > 5σ 2σ3σ 4σ 5σ > 5σ amplitude and 3° in phase over the frequency range 20– 2σ 3σ 4σ 5σ > 5σ +4 104 104 2σ 3σ 4σ 5σ > 5σ m1 = 13 5 M 1024 Hz. − 3 Search Result 3 Search Result +18 +0.3 10 At the time of GW170104, both LIGO detectors were 10 m2 = 23 6 M a1,a2 =0.0 0.2 2 Search Background Background including all search results − − 10 102 +14 operating with sensitivityBackground excluding typical of GW150914 the observing run to Background excluding only GW150914 M = 35 4 M 101 1 − date and were in an observation-ready state. Investigations 10 +0.09 0 0 a = J/M =0.66 0.10 10 10 − similar to the detection validation procedures for previous +0.5 +0.09 10 1 10 1 DL =1 0.5Gpc z =0.20 0.09 events− [2,14] found no evidence that instrumental or − − − 2 LV T 1 5 1 0 1 2 2 10− 10 environmental disturbances contributed to GW170104.GW150914 − GW150914 10 3 3 the significance is ≤ 2 σ − 10− 10 4 10 4 − III. SEARCHES − 5 5 Number of events 10 Number of events − 10− 10 6 GW170104 was first identified by inspection of low- 6 − 10− 10latency7 triggers from Livingston data [15 17]. An auto- 7 − – 10− 10mated8 notification was not generated as the Hanford 8 Third detection :GW170104 − 10− detector8 10’s calibration12 14 state16 was18 temporarily20 22 set incorrectly24 10 20 30 40 50 60 70 80 90 Detection statistic ρˆc Detection statistic ln in the low-latency system. After it was manually deter- L mined that the calibration2σ 3σ 4 ofσ both5σ detectors> was5σ in a 2σ 3σ 4σ 5σ 4 2σ 3σ 4σ 5σ > 5σ 2σ 3σ 4σ 5σ 10nominal state,+5 an.3 alert with anSNR= initial 13 source localization 104 m1 = 19.4 5.9 M 10[18,19]3 was distributed− toSearch collaborating Result astronomers [20] 103 Search Result m = 31.2+8.4 M Background excluding GW150914 Background excluding only GW150914 10for2 the2 purpose6 of.0 searching for a transient counterpart. 102 − Background excluding Background excluding 1 2 1 10About 30 groups of observersGW150914radiated covered and GW151226 E theGW parts = 2 M of☉ the c sky 10 GW150914 and GW151226 10localization0 using+5.7 ground- and space-based instruments, 100 M = 48.7 4.6 M 10spanning1 from−γ ray to radio frequencies as well as high-10 1 − a = J/M =0.64+0.09 − 2 0.20 2 10energy− neutrinos [21]−. 10 +450 +0GW151226.08 − GW151226 10 3 OfflineDL = analyses 880 390Mpc are used to z determine=0.18 0.07 the significance of 3 − − − 10− 10 4 4 candidate− events.