Solar Cycles 18–25 Show Multiscale Periodic Variations in 10.7 cm Radio Flux

The Sun’s activity has long been summarized by a single number: the 10.7-centimeter radio flux, known to space-weather forecasters simply as F10.7. Measured continuously since 1947 from the ground in Canada, this quiet stream of microwave emission traces the thermal glow of hot plasma trapped in the Sun’s corona and has become one of the most trusted proxies for solar ultraviolet output. Now, a team of Chinese researchers has taken the longest F10.7 record ever assembled and, using a sophisticated statistical technique borrowed from signal processing, peeled it apart layer by layer to reveal the hidden rhythms within. Their findings, published in the journal Solar Physics, shed new light on one of solar physics’ most stubborn puzzles: the origin and behavior of the Sun’s quasi-biennial oscillation, a mysterious fluctuation in magnetic activity that rises and falls roughly every two years.

The study, led by Yu Fei and Lei Zhang of Yunnan University of Finance and Economics, together with colleagues at Honghe University, Yunnan Minzu University, and Kunming University of Science and Technology, analyzed daily F10.7 measurements spanning Solar Cycles 18 through 25, covering an impressive 78 years of observations from 1947 to 2025. Their central challenge was a technical one that has plagued solar variability studies for decades: spectral overlap. The Sun’s output contains fluctuations at many different timescales simultaneously, from the famous 11-year Schwabe cycle down to the 27-day rotation of the solar surface and everything in between. Conventional filtering methods tend to smear these signals into one another, blurring the boundary between genuine periodicities and artifacts of the analysis itself.

To overcome this, the researchers deployed a hybrid framework combining Singular Spectrum Analysis, or SSA, with a log-frequency hierarchical clustering algorithm. SSA works by embedding a time series into a high-dimensional space of delayed copies of itself, then decomposing that space using eigenvector techniques. The result is a set of orthogonal components that capture trend, oscillations, and noise without imposing any preconceived functional form. The team’s innovation was to group these components hierarchically in log-frequency space, which allowed them to objectively separate fluctuations that standard filters would conflate. In effect, the method lets the data declare its own natural frequency bands rather than forcing them into predefined boxes.

The decomposition succeeded in isolating four distinct layers of variability. At the top sits a secular trend, the slow multi-decadal drift in the baseline level of solar activity. Above that rises the familiar 11-year Schwabe cycle, the grand pulse of the solar dynamo that governs the appearance and disappearance of sunspots. Below it lies the 27-day rotational modulation, produced as active regions on the rotating Sun swing into and out of view of Earth-based instruments. And between the 11-year cycle and the rotation period, the analysis uncovered a family of intermediate-period components, including a clear quasi-biennial signal.

The quasi-biennial oscillation, or QBO, appeared in the decomposition as an intermittent wave packet concentrated in the one-to-three-year period band, with dominant periodicities near 2.39 and 1.78 years. The team also identified a 3.36-year component consistent with a quasi-triennial oscillation, or QTO, a related but distinct fluctuation that some researchers regard as part of the same family of sub-Schwabe variability. The wave-packet character of the QBO is significant: rather than ringing continuously like a tuning fork, the signal switches on and off, strengthening and weakening across different phases of the solar cycle and from one cycle to the next.

Perhaps the most provocative finding concerns how the QBO’s strength relates to the overall level of solar activity. The researchers found that QBO variability is preferentially enhanced during the ascending and maximum phases of the 11-year cycle, when the solar dynamo is working hardest to generate new magnetic flux. But crucially, the amplitude of the QBO does not scale monotonically with the peak activity of a given cycle. The largest QBO excursions in the 78-year record occurred during Solar Cycle 22, a moderately strong cycle. Solar Cycle 19, by contrast, was the most intense cycle of the entire instrumental era, yet its QBO response was comparatively muted. This decoupling between cycle amplitude and QBO amplitude suggests that the two phenomena arise from different physical mechanisms rather than the QBO simply being a scaled-down echo of the main dynamo.

The team’s interpretation, grounded in the intermittent wave-packet morphology and the erratic cycle-to-cycle variability they observed, is that the QBO is best understood as an instability-related secondary component of the solar dynamo rather than a persistent, independent oscillator. This view aligns with theoretical work proposing that magnetic Rossby wave instabilities in the solar tachocline, the shear layer at the base of the convection zone where the dynamo’s magnetic field is thought to be anchored, can spontaneously generate quasi-biennial periodicities. It also resonates with observational studies that have traced QBO signatures in helioseismic data, solar flare records, and the topology of the Sun’s magnetic activity bands, all of which point toward an intermittent, instability-driven phenomenon rather than a clockwork oscillation.

Beyond its intrinsic interest for solar dynamo theory, the F10.7 index has immense practical importance. Because it tracks the Sun’s extreme-ultraviolet output, which heats and inflates Earth’s upper atmosphere, F10.7 serves as a key input to models of thermospheric density used to predict satellite orbital decay, to ionospheric models that shape radio communication and GPS accuracy, and to space-weather forecasting systems worldwide. Understanding the full spectrum of variability embedded in the F10.7 record, including the intermittent QBO, therefore carries tangible benefits for anyone who operates spacecraft, communicates over long distances by radio, or models the space environment. Better decomposition of the signal could eventually translate into more accurate empirical models and improved forecasts of how the upper atmosphere will respond to solar forcing.

The study also highlights the enduring scientific value of long, continuous observational records. The F10.7 time series, maintained with remarkable consistency for nearly eight decades, has proven to be far more than an operational convenience. As analysis techniques grow more sophisticated, old data sets continue to yield new insights, and the record now stands as a unique window onto the Sun’s behavior across eight complete solar cycles. The researchers note that their data, drawn from the Canadian solar radio flux program, are publicly available, allowing independent verification and further exploration of the multiscale structure they have documented.

As the Sun progresses through Solar Cycle 25 toward its current maximum and eventual decline, the intermittent quasi-biennial oscillation will no doubt continue its irregular pulse, waxing during the active years and fading during the quiet ones. What this study makes clear is that the Sun’s rhythms are richer and less orderly than the familiar 11-year heartbeat alone would suggest, and that careful statistical archaeology of the longest observational records remains one of the most powerful tools available for deciphering the inner workings of our nearest star.