Application of time-series analysis methods to a multiple-sector TESS observations: the case of the radio-loud blazar 3C 371

We present various time series analysis methods to analyze multiple-sector observations of bright AGN from the Transiting Exoplanet Survey Satellite (TESS) and examine whether issues such as gaps and noise in these data can be mitigated. We determine variability timescales and search for quasi-periodicity using these methods and assess any differences. In this paper, we present an analysis of the $\approx$300-day TESS observation of a blazar 3C 371 using power spectrum density, structure-function, and weighted wavelet Z-transform approaches. To reduce the effect of gaps and noise, Continuous auto-regressive moving averages, Bartlett periodogram, and wavelet decomposition methods are used. We have also used recurrence analysis to account for the nonlinearity present in the data and to quantify variability or periodicity as the recurrent state. Considering the entirety of the TESS observations, we derive the variability timescale to be around 4.5 days. Sector-wise analysis found variability timescales in the range of 3.0–7.0 days, values that are found to be consistent using different methods. When analyzing multiple sectors together, significant variability, which could be quasi-periodic oscillations (QPOs), of duration 3–6 days in individual segments, is detected. These may be attributed to the kink instabilities developed in the jet or the existence of mini-jets inside a jet undergoing precession. We find that these methods, when applied appropriately, can be used to study the variability in TESS data. The noise present in these TESS observations can be minimized using Bartlett’s periodogram and wavelet decomposition to recover the real stochastic variability.

💡 Research Summary

This paper presents a comprehensive analysis of approximately 300 days of high-cadence optical photometric data for the radio-loud blazar 3C 371, obtained by NASA’s Transiting Exoplanet Survey Satellite (TESS). The primary objective is to demonstrate and evaluate the application of multiple time-series analysis techniques to real astronomical data, which is often plagued by issues like irregular sampling, data gaps, and various sources of noise. The study aims to mitigate these issues to reliably extract intrinsic variability signals originating from the physical processes within the blazar.

The data comprises TESS Cycle 2 observations from Sectors 14 to 26 (excluding Sector 19), spanning from July 2019 to July 2020. The light curves were processed using the specialized ‘Quaver’ pipeline, which is designed to preserve the stochastic variability of Active Galactic Nuclei (AGNs). The authors employed the ‘fully hybrid’ reduction method, which rigorously removes high-frequency instrumental systematics, making it suitable for analyzing rapid variations, despite potentially overfitting longer-term trends.

The methodological framework is threefold. First, traditional variability characterization using Power Spectral Density (PSD) and the Structure Function (SF) was performed to estimate the characteristic timescale at which variability power is most prominent. Second, gap and noise mitigation techniques were applied. This includes modeling the light curve in the time domain using a Continuous-time Auto-Regressive Moving Average (C-ARMA) process, specifically a Damped Harmonic Oscillator model, to interpolate across gaps. In the frequency domain, Bartlett’s method (averaging periodograms of data segments) and Wavelet Decomposition were used to reduce random noise and enhance the signal-to-noise ratio, particularly at lower frequencies. Third, non-linear dynamical analysis was introduced via Recurrence Analysis (RA). This technique reconstructs the phase space of the system and creates Recurrence Plots, which can distinguish deterministic (potentially quasi-periodic) processes from pure stochastic noise, offering insights beyond linear correlation measures.

The key results are as follows. Analyzing the entire ~300-day dataset, the characteristic variability timescale for 3C 371 was found to be approximately 4.5 days. A sector-by-sector analysis (each sector is ~27 days long) yielded variability timescales in the range of 3.0 to 7.0 days, with consistent values obtained from both PSD and SF methods, reinforcing the reliability of the measurement. Furthermore, when analyzing connected segments across multiple sectors, significant variability with durations of 3 to 6 days was detected in individual epochs. The authors suggest this could be evidence of Quasi-Periodic Oscillations (QPOs). They propose that such short-timescale oscillations might be attributed to physical processes within the blazar’s relativistic jet, such as kink instabilities developing in the jet flow or the presence of mini-jets undergoing precession inside the main jet.

In conclusion, the study successfully demonstrates that a multi-method approach is essential for robust time-series analysis of TESS data for AGNs. By combining traditional tools (PSD, SF) with advanced techniques for handling data imperfections (C-ARMA, Bartlett’s method, Wavelet Decomposition) and methods for uncovering non-linear dynamics (Recurrence Analysis), astronomers can more effectively separate true astrophysical signals from artifacts. The methodologies validated in this work for 3C 371 provide a powerful and transferable framework for analyzing the variability of a wide range of celestial objects monitored by TESS and future high-cadence space observatories.