# Study of optical and gamma-ray long-term variability in blazars ††thanks:
Presented at Krakow Epiphany 2022 international conference

Gopal Bhatta  Institute of Nuclear Physics, Polish Academy of Sciences PAN
PL-31342 Krakow, Poland

###### Abstract

Blazars, a subset of powerful active galactic nuclei, feature relativistic
jets that shine in a broadband electromagnetic radiation, e. g. from radio to
TeV emission. Here I present the results of the studies that explore gamma-ray
and optical variability properties of a sample of gamma-ray bright sources
Several methods of time-series analyses are performed on the decade-long
optical and Fermi/LAT observations. The main results are as follows: The
sources are found highly variable in both the bands, and the gamma-ray power
spectral density is found to be consistent with flicker noise suggesting long-
memory processes at work. While comparing two emission, not only the overall
optical and the $\gamma$-ray emission are highly correlated but also both the
observation distributions exhibit heavy tailed log-normal distribution and
linear RMS-flux relation. In addition, in some of the sources indications of
quasi-periodic oscillation were revealed with similar characteristic
timescales in both the bands. We discuss the results in light of current
blazar models with relativistic shocks propagating down the jet viewed close
to the line of sight.

##  1 Introduction

Active galactic nuclei (AGN) are one of the most luminous sources in the
Universe. The sources are powered by the accretion on to the supermassive
black holes at the center of the distant galaxies. The objects can be broadly
classified in two main groups: radio-loud AGN and radio-quiet AGN. While a
large fraction of AGN do not show prominent radio emission, about 10% of them
output a significant amount of radio emission [1]. The emission can be linked
to the presence of kpc/Mpc scale radio jets as seen in the VLBI images. The
bipolar jets are often found to remain highly collimated over large distances
and mostly contain plasma matter traveling at the nearly at the speed of the
light. In a small sub-group of the radio-loud AGN, the jet is aligned to the
line of sight at $\lesssim 6^{o}$ [2], such that the relativistic beaming
effects dominate lending the sources some of their extreme observational
properties such as high luminosity, TeV emission and rapid variability.

The broadband emission from blazars can be characterized by a double-hump
feature in the frequency-flux plane. It is widely accepted that the low
frequency feature of the spectrum, lies between radio and X-ray, arises due to
the synchrotron emission by the energetic charged particle moving in the jet
magnetic field; whereas the high frequency feature, that lie between UV and
gamma-rays, probably results due to the inverse-Compton scattering of the low
energy photons by high energy particles. In the synchrotron self-Compton (SSC)
leptonic models, the same population of electrons up-scatters the co-spatial
synchrotron photons. But in the external Compton (EC) models the low energy
seed photon could be contributed by accretion disk, dusty torus and broad-line
regions (BLR). Blazars can be further sub-classified into two groups: the more
powerful flat spectrum radio quasar (FSRQ) that show emission line over the
continuum emission and the less powerful BL Lacs showing weak or no presence
of emission lines. The sample of TeV blazars is mostly dominated by BL Lacs.

Blazars display multi-timescales variability across a broad range of
electromagnetic spectrum (see e. g. [3, 4, 5, 6]). The basic character of
variability appears to be stochastic in nature such that the statistical
properties of the variability can be fairly represented by power-law models in
the frequency domain. In addition, the sources light curves also show
occasional rapid flares and quasi-periodic oscillations [7]

As multi-wavelength (MWL) variability is defining properties of AGN,
variability studies are important tool to probe the energetics of the central
engines of AGN. In this proceedings, I discuss the recent results of the
studies focused on the time series analysis of a sample of gamma-ray bright
blazars. The decade-long gamma-ray observations from Fermi/LAT and the optical
observations from four different observatories were analyzed and the results
in the two bands were compared.

Table 1: Sample sources for study of gamma-ray and optical variability of blazars Source name | 3FGL name | Source class | Red-shift
---|---|---|---
3C 66A | J0222.6+4301 | BL Lac | 0.444
AO 0235+164 | J0238.6+1636 | BL Lac | 0.94
PKS 0454-234 | 3FGLJ0457.0-2324 | BL Lac | 1.003
S5 0716+714 | J0721.9+7120 | BL Lac | 0.3
Mrk 421 | 3FGLJ1104.4+3812 | BL Lac | 0.03
TON 0599 | J1159.5+2914 | BL Lac | 0.7247
ON +325 | J1217.8+3007 | BL Lac | 0.131
W Comae | J1221.4+2814 | BL Lac | 0.102
4C +21.35 | 3FGLJ1224.9+2122 | FSRQ | 0.432
3C 273 | J1229.1+0202 | FSRQ | 0.158
3C 279 | J1256.1-0547 | FSRQ | 0.536
PKS 1424-418 | 3FGLJ1427.9-4206 | FSRQ | 1.522
PKS 1502+106 | 3FGLJ1504.4+1029 | FSRQ | 1.84
4C+38.41 | J1635.2+3809 | FSRQ | 1.813
Mrk 501 | J1653.9+3945 | BL Lac | 0.0334
1ES 1959+65 | J2000.0+6509 | BL Lac | 0.048
PKS 2155-304 | J2158.8-3013 | BL Lac | 0.116
BL Lac | J2202.7+4217 | BL Lac | 0.068
CTA 102 | J2232.5+1143 | FSRQ | 1.037
3C 454.3 | J2254.0+1608 | FSRQ | 0.859

##  2 Observations and Data

Gamma-ray variability of blazars was investigated using Fermi/LAT observations
spanning nearly 10 year from 2008-2018 in the spectral range 100 MeV to 300
GeV. The sample source along with their Fermi/LAT 4-year Source Catalog (3FGL)
name, source classification and red-shift are listed in Table 1. The data
processing was performed using the standard procedure of likelihood analysis
of the unbinned analysis and weekly binned source light curves were produced.
111https://fermi.gsfc.nasa.gov/ssc/data/analysis/scitools/likelihood_tutorial.html
(For details see [8])

That optical data for the sources marked in the fold fonts in Table 1 were
gathered from four ground based observatories:
SMARTS222http://www.astro.yale.edu/smarts/glast/home.php, Steward
observatory333http://james.as.arizona.edu/~psmith/Fermi/,
Catalina444http://nesssi.cacr.caltech.edu/DataRelease/ and
AAVSO555https://www.aavso.org/. The data were complied to create a dense
observations constructing 10 year-long optical light curves (For details see
[9]).

##  3 Analysis and Results

The decade-long optical and gamma-ray observations were analyzed using several
methods of time-series analysis. In particular, the observed variability was
quantified by computing fractional variability of the source light curves [10,
11]. The large fractional variability values are the indications that blazars
exhibit remarkable variability on diverse time-scales. Also to compare the
variability in the optical and the gamma-ray band, the results show that the
variability amplitude are larger in the gamma-ray.

Power spectral density analysis of the gamma-ray light curves was performed by
computing the discrete Fourier periodogram of the source light curves. The
effects of unevenly sample, discrete observations and finite observation
lengths were corrected by the use of a large number mock light curves that
were simulated by the Monte Carlo method described in [12]. It is found that
the power spectral density of the gamma-ray observations are consistent with
single power law model with spectral index $\sim$ 1, often known as long-
memory flicker noise. The result implies a strong dik-jet connection in the
sense that the jet modulations are somehow coupled to the disk modulations.
The optical PSD is however steeper, closer to the Brownian motion, than that
of the gamma-ray PSD slope index.

The flux distribution of the gamma-ray and optical flux of the blazar was
explored by fitting the flux histograms with normal and log-normal probability
distribution function (PDF). The analysis revealed that flux distribution can
be represented by log-normal PDF [8]. Similar results were obtained in a study
of optical variability of blazars using decade-long optical observations [9].
In addition, the source light curves in both the bands were divided into
several segments and relation between the mean and RMS of the segments were
analyzed. It was found that majority of the sample sources displayed a linear
dependence between the RMS and the flux, so called linear RMS-flux relation.

In addition to the PSD and PDF, the light curves were studied to look for
possible quasi-periodic oscillations (QPO) in the light curves. For the
purpose the gamma-ray observations were analyzed using the methods Lomb-
Scargle periodogram [13, 14] and Z-transformed Weighted Wavelet methods [15].
The results showed that the light curves of the sources Mrk 501, Mrk 421, S5
0716+714, PKS 1424-418, ON +325 and PKS 2155-314 revealed year timescale QPOs
which were found to be significant over the red-noise inherent in blazar light
curves [8, 7]. Moreover, in the sources Mrk 501, Mrk 421, S5 0716+714 and PKS
2155-314 the observed QPOs were found to have similar characteristic
timescales (See Table 4 in [9]).

Furthermore, a cross-correlation study between the optical and gamma-ray light
curves was conducted using z-transformed discrete correlation function (ZDCF)
[16], a method frequently used in the discretely sampled data sets with gaps.
Moreover, significance of the ZDCF peaks against any spurious correlation
arising due to red-noise is computed. The results suggest that both optical
and gamma-ray emission from the sources highly correlate with each other
within the timescales of a few weeks (See Table 5 in [9]).

##  4 Discussion

A study of long-term variability properties of gamma-ray bright blazar was
performed using the gamma-ray observations from the Fermi/LAT space telescopes
and the optical observation. In the standard model of blazars the observed
variability can be mainly ascribed to the processes occurring at accretion
disk and jets of AGN. In the disk scenario, the magneto-hydrodynamics
instabilities arising from modulations in the accretion rates, viscosity
parameter and the magnetic field can lead to the observed variability.
Similarly in jets related scenarios some of the widely discussed models are
based on particle acceleration due to shock waves and/or due to turbulence
wide spread in the jets, and the subsequent cooling of the particles via
dissipative processes such as synchrotron and inverse-Compton emission [17,
18, 19, 20]. In such scenarios, variable injection rates could also produce
the optical variability [3]. Moreover, strong correlation between the optical
and the gamma-ray emission suggests existence of co-spatial particle that
contribute to both the emission. In the case of magnetized jets, magnetic
reconnection could be a dominant particle accelerating mechanism, and several
mini-jets could form within the main jets such that it could be source of TeV
emission [21]. The observed log-normal PDF of blazar flux could be indication
of such processes [22]. Power-law PSD of slopes of unity in particular
describe the long-memory processes at work such that the flux changes in the
accretion disk can propagate along the jets and somehow affect the variable
processes along the jets. The fact that the source flux distribution are
consistent with the log-normal PDF indicates the processes being
multiplicatively coupled to result in the total observed variable emission, as
opposed to linear combination of additive processes such as shot noises[23].
Moreover, the linear dependence between the flux and the RMS, which are more
relevant to the galactic X-ray binary systems, are often explained in terms of
the propagation of viscosity modulations at the disk [24]. That fact that we
observe similar trend in the blazar sample sources, where the disk emission is
completely swamped by the jet emission, indicates a strong coupling between
the jet and disk.

The peaks in the periodogram that appear in both the bands on similar
timescales imply plausibility of MWL QPOs with a common origin. Such QPO can
arise either from the accretion disk and the jets. Some of the widely
discussed blazar QPO models include binary supermassive black holes, passage
of the emission region along helical jets, Lense-Thirring precession, and
periodic jet angle modulations(readers are directed to [4, 5, 7] for detailed
discussion on the topic)

### Acknowledgment

I acknowledge financial support by the Narodowe Centrum Nauki (NCN) grant
UMO-2017/26/D/ST9/01178.

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