On the detection of gravitational waves by the Laser Interferometer Gravitational-Wave Obsevatory (LIGO)

The direct detection of gravitational waves is one of those events long-expected by physicists that are nevertheless a significant occurrence which excites the world scientific community as if something unexpected has happened. The event that happened on September 14, 2015 was not kept in utmost secrecy; however, everybody was waiting for the press conference that took place on February 11, 2016

(the link can be found, e.g., here ) and, most importantly, the paper. Many rumors leaked ahead of the conference, and the fact that something (that is, a signal corresponding to gravitational waves) was discovered by LIGO (Laser Interferometer Gravitational-Wave Observatory) was discussed on the sidelines. The details of the observations and data analysis by the LIGO collaboration (over 1000 people) became available on the arXiv server on February 12, 2016. These papers, including the technical ones, are listed below:

• The LIGO Scientific Collaboration, the Virgo Collaboration. Astrophysical Implications of the Binary Black-Hole Merger GW150914. ApJL, 818, L22, 2016. arXiv:1602.03846
• B. P. Abbott, R. Abbott, T. D. Abbott, et al. The Rate of Binary Black Hole Mergers Inferred from Advanced LIGO Observations Surrounding GW150914. arXiv:1602.03842
• The LIGO Scientific Collaboration, the Virgo Collaboration. GW150914: Implications for the stochastic gravitational wave background from binary black holes. arXiv:1602.03847
• The LIGO Scientific Collaboration: B. P. Abbott, et al. Calibration of the Advanced LIGO detectors for the discovery of the binary black-hole merger GW150914. 1602.03845
• The LIGO Scientific Collaboration, the Virgo Collaboration. Characterization of transient noise in Advanced LIGO relevant to gravitational wave signal GW150914. arXiv:1602.03844
• The LIGO Scientific Collaboration, the Virgo Collaboration. Observing gravitational-wave transient GW150914 with minimal assumptions. 1602.03843
• The LIGO Scientific Collaboration, the Virgo Collaboration. Properties of the binary black hole merger GW150914. arXiv:1602.03840
• The LIGO Scientific Collaboration, the Virgo Collaboration. GW150914: First results from the search for binary black hole coalescence with Advanced LIGO. arXiv:1602.03839
• The LIGO Scientific Collaboration, the Virgo Collaboration. GW150914: The Advanced LIGO Detectors in the Era of First Discoveries. arXiv:1602.03838
• The LIGO Scientific Collaboration, the Virgo Collaboration. Observation of Gravitational Waves from a Binary Black Hole Merger. Physical Review Letters 116, 061102 (2016), arXiv:1602.03837.

At the same time, papers by authors who, apparently, expected this day knowing about the LIGO results, appeared on arXiv:

• P.A. Evans, J.A. Kennea, S.D. Barthelmy, et al. Swift follow-up of the Gravitational Wave source GW150914. To be submitted to MNRAS letters. arXiv:1602.03868
• I.Bartos, B.Kocsis, Z.Haiman, S.Marka. Rapid and Bright Stellar-mass Binary Black Hole Mergers in Active Galactic Nuclei. arXiv:1602.03831
• J. J. Eldridge, E. R. Stanway. BPASS predictions for Binary Black-Hole Mergers. Submitted to MNRAS. arXiv:1602.03790
• T.L. Campante, I.Lopes, D.Bossini, et al. Asteroseismology of red-giant stars as a novel approach in the search for gravitational waves. Submitted to Astronomy in Focus, to appear in the Proc. IAU XXIX GA. arXiv:1602.03667
• J. P. W. Verbiest, L. Lentati, et al. The International Pulsar Timing Array: First Data Release. Accepted for publication in MNRAS. arXiv:1602.03640
• Maurice H.P.M. Van Putten. Directed searches for broadband extended gravitational-wave emission in nearby energetic core-collapse supernovae. To appear in ApJ. arXiv:1602.03634
• R. Ruffini, J. A. Rueda, M. Muccino, et al. On the rate and on the gravitational wave emission of short and long GRBs. arXiv:1602.03545
• E.Calabrese, N.Battaglia, D.N. Spergel. Testing Gravity with Gravitational Wave Source Counts. (Comments: Comments welcome, congratulations to the LIGO team) arXiv:1602.03883
• M.A.Resco, A. de la Cruz-Dombriz, F.J. Llanes Estrada, et al. On neutron stars in f(R) theories: small radii, large masses and large energy available for emission in a merger. arXiv:1602.03880

 

We can note the FERMI collaboration preprint (V. Connaughton, E. Burns, A. Goldstein, Fermi GBM Observations of LIGO Gravitational Wave event GW150914. ) which was not posted to arXiv at the time [ the paper appeared on arXiv on February 15, 2016: arXiv:1602.03920. ]. Also, several important popular-science comments from physicists and astrophysicists appeared on the RuNet during the first three days, and some even earlier (we list only a few of them here):

• Postnauka website:
  1) K. Postnov Gravitational waves: research history and the LIGO discovery.
  2) S. Popov, E. Akhmedov, V. Rubakov, A. Zasov. Point of view: What will the discovery of gravitational waves change?
• Elementy.ru website:
  1) I. Ivanov. Gravitational waves - discovered! , and numerous links at the end of the article.
  2) Discussion on the "Science 2.0" TV channel (video). A. Semikhatov and K. Postnov.
• "Troitsky Variant - Science"  newspaper:
  1) B. Stern. What the LIGO detectors saw.
  2) A. Levin. Gravitational waves: road to discovery.

We should point out straight away that the attempts to register and investigate experimentally the gravitational waves, which were predicted in Albert Einstein's general theory of relativity, were started in the 60's by Joseph Weber, a professor of physics at the University of Maryland (USA). Despite the pessimistic results of the experiments, the research was continued in many countries, including the USSR. We should mention that the principle of using a laser interferometer (also employed in LIGO) to detect gravitational waves was proposed in the works of Soviet physicists (M.E. Gertsenshtein, V.I. Pustovoit, JETP, 43, 605, 1962) back in 1962, and later also by J. Weber. Active investigations in this field are (and have been) carried out by members of the group lead by V.B. Braginsky at the physics faculty of MSU (see the interview with Sergey Vyatchanin and the book by Kip Thorne "Black Holes and Time Warps"), also included in the LIGO collaboration [among the useful Russian-language links we note also (V.M. Lipunov The gravitational wave sky. ISSEP, V.6, No 4, p. 77 (2000); V. N. Rudenko. "The search for gravitational waves". Chapter in a book published by "Vek 2", 2007)].

The construction of LIGO began in the 90's (by the initiative of Rainer Weiss, Ronald Drever, and Kip Thorne). Observations were conducted with LIGO in 2002-2010, with no results. In September 2015, during the calibration measurements for the modernized "Advanced LIGO" project, a signal was detected with a significance above 5.1 sigma, corresponding to the one expected for the merger of two massive compact objects.

Here we need to show several figures available from the LIGO website.

Fig.1. Scheme of the LIGO laser interferometer.


Fig.2. Photo of the gravitational wave detector in Hanford:


Fig.3. The signal of the event GW150914, registered by the two LIGO detectors, interpreted as a result of a gravitational wave (which developed as a result of a merger of two black holes) passing through the interferometer. Right: data from the facility in Hanford, Washington; left: data from the facility in Livingston, Louisiana. Top: the signal from the detectors; bottom: the result of the numerical simulations. The figure was taken from the following paper: Physical Review Letters 116, 061102 (2016), arXiv:1602.03837.

Based on the analysis results, the collaboration obtained a set of physical quantities: the masses of the compact objects (black holes) - the pair M1=29(+/-4)Msun and M1=36(+5,-4)Msun before the merger and M=62(+/-4)Msun after the merger; the mass that converted to gravitational waves, Mgw=3.0(+/-0.5)Msun (with a factor of c^2); the estimate of the redshift z_gw=0.09(+0.03,-0.04), and even the metallicity in the neighborhood of GW150914 of the order of Z~0.5Zsun. In addition, the region in the sky where the signal came from was determined (although with poor accuracy). Also, the graviton mass limit was obtained as <1.2x10^(-22)eV.

A third-party researcher, after reviewing the data presented in Fig.3, would naturally have the following questions: 1) how do we know the registered signal is not a noise fluctiation? 2) why does the paper talk about black holes? 3) how were the physical parameters obtained from the presented recordings?

1) The registered signal with the decreasing frequency and increasing amplitude strictly corresponds to the theoretically predicted gravitational wave signal from merging compact objects. The "frequency-time" dependence (Fig.4) is a distinctive characteristic of such a signal.
Fig.4. The gravitational wave signal as a frequency-time dependence. Top: Hanford data; bottom: Livingstone data.

2) The type of the time dependence of frequency characterizes the distance between the two merging compact objects. If we can estimate the masses of the objects, then the frequency and its rate of change give us the distance between the objects and thus impose a limit on their size (see (Physical Review Letters 116, 061102 (2016), arXiv:1602.03837) for details).


3) The determination of the physical parameters is related to point 2) above. A simple estimation is given in the popular article by B. Stern in the "Troitsky Variant" (we quote the part which is very useful for the understanding of the physics of the process):

"How would one, looking at Fig. [here, Fig.3], estimate the mass of the merging black holes and the distances to them? One should estimate the rotation period of the merging objects at the last moment. Looking at the figure we see that the distance between the last few peaks is about ten times less than the distance between the marks, i.e. about 5 milliseconds, which is roughly the rotation half-period of a still strongly deformed black hole. What is the linear rotation velocity of its surface? Comparable to the velocity of light, but smaller, about a third (Kerr black hole limit) - regardless of size. The half-circle of rotation will then be approximately 500 km; we then divide by pi to obtain the radius of 170 km. The radius of a Solar-mass black hole is 3 km; therefore, the mass of the system is about 60 Solar masses (62 in reality). Such accuracy is astonishing, especially considering that the time between the peaks was estimated by eye. Now let us try to estimate the distance. This is slightly more complicated. The amplitude of a gravitational wave (the relative deformation of space) is inversely proportional to the distance of the source. The deformation in the source is huge, not unity, of course, but 0.1 is quite realistic (computations yield values of this order of magnitude). Here we have 10^(-21) (see the units along the vertical axis), therefore, we are situated about 10^(20) times farther from the source than its size - 170 km (see above). We obtain 1,7 x 10^7 cm x 10^(20) = 1,7 x 10^(27)cm = 0,6 Gpc (0,4 Gpc in reality). Again we are right on target, considering that there is an additional uncertainty in the orientation of the equatorial plane of the system relative to the line of sight." (B. Stern. What the LIGO detectors saw. , TrV, February 2016).

In the precise computational approach, the estimates of the objects' masses (and the distances between them) are obtained as a result of parameterization of the masses of the system components and their merger process (taking into account their rotation axes) and constructing the likelihood function to determine the most probable parameter values and the corresponding significance levels. The estimates are given in Properties of the binary black hole merger GW150914, arXiv:1602.03840. In this approach, the masses and rotation components of the objects are free parameters. Furthermore, considering the fact that the observed signal has a cosmological redshift z, it (the signal) can be matched by a mass scale varying by the same factor. The mass selected through the likelihood function is then itself a function, m(z)=(1+z)m_real , with an unspecified redshift that can be varied when minimizing the functional constructed from the likelihood function. The additional parameter (redshift) can thus be determined, and therefore, we can also determine the luminosity distance). Figs.5 and 6 show several likelihood functions from (arXiv:1602.03840). The presence of massive black holes at z~0.1 implies a relatively weak stellar wind in the vicinity of GW150914 and an approximately 1/2 Solar metallicity (arXiv:1602.03846).

Fig.5. Posteriori likelihood functions for the masses of the compact objects - system components m1_source and m2_source, where m2_source <= m1_source.


Fig.6. Posteriori likelihood functions for the pairs of determined parameters. Left: for the luminosity distance D_L to the object and the inclination of the system theta_JN. Right: for the mass and spin of the merged object.

The 7 ms registration delay between the two LIGO instruments and the different orientation of the arms of the installations made it possible to estimate the direction in the sky where the signal may have come from (Fig.7).


Fig.7. Approximate direction of the signal. The purple contours show the 90% probability zone.

Note that after the registration, the LIGO team appealed to the SWIFT team to search for a signal in other spectral regions, but the latter did not find any signals in this sky area either in the X-ray, the hard X-ray, or the UV ranges (arXiv:1602.03868). Simultaneously, the FERMI satellite saw a faint transient source (gamma-ray burst) with an amplitude of over 50 keV 0.4 s after the GW150914 event with a false alarm probability level 0.0022 (see arXiv:1602.03920). The location of the gamma-ray burst does not contradict the GW150914 region.

Let us also note among the February 12, 2014 arXiv preprints the following works: the paper about massive pulsars with a stable rotation used to search for and determine the parameters of the passing gravitational waves (arXiv:1602.03640); proposals to observe massive resonators based on red giants that exhibit asteroseismic activity (arXiv:1602.03667), and also (arXiv:1602.03883), from the group of David Spergel [one of the leaders of the NASA WMAP space mission, which targeted the cosmic microwave background], dedicated to the information that can be obtained from gravitational wave burst event counts. Note that the latter paper includes congratulations to the LIGO team in the comments, and the abstract has the [vague] phrase "the distribution of the candidate black holes binary systems observed by Advanced LIGO".

To conclude, we can note that the formal (indirect) discovery of gravitational waves was already marked by a Nobel prize, received by the American radio astronomer Joseph Taylor and his student Russell Hulse for the detection in 1974 and study of a pair of neutron stars orbiting each other, one of which is the pulsar PSR B1913+16. Moreover, from the decrease of the period of the binary, it was possible to verify the General Theory of Relativity, which describes gravitational radiation losses. After 2014, when the discovery of the primordial gravitational waves based on BICEP2 measurements of the B-mode of CMB polarization did not take place, it would seem that there should be nothing surprising in the direct detection of gravitational waves. However, the strong signal GW150914 has shown that a new window has really been opened into deep space. Apparently, a new, powerful, competitive field in astronomy, related to both the new technologies and the possibility to reach the most secret places in the Universe, was demonstrated to the international science foundations.

Oleg Verkhodanov.
February 14, 2016.
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