Titanium Oxide Absorption as a Proxy to Detect Long term Variation and Activity Cycle in Proxima Centauri

The paper introduces a method to detect long-term stellar activity cycles in M-type stars using a molecular index based on Titanium Oxide (TiO) absorption at 567 nm, and applies it to Proxima Centauri. The authors previously introduced this B-index in earlier work, which compares the absorption line strength of TiO at 567 nm with its nearby continuum at 610 nm. In this study, they use the B-index to evaluate long-term activity variations for Proxima Centauri, using 170 high-resolution spectra from the HARPS spectrograph, spanning from February 25, 2004, to August 14, 2017, covering over 13 years.

The analysis uses a generalized Lomb-Scargle periodogram (GLS) to search for periodicities in the time series, with a period range of 1.5 to 20 years. The lower limit of 1.5 years was chosen to avoid the star's known rotational period of approximately 80 days, and the upper limit was set by the observation time span. The results show a significant periodicity with an activity period of 2873+47.4−53.9 days (approximately 7.9 years), with a semi-amplitude of about 0.13 mag. The peak in the periodogram is above the 1% false-alarm probability, indicating a definite stellar cycle.

This 7.9-year period confirms previous measurements from other indicators, including the 7-year cycle reported by Wargelin et al (2017), the 6.8 ± 0.3 year period from Suárez Mascareño et al (2016) using ASAS data, and the wide peak around 8 years from Savanov et al (2012). The results do not support the shorter periods of 1.2 years (Cincunegui et al, 2007) or 3 years (Benedict et al, 1998). The authors note that their maxima and minima are approximately in phase with Wargelin et al (2017), but with a slightly longer period. They also discuss that the TiO absorption appears to have a longer activity cycle than the visual light curve, similar to observations of λ Andromedae by Mirtorabi et al (2003), possibly due to the spatial distribution of bright and dark spots on the star's surface.

The study concludes that since TiO is a major spectral feature of cool M-type stars, the B-index can serve as an effective indicator of magnetic activity cycles, especially in the absence of the usual indicators like CaII H&K lines, which are not very visible in M-stars. The average cycle length of 7.9 years for Proxima Centauri is consistent with the mean cycle lengths of 7.4 years for early M-types and 7.5 years for mid M-types found by Suárez Mascareño et al (2016).

Improvements to AI Systems:

1. Enhanced Stellar Activity Detection for Exoplanet Studies

• Improvement: Integrate the B-index (TiO absorption at 567 nm vs. continuum at 610 nm) as a new feature in AI models that analyze stellar spectra to disentangle stellar activity signals from planetary radial velocity (RV) signals.

• What the improved AI can do: Automatically identify and model long-term magnetic cycles (like the 7.9-year cycle in Proxima Centauri) in M-dwarf stars, reducing false positives in exoplanet detection by correcting RV variations caused by activity cycles. This is critical for habitable-zone planet searches around M-stars.

2. Multi-Wavelength Activity Cycle Forecasting

• Improvement: Train a time-series AI (e.g., transformer or LSTM) on multi-indicator activity data (CaII H&K, Hα, photometry, and now B-index) to predict the phase and amplitude of stellar cycles.

• What the improved AI can do: For a given M-star, forecast the timing of activity maxima/minima and cycle length, enabling observatories to schedule high-precision RV measurements during quiet phases to maximize exoplanet signal-to-noise.

3. Automated Cycle Detection in Sparse or Noisy Spectroscopic Data

• Improvement: Use the GLS periodogram results (2873 days, semi-amplitude 0.13 mag) as a labeled training set to build a deep learning classifier that detects periodicities in unevenly sampled time series from other stars, even with gaps or low signal-to-noise.

• What the improved AI can do: Automatically flag candidate magnetic cycles in large surveys (e.g., ESPRESSO, CARMENES) without manual periodogram inspection, and distinguish real cycles from aliases or rotational modulation.

4. Cross-Indicator Consistency Validation

• Improvement: Develop an AI-based anomaly detector that compares cycle periods derived from different activity indicators (e.g., B-index vs. photometric ASAS data vs. X-ray) to validate or reject conflicting claims (e.g., the 1.2-year or 3-year periods).

• What the improved AI can do: Quantify the statistical agreement between indicators, automatically flag outliers, and provide a unified, robust cycle period for a star by weighting evidence from multiple datasets—reducing human bias in literature comparisons.

5. Synthetic Spectral Modeling for M-Star Atmospheres

• Improvement: Use the B-index’s sensitivity to TiO absorption to train a generative AI (e.g., diffusion model) that synthesizes M-star spectra under varying activity levels, including spot coverage and temperature distributions.

• What the improved AI can do: Generate realistic mock spectra for training other AI models (e.g., RV extraction pipelines) under different activity scenarios, improving their robustness to stellar noise without needing new observations.

6. Real-Time Activity Monitoring for Space Missions

• Improvement: Embed the B-index calculation into an AI-driven pipeline for space telescopes (e.g., PLATO, JWST) that monitors M-dwarfs continuously.

• What the improved AI can do: Automatically detect the onset of an activity cycle in real time, trigger alerts for follow-up observations, and adjust exposure times or target priorities to maximize science yield (e.g., catching a planet transit during a quiet stellar phase).

7. Cycle–Magnetic Field Correlation Mapping

• Improvement: Train a regression model linking B-index cycle periods to stellar parameters (mass, rotation, metallicity) using Proxima Centauri and other M-dwarfs as training data.

• What the improved AI can do: Predict the expected activity cycle length for any M-star from its fundamental properties, aiding in stellar evolution models and habitability assessments (e.g., knowing when a star will be most hostile to planetary atmospheres).