An international team led by the Institute of High Energy Physics (IGFAE) of the University of Santiago de Compostela in Spain jointly measured the "recoil" speed and direction of black holes after their merger for the first time. This result has been published in Nature Astronomy. Research shows that gravitational waves not only carry energy, but also momentum, giving the final black hole a "kick-off" recoil after the black holes merge, allowing it to move through the universe at a considerable speed.
Gravitational waves are ripples in space-time predicted by Einstein in his 1916 general theory of relativity. When extremely dense and massive celestial bodies such as black holes collide violently, such fluctuations will be stirred up and spread in all directions of the universe. Since gravitational waves carry the energy and momentum of the system, once the wave radiation is not completely symmetrical in spatial distribution, the resulting black hole will recoil under the "unbalanced" thrust, which is also vividly called "the black hole was kicked." The strength of the recoil is closely related to the mass and spin of the two initial black holes, while the direction of the recoil depends on the geometric configuration of the entire system in space.
In the past, scientists were mainly able to measure a few geometric parameters such as orbital inclination from gravitational wave signals. Another key angle, the azimuthal angle, has been difficult to obtain accurately. This research team found that the "higher-order modes" in gravitational waves contain geometric information that was previously difficult to read, which can be used to restore this missing angle and calculate the three-dimensional direction of the recoil.
The researchers used the gravitational wave event GW190412, which was jointly detected by Advanced LIGO and Virgo observatories in 2019, as a sample to verify the method. In this event, the masses of the two black holes are obviously not equal, so they show clearly discernible high-order mode features in the signal, which is very suitable for fine analysis. Through accurate numerical simulations based on Einstein's equations, the team calculated that the recoil speed of the merged black hole exceeds 50 kilometers per second, which is fast enough for it to escape from some dense star clusters (such as some globular star clusters). The Bayes factor given by statistical analysis is about 21, corresponding to a confidence level of about 95%, which provides strong support for this conclusion.
While determining the speed, the team also compared the recoil direction with reference directions such as the system orbit axis and the Earth observation direction. The results showed that the "kick" was not along the orbital plane, nor was it pointed directly at the Earth, but in an intermediate direction between the two. Professor Juan Calderon-Bustillo, one of the project members, made an analogy: the gravitational wave signal is like an orchestra. Depending on the position of a person, the "instruments" heard will be different, and this "tone color difference" helps scientists reconstruct the movement trajectory of the black hole in the three-dimensional space. Dr. Kustav Chandra of Pennsylvania State University pointed out that this method is equivalent to reconstructing the true movement of celestial bodies billions of light-years away using only "ripples" in space and time.
The author said that such precise recoil measurements are particularly important for studying black hole mergers that occur in special environments. For example, in active galactic nuclei with accretion disks, black hole mergers may be accompanied by signals such as visible light and electromagnetic radiation. Whether we can observe these flashes depends largely on the relative geometric relationship between the recoil direction and the Earth. Therefore, knowing the recoil direction can help astronomers judge whether a certain gravitational wave event and an electromagnetic burst really come from the same cosmic event, or whether it is just a coincidence in time.
The research team believes that this work marks that gravitational wave astronomy is gradually moving out of the stage of "only hearing mergers occur" and entering a new stage that can meticulously map the spatial structure and dynamic processes of events. In the future, as detector sensitivity increases and event samples increase, simultaneously measuring the recoil velocity and direction of black holes will become a routine method, helping the scientific community to more clearly understand how black holes grow and migrate in the universe, and shape the evolution of galaxies and large-scale structures.