Betelgeuse: Šumový budget a pre-dimming variabilita

Motivation

The Great Dimming of Betelgeuse (α Ori) during October 2019 – February 2020 represents the most dramatic observed brightness change of a first-magnitude star in modern astronomy. Brightness dropped from V ≈ 0.5 to a record minimum of V ≈ 1.614 (February 10, 2020), a factor of ~3× in flux.

Standard approach: remove pulsation periodicity (~400d, ~2200d, ~185d), explain the dimming as a combination of surface cooling and a dust cloud (Montargès et al. 2021, Dupree et al. 2022). Case closed.

Noise-preserving approach (this scroll): Do not remove variability automatically. Construct a noise budget, identify individual sources of scatter, and examine the structure of the clean residual — especially in the period before the Great Dimming.

Research question: Does statistically significant signal exist in the residual variability — after removal of identified noise sources and known pulsation — in the 100–200 days preceding the Great Dimming? If so, was the noise telling us something about the approaching event?

Data

Available sources: AAVSO visual (1893–present, ~36,000 points, low precision), AAVSO V-band PEP (1980s–present, ~1,500 points, photoelectric), Harper+ 2020 VizieR J/ApJ/905/34 (2015–2020, 209 + 118 points, most precise ground-based), SMEI Joyce+ 2020 (2003–2011, ~2,500 points, space-based), ASAS-SN Sky Patrol (2012–present, robotic V/g, saturated stars with ML correction).

Version 1.0 uses synthetic data calibrated to published parameters. Real data will be integrated in the next session.

The synthetic generator reproduces key properties of Betelgeuse: three pulsation periods (416d, 2170d, 185d), seasonal visibility with ~5-month gaps, inter-observer systematics (15 simulated observers), atmospheric extinction, and injected pre-dimming activity (elevated variance 100–200 days before minimum). Total of 622 data points over 2,400 days.

Method — Noise Budget for Ground-Based Photometry

Scroll 009 worked with Kepler space data, where identified noise sources were pointing jitter, background flux, and photon noise. Ground-based data require a different catalog of sources.

Identified sources of scatter:

a) Per-season polynomial trend. Each observing season (separated by gaps >60 days) is fitted with a degree-2 polynomial. This trend absorbs instrumental drift, seasonal atmospheric changes, and slow stellar variations.

b) Inter-observer systematics. Each observer has a systematic offset from the global median. Removed by subtracting the per-observer median.

c) Photometric error. Reported measurement uncertainty (mag_err). Represents photon noise + scintillation.

d) Known pulsation. Three-period sinusoidal model fitted to detrended data using Lomb-Scargle identification + nonlinear optimization.

After removal of components a–d, the clean residual remains, containing: astrophysical signal not captured by the pulsation model (convective cells, episodic mass loss, pre-event activity), unidentified systematics (seeing, differential refraction, color term effects), and stochastic noise.

Results (Synthetic Data)

Variance Budget: Seasonal trend 97.0% of variance, inter-observer systematics 1.0%, photometric error 1.0%, known pulsation (after detrending) ~0%, unexplained 0.9%. The high share of seasonal trend is an artifact of synthetic data, where the per-season polynomial absorbs most of the pulsation signal. With real data, the ratios will redistribute.

Pre-Dimming analysis: Pre-event window with 20-day buffer shows variance ratio 4.79× compared to quiet period (RMS 114.7 mmag, 23 points). Pre-event window with 50-day buffer shows 4.59× (RMS 112.2 mmag, 11 points). Control window (1,000–1,200 days before dimming) shows 0.55× — below the reference level.

In synthetic data, pre-dimming activity is intentionally injected. The numbers demonstrate pipeline sensitivity, not a discovery.

Pipeline detects injected pre-dimming activity with variance ratio 4.6–4.8× versus control (0.55×). Demonstrated sensitivity, not a discovery.

Key Differences from Tabby's Star

Instrument: KIC 8462852 has space-based Kepler (1 detector), Betelgeuse has ground-based AAVSO (dozens of observers). Cadence: Kepler 29.4 min, AAVSO irregular (days–weeks). Noise sources: Kepler has pointing and background, AAVSO has atmosphere, observers, and seeing. Known variability: KIC 8462852 is a quiet star, Betelgeuse has strong multi-periodic pulsation. Event: KIC 8462852 has aperiodic dips, Betelgeuse has the single Great Dimming. Control: Kepler uses other stars on the CCD, Betelgeuse uses quiet periods of the same star.

Critical difference: Betelgeuse is a known variable star. The pulsation signal must be removed before noise-budget analysis, otherwise it dominates the entire budget. This requires caution — overly aggressive detrending may remove pre-event signal as well.

Betelgeuse requires pulsation signal removal before noise-budget analysis — overly aggressive detrending may remove pre-event signal as well.

Open Questions for Version 2.0

Data: Download AAVSO V-band PEP data (JD 2455000–2459500). Download Harper+ 2020 from VizieR (J/ApJ/905/34). Consider ASAS-SN saturated star ML photometry.

Methodology: Optimize per-season polynomial order (1 vs 2 vs spline). Test sensitivity to pre-dimming window size. Compare pulsation fit: 3-period sinusoid vs Gaussian Process. Define control class: other RSGs (Antares, μ Cep) + stable stars.

Physical context: Dupree et al. (2022) identified a surface mass ejection (SME) in HST UV data — material was ejected months before the optical dimming. If residual variance rises 100–200 days before the V-band minimum, it may be a photometric imprint of the same process. This is a testable prediction: HST UV data show activity in September–November 2019. The noise budget should detect elevated residual variance in the same period.

What We Claim and What We Don't

We claim: The pipeline for noise-budget analysis of ground-based photometry is functional and adaptable. The method successfully separates seasonal trends, inter-observer effects, and the pulsation model. Synthetic data confirm that the pipeline has sensitivity to injected pre-event activity at the ~5× variance ratio level.

We do not claim: Any discovery in real data (version 1.0 is purely synthetic). That a pre-dimming signal exists in real data (this is a hypothesis to be tested). Causal connection between residual variance and the Great Dimming (even if the effect exists, causality requires independent confirmation).

Where We Meet Standard Physics

Dupree et al. (2022) identified a massive surface ejection from Betelgeuse months before the optical dimming. HST UV data confirmed it. Did a photometric precursor exist in optical data? Noise-budget methodology is standard in space missions. Nobody has systematically applied it to ground-based data yet.