Searching for the signal and explanation of the GW event with balanced equations of motion

Transcription

1 Searching for the signal and explanation of the GW event with balanced equations of motion Osvaldo M. Moreschi collaborators in dierent parts of this program: Emanuel Gallo & José Nieva Facultad de Matemática Astronomía, Física y Computación (FaMAF) Universidad Nacional de Córdoba, Instituto de Física Enrique Gaviola (IFEG), CONICET, Ciudad Universitaria, (5000) Córdoba, Argentina IV CosmoSul; July 31-August 2, 2017 O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW150914IVevent CosmoSul with balanced 1 / 46 equ

2 Content 1 Introduction 2 New analysis to the GW LIGO signals The whitening procedures Observed data with LIGO lters Filtering without whitening Observed data with new lters 3 The balanced equation of motion approach Presentation Basic assumptions of our models The general form of the equation of motion The equation of motion in the harmonic gauge Radiation force in the harmonic gauge Composite equations of motion Crude calculation with the composite model 4 Final comments O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW150914IVevent CosmoSul with balanced 2 / 46 equ

3 Content 1 Introduction 2 New analysis to the GW LIGO signals The whitening procedures Observed data with LIGO lters Filtering without whitening Observed data with new lters 3 The balanced equation of motion approach Presentation Basic assumptions of our models The general form of the equation of motion The equation of motion in the harmonic gauge Radiation force in the harmonic gauge Composite equations of motion Crude calculation with the composite model 4 Final comments O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW150914IVevent CosmoSul with balanced 3 / 46 equ

4 Introduction: I Gravitational waves have been detected [Abbott et al.(2016)] We have the rst observed signal, which we must use to describe the astrophysical system and test our understandings. We present recent advances in our program for constructing balanced equations of motion for compact objects in GR. The explicit form of the back reaction gravitational radiation force is presented for the harmonic gauge. The GW LIGO signals are analyzed with a minimal set of ltering to give light on possible hidden physical information. We apply the composite equations of motion model to these type of systems and argue that our tools could help in studying new points of view on the nature of the astrophysical systems that generated those signals. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW150914IVevent CosmoSul with balanced 4 / 46 equ

5 Content 1 Introduction 2 New analysis to the GW LIGO signals The whitening procedures Observed data with LIGO lters Filtering without whitening Observed data with new lters 3 The balanced equation of motion approach Presentation Basic assumptions of our models The general form of the equation of motion The equation of motion in the harmonic gauge Radiation force in the harmonic gauge Composite equations of motion Crude calculation with the composite model 4 Final comments O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW150914IVevent CosmoSul with balanced 5 / 46 equ

6 New analysis to the GW LIGO signals I This is the Amplitude Spectral Density (ASD) of both LIGO strains for the lapse of 4096s around the GW event. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW150914IVevent CosmoSul with balanced 6 / 46 equ

7 New analysis to the GW LIGO signals II The whitening procedures This is how the original LIGO whitening procedure looks like in the Amplitude Spectral Density (ASD). O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW150914IVevent CosmoSul with balanced 7 / 46 equ

8 New analysis to the GW LIGO signals III This is our whitening procedure with a normalization that preserves the units. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW150914IVevent CosmoSul with balanced 8 / 46 equ

9 New analysis to the GW LIGO signals IV This is another version of the whitening procedure using a Chebyshev window. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW150914IVevent CosmoSul with balanced 9 / 46 equ

10 New analysis to the GW LIGO signals V This is another version of the whitening procedure using a Blackman window. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 10 / 46 equ

11 New analysis to the GW LIGO signals VI Observed data with LIGO lters This is how the observed data looks like after LIGO whitening lters are applied[abbott et al.(2016)]; using data sampled at 2048Hz. Notice how the signal is attenuated before 0.1s of the event time. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 11 / 46 equ

12 New analysis to the GW LIGO signals VII One can see that the lapse of time very close to the time of the event is emphasized by this type of ltering. This is related to the physical picture they have in mind, namely: This is extracted from the same publication, in which they remark that no eccentricity is considered. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 12 / 46 equ

13 New analysis to the GW LIGO signals VIII Filtering without whitening Suppose that there is signicant signals at low frequencies. In that case, the whitening procedure will wash away these physically interesting information of the observed data. This suggests to consider a more delicate ltering procedure in which one gets rid of the unwanted noise by a selective lter scheme. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 13 / 46 equ

14 New analysis to the GW LIGO signals IX Initial smooth pass band lter of H1 data around the GW event. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 14 / 46 equ

15 New analysis to the GW LIGO signals X ASD of the H1 strain after applying selective narrow stopband lters to suppress the intrinsic noise of the instrument. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 15 / 46 equ

16 New analysis to the GW LIGO signals XI ASD of the L1 strain after applying initial smooth pass band lter and selective narrow stopband lters to suppress the intrinsic noise of the instrument. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 16 / 46 equ

17 New analysis to the GW LIGO signals XII In our analysis we have applied: an initial smooth pass band lter (to hide unphysical high and low frequency noise) narrow stop band lters (to suppress the intrinsic noise of the instrument) nal sharp low pass lter at 1024Hz (respecting LIGO high frequency bound) nal sharp carefully chosen high pass lter (to allow for possible low frequency signal) This is a minimum type of ltering that respects possible high an low frequency physical interesting information encoded in the observed data. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 17 / 46 equ

18 New analysis to the GW LIGO signals XIII Observed data with new lters Signal after our ltering is applied with new relative shift of s, using data sampled at 8192Hz. They only considered the yellow shaded region of data for the analysis and used a shift of s. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 18 / 46 equ

19 New analysis to the GW LIGO signals XIV Template (chosen by LIGO) over minimum ltered signal in the region considered by LIGO. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 19 / 46 equ

20 New analysis to the GW LIGO signals XV We claim that there is physically interesting data at least in the previous 0.5s interval. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 20 / 46 equ

21 New analysis to the GW LIGO signals XVI We clean the signal with a low pass lter at 350Hz, and show the interesting data in the shaded green region. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 21 / 46 equ

22 New analysis to the GW LIGO signals XVII Let us remark that in the previous graph one nds: The proposed physical signal is very closed to the time of the event. The proposed physical signal matched perfectly in phase with the theoretical calculation proposed by LIGO people. The proposed physical signal matched perfectly in amplitude with the theoretical calculation proposed by LIGO. The proposed physical signal matched perfectly in frequency for about six cycles with the theoretical calculation proposed by LIGO. Many previous techniques designed to deal with very bad signal to noise ratios, can now be adapted to the new generation of observatories taking into account the new sensitivities of the interferometers and the details of their intrinsic generated noise. New views to the data might give new interpretations on the astrophysical parameters of the observations of the binary system. Common assumptions in the theoretical calculations might need to be revised, as for example the general use of very low (zero) eccentricity. Common assumptions in the numerical calculations might need to be revised. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 22 / 46 equ

23 New analysis to the GW LIGO signals XVIII This can also be seen in the following spectrogram in the time region of interest. It can be seen that there is a strong coincidence of the two detectors in the approximate lapse of time [-0.5, -0.2]s prior to the event time. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 23 / 46 equ

24 New analysis to the GW LIGO signals XIX Are there other indications for the existence of more physically interesting signals at earlier times? We have also made a brief study of a notion of likelihood of having the same unknown signal in both detectors. The above graph shows such quantity for a particular chosen window length. One can see that for a 0.5s window, the peak is close to the time of the event and above the other local peaks. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 24 / 46 equ

25 New analysis to the GW LIGO signals XX Taking a look in more detail, one can see that for a 0.5s window, the peak is about at -0.25s; which gives support for the existence of physical signal up to -0.5s of the time of the event. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 25 / 46 equ

26 Content 1 Introduction 2 New analysis to the GW LIGO signals The whitening procedures Observed data with LIGO lters Filtering without whitening Observed data with new lters 3 The balanced equation of motion approach Presentation Basic assumptions of our models The general form of the equation of motion The equation of motion in the harmonic gauge Radiation force in the harmonic gauge Composite equations of motion Crude calculation with the composite model 4 Final comments O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 26 / 46 equ

27 The balanced equation of motion approach I Presentation Equations of motion have been studied in dierent frameworks, as for example the PostNewtonian and the self-force approaches. Our program involves the idea of obtaining the equations of motion from the requirement of balanced of the radiated momentum. Therefore our approach diers conceptually and in the algebra to the two previous mentioned approaches. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 27 / 46 equ

28 The balanced equation of motion approach II The directions of our study: 1 There is a general framework that it can be described previous to any reference to specic eld equations and/or gauge selection. The form of the general equation of motion can be expressed at this stage 2 We are studying the approach in the harmonic gauge. We have calculated the details of the radiation eld. We have recently calculated the explicit form of the radiation force term; that we use in this presentation. 3 We are studying the approach in the null gauge. We have calculated the radiation eld. 4 In order to be able to test the basics of the back reaction ideas we have constructed the composite model, which combines the conservative terms of the PostNewtonian calculations with the radiation force term, we have calculated in the harmonic gauge. We show here preliminary results using this model. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 28 / 46 equ

29 The balanced equation of motion approach III Basic assumptions of our models In the construction of our model we have in mind the shortcomings of the other approaches and therefore we do not restrict to small velocities or weak elds. It is the intention to provide with a spacetime that can appropriately represent a system of compact objects; with a dynamics that takes into account the back reaction due to gravitational radiation, and with a complete asymptotic region, where all the total physical quantities can be calculated without ambiguities. Minimum requirement to the model for compact objects: 1 It is an approximate solution of Einstein equations. 2 The model presents a single spacetime description (M, g ab ) of the system. 3 The spacetime (M, g ab ) is asymptotically at at future null innity. 4 Each compact object satises an equation of motion that takes into account the back reaction due to gravitational radiation, at the appropriate retarded time of (M, g ab ). O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 29 / 46 equ

30 The balanced equation of motion approach IV η ~ ab η ab This sketch depicts the global spacetime of the model, in which the black lines at 45 degrees represent future null innity, with one of an innite possible set of at asymptotic metrics η ab. The world line of each compact object is represented in color lines, gravitational radiation is represented by the blue arrows, and the internal at background metric is denoted by η ab. One of the diculties in this subject is how to relate η ab with an appropriate η ab. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 30 / 46 equ

31 The balanced equation of motion approach V The general form of the equation of motion With this geometry one can calculate the time derivative of the total momentum at future null innity; which is related to the instantaneous momentum ux F µ with V respect to the time u by dp µ du = 1 l 0 µ 4π Ṽ σ 0 σ 0 ds 2 = F µ ; (1) V S where σ 0 is the leading order behavior of the σ GHP spin coecient. Using the value of the radiation eld presented above one can dene the back reaction force F 0 by F µ 0 = 1 l 0 µ 4π V0 σ 0 σ 0 ds 2 ; (2) S where V 0 = ũ τ 0, and write the equation of motion as ( M A v a a v b + γ b a c v a v c ( 1 du ) d dτ 0 2 u dτ 2 0 v b + ( du ) ) b w v (τ 0) = ( du ) µ F dτ 0 dτ 0. (3) 0 O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 31 / 46 equ

32 The balanced equation of motion approach VI From the contraction in the direction of v one obtains: M A ( ( 1 du ) d dτ 0 2 u dτ 2 0 and one also has the equation + γ b a c v a v c η bd v d + ( du ) ) w = ( du ) b F0 η bd v d ; (4) dτ 0 dτ 0 M A v a av b = M A a b + ( du dτ 0 ) F d 0 ( η b d v d v b) ; (5) where we have used the denition for the acceleration vector a b as the component of the acceleration vector which is orthogonal to v, namely: a b γ d a c v a v c( η b d v d v b). (6) It is curious that this general form of the equation of motion can be derived[gallo and Moreschi(2016)] from our basic assumptions, before determining the specic eld equations and previous to the xing of a particular gauge. It is only required the validity of the linear structure of the Hilbert-Einstein eld equations. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 32 / 46 equ

33 The balanced equation of motion approach VII Our general discussion[gallo and Moreschi(2016)] also indicates that these equations of motion must be calculated in the rest frame of the system. This in turn forces to make a link between the notion of rest frame and center of mass in the interior and in the asymptotic region[moreschi and Dain(1998)] (O.M. Moreschi and S. Dain, Rest frame system for asymptotically at space-times, J. Math. Phys., 39, 12, , 1998), [Moreschi(2004)] (O.M. Moreschi, Intrinsic angular momentum and center of mass in general relativity, Class.Quantum Grav., 21, , 2004), [Gallo and Moreschi(2014)] (E. Gallo and O.M. Moreschi, Intrinsic angular momentum for radiating spacetimes which agrees with the Komar integral in the axisymmetric case, Phys.Rev., D89, , 2014). The equation of motion in the harmonic gauge For a particle of mass M A and velocity eld v a, the rst order solution in the harmonic gauge is h (1) = 4M v av b 1 2 η ab ab A ; (7) r so that one has ( g (1) (A) = 1 + 2M ) A η ab ab 4M A v av b. (8) r r O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 33 / 46 equ

34 The balanced equation of motion approach VIII In these equations we have considered the denition v a η ab v b ; however it should be emphasized that the vector v b is not normalized with the at metric η but with g B. Expressing the leading order behavior of the radiation eld σ in terms of the dynamical time τ 0, one has ( σ 0 Υ 2 ( dvη ) dτ = 4M A ð 0 0 ð 0V η + Υ V η V η V η Radiation force in the harmonic gauge dυ dvη dτ 0 ) 2 1 dτ ( ð 0V η 0 Υ 2 V η 2 V η Vη 2 ( ð 0V η) ). 2 (9) With the previous information one can calculate the explicit expression for the radiation force in the harmonic gauge, in terms of the usual dynamical variables. ( F0 i = 4M2 A Υ 4 Γ 5 a0( a i 0 v) ( 8v 2) ( Γ 2 v0 i ( a 0 v) 2 Γ 6( 6 6v v 4 2v 8) 35 (10) + 10Γ 4 a 0 2 v 2 ) ). O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 34 / 46 equ

35 The balanced equation of motion approach IX Composite equations of motion The calculation of the complete balanced equations of motion for a binary system in the harmonic gauge is intricate, since in particular involves retarded eects that should be calculated without approximation. In the meantime, in order to obtain some preliminary results, we propose the composite equations of motion model, which consists in using the advances made in postnewtonian works, in which the conserved part of the equations of motion are calculated at high orders, and supplement them with our calculation of the dissipative radiation force. We use the equations as presented in [Blanchet(2014)]; since they are complemented by the conserved quantities calculated in [de Andrade et al.(2001)de Andrade, Blanchet, and Faye]. This allows for easy checking of the numerical codes. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 35 / 46 equ

36 The balanced equation of motion approach X The accelerations of the black holes is given in this model by: a 0 = a BN + 4M A Υ 4 Γ 3( ) ( du dτ 0 a BN ( a BN v) ( 8v 2) 35 ( v ( a BN v) 2( v v v v 8) (11) + 10 a BN 2 (v 2 + 2v 4 + 2v 6 )) ) ; where a BN is the expression for the conservative postnewtonian acceleration; which we have considered up to the 3PN order. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 36 / 46 equ

37 The balanced equation of motion approach XI Crude calculation with the composite model Although our models for the dynamics of black holes intend to supply a new tool that extend beyond the limitations of previous approaches; in this occasion, in order to be able to carry out some preliminary calculations, we recur to the composite model. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 37 / 46 equ

38 The balanced equation of motion approach XII An example of our crude composite model (green) and the numerical relativity calculation, for qualitative analysis. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 38 / 46 equ

39 The balanced equation of motion approach XIII O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 39 / 46 equ

40 The balanced equation of motion approach XIV In this preliminary calculation in the composite model we have used initial data corresponding to: m 1 = 52M and m 2 = 13M (same initial total mass as suggested by LIGO papers) Keplerian elements: a = 6total mass, e = 0.08 Although we use a dierent mass ration, the main dierence is that we consider a non-zero initial eccentricity. Only 8 of the more than 300 numerical calculations presented in are in the range of the eccentricity we have considered; the rest are smaller O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 40 / 46 equ

41 Content 1 Introduction 2 New analysis to the GW LIGO signals The whitening procedures Observed data with LIGO lters Filtering without whitening Observed data with new lters 3 The balanced equation of motion approach Presentation Basic assumptions of our models The general form of the equation of motion The equation of motion in the harmonic gauge Radiation force in the harmonic gauge Composite equations of motion Crude calculation with the composite model 4 Final comments O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 41 / 46 equ

42 Final comments I We have presented a new look to the GW LIGO data that suggests that there is more physically interesting data than the one used by the LIGO Scientic Collaboration. The astrophysical system might actually include non-trivial eccentricity. Our better understanding of the problem of balanced equations of motions has allowed us to treat in a unied way the problem for dierent gauge choices[gallo and Moreschi(2016)]. We have presented the explicit force and balanced equations of motion in the harmonic gauge. The composite balanced equations of motion model has been used in preliminary studies of binary systems with data similar to that of the GW LIGO event. We plan to use our models in the harmonic and null gauge settings to study in detail these types of binary systems. It is unlikely that the same techniques can be applied to the new reported event GW170104; since it has a much worse signal to noise ratio. O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 42 / 46 equ

43 Final comments II I am especially grateful to LIGO people who kept the observed data available to us. Thank you all! O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 43 / 46 equ

44 Bib I Virgo, LIGO Scientic Collaboration, B. P. Abbott et al., Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett. 116 (2016), no. 6, , arxiv: E. Gallo and O. M. Moreschi, Constructing balanced equations of motion for particles in general relativistic theories: the general case, arxiv: O. M. Moreschi and S. Dain, Rest frame system for asymptotically at space-times, J. Math. Phys. 39 (1998), no. 12, O. M. Moreschi, Intrinsic angular momentum and center of mass in general relativity, Class.Quantum Grav. 21 (2004) E. Gallo and O. M. Moreschi, Intrinsic angular momentum for radiating spacetimes which agrees with the Komar integral in the axisymmetric case, Phys.Rev. D89 (2014) , arxiv: L. Blanchet, Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries, Living Rev. Rel. 17 (2014) 2, arxiv: O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 44 / 46 equ

45 Bib II V. C. de Andrade, L. Blanchet, and G. Faye, Third postnewtonian dynamics of compact binaries: Noetherian conserved quantities and equivalence between the harmonic coordinate and ADM Hamiltonian formalisms, Class.Quant.Grav. 18 (2001) , arxiv:gr-qc/ Virgo, LIGO Scientic Collaboration, B. P. Abbott et al., Properties of the Binary Black Hole Merger GW150914, Phys. Rev. Lett. 116 (2016), no. 24, , arxiv: O. M. (FaMAF, IFEG) Searching for the signal and explanation of the GW IV CosmoSul event with balanced 45 / 46 equ