Long-Term Optical and Spectral Variability of FSRQ 3C454.3

3C454.3 is a widely studied and monitored flat spectrum radio quasar. We use the observations from the Small and Moderate Aperture Research Telescope System (SMARTS) to analyze the long-term optical and spectral variabilities of 3C454.3 at B, V, R, J, and K (BVRJK) bands. Based on the relation: F] ∝ ], we calculate the multiband spectral indices (α) and analyze the relations between α and F], where F] is the flux density at ] band (]=B, V, R, J, K). Main results are as follows. (1) The largest variations at BVRJK bands are ΔB = 3.37±0.08 mag, with the timescale ΔTB ≈ 1015 days, at B band; ΔV = 3.31±0.07 mag, with the timescale ΔTV ≈ 1014 days, at V band; ΔR = 3.62±0.12 mag, with the timescale ΔTR ≈ 679 days, at R band; ΔJ = 4.08±0.01 mag, with the timescaleΔTJ ≈ 763 days, at J band; andΔK = 5.03±0.03mag, with the timescaleΔTK ≈ 2715 days, at K band. (2)We analyze the long-term BVRJK lightcurves and obtain the quasiperiodicities: P1 = 86.92 ± 2.21 days, P2 = 204 ± 8.1 days, and P3 = 1.24 ± 0.19 years. (3) Multiband lightcurves show time delays: τVB = 0.15 ± 0.12 days, τRB = 0.37 ± 0.28 days, τJB = 0.58 ± 0.40 days, and τKB = 1.02 ± 0.47 days. (4) The relations between α and F] show strong correlations, which are typical RWB behaviors; when the source turns to be brighter, the spectral indices turn to be redder.


Introduction
Blazars show some extreme properties, such as violently optical variability, core dominance, and superluminal motion [1,2]. Blazars can be divided into two subclasses: BL Lacs and FSRQs (flat spectrum radio quasars). BL Lacs are characterized by featureless optical spectra or weak emission line [3], and FSRQs are composed of the flat-spectrum radio spectrum and show typically broad emission lines [1].
Blazars have relativistic jets. eir jets can produce the nonthermal emission, which can dominate the total observed emission. Many works analyzed the relations between spectral indices (or spectrum) and flux densities (or brightness) (e.g., [4][5][6][7][8][9][10]). ose studies can explain the reasons behind the characteristic of blazar variability and can also help us to constrain the emitting region. BL Lacs and FSRQs show different correlations. Generally, BL Lacs show that when the sources become brighter, the spectrums become harder and when the sources become fainter, the spectrums become softer. FSRQs show that when the sources become brighter, the spectrums become softer (redder). The redderwhen-brighter (RWB) behavior of FSRQs can be explained as the contribution from less variable, bluer accretion disk to the variable, redder jet emission. Kirk and Mastichiadis (1999) [11] put forward that, for blazars, the spectral shape can be influenced by the synchrotron particle acceleration and synchrotron cooling. The spectral shape can reflect the intrinsic variability of jet [12][13][14][15]. Fiorucci, Ciprini, and Tosti (2004) [16] pointed out that the optical spectrum of QSOs (subclass of Active Galactic Nuclei) consisted of two components, the first one was variable ( V , with a flatter slope), which came from synchrotron emission, and the other part was stable ( ), which might come from the thermal emission. Fan et al. (2014) [17] pointed out that the correlation between brightness and spectral index can be influenced by the brightness intensity.
This paper is arranged as follows: in Section 2, we introduce observations and data reductions; in Section 3, results are proposed; Section 4 includes discussion and conclusion.

Results
. . Periodicity Analysis. It is very important to choose suitable methods to analyze the long-term optical variability. Considering the uneven lightcurves, we avail the power spectrum to deal with this question and choose the common part as the quasiperiodicity.  The mostly common tool for periodicity analysis of both evenly and unevenly sampled signals is the Periodogram method, which is an estimator of the signal energy in the frequency domain by Deeming (1975) [33]. Lomb (1976) [34] introduced a modified form of this method, and additionally it was elaborated by Scargle (1982) [35], which can be described in the following. Considering a series ( ) with N points, is the frequency and is a variable timescale. Their mean and deviation are given by = (1/ ) ∑ =1 ( ) and The normalized Lomb's , i.e., the power spectrum as a function of the angular frequency ≡ 2 > 0 is defined as and is defined by the equation: The errors of the period are estimated by the half width at half-maximum (HWHM) of the minimum standard deviation ( 2 ). We use the Periodogram method to analyze the BVRJK lightcurves and obtain the periodicities 1 = 86.92 ± 2.21 days, 2 = 204 ± 8.1 days, 3 = 1.24 ± 0.19 years.
The periodic signals are shown in Figure 2. Red noise is a random signal, which has been filtered in order to generate a lot of energy at low frequencies. In order to check the strength of the periodic signal, we compare the periodic signal with the red noise. The red noise [36] with the noise levels 80%, 90%, 95%, and 99% is shown in Figure 2. Based on the results, we can find that at the whole five bands, 1 is higher than 99% noise level, at J and K bands, 2 is higher than 90% noise level, and only K band 3 are higher than 99%.
. . e Spectral Indices. We use the following method to obtain the spectral indices. Firstly, we make Galactic Extinction correction, using After calculation, there are 752 spectral indices ( ), which are in the range from 0.33 ± 0.01 to 2.02 ± 0.07, with the averaged value = 1.26 ± 0.31.

. . Relations between Flux Densities and Spectral Indices.
Because the linear relations can clearly show the interdependence between the two parameters, so many works used the linear correlations to analyze the relations between spectral indices ( ) and flux densities (^). To compare with the others, we use linear correlations to analyze = k log ] + , with the correlation coefficient r and the chance probability p, the slope k, and the intercept b. When the absolute value of r is higher than 0.5 and p is lower than 0.05, the correlations show strong correlation.
e results are as follows:

Discussion
. . Optical Variability. e optically variable timescale is an important physical quantity and is often used to probe the physics process of blazars. Based on the optical-infrared lightcurves, we obtain the spectral indices ( ) and analyze the long-term variability; see Figure 4 (the upper subpicture). The spectral variability shows quasiperiodic properties, |1 = 0.55 ± 0.08 years, |2 = 0.85 ± 0.07 years, and |3 = 1.21 ± 0.06 years, among which |3 shows the strongest signal and is consistent with the result calculated from the lightcurves; see Figure 4 (the lower subpicture). The upper results show that the lightcurves and spectral variability have the same long-term variation tendencies.
If the long-term periodicity (P) is caused by a slim disk, the periodicity can be expressed as / = 9.0 ( /0.1) −0.62 ( /10 6 ⊙ ) 1.37 , where is the viscosity coefficient [18], is periodicity (in unit of years), and is the central black hole mass. e mass calculated from this method is about ∼ 10 6 ⊙ , which is smaller than the others, Advances in Astronomy  [37]. Long-term periodicity might come from the influence of binary black hole. OJ287 is considered as a binary black system [38]. Some authors [39,40] consider PKS 1510-089 as a binary black hole.
3C454.3 might be a binary black hole system. Based on the variability timescales, Li et al. (2007) [40] gave a method about how to calculate the masses of the primary black hole ( 1 , PBH) and secondary black hole ( 2 , SBH). The methods are as follows.
(1) The distance (a) between the two black holes can be calculated from the following relation: where Δ is variable timescale, is the quasiperiodicity, and is the ratio between the jet diameter and radius of secondary black hole.
. . Time Delay among Different Bands. The analysis about the multiband time delays can help us to study the emission properties and can reflect the terms of electron cooling timescales [42,43]. For S + , Gupta [46,47] to explore time delays among different bands. In order to get the delay time more accurately, we use three methods to fit the DCF results: local polynomial regression (LOESS) [48], local Kernel regression (LOCFIT) [49], and Gaussian regression. The fitting curves have been added in Figure 5, in which red lines stand for Gaussian regression, blue lines stand for Locfit regression,

. . Relation between Flux Density and Spectral Index.
In this work, we analyze the relations between flux densities and spectral indices. At the whole five bands (B,V,R,J,K), log ] and show strong correlations. When the source turn to be brighter, the spectrum turn to be redder, which is a typical RWB behavior and consistent with the other FSRQs [32,50,51].
We check those distributions and find that there lie break points; see Figure 6. We use a broken power law to fit them and obtain the break points: log 10 ( | ) = 0.58 mJy, log 10 ( | ) = 0.69 mJy, log 10 ( | ) = 0.78 mJy, log 10 ( | ) = 1.12 mJy, log 10 ( | ) = 1.49 mJy, which are noted in Figure 6. When the source becomes fainter, the relations show correlations and when the source becomes brighter, their relations turn to be anticorrelations.
In this paper, we use the observations of 3C454.3 from SMARTs to analyze the lightcurves and calculate the optical spectral indices. Our results show that except K band, the largest variances at B, V, R, and J bands are similar (about 3.5 mag) within about 3 years. The long-term bright variability and spectral variability have the same quasiperiodicities. There lie time delays among different optical and near-IR bands (B, V, R, J, K).

Data Availability
The text formatting data used to support the findings of this study have been deposited in the "http://www.astro.yale.edu/ smarts/glast/home.php" repository. The data on the upper website are public and may be used by other investigators. If others intend to make use of the data, please inform the SMARTs group by email to glast@elilists.yale.edu and send copies of any resulting publications, including telegrams. Please acknowledge them in your paper by including a citation to the Bonning et al. (2012), mentioned above, and with the following: "This paper has made use of upto-date SMARTS optical/near-infrared lightcurves that are available at http://www.astro.yale.edu/smarts/glast/home .php." Please also include "SMARTS" as a facility keyword.
Advances in Astronomy

Conflicts of Interest
The authors declare that they have no conflicts of interest.