[Paper Review] A Detection Threshold in the Amplitude Spectra Calculated from TESS Time-Series Data

A. S. Baran, C. Koen|arXiv (Cornell University)|Jun 17, 2021

Spectroscopy and Chemometric Analyses26 citations

TL;DR

The paper estimates the S/N detection threshold for amplitude spectra of simulated TESS time-series data at a false alarm probability (FAP) of 0.1%, deriving empirical S/N as a function of data coverage and cadence, and provides a formula to adjust thresholds for other FAPs and data lengths.

ABSTRACT

We present results of time-series data simulation. We aimed at estimating the threshold used for detecting signals in amplitude spectra, calculated from simulating TESS photometry of up to one year duration. We selected the threshold at a false alarm probability FAP=0.1% and derived S/N ratios between 4.6 and 5.7 depending on the data cadence and coverage. We also provide a formula to estimate the threshold for any FAP adopted and a given number of data points. Our result confirms that, to avoid spurious detection, space-based photometry may require substantially higher S/N than that typically being employed for ground-based data.

Motivation & Objective

• Motivate the need for robust detection thresholds in space-based time-series analysis due to higher spurious peak rates than ground-based data.
• Estimate the S/N threshold corresponding to FAP = 0.1% for TESS ultra-short, short, and long cadences across 1–13 observing sectors.
• Provide a practical formula to estimate thresholds for any chosen FAP and number of data points.
• Show that space-based photometry generally requires higher S/N than ground-based data to avoid false detections.

Proposed method

• Simulate Gaussian-noise TESS time-series data for ultra-short (20 s), short (120 s), and long (1800 s) cadences over 1–13 sectors.
• Compute amplitude spectra using a fast Fourier transform and standardise the spectrum (via median-based standardisation).
• Model detection thresholds as the maximum amplitude in the spectrum with a specified false alarm probability (FAP) and derive S/N ratios as a function of the number of sectors (Ns).
• Derive analytical expressions for cumulative distribution functions of spectrum maxima using standardisations W and U (Eqs. A2–A8) and compare with simulation results.
• Provide a closed-form relation for S/N versus Ns (Eq. 3) and discuss effective Np adjustments when restricting the frequency range (N_eff).
• Present tabulated S/N thresholds for FAP = 0.1% across cadences and Ns.

Experimental results

Research questions

• RQ1 What S/N threshold must be exceeded in amplitude spectra to claim a detection at FAP = 0.1% for TESS time-series data?
• RQ2 How does the required S/N threshold depend on cadence (ultra-short, short, long) and the number of observed sectors?
• RQ3 How can one adjust the threshold for different FAPs or when restricting the frequency range of interest?
• RQ4 To what extent do data gaps or cadenced observing impact the false-alarm thresholds?
• RQ5 What practical guidelines emerge for avoiding spurious detections in space-based photometry compared to ground-based data?

Key findings

• For FAP = 0.1%, the S/N thresholds range from about 5.3–5.6 (ultra-short), 5.0–5.4 (short), and 4.6–5.0 (long cadence) depending on Ns.
• S/N thresholds increase with more sectors and higher cadence data, indicating space-based photometry requires higher S/N than typical ground-based thresholds (S/N = 4).
• The S/N thresholds can be predicted by logarithmic fits in Ns (Eq. 3) and can be adjusted for different FAPs using the derived CDFs (Appendix).
• Restricting the frequency range to a fraction f of the Nyquist interval reduces the effective data points to N_eff = N_p f, lowering the required S/N threshold for a given FAP.
• Gaps in sector data can raise the threshold by up to about 0.25 in S/N compared to gap-free data with the same point count, and aliasing may occur with long gaps.
• The paper provides a table (Table 1) of S/N thresholds across Ns for the three cadences at FAP = 0.1%.