The LIGO, Virgo, and KAGRA detectors routinely register mergers of stellar-mass black holes, but the origin of these objects remains a mystery. Primordial black holes, which could have formed in the early Universe, are considered candidates for dark matter. Black holes with masses below that of the Sun are of particular interest: they cannot be explained by stellar evolution, so a detection would be a direct indication of a primordial origin. Existing gravitational-wave searches for such objects fall into two camps: matched filters for masses near the solar mass and semicoherent methods for planetary masses. Between them yawns a gap in the chirp-mass range from 0.01 to 0.1 solar masses, where signals last from minutes to hours and evolve rapidly in frequency. This work fills exactly that niche, using data from the O4a and O4b LIGO observing runs.
The authors applied the BinaryGFH-v2 method, which works with peak maps: time-frequency representations of the data in which local power maxima above a threshold are selected. For a power-law evolution of the binary's frequency, the method maps peaks from the detector time-frequency plane onto lines in the plane of initial frequency and chirp mass. The search was conducted in the frequency range 71–169 Hz, split into five configurations with coherent Fourier transform durations from 4 to 0.5 seconds. Candidates were selected independently in the Hanford and Livingston detectors, after which a coincidence in parameters within three bins and an excess over the average critical threshold ratio of about 6 were required. To vet candidates, phase demodulation was used, followed by a search for residual frequency drift with the frequency Hough method. The entire analysis took about 350 CPU hours, which is two to three orders of magnitude less than previous semicoherent searches and four to five orders of magnitude less than matched filtering.
No significant candidate survived in the O4a and O4b data. After the coincidence stage, there were 158870 candidates in O4a and 139260 in O4b, but after applying the critical-ratio threshold one candidate remained in O4b, and after accounting for subthreshold events down to CR=5, three candidates. All were rejected at the follow-up stage because their time-frequency tracks overlapped with known instrumental lines and combs. The absence of events allowed 90% upper limits to be set on the merger-rate density in the chirp-mass range 0.01–0.1 solar masses. These limits bridge the constraints from long-duration planetary-mass searches and from matched filtering at higher masses. Assuming that primordial black holes form binaries in the early Universe without merger suppression, the first gravitational-wave constraints on the fraction of primordial black holes in dark matter were obtained: fPBH < 1 for equal masses and for asymmetric systems with secondary mass from 0.0003 to 0.01 solar masses at a primary mass of 2.5 solar masses.
The work fills an important gap in gravitational-wave searches for subsolar objects, connecting two previously separate regimes. Unlike neighboring studies, which either cover planetary masses with long-duration semicoherent methods or use matched filtering for masses near the solar mass, this study systematically explores the intermediate range with rapid frequency evolution for the first time. The BinaryGFH-v2 method demonstrates that such a search is possible with computational costs orders of magnitude lower than alternatives. The resulting constraints on primordial black holes do not depend on a specific mass function or suppression factor, which allows other researchers to recalculate them for their own models.
Further development could include applying the method to data from future LIGO, Virgo, and KAGRA observing runs, as well as to data from planned next-generation detectors such as the Einstein Telescope and Cosmic Explorer. Improving the power spectral density estimate on short coherent intervals could boost sensitivity in the upper part of the mass range. In addition, the analysis could be extended to a wider frequency and mass range, as well as to triple systems or eccentric orbits.
The results directly affect constraints on the fraction of primordial black holes in dark matter, providing a test method independent of microlensing. They also set benchmarks for future gravitational-wave surveys and for theoretical models of binary formation in the early Universe.
The next step will be to apply BinaryGFH-v2 to the full O4 data, including periods of triple coincidence with Virgo, and to O5 data. In parallel, it is worth improving noise estimation algorithms for short Fourier transforms in order to increase sensitivity at high chirp masses.
In gravitational-wave astronomy, the question of the nature of dark matter and the existence of primordial black holes remains unresolved. This work contributes to solving that problem by providing the first constraints in a previously unexplored mass range. In addition, it demonstrates that semicoherent methods can efficiently cover intermediate regimes, which opens the way to a more complete mapping of the population of subsolar compact objects.
Chirp mass is a combination of the masses of the two components of a binary system that determines the rate of change of the gravitational wave's frequency. For a system of two objects of 0.05 solar masses each, the signal in the LIGO detector would last about 20 minutes, changing frequency from 169 to 71 Hz.
The idea of primordial black holes as dark matter is explored in Greg Egan's novel Schild's Ladder, where exotic compact objects affect the structure of space. The search for invisible subsolar objects echoes the plot of the film Interstellar, where black holes play a key role in the fate of humanity.