Distortions in Periodicity Analysis of Blazars II: The Impact of Gaps

TL;DR

This work analyzes how irregular sampling and gaps in blazar gamma ray light curves affect periodicity searches. It systematically compares LSP, PDM, and SSA on simulated red-noise and periodic signals under diverse gap patterns, revealing that SSA is robust to moderate data loss but can introduce 1-year artifacts under seasonal sampling. The study further shows that gap effects can mimic or distort true periodicities, and that a 50% gap threshold is a practical cutoff for reliable analyses. Real data tests on a large gamma ray blazar sample yield no robust periodic detections, underscoring the need for gap aware methods and careful interpretation of apparent periodicities in the presence of incomplete data.

Abstract

Time series analysis is fundamental to characterizing the variability inherent in multi-wavelength emissions from blazars. However, a major observational challenge lies in the need for well-sampled, temporally uniform data, which is often hindered by irregular sampling and data gaps. These gaps can significantly affect the reliability and accuracy of methods used to probe source variability. This paper investigates the impact of such observational gaps on time series analysis of blazar emissions. To do so, we systematically evaluate how these gaps alter observed variability patterns, mask genuine periodic signals, and introduce false periodicity detections. This evaluation is conducted using both simulated and real observational data. We assess a range of widely used time series analysis methods, including the Lomb-Scargle periodogram, Phase Dispersion Minimization, and the recently proposed Singular Spectrum Analysis (SSA). Our results demonstrate a clear and significant degradation in period detection reliability when the percentage of gaps exceeds 50\%. In such cases, the period-significance relationship becomes increasingly distorted, often leading to misleading results. Among the tested methods, SSA stands out for its ability to yield consistent and robust detections despite high data incompleteness. Additionally, the analyzed methods tend to identify artificial periodicities of around one year, likely due to seasonal sampling effects, which can result in false positives if not carefully recognized. Finally, the periods detected with $\geq$3$σ$ confidence are unlikely to result from stochastic processes or from the presence of gaps in the analyzed time series.

Figures (19)

• Figure 1: Right: Distribution of the number of ULs (interpreted as observational gaps in this paper) of the sample of 3,300 AGN analyzed in penil_trends. The median of this distribution is $\approx$32%, denoted by the dotted vertical line. The majority of the objects are in the range 20%-50% (denoted by the 25th and 75th percentiles). Left: Distribution of consecutive gaps of the LCs in our sample, using a bin size of 28 days. The histogram illustrates that the majority of ULs appear as isolated points, with a maximum observed consecutive UL sequence of 161. Additionally, most UL sequences remain short, while consecutive UL lengths of $\geq$12 are grouped in the final bin to highlight extended sequences.
• Figure 2: Examples of noise LCs and random gaps distribution. Top Left: Pure noise. Top Right: 40% of gap distribution. Bottom: 90% of gap distribution.
• Figure 3: Examples of LCs to illustrate the different annual variability distribution using as a test. The LCs are pure sinusoidal without adding any noise to help see the differences in the gap distribution. We consider a percentage of gaps of 60%. Left: Annual variability with periodic gap distribution. Right: Annual variability with random gap distribution, denoting in the legend as "Aperiodic Annual Distribution".
• Figure 4: SSA decomposition showing the underlying oscillatory structure using a window length of 20%. Top: NVSS J095501+083342 and FBQS J111056.8+353907 (see Figure \ref{['fig:example_use_cases']}). Bottom: PG 1553+113 (see Figure \ref{['fig:example_use_cases']}). The flux axis shows negative values because it represents only the oscillatory component, excluding the overall emission behavior of the source. As a result, the oscillatory component is centered around zero, reflecting deviations from the mean rather than the total flux.
• Figure 5: Distributions for the period and significance for pure noise LCs, for LSP. Left: no gaps. Center: 50% of randomly distributed gaps. Right: 70% of randomly distributed gaps. The results denote the evolution of the period according to the increase in the percentage of gaps. When there are no gaps, the period distribution is approximately homogeneous in the period range, with an excess in the higher period expected for the red noise LCs. With the introduction of gaps, this disruption is modified to a lower period. The dotted red vertical and horizontal lines indicate the median values for both the period and the significance of the test. The blue dotted vertical line highlights the most frequently occurring period in the tests (and the associated significance), emphasizing its prominence in the distribution. The "Percen. of Gaps" refers to the percentage of gaps injected in the LC. The "Median Period" represents the median of all periods resulting from the test, and the "Std Period" is the standard deviation of such periods' distribution. The "Median Significance" represents the median of the significance distribution associated with the test, and the "Std Significance" is the standard deviation of this significance distribution. "Mfp" represents the most frequent period resulting from the test.