In May 2020, the LIGO and Virgo detectors picked up a gravitational-wave burst known as GW200105. Among the many similar gravitational waves recorded, this one stood out for an oddity: the orbit of the colliding neutron star and black hole was not a perfect circle, but a stretched ellipse. A measurable eccentricity is a rarity for such systems. Most of them, born from isolated binary star systems, manage to radiate away all their 'excess' energy as gravitational waves and settle into circular orbits long before merger. This feature turned out to be not just an exotic quirk but a genuine magnifying glass, through which the system's details become far clearer. Researchers showed that eccentricity multiplies the information yield of each event, turning a small sample into a powerful population probe.

Take the effective spin χeff — the averaged projection of the spins onto the orbital angular momentum. In circular neutron star–black hole mergers, only 22% of events confidently indicate a negative value for this quantity. But once eccentricity is added, that fraction jumps to 43%. This means that roughly every two and a half eccentric mergers clearly signal that the black hole is spinning opposite to the orbital direction — a telltale sign that the pair formed dynamically. The magnifying-glass analogy is direct: a faint detail becomes crisp and unambiguous.

Improved mass measurements of neutron stars unveil their hidden structure. A hypothesis suggests that these objects fall into two families, with peaks around 1,3 and 1,8 solar masses. Ordinary circular events cannot confirm this bimodal picture even with 30 detections. But eccentricity boosts the Bayes factor — a measure of model preference — by a factor of 7,5. The mass boundaries become more precise by a factor of two to two and a half. This is a direct step toward understanding the equation of state of nuclear matter — the very “recipe” by which matter gets compressed in a neutron star's core. Another trick of the magnifying glass is distinguishing between metallicity models of black hole progenitors. For intermediate progenitor metallicity, the Bayes factor jumps by 14 orders of magnitude in favor of the correct scenario when eccentricity is accounted for. The eccentricity distribution law itself can be recovered from just ten events. This turns each signal into a mini-laboratory, testing theories of stellar evolution and cluster dynamics.

When O5 runs at full capacity, and next-generation observatories like Einstein Telescope come online, the eccentricity magnifying glass will let us not only take a census of the population but also peer into the darkest corners of compact-object astrophysics. From a blurry circular smudge to a sharp snapshot — that is how the tale of one anomaly, GW200105, opened the door to a mature era of gravitational-wave population astronomy.