A mysterious background of ultra-low-frequency gravitational waves detected using pulsar timing arrays may contain information about events that occurred more than 13 billion years ago, including the formation of the first supermassive black holes in the Universe.
In a new study published in Physical Review D, physicists Sohan Ghodla and Cosmin Ilie of Colgate University investigated whether supermassive black holes that formed in the early Universe could have been responsible for a significant portion of the gravitational-wave background currently detected by pulsar timing arrays.
The researchers identified a possible connection between two observational phenomena that initially appear unrelated: unexpectedly massive black holes in the young Universe and gravitational waves produced by mergers of supermassive black holes billions of years later.
One particularly interesting possible scenario for the origin of the first black holes is the collapse of supermassive dark stars. According to the calculations, their remnants could have been responsible for a significant — and under certain conditions even dominant — portion of the observed gravitational-wave background.
Cosmic Clocks for Searching for Black Holes
Pulsar timing arrays use rapidly rotating neutron stars as extremely precise cosmic clocks. Gravitational waves slightly alter the arrival time of radio pulses from pulsars reaching Earth.
By observing many pulsars over many years, astronomers can detect a common signal produced by gravitational waves with frequencies on the order of nanohertz.
The leading explanation for this signal is a population of supermassive black-hole binaries that gradually move closer together and eventually merge. Systems with a combined mass exceeding one billion solar masses are expected to make a particularly significant contribution.
However, an important question arises: where did the first “seeds” of these enormous black holes come from?
Observations using telescopes, including the James Webb Space Telescope and Chandra, have shown that unexpectedly massive black holes already existed in the early Universe. This has prompted researchers to search for mechanisms capable of rapidly producing their initial seeds.
Ghodla and Ilie investigated whether such early black holes could have survived, grown together with their host galaxies, formed binary systems, and ultimately produced the gravitational-wave background observed today.
Dark Stars as a Source of the First Black Holes
The scientists considered two scenarios for the formation of early black holes: the direct collapse of massive gas clouds and the collapse of supermassive dark stars.
Dark stars are hypothetical objects whose existence has not yet been confirmed. In the model considered, their energy is sustained not by conventional nuclear fusion but by heating associated with the annihilation of dark-matter particles.
Such stars could have remained relatively cool and extended while continuing to accumulate surrounding matter. According to the model, their masses could have reached one million solar masses or more, after which they could have collapsed and transformed into massive black holes.
The researchers modeled the subsequent evolution of these black holes, their interactions with galaxies and dark-matter halos, their merger rates, and the gravitational-wave background produced as a result.
The calculations showed that if the density of supermassive dark-star remnants was approximately 10⁻³ per cubic megaparsec, their descendants could have contributed a significant — and potentially dominant — portion of the gravitational-wave signal observed by pulsar timing arrays.
By comparison, the direct-collapse black-hole scenario considered in the study assumes a substantially lower characteristic density of approximately 10⁻⁶ per cubic megaparsec, resulting in a much weaker contribution to the gravitational-wave background.
Gravitational Waves as Evidence of the First Black Holes
The main result of the study is that modern gravitational-wave observations can be used to constrain the number of supermassive black holes that existed in the early Universe.
If there had been too many such objects, their descendants would eventually have produced too many supermassive black-hole binaries, creating a gravitational-wave background stronger than the one observed.
For the models considered, an initial seed density of approximately 10⁻²–10⁻¹ per cubic megaparsec could already have resulted in a gravitational-wave background exceeding the observed level.
The precise constraint depends on the mass of the dark-matter halos in which these objects formed.
Thus, pulsar timing-array observations make it possible to indirectly investigate populations of objects that existed at redshifts z > 10, even though the black-hole mergers producing the gravitational waves detected today occurred much later.
The calculations also confirmed that the dominant contribution to the signal should come from binary systems with a combined mass of approximately 10⁹ solar masses or more. Less massive systems produce a significantly weaker signal at the frequencies of interest.
The results connect several major areas of modern astrophysics: the nature of dark matter, the formation of the first stars and galaxies, the origin of supermassive black holes, and gravitational-wave astronomy.
If dark stars actually existed, their descendants may have left an observable imprint in the gravitational-wave background that has persisted to the present day.
Future observations by pulsar timing arrays, together with more precise data on black holes in the early Universe and their host galaxies, will help test this scenario and compare it with other models for the origin of the first supermassive black holes.