When two black holes merge, they produce gravitational waves, which are fluctuations in space-time that can be captured by detectors on Earth. The signal of gravitational waves can be divided into three phases: the early helical phase, the mid-phase merging phase, and the late attenuating phase.
In the decay phase, the merged black hole will radiate some excess energy outward, so that it will eventually reach a stable state. This process is like a bell that rings, it makes a series of sounds that gradually weaken until it disappears. These sounds are the quasi-oscillation spectrum of black holes, or quasi-normal patterns of black holes.
According to the black hole theorem, the properties of a black hole depend only on its mass and angular momentum, and not on its shape or other factors. This means that the quasi-normal spectrum of a black hole is also determined only by its mass and angular momentum, and not by its initial state or merging process. This is a fundamental prediction of general relativity, and if we can observe multiple quasi-normal patterns, we can test whether this prediction is true.
Each quasi-normal mode has a specific frequency and decay time, which can be calculated from the mass and angular momentum of the black hole. Different quasi-normal modes also have different angular distributions, which can be described by spherical harmonic functions. For example, the mode =m=2 is the dominant mode, which corresponds to an oscillation of the dipole moment in the direction of the spin of the black hole. The mode =m=3 is the sub-major mode, which corresponds to an oscillation of the tripolar moment along the spin direction of the black hole. In general, the larger the pattern, the faster it decays.
If we can observe more than one black hole oscillation pattern, we can use them to test the predictions of general relativity and explore the properties of black holes. However, this is not easy, because we need to have a strong enough gravitational wave signal, and a sensitive enough detector to be able to distinguish the different patterns.
Currently, we already have some advanced gravitational-wave detectors, such as Ligo and Virgo, that can detect black hole merging events from distant galaxies. One of the most notable events is GW190521, which occurred on May 21, 2020, and was produced by the merger of two black holes with masses of 85 and 66 solar masses, respectively. This is the largest known black hole merger event, resulting in the formation of a black hole with a mass of 142 solar masses and at the same time radiating outward energy in the form of gravitational waves at **8 times the mass of the sun.
The gravitational wave signal of this event is very strong and lasts for a short period of time, only a few cycles. This means that it mainly contains information about the oscillation spectrum of the black hole after the merger, rather than about the rotation and proximity before the merger. Therefore, this is a good opportunity to try to observe multi-mode black hole oscillation spectra, as well as to test the black hole theorem. In order to do this, we need to use some mathematical and physical tools to analyze the data of gravitational wave signals and compare the possibilities of different hypotheses or models.
In the latest study, scientists analyzed gravitational wave data from GW190521 and compared two hypotheses: one is an oscillation spectrum with only one mode, and the other is an oscillation spectrum with two modes. They found that the latter was more likely than the former, with a Bayesian factor of 56 1. This is a strong evidence in favor of the existence of multi-mode black hole oscillation spectra. They further estimated the frequency and decay time of the two modes, as well as the mass and spin of the eventual black hole. They found that in the end, black holes conform to the black hole theorem.
The significance of this study lies in the fact that it is the first time that a multi-model quasi-normal spectrum of a black hole has been observed, which is an important test of general relativity and an in-depth exploration of black hole physics. These results not only improve our understanding of black holes, but also provide new opportunities and challenges for future gravitational wave detection.