What question did this study set out to answer?

The research aims to understand how total solar irradiance varies across different observational scales using a framework for null-model diagnostics.

January 22, 2026Open Access

Solar phase transitions in null-model diagnostics: window-dependent regimes in total solar irradiance

Key Points

The research aims to understand how total solar irradiance varies across different observational scales using a framework for null-model diagnostics.
Defined four scale-sensitive indicators for scalar time series analysis.
Used a hierarchical decision rule for classifying time-series behavior based on null assumptions.
Applied this framework to SORCE/TIM Total Solar Irradiance data from 2003 to 2020.
Identified period instability at 27-day windows.
Found stable rotation signatures in the 54-81 day range.
Noted a 'silence band' from 108-182 days where no null assumption is violated.
Discovered destabilization of activity cycles in periods greater than 365 days.

Abstract

Overview We introduce a null-diagnostic framework in which null-model selection is treated as a physical statement about time-series structure. Rather than asking whether the Sun is anomalous, we ask under which null assumptions the series becomes statistically indistinguishable from its reference distribution—and how this depends on observational scale. Method For a scalar series F (t), we define four scale-sensitive indicators: D★ (Drift): Secular trend strength A★ (Autocorrelation): Integrated autocorrelation time G★ (Degeneracy): Period estimation uncertainty (σP / P) η★ (Coverage): Window length / rotation period Using fixed thresholds and a hierarchical decision rule: DEGENERACY → DRIFT → AUTOCORR → SILENCE we classify time-series behaviour according to which null assumption fails first. Key Finding Applying this framework to SORCE/TIM Total Solar Irradiance (2003–2020), we find: Window Length Class Interpretation 27 d DEGENERACY Period unstable 54–81 d AUTOCORR Rotation signature stable 108–182 d SILENCE No null assumption violated ≥365 d DEGENERACY Activity cycle destabilizes period The "silence band" at ~108–182 days is a new, data-driven discovery absent in synthetic validation. Significance The Sun is a diagnostic boundary case, transitioning across multiple regimes as window length changes The framework is explicitly falsifiable and transferable to other astrophysical contexts This establishes null-model selection as a physical diagnostic tool Contents manuscript/ — LaTeX source (MNRAS Letters format) figures/ — Phase diagrams (synthetic validation + real data) code/ — Python analysis pipeline data/ — Results table (CSV) Citation Takagi, T. (2026). Solar phase transitions in null-model diagnostics: window-dependent regimes in total solar irradiance. Zenodo. https: //doi. org/10. 5281/zenodo. 18309608 Author Takayuki TakagiIndependent Researcher, Higashimatsuyama, Saitama, JapanORCID: 0009-0003-5188-2314

Solar phase transitions in null-model diagnostics: window-dependent regimes in total solar irradiance

Key Points

Abstract

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