# PKS 2155-304: A Case Study of Blazar Variability Power Spectrum at the Highest Energies and on the Longest Timescales

## Abstract

**:**

## 1. Introduction

## 2. Methodology: CARMA Modeling of the H.E.S.S. Light Curves

## 3. Results

## 4. Discussions and Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

PSD | Power Spectral Density |

CARMA | Continuous-time Auto-Regressive Moving Average |

## References

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4. | Data for the period 2004–2012 were obtained upon request from David Sanches. |

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**Figure 2.**Results of CARMA modeling on the long-term light curve (Figure 1a). Panel (

**a**) gives the logarithmically-transformed light curve along with the modeled values based on the best-fit Continuous-Time Auto-Regressive Moving Average (CARMA) process. Panel (

**b**) shows the standardized residuals and their distribution compared with the expected normal distributions. Panel (

**c**) gives the corresponding ACF compared with the $95\%$ confidence regions, shown by dotted lines, for a white-noise process. Panel (

**d**) gives the squared ACF compared with the $95\%$ confidence regions, shown by dotted lines, for a white-noise process. Panel (

**e**) gives the AICc values for different $(p,q)$ pairs (bands within the dotted lines refer to AICc values ranging from the lowest AICc to the lowest AICc + 10, which marks all the model sets, which are statistically indistinguishable from each other). Panel (

**f**) shows the resulting PSD with the $2\sigma $ confidence region, as well as noise floor levels, ${P}_{\mathrm{stat}}$, marked by horizontal black (=10.4 rms${}^{2}$ day, corresponding to the mean sampling interval of 13 days) and red (=0.08 rms${}^{2}$ day, corresponding to the median sampling interval of two days) lines, respectively. The best-fit CARMA model is obtained for $p,q$ = 2,1.

**Figure 3.**Results of CARMA modeling on the intra-night light curve (Figure 1b). The layout is the same as that of the Figure 2. ${P}_{\mathrm{stat}}$ is 0.000053 rms${}^{2}$ day, which corresponds to a mean (=median, in this case) sampling interval of 1.1 min. The best-fit CARMA model is obtained for $p,q$ = 1,0.

**Figure 4.**The combined long-term (shown in red color) and intra-night (shown in blue color) PSD from the H.E.S.S. monitoring, extending up to ∼6 decades in the temporal frequency range. The shaded area corresponds to the $3\sigma $ confidence regions, and the dashed horizontal lines mark the ${P}_{\mathrm{stat}}$, for the two datasets.

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**MDPI and ACS Style**

Goyal, A.
PKS 2155-304: A Case Study of Blazar Variability Power Spectrum at the Highest Energies and on the Longest Timescales. *Galaxies* **2019**, *7*, 73.
https://doi.org/10.3390/galaxies7030073

**AMA Style**

Goyal A.
PKS 2155-304: A Case Study of Blazar Variability Power Spectrum at the Highest Energies and on the Longest Timescales. *Galaxies*. 2019; 7(3):73.
https://doi.org/10.3390/galaxies7030073

**Chicago/Turabian Style**

Goyal, Arti.
2019. "PKS 2155-304: A Case Study of Blazar Variability Power Spectrum at the Highest Energies and on the Longest Timescales" *Galaxies* 7, no. 3: 73.
https://doi.org/10.3390/galaxies7030073