A Possible Optical Quasi-periodic Oscillation of 134 day in the Radio-loud Narrow-line Seyfert 1 Galaxy TXS 1206+549 at $z=1.34$

Zwicky Transient Facility is a new 48 inch Samuel Oschin Telescope at Palomar Observatory with a 47 square degree field of view camera in optical wavelength (Graham et al., 2019; Bellm et al., 2019). It has scanned the entire Northern sky every two days started in 2018, and released high quality data products every two months. Such an observation cadence makes ZTF archival data very suitable for time-domain science, especially for the exploring of periodic variabilities in the timescales of sub-year-long ones. The ZTF released data can be obtained from the website of the archive science data¹¹1https://irsa.ipac.caltech.edu/Missions/ztf.html.

The source TXS 1206+549 (at the same coordinate as it in 4FGL) is one of ZTF targets. It has been monitored more than 1300 day spanning from 2018 March 23 to to 2021 December 2 (MJD 58,200-59,550) in the g-, r-, and i-bands. We show the optical light curves of g-, r-, and i-bands by ZTF in the panels A, B, and C of Figure 1, respectively. The median and minimum time intervals of two adjacent data points of g-band (r-band) are $\sim 0.927$ (0.829) and 0.001 (0.001) day, respectively, the maximum interval is 126.266 (126.262) day at MJD 59,454 (marked with a pink star in Figure 1). For g-band, the brightest and faintest epochs of target are at MJD 58,561.3 and 59,265.4 with the magnitudes of 19.1 (indicated with a red arrow) and 20.8 (a green arrow), respectively. The weighted magnitude was calculated and weighted by the errors of data points with a formula of $\overline{M}=\sum{w_{i}*M_{i}}$, where $w_{i}=\frac{1}{\sigma^{2}_{i}}\frac{1}{W}$, $W=\sum{\frac{1}{\sigma^{2}_{i}}}$, and $\sigma_{i}$ indicating the errors. And the weighted standard deviation ($\rm\sigma_{d}$) was calculated by $\rm\sigma_{d}$=$\sum{w_{i}*(M_{i}-\overline{M})^{2}}$, its value is 34.4%. For r-band, the corresponding epochs are MJD 58,306.2 and 58,227.3 at the magnitudes of 18.5 and 20.3 shown with red and green arrows in B panel of Figure 1. Its values of $\overline{M}$ and $\rm\sigma_{d}$ are 19.53 and 38.0%. We show that weighted results of g- and r-bands as horizontal gray lines and yellow shaded regions, respectively.

Asteroid Terrestrial-impact Last Alert System²²2https://fallingstar-data.com/forcedphot/ consists of four 0.5 m telescopes with two of them in Hawaii, one each in Chile and South Africa (Tonry et al., 2018), which provides public access to photometric measurements over its full history survey. TXS 1206+549 is one of the objects monitored by ATLAS. We obtained its o-band light curve from the website of archive data³³3https://fallingstar-data.com/forcedphot/queue/. ATLAS observations for TXS 1206+549 span from 2015 December 9 to 2023 March 28 (MJD 57,365.6-60,031.4), we show the o-band light curve with a simultaneous observations of ZTF in D panel of Figure 1. For the simultaneous o-band light curve, the median, minimum and maximum time intervals of two adjacent data points are 1.6, 0.0005 and 146.3 day. Its minimum, maximum, and median magnitudes are $\sim$15.3, 25.6 and 19.7 respectively. It should be noted that data quality of ATLAS light curve is poorer than that obtained by ZTF (see D panel of Figure 1), and the ATLAS light curve is used only as an independent check for that QPO detected by ZTF observations.

The source TXS 1206$+$549 was cataloged in the fourth Fermi Large Area Telescope catalog (4FGL-DR3, Fermi-LAT collaboration et al., 2022) and named as $\gamma$-ray point source 4FGL J1208.9$+$5441 with a coordinate (R. A. = $\rm 12^{h}08^{m}54^{s}.264$, decl. = $+54^{\circ}41^{{}^{\prime}}58^{{}^{\prime\prime}}.208$). In the $\gamma$-ray data analysis, the Pass 8 $Front+Back$ SOURCE class events (i.e., evclass=128 and evtype=3) were selected with the energy range of 0.1–500 GeV spanning from 2008 August 4 to 2022 June 22 centered at target’s position within a $20^{\circ}\times 20^{\circ}$ region of interest (RoI). The events were reduced by a selection of the zenith angle $\leq 90$ and an expression of ”DATA_QUAL$>$0&&LAT_CONFIG==1” to obtain those high-quality events in the good time intervals. Then a binned maximum likelihood analysis was performed between the whole data and a model file. The model contains the parameters of the flux normalizations and spectral shapes for all known 4FGL sources in the RoI. In 4FGL-DR3, the $\gamma$-ray emissions from TXS 1206$+$549 was described by a log-parabolic spectrum model with a form of $dN/dE=N_{0}(E/E_{b})^{-\alpha-\beta\log(E/E_{b})}$. We obtained an average photon flux of $3.13(2)\times 10^{-8}$ photons cm^-2 s^-1 in the 0.1–500 GeV energy range with a test statistic (TS) value of 2,810.18. Its best-fit spectral parameters $\alpha$, $\beta$, and $E_{b}$ are 2.53(1), 0.07(1), and 0.42(1) GeV, respectively. Those values are in agreement with those reported in 4FGL-DR3. All the corresponding best-fit parameters were saved as a new model file, and the following light curve analysis was carried out based on this model.

Then a monthly light curve with 0.1–500.0 GeV energy range was constructed by performed an unbinned likelihood analysis during the corresponding observations. In this analysis, we only freed the flux normalizations for the sources within $5^{\circ}$ RoI, others were fixed at their best-fit values. In order to catch the variations as complete as possible, the data points with TS $\geqslant$ 4 are included in the following periodic analysis. We show flux variations and their corresponding TS values for each time-bin as black crosses and pink shaded regions in Figure 2, respectively. And the nearly simultaneous light curve with ZTF observations is shown in E panel of Figure 1 to facilitate comparison of multi-wavelength variabilities. The average photon flux over the whole Fermi-LAT observations in 0.1–500.0 GeV is shown as a blue dashed-dotted line.

Two different mathematical techniques, the generalized Lomb-Scargle periodogram (LSP; Lomb, 1976; Scargle, 1982; Zechmeister & Kürster, 2009) and the weighted wavelet Z-transform (WWZ; Foster, 1996), were employed in the periodic variability analysis for optical and $\gamma$-ray light curves. These independent techniques were used to check each other results. In the optical g- and r-bands data from ZTF observations, we found a periodic signal with a sharp peak at the similar period in their power spectra.

For the g-band light curve, we constructed its LSP power spectrum and show it in left panel of Figure 3 with red histogram in log-log units. From it, a significant QPO signal presents in the LSP power spectrum. The periodical variations can be described by a sinusoidal function with a form of $A\sin([2\pi(t-t_{0})/P])+A_{0}$. Their parameters and uncertainties were derived by the LSP code, and their values are 0.300$\pm$0.016, 132.8$\pm$0.7 day, 58197.5$\pm$1.2, and 19.99$\pm$0.01 for $A$, $P$, $t_{0}$ and $A_{0}$, respectively. We show the sine in A panel of Figure 1 with an orange dashed sine. From it, about ten cycles of periodic modulation appears in the light curve.

A periodic signal or statistical fluctuations in a time-series may lead to a power peak in a power spectrum. In order to determine the significance level for periodicity signal, we employed a program for simulating light curve basing the power spectral density (PSD) and probability density function (PDF) of variations derived from the original light curve, as that provided by Emmanoulopoulos et al. (2013). In general, the power spectra of AGN light curves are typically described using a power-law (PL) or a smoothly bending power law plus a constant (SPL) models (González-Martín & Vaughan, 2012). In our analysis, the SPL model yielded the better maximum likelihood fitting results than the PL one. So, in the subsequent simulated light curve, we adopted the SPL model as the underlying best-fit PSD. We used the SPL, $PSD(f)=Kf^{-\alpha}[1+(f/f_{\rm bend})^{\beta-\alpha}]^{-1}+c$, to estimate the underlying PSD (González-Martín & Vaughan, 2012). Then the maximum likelihood fitting was employed to obtain their best-fit parameters for the PSD (Barret & Vaughan, 2012). In the fitting, we make the assumption that the components of the periodogram asymptotically follow a $\chi^{2}$ distribution around the underlying PSD model. Employing maximum likelihood estimation and minimizing the negative logarithmic likelihood function, we obtained the best-fit parameters. We present the best-fit parameters along with their associated relative uncertainties in Table 1. Based on them, the program generated the artificial light curves. The artificial light curves have similar PSD and PDF comparing with them derived from the original light curve. Using the simulation code, we generated $10^{6}$ artificial light curves for g-band data. The 4$\sigma$ significance curve built based on these light curves is shown in left panel of Figure 3 with a green dashed line. And the significance level of the QPO signal in the g-band is $\sim 4.4\sigma$ (with $p$-value of $1\times 10^{-5}$).

The same process was carried out for r-band data, and the results are shown in right panel of Figure 3. A power peak presents in its power spectra with a similar period as that detected in g-band. The sine parameters and uncertainties are 0.334$\pm$0.016, 133.9$\pm$0.6 day, 58196.1$\pm$1.1, and 19.58$\pm$0.01 corresponding to $A$, $P$, $t_{0}$ and $A_{0}$, respectively. We show it in B panel of Figure 1 with a blue dashed-dotted sine and the 4$\sigma$ significance curve in right panel of Figure 3 with a green dashed line. Its significance of the periodic signal is $\sim 4.1\sigma$ (with $p$-value of $4.5\times 10^{-5}$).

Considering the observation cadence performed by ZTF for the target, in our analysis, we searched the QPO signal in a scale of frequencies between $f_{\rm max}$ = 1/7 and $f_{\rm min}$ = 1/1350 day^-1 by employed the LSP method, where 1350 day is approximately the total length of the data. In order to evaluate the precise significance for the QPO signal, we take a trial factor into our significance level calculation. The false-alarm probability (FAP) is derived by a form of FAP=1-(1-$p$)^N, where $N=192$ is the number of independent frequencies in the frequency range. The trial number is calculated by a form of $N=\frac{f_{\rm max}-f_{\rm min}}{\delta f}$, where $\delta f$ is determined by the mean total length of the g- and r-band data (i.e. the frequency resolution). After considering that the trial factor in the periodic signal searching, the significance of the QPO in the g-band is 3.1$\sigma$, while in the r-band, it is 2.6$\sigma$.

Then a independent method of WWZ was used to check the results obtained by the LSP. And a time–frequency WWZ power spectra were obtained for g- and r-band light curves, the suitable WWZ power values were calculated by changing the parameters of wavelets to match the LSP results. In g- and r-band data, a QPO signal presents in time–frequency power spectra over the whole-data time range, we show them in Figure 3 by scaled the power values with a colorbar. A time-averaged power spectra along the time-dimensionality were also created for WWZ power spectra, we show them in Figure 3 with a black curves, and a QPO signal presents in them too, which has the same shape and period as the LSP power spectra.

For the i-band light curve, a weak peak was also seen in its power spectra with a frequency corresponding to the periods determined from the g- and r-band light curves. It is worth mentioning that the i-band light curve comprises only 133 data points, which are concentrated in three time intervals with large gaps between them, namely 2018 June, 2019 May, and 2020 May (see C panel in Figure 1). It is possible that the properties of QPO variabilities may not be fully captured by i-band light curve because of these intervals. These causes may result in the QPO signal not being statistically significant in i-band.

By the same procedure, we searched the periodicity in the o-band light curve from the whole ATLAS observations, and no significant power peak in the power spectra was found. When we focused on the simultaneous light curve as the time scale of ZTF observations, a potential QPO signal with a similar period as that found in ZTF reveals in power spectra. We show them in left panel of Figure 4. The same case was also shown in the gamma-ray light curve, when we focuses on the simultaneous time scale of ZTF, a weak periodic signal was detected at similar period. We show the $\gamma$-ray results in right panel of Figure 4. For comparison, we show the QPO found in ZTF data with a blue dashed-dotted line in Figure 4.

Based on the results of the periodic analysis, we folded the light curves with the respective periods that detected in g- and r-bands. The folded light curves have a same phase zero at MJD 58200.0, which corresponding to the start time of ZTF observations. We show the folded data points with the raw data in lower panel of Figure 5. Based on the lower panel, we defined 30 phase bins to average the weighted magnitudes for each data point which falls into the corresponding phase bin. The weighted magnitudes and their errors were calculated with the same procedure presented in Section 2.1. In lower panel, for g-band (r-band), the minimum, maximum, and mean values are $\sim$19.55(19.10), 20.31(19.98), and 20.01(19.61) Mag, respectively. From the folded light curves, we can see that a near-sinusoidal profile show in it.