Hercules X-1’s 35-day X-ray cycle is shortening, preprint reports

A changing cycle, not a shrinking orbit

Hercules X-1 is an X-ray binary: a system containing a neutron star and a companion star, called HZ Her. Gas supplied by the companion forms an accretion disc around the neutron star—a disc through which material moves inward.

The system’s roughly 35-day brightness pattern is called a superorbital cycle because it lasts longer than the stars’ orbit. Each cycle normally contains a bright interval, known as the main-on, and a fainter interval, the short-on, separated by low-emission states.

The new study concerns this brightness cycle, not the 1.7-day orbit or the neutron star’s much faster rotation. Posted as a preprint on 6 November 2026, it reports an overall shortening of the superorbital period in monitoring data described as covering 1995–2025. Earlier measurements extend the timing record back to the 1970s.

How the researchers tracked the timing

The team used five X-ray monitors: CGRO/BATSE, RXTE/ASM, Swift/BAT, Fermi/GBM and MAXI/GSC. Their light curves—records of detected X-ray intensity over time—provide overlapping coverage across approximately three decades.

These instruments do not all measure the same thing. Three record total X-ray intensity in their respective energy ranges, while BATSE and GBM record the pulsed component. The researchers adjusted the relative intensity scales using overlapping observations and used the combined record to study timing rather than absolute brightness.

Two methods tested how the cycle changed. Epoch folding stacks observations according to a trial cycle length to see how clearly a repeating pattern emerges. The researchers searched both for the period and for a gradual change in that period.

The second method tracked the peaks of individual main-on intervals. It compared each observed peak with the time predicted by a constant-period clock. This produces an observed-minus-calculated, or O−C, diagram. A sustained curve in these timing differences indicates that the assumed clock is not keeping a constant period.

A downward trend with sizeable departures

Both methods returned a shortening rate close to −5 × 10⁻⁵ seconds per second. The negative sign means that the cycle is getting shorter. The paper describes the trend as approximately a 0.05% decrease in period per year.

Epoch folding gave a rate of (−5 ± 2) × 10⁻⁵ seconds per second. The peak-timing analysis gave (−4.7 ± 0.1) × 10⁻⁵ seconds per second. These quoted uncertainties are one-standard-deviation estimates, but the authors explicitly caution against taking the narrow timing-fit uncertainty at face value: a smooth, constant-rate shortening does not adequately describe the observations.

Instead, the timing record contains departures that develop and subside over about 10–38 superorbital cycles, or roughly one to four years. Period differences across these excursions can reach about 5% between their maximum and minimum values.

The authors also divided the post-1999 timing curve into 24 locally straight segments. Across those segments, longer periods tended to accompany higher mean X-ray count rates—the rate at which the instruments registered events. They report a Pearson correlation coefficient of 0.73, indicating a positive association. That association does not establish which physical process causes either change.

Two explanations remain in contention

One explanation involves a tilted, warped accretion disc that slowly changes its orientation. This motion, called precession, could periodically move the disc into and out of our view of the X-ray-emitting region, producing the brightness cycle.

In this picture, radiation from the neutron star can help warp the disc. Changes in the disc’s shape, gas supply or interacting patterns of warping could alter its precession period. The authors suggest that the brightness–period correlation and the excursions may reflect radiation-driven feedback that helps the system recover after a disturbance. They do not directly demonstrate such a restoring mechanism.

The alternative is free precession of the neutron star: a wobble associated with a spinning body that is not perfectly symmetrical. In this model, the star supplies the underlying clock, and the disc’s motion becomes coupled to it.

Under particular assumptions about the neutron star’s shape and orientation, the authors estimate that a decrease in its spin-axis misalignment of about 0.002 degrees per superorbital cycle could reproduce the gradual shortening. Changes in the star’s small departure from a symmetrical shape, caused by accumulating material, might also contribute to the long-term trend. These are model-based possibilities, not measured changes in the star’s interior or orientation.

The paper argues that the observed speeding-up of the neutron star’s rotation is insufficient, by itself, to explain the superorbital evolution.

Why the longer history matters

The extended record does not support a simple, uninterrupted shortening across the entire approximately half-century baseline. Earlier studies found fluctuations without a clear long-term trend, and the new paper particularly identifies a declining trend after the prolonged anomalous low state around 1999.

Such low states interrupt the usual bright-cycle markers. The researchers excluded data from that prolonged low interval, and the number of cycles that elapsed through it remains uncertain. They therefore examined alternatives with 18 or 19 cycles across the affected gap. For older observations, they also converted published turn-on times into estimated peak times by adding a fixed, approximate seven-day offset.

These assumptions, the combination of different instruments and the inadequacy of a smooth timing model limit how precisely the trend can be interpreted. The preprint’s central result is a shortening superorbital cycle over the recent monitoring interval, accompanied by substantial shorter-term variability—not a definitive identification of the mechanism behind the 35-day clock.