Yu-Xin Xin , Ding-Rong Xiong, Jin-Ming Bai, Hong-Tao Liu, Kai-Xing Lu , and Ji-Rong Mao

1Yunnan Observatories, Chinese Academy of Sciences, Kunming 650216, China; xiongdingrong@ynao.ac.cn, baijinming@ynao.ac.cn

2 University of Chinese Academy of Sciences, Beijing 100049, China

3 Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, Kunming 650216, China

4 Center for Astronomical Mega-Science, Chinese Academy of Sciences, Beijing 100101, China

Received 2022 February 28; revised 2022 April 1; accepted 2022 April 18; published 2022 June 14

Abstract In order to study the physical properties of the γ-ray emitting narrow-line Seyfert 1 (NLS1) galaxy population,photometric and spectral observations of the γ-ray emitting NLS1 PMN J0948+0022 were made with the Lijiang 2.4 m optical telescope of Yunnan Observatories,Chinese Academy of Sciences.Photometric data in the B and R bands were collected for 50 nights from 2020 January to 2021 December. During the observation epoch, the variability amplitudes are 73.67% in the B band and 79.96% in the R band. Intra-day variability is found in two observation nights, and the duty cycle value is 29% with variability amplitude>12.9% in the R band, which support the presence of the relativistic jets in the target. The redder-when-brighter (RWB) chromatic trend (or steeper-when-brighter trend) appears on intra-day and long timescales. The RWB trend is dominated by the radiation of accretion disk and jet,and resembles those in flat spectrum radio quasars.When PMN J0948+0022 is brighter than 17 5 in the R band, there is no color change trend. By analyzing the spectral data of PMN J0948+0022,we obtained the black hole mass of M?=1.61×107M⊙and accretion rate ofM˙=93,and confirmed that PMN J0948+0022 is a super-Eddington accreting NLS1. The redshifts of reverberation mapped super-Eddington accreting active galactic nuclei can be expanded by PMN J0948+0022 up to above 0.5.Super-Eddington accreting NLS1 galaxies were chosen as a new type of cosmological candle in the literature.PMN J0948+0022 may be used as a target for the next step of reverberation mapping monitoring project of super-Eddington accreting massive black holes.

Key words: galaxies: jets – galaxies: photometry – galaxies: Seyfert – galaxies: active

1. Introduction

Active galactic nuclei(AGNs)are very energetic phenomena in the central regions of galaxies and are powered by accretion processes of black holes other than the nuclear fusion that powers stars(Urry&Padovani 1995).Seyfert galaxy is a subclass of AGNs. Osterbrock & Pogge (1985) first proposed the concept of narrow-line Seyfert 1 (NLS1) galaxies when they classified the Seyfert galaxies. Compared to normal Seyfert 1 galaxies,the optical spectra of NLS1 galaxies contain narrower permitted broad emission lines from broad-line region (BLR),with full width at half maximum (FWHM)<2000 km s?1for broad emission line Hβ(Goodrich 1989;Pogge 2000).Besides,they have a line ratio [O III]/Hβ<3, strong permitted Fe II emission lines, a steep soft X-ray spectrum, and rapid variabilities in the optical and X-ray bands (Shuder &Osterbrock 1981; Boller et al. 1996; Yuan et al. 2008; Liu et al.2010;Paliya et al.2013;Berton et al.2015;Kshama et al.2017; Wang et al. 2017; D’Ammando 2020; Ojha et al. 2020,2021). Though controversial, it is widely believed that the centers of NLS1 galaxies possess black holes with relatively small masses and high accretion rates (Williams et al. 2002;Zhou et al.2003;Yuan et al.2008;Abdo et al.2009a;Calderone et al. 2013; Berton et al. 2015; Baldi et al. 2016; Ojha et al.2020). According to radio-loudness parameter R, NLS1 galaxies are divided into two categories: radio-loud (R>10)and radio-quiet (R<10). Most of them belong to radio-quiet NLS1 galaxies (93%) while the fraction of radio-loud NLS1 galaxies is only 7% (Komossa et al. 2006; Zhou et al. 2006;Kellermann et al. 2016). For the extremely radio-loud NLS1 galaxies(R>100),the fraction falls to 2%–3%(Komossa et al.2006;Yuan et al.2008).

Similar to blazars, a few radio-loud NLS1 galaxies show high radio brightness temperatures, flat radio spectrum, and optical intra-day variability (IDV) (Zhou et al. 2003; Yuan et al. 2008; Liu et al. 2010; Gu et al. 2015). These characteristics support that at least these radio-loud NLS1 galaxies carry relativistic jets.Owing to high sensitivity,Fermi Large Area Telescope (LAT) has detected high-energy γ-ray emission (E>100 MeV) from radio-loud NLS1 galaxies,definitely confirming relativistic jets in these radio-loud NLS1 galaxies (Abdo et al. 2009a, 2009b, 2009c; Foschini et al.2011). In addition to blazars and radio galaxies, radio-loud Seyfert 1 galaxies also join the catalog of γ-ray AGNs. About 15 NLS1 galaxies have been detected in the γ-ray band (Yao et al.2019),nine of which are contained in the fourth catalog of AGNs from the Fermi LAT (4LAC) (Ajello et al. 2020). The detections of γ-ray emitting NLS1 galaxies open new and interesting questions on the unified model of AGNs, development of relativistic jets, and evolution of radio-loud AGNs(Yuan et al. 2008; Abdo et al. 2009b). Finding evidence of blazar-like behavior in γ-ray emitting NLS1 galaxies would help to understand the evolution of relativistic jets (Itoh et al.2013)and to answer whether γ-ray emitting NLS1 galaxies are a new blazar population (Eggen et al. 2013).

Based on the fact that the bolometric luminosities of AGNs tend to saturate at super-Eddington accretion rates,Wang et al.(2013) suggest that super-Eddington AGNs can be used as a new type of cosmological candle. In order to test this suggestion, a large reverberation mapping monitoring project is developed by group of Super-Eddington Accreting Massive Black Holes(SEAMBHs)to measure the masses and accretion rates of supermassive black holes(SMBHs)(Du et al.2014;Hu et al. 2015). An interesting fact is that almost all the NLS1 galaxies selected as the SEAMBH candidates are confirmed to be super-Eddington accreting AGNs, but they are radio-quiet and no γ-ray emitting.The radio-loud and γ-ray emitting NLS1 galaxies are the potential candidates of super-Eddington accreting AGNs, and their physical properties and their connections with the normal AGNs are not yet fully understood. Therefore, it is quite interesting to perform observation of the γ-ray emitting NLS1 galaxies.

PMN J0948+0022 (R.A.=09:48:57.32, decl.= +00:22:25.56, J2000, z=0.5846) is the first radio-loud NLS1 galaxy(R>1000) detected in γ-rays (Abdo et al. 2009a, 2009b), and is considered as the prototype for γ-ray emitting NLS1 galaxies. Abdo et al. (2009a) discovered that the NLS1 galaxy strongly displays variable emission in the radio and γ-ray bands,high brightness temperatures,variability of the compact radio core, and a flat and inverted radio spectrum. Liu et al.(2010) first found the optical IDV in the NLS1 galaxy. The high polarization degree in the optical band was also reported(e.g., Ikejiri et al. 2011; Eggen et al. 2013; Itoh et al. 2013).The above results indicate the presence of a relativistic jet for the γ-ray emitting NLS1 galaxy. Although PMN J0948+0022 is a good target to study the properties of new γ-ray emitting NLS1 galaxy population and to find similarities to blazars, its optical flux variability on different timescales is still not fully studied. Optical flux variability is often associated with color/spectral behavior in blazars, which can be used to explore the radiation mechanism and origin of flux variability (Wu et al.2007;Gu 2011;Dai et al.2015;Xiong et al.2016,2017;Feng et al. 2020a, 2020b). For γ-ray emitting NLS1 galaxies, the relationships between optical flux and color have been hardly explored.

In view of these facts and in order to analyze flux variability and spectral properties, we carried out multicolor optical monitoring and spectroscopic observations of the target from 2020 to 2022 using the Lijiang 2.4 m optical telescope. This paper is organized as follows. We describe photometric and spectroscopic observations and data reduction in Section 2.The results are given in Section 3. Discussion and conclusions are presented in Sections 4 and 5, respectively.

2. Observations and Data Reduction

2.1. Photometry

The long-term optical monitoring program of γ-ray emitting NLS1 galaxy PMN J0948+0022 was carried out using the Lijiang 2.4 m telescope with the primary scientific instrument-Yunnan Faint Object Spectrograph and Camera (YFOSC, Fan et al. 2015; Wang et al. 2019). The instrument is mounted on the straight Cassegrain focal plane of the Lijiang 2.4 m telescope, covers the wavelength range from 350 nm to 1100 nm, and has an image scale of 0 283 pixel?1in the standard readout mode and a field of view (FoV) of 10×10 arcmin2. The detector is CCD42-90 back illuminated deep depletion 2048×4612 pixel E2V Scientific CCD Sensor,with pixel size 13.5×13.5 μm2. The full frame was for spectroscopic observation and the half frame of 2148x2200 was for photometric observation.

Our photometry observations were performed in a cyclic mode among the standard Johnson B and R bands.Before 2020 December 19, the exposure times were 300 s and 150 s for the B and R bands,respectively,under CCD readout mode of bin2.Afterwards, the exposure times were 600 s and 300 s for the B and R bands, respectively, under CCD readout mode of bin1.The bin2 mode combined 2×2 pixels into 1 pixel and its readout noise is 2.8 e?. The bin1 mode had not merged pixels and its readout noise is 6.3 e?.Both of them have the same gain 0.3 e?ADU?1. The time resolutions per night for the same bands were from 8 to 16.5 minutes. The time interval between the B and R bands in the same cycle was less than 15 minutes.So,the B band and R band observations could be considered as quasi-simultaneous measurements.

The photometric data processing program is implemented based on Python3, which mainly includes astronomy package—Astropy (Thomas et al. 2013; Price-Whelan 2018), astrometry software—Astrometry.Net and photometric software—SExtractor.5https://sextractor.readthedocs.io/en/latest/The details are described below.

(i) Data classification: All photometric observations on YFOSC were automatically classified into three groups: bias,flat and science data.Based on the bias and flat data,we could get the gain and readout noise values(Howell 2006).Flat field images were observed during the twilight when clear. If there were no flat field images on that night, the flat field images on the latest date was selected. The bias images were observed at the beginning and end of the observations. We need to check every fits image before using it.

(ii) Pre-processing: We stacked 10 bias images and calculated the median value as the masterbias. For flat field image, first we trimmed the flat image data as the same size of the trimmed object image; second we used the median of the image data as the divisor to achieve flat field normalization;finally use the median of the normalized flat field as the masterflat. During the data pre-processing, the science data were trimmed (remove invalid areas around the FoV) and corrected by masterbias and masterflat. Furthermore, the cosmic ray elimination program would be performed when the cosmic ray contaminated the target or the reference stars,and this program has the same function as IRAF by using the Laplacian Cosmic Ray Identification6http://www.astro.yale.edu/dokkum/lacosmic/(Pieter&van 2001).We used Astrometry.net to get new world coordinate system coordinates and updated them in fits header. The higher photometric coordinates could be obtained by SExtractor(Bertin & Arnouts 1996).

(iii) Aperture photometry: We extracted instrument magnitudes of all the objects using the SOURCE-EXTRACTOR(SExtractor2.19.5,Kron 1980).SExtractor’s automatic aperture photometry routine was derived from Kron’s “first moment”algorithm(Kshama et al.2017).Since there are no nearby stars around the target and comparison stars, we utilized MAG_AUTO to get the best magnitudes. The MAG_AUTO could automatically select the best aperture to measure the instrument magnitudes in each measurement.The aperture radii ranged from 2×FWHM to 5×FWHM and the average value is 3.8×FWHM, where FWHM denotes seeing. We checked the aperture radius of 5×FWHM,but could not find any stars other than the target within the aperture.

Figure 1.The finding chart of of PMN J0948+0022.The red circle is the target and the blue circles are two comparison stars (FoV is 7 6×7 6).

(iv) Differential photometry and errors: We obtained the source magnitude from the average of the values derived with respect to two comparison stars in the same frame(e.g.,Zhang et al. 2008; Fan et al. 2014; Xiong et al. 2016, 2017). The finding chart of the target is presented in Figure 1. The Landessternwarte K?nigstuhl (LSW)7https://www.lsw.uni-heidelberg.de/projects/extragalactic/charts/0948+002.htmlat the University of Heidelberg provided the chart for the same field. The LSW marks out three stars(A,B and C)as comparison stars.A and B comparison stars were chosen because their magnitudes are known and their locations are close to the target. Maune et al.(2013) confirmed that the two comparison stars were stable.The magnitudes of the two comparison stars were obtained from the LSW(A:mB=17 84,mR=16 35;B:mB=17 23,mR=16 33). In order to further illustrate that the two comparison stars are stable during our observation period, the differential instrumental magnitudes between them are shown in Figure 2. As shown in Figure 2, the comparison stars are stable. The standard deviations of differential instrumental magnitudes between them are 0.017 in the R-band and 0.048 in the B-band. Although a few values in the B-band have large deviations from average value of differential magnitudes between A and B stars, the rms errors of the differential magnitudes can reflect these deviations. The rms errors of the differential magnitudes between two comparison stars on a certain night were regarded as photometry errors (see Zhang et al. 2008; Fan et al. 2014; Xiong et al. 2016, 2017). The photometric data are given in Table 1. For a few nights,insufficient sampling (once or twice a night) caused that there was no rms errors or the errors were zero.We used the average error in each band as the error of the night observed only once,and the minimum error instead of the zero error.

2.2. Spectroscopy

Figure 2.The long-term light curves of PMN J0948+0022 in different bands.The black circles represent the light curves of PMN J0948+0022.The red circles are the differential instrumental magnitudes between two comparison stars.The differential instrumental magnitudes are offset to avoid their eclipsing with the light curves of PMN J0948+0022.

Using the Lijiang 2.4-m telescope, we obtained an optical spectrum of PMN J0948+0022 on 2022 February 11,which is near to the photometric period. The optical spectrum can be used to estimate the mass and accretion rate of the supermassive black hole in PMN J0948+0022. During the spectroscopic observation,we oriented the long slit to take the spectra of PMN J0948+0022 and a nearby comparison star simultaneously, and this method was widely used by many spectroscopic monitoring campaigns for spectral calibration (e.g.,Du et al. 2015; Lu et al. 2021a). Meanwhile, a standard star with a similar airmass to PMN J0948+0022 was selected.The two-dimensional spectroscopic image of PMN J0948+0022 was reduced using the standard IRAF procedures.We extracted the spectrum using the aperture of 20 pixels (5 7), and background was determined from two adjacent regions (+7 4～+14?and ?7 4 ～?14?) on both sides of the aperture region.The red side of optical spectrum is contaminated by the variable absorptions of the telluric atmosphere, as a part of broad Hβ line drops into the absorption band of Oxygen in the observed frame. We used the correction method of the telluric absorption presented in Lu et al. (2021b) to correct the telluric absorption lines. In briefly, the spectra of PMN J0948+0022 and the comparison star have the same telluric transmission spectrum.The telluric spectrum can be constructed by dividing the observed spectrum of the comparison star with its stellar template. It was used to correct the telluric absorption lines in the observed spectrum of PMN J0948+0022. Then we calibrated the spectral flux of PMN J0948+0022 using the spectrum of standard star,and corrected the Galactic extinction using the extinction map of Schlegel et al. (1998) and the redshift.Meanwhile,we also took the photometric observations for PMN J0948+0022 at the night, 25 minutes before the Spectroscopic observations. The result shows that B = 17.m85 and R = 17.m74 with corrected for Galactic extinction.

3. Results

3.1. Long-term Optical Variability

The B band and R band magnitudes are corrected for the Galactic extinction with AB=0.285 and AR=0.17 from the NASA/IPAC Extragalactic Database (NED) and Schlafly &Finkbeiner (2011). Throughout, the rest of the article, the B band and R band magnitudes refer to the magnitudes corrected for the Galactic extinction. Figure 2 shows the long-term light curves in different bands from 2020 January 29 to 2021 December 11. In order to better display the light curves, we divide the observation epoch into two parts, in which the first epoch is from 2020 January 29 to 2020 May 19 (the left panel in Figure 2)and the second epoch is from 2020 December 19 to 2021 December 11 (the right panel in Figure 2).

Table 1 Raw Photometric Data of PMN0948

Table 1(Continued)

For long timescales,the object displays significant variability in the B and R bands. The variability amplitude (Amp) is calculated as (Heidt & Wagner 1996)whereAminandAmaxrepresent the minimum and maximum magnitudes respectively, and σ is the rms error. The Amp is 73.67%for the B band and 79.96%for the R band.The Amp in the R band is larger than that in the B band.PMN J0948+0022 brightens by ΔR=0 66 in about 6 days from MJD=58885.71 to MJD=58891.64, and fades by ΔR=0 65 in about 4 days from MJD=58909.6 to MJD=58913.72,which is the fastest variability of this magnitude during our observation epochs. The magnitude changes are ΔR=0 59 in about 7 days from MJD=58933.56 to MJD=58940.83 and ΔR=0 29 in about 10 days from MJD=59247.78 to MJD=59257.73. The brightness increases by ΔR=0 64 in 21 days from MJD=58959.65 to MJD=58980.67. Sub-flares are superimposed on the entire brightening trend.The magnitude variation in the B band is much smaller than that in the R band during the same time (ΔB=0 5 from MJD=58885.71 to MJD=58891.64;ΔB=0 53 from MJD=58909.6 to MJD=58913.72; ΔB=0 37 from MJD=58933.56 to MJD=58940.83; ΔB=0 27 from MJD=59247.78 to MJD=59257.73; ΔB=0 57 from MJD=58959.65 to MJD=58980.67).The average magnitudes are〈mR〉=17.72±0.01 and〈mB〉=17.88±0.01.

3.2. Optical IDV

In order to search for optical IDV, F-test and one-way analysis of variance (ANOVA) are employed. The F-test and ANOVA are two different methods based on different principles to evaluate microvariability. The F-test is considered as a proper statistics to quantify optical IDV(e.g.,de Diego 2010;Joshi et al. 2011; Goyal et al. 2012; Hu et al. 2014; Xiong et al.2016, 2017). It can be written as

Table 2 Results of Optical IDV of PMN J0948+0022

The target is variable(V)when the light curves meet both of the variability criteria of F-test and ANOVA. The target is probably variable (PV) when the light curves meet one of the variability criteria of ANOVA and F-test. The target is not variable (N) when the light curves cannot meet any one of the variability criteria of ANOVA and F-test.We only analyze the night with the number of data points more than ten, so six nights are selected. The results of data analysis are given in Table 2. The V status is found in two nights (the R band on 2020 May 11 and 2021 February 12). The B band light curves on the two nights are detected as PV. The R band light curves in the rest of four nights are detected as PV. The light curves detected as PV and V status are shown in Figure 3. On 2020 May 11,the target fades by ΔR=0 14 in 40.32 minutes from MJD=58980.554 to MJD=58980.582,and then brightens by ΔR=0 3 in 120 minutes from MJD=58980.582 to MJD=58980.665, which correspond to Amp=29.9%.

In order to quantify the reliability of variability, the differential instrumental magnitudes between two comparison stars (i.e., the instrumental magnitude of Ref A minus that of Ref B) are displayed in Figure 3. The differential instrumental magnitudes between two comparison stars are almost constant for the R band on 2020 May 11. For the B band on the same night,the trend of magnitude changes is consistent with that in the R band, but its Amp is much smaller compared to Amp in the R band.Although the light curve is considered as PV for the B band on 2020 May 11 (the ANOVA detects IDV but the Ftest does not detect IDV), the F value of F-test is close to the critical value (see Table 2). On 2021 February 12, the R band light curve of PMN J0948+0022 continues to brighten by ΔR=0 13 in 229 minutes from MJD=59257.67 to MJD=59257.83. For the B band on 2021 February 12, the ANOVA detects IDV but the F-test does not detect IDV. The daily average magnitudes on both 2020 May 11 and 2021 February 12 are above the average magnitudes during the whole monitoring epoch. For the R band light curves on 2021 December 11, 2020 December 20, 2020 December 19 and 2020 May 15,the F-test detects IDV but the ANOVA does not detect IDV.

Figure 3. The light curves detected as PV and V status (same symbols as Figure 2).

The duty cycle (DC) of IDV is calculated by

where ΔTi=ΔTi,obs(1+z)?1, z is the redshift and ΔTi,obsis the duration of the monitoring session of the ith night(Romero et al.1999;Hu et al.2014;Xiong et al.2016).Niwill be set to 1 if IDV is detected, otherwise Ni=0 (Goyal et al. 2013). For the R band, DC=29% with Amp > 12.9%, and DC will be 100% with Amp > 3.9% when PV status is also considered.For the B band,only two nights are detected as PV status(2020 May 11 and 2021 February 12), DC=0% for V status, and DC=29% with Amp > 6.7% for PV status.

3.3. Correlation between Magnitude and Color Index

There are correlations between the B ?R index and R magnitude on intra-day and long timescales(see Figure 4).The spectral index is calculated as

where νBand νRare the effective frequencies of the respective bands (Wierzcholska et al. 2015). The average optical spectral index is 〈αBR〉=0.32±0.01 when considering all the observed data. The spectral index as y-axis is plotted in Figure 4. The error-weighted linear regression analyses show strong or moderate negative correlations between the B ?R index and R magnitude on intra-day timescale (see Table 3).For long timescale, a strong negative correlation between the B ?R index and R magnitude is found. Therefore, a redderwhen-brighter (RWB) chromatic trend is significant for PMN J0948+0022 on intra-day and long timescales. When the R band magnitude is brighter than 17 5, color change trend disappears (r=0.17, P=0.6;the last panel in Figure 4).

3.4. Mass and Accretion Rate of SMBH

In light of the standard model of accretion disk (Shakura &Sunyaev 1973), the dimensionless accretion rate is defined as(Du et al. 2015)

where ?44=L5100/1044erg s?1is the optical luminosity at rest wavelength 5100 ?, M7=M?/107M⊙is the mass of SMBH and i is the inclination of accretion disk.We takecosi=0.75,which represents a mean disk inclination for type 1 AGNs.Therefore, we need to measure L5100and estimate M?before calculating the dimensionless accretion rate. Based on the single-epoch spectrum for PMN J0948+0022, M?can be estimated using the virial equation

where RHβis the radius of BLR for broad emission line Hβ,vFWHMis the velocity FWHM of broad Hβ, G is the gravitational constant,and f is the virial factor which is usually taken as f=1.0 for vFWHM.

The spectral fitting scheme is widely used in spectral analysis(e.g., Hu et al. 2015; Lu et al. 2019), which can eliminate the contamination of other blended components in our measurement.Following the work of Lu et al.(2021a),we decomposed the spectrum into multi-components in the Hγ and Hβ region(see Figure 5).The main fitting models include power law for AGN continuum (blue), Fe II template for strong iron lines(green),two Gaussians for the broad Hβ(pink),two Gaussians for the broad Hγ (pink), and one Gaussian for the broad He II line(cyan).From the decomposed spectrum,we measured the continuum flux density at 5100 ? F5100,disk+jet=9.39×10?17erg s?1cm?2??1and vFWHM=1659 km s?1for the broad Hβ, and calculated the flux ratio of Fe II to Hβ RFe=1.26. The RWB trend of PMN J0948+0022 appears/disappears when the magnitude is fainter/brighter than R=17 5 (more details see Section 4), which indicates that the optical contributions from thermal radiation of accretion disk and non-thermal radiation of jet reach an equilibrium when R=17 5,that is,the continuum flux density from the accretion disk F5100,diskshould be half of F5100,disk+jet. Therefore, we calculated F5100,disk=5.85×10?17erg s?1cm?2??1by the difference between R=17 5 and 17 74 (R=17 74 during the spectroscopic observation, see Section 2.2). The optical luminosity L5100is derived from F5100,diskwith the cosmological parameters of H0=72 km s?1Mpc?1, ΩΛ=0.7, and ΩM=0.3. Therefore, using the latest scaling relation of Du&Wang (2019), we estimated M?=1.61×107M⊙for PMN J0948+0022. With L5100and M?, we obtainedM˙=93.According to the classification of sub-Eddington and super-Eddington (M˙≥3) of Du et al. (2015), we found that PMN J0948+0022 is a super-Eddington accreting AGN.

4. Discussion

For nearby AGNs, when performing aperture photometry,the contribution from a strong host galaxy component has a significant impact on the photometry results (Cellone et al.2000; Nilsson et al. 2007). If there is a large seeing change,false microvariability is likely to occur.PMN J0948+0022 has no clear features of host galaxy, and its host galaxy is much fainter than its AGN core (Liu et al. 2010). Moreover, the photometric aperture was always greater than 2×FWHM, so the host galaxy was included in the aperture even if the target had a host galaxy. An aperture radius of 2×FWHM is expected to yield fairly reliable light curves for the AGN even if its host galaxy is up to 2 mag brighter (Cellone et al. 2000;Ojha et al. 2020). Therefore, the host galaxy cannot significantly take effects on our photometry results, i.e., the contamination of the host galaxy is negligible.

Figure 4. Correlations between the B ?R index (spectral index αBR) and R magnitude. The y-axis on the left represents the B ?R index and the right represents spectral index αBR.The left panel in the last row represents the data of for the whole monitoring epoch.The right panel in the last row is for the data when considering brightness more than 17 5. The red lines are the results of error-weighted linear regression analysis.

Table 3 Results of Error-weighted Linear Regression Analysis

There is IDV in two nights for the R band and possible IDV in all the six nights. DC=29% with Amp > 12.9% in the R band. In fact, the target had a higher IDV duty cycle (DC >50%) (Liu et al. 2010; Paliya et al. 2013; Ojha et al. 2020,2021). For the B band light curves, the possible IDV was detected only in the two nights.The following three factors are likely to make a lower DC value for our results: short time spans per night (<4 hr), a larger scatter in the differential instrumental magnitudes between two comparison stars, and lack of enough data points. Previous studies demonstrated a longer duration per night and a higher possibility of IDV detection (Gupta & Joshi 2005; Rani et al. 2011). The larger scatter may cause a lower F value of F-test.The lack of enough data points may reduce the possibility of detecting IDV. It’s also possible that during our monitoring epochs the target indeed has a lower DC value compared to other epochs.Goyal et al. (2013) found DC ≈32% with Amp > 3%for TeV γ-ray blazars. If higher Amp is considered, DC should be lower for TeV γ-ray blazars.Thus,DC=29%with Amp>12.9%in our results is comparable to that of TeV γ-ray blazars. These comparable DC values support a similar IDV nature and the presence of relativistic jets with a small angle of view in the γray emitting NLS1 galaxies.High IDV is often considered to be an important feature for blazars,and is related to the relativistic jets with a small angle of view (e.g., Wagner & Witzel 1995;Sagar et al. 2004; Goyal et al. 2013). We found the high IDV on 2020 May 11 when the target brightened by ΔR=0 3 in 120 minutes, corresponding to Amp=29.9%. The average magnitude on the night is above that during the whole monitoring epoch. Such high IDV also supports a similar IDV nature between γ-ray emitting NLS1 galaxies and blazars,and the presence of relativistic jets with a small angle of view.For long timescale,the object displays significant variability in the B and R bands, which is similar to variability of blazars.

Figure 5. Fitting and multi-component decomposition of the spectrum observed from the Lijiang 2.4 m telescope (JD=2459622). The top panel shows the details of spectral fitting and decomposition and the bottom panel shows the residuals.

Amp=73.67%for the B band and Amp=79.96%for the R band when considering all the observed data. For many obvious flares, |ΔB| is much smaller than |ΔR| (see Section 3.1). Amp in the R band is larger than that in the B band for the two nights detected as IDV (see Table 2), i.e.,variability in higher frequencies exhibits lower amplitude. Our results show that an RWB chromatic trend is significant for PMN J0948+0022 on intra-day and long timescales. The shock-in-jet model is often used to explain the variability and bluer-when-brighter (BWB) trend in blazars (e.g., Marscher &Gear 1985; Xiong et al. 2017; Liu et al. 2019; Feng et al.2020a, 2020b). Disturbances in the flow of a jet cause a shock to propagate along the jet. When the shock sweeps emitting regions, variability/flare occurs. Higher frequency photons from the synchrotron mechanism typically emerge sooner and closer to the shock front than lower frequency radiation,resulting in higher variability amplitude of higher frequency photons and a BWB trend(Agarwal&Gupta 2015).However,the shock-in-jet model is hard to explain our results, i.e., an RWB trend.

The BWB chromatic trend is significant in most blazars,especially BL Lac objects (e.g., Feng et al. 2020a, 2020b),whereas the RWB trend is also found for flat-spectrum radio quasars (FSRQs) (e.g., Gu et al. 2006; Wu et al. 2007; Ikejiri et al. 2011; Bonning et al. 2012; Dai et al. 2015; Xiong et al.2020).The different relative contributions of the thermal versus non-thermal radiation to the optical emission may be responsible for the different trends of the color index with brightness in FSRQs and BL Lac objects(Gu et al.2006).The color change trend may be dominated by the relative position changes of the synchrotron peak frequency of spectral energy distribution (SED) with respect to the observational window(e.g.,Feng et al.2020a,2020b).So,the color change trend may be controlled by the observational window and the underlying broadband SED. The broadband SED fitting shows that accretion disk dominates the total optical flux in a lower state,and our observational window is to the left of the peak of accretion disk SED and to the right of the peak of synchrotron SED of jet (see Figure 4 in Abdo et al. 2009a). A BWB trend emerges for radiation of accretion disk and jet as they brighten,and furthermore our observational window is to the left of the peak of accretion disk SED and to the right of the peak of synchrotron SED of jet as PMN J0948+0022 is between the lowest and highest states(see Figure 6 in Foschini et al.2015).From lower to higher state,a superposition of the BWB trends of the jet and disk components will lead to an RWB trend because that the jet component is much redder than the disk one and that the jet component contributes more relative to the disk one.The BWB trend in disk emission of PMN J0948+0022 is consistent with the results that the thermal component of accretion disk dominates the total emission in low flux state and that accretion disk model can produce the BWB trend (Li& Cao 2008; Gu & Li 2013; Xiong et al. 2020). When PMN J0948+0022 is in the highest state, the total SED seems to be flat in our observational window (nearly equal jet and disk contributions), and the color change trend likely becomes saturated(see Figure 6 in Foschini et al.2015).This saturation is consistent with the result of Isler et al. (2017) that the color change trend remains unchanged when jet and disk contributions are equal. Also, this saturation is consistent with the disappearance of the color change trend in PMN J0948+0022 when brighter than 17 5 in the R band.

The jet component on short timescale might be more variable compared to the accretion disk component due to the jet beaming effect. The accretion disk component seems more variable on long timescale. Liu et al. (2010) found that PMN J0948+0022 emerges ΔR=0 5 within a few hours when the brightness is higher than 17 33. Our results show that the target brightened by ΔR=0 3 in 120 minutes when the brightness is lower than 17 4. Therefore, the target shows higher variability amplitude when brighter.With respect to the optical emission of accretion disk,the jet in PMN J0948+0022 may be weak on long timescale. Interestingly, PMN J0948+0022 is a super-Eddington accreting NLS1 galaxy with the highest redshift among those known super-Eddington accreting NLS1s, some of which were used as candidates of cosmological candle (e.g., Wang et al. 2014). PMN J0948+0022 expands the redshifts of those NLS1s by almost an order of magnitude up to above 0.5, and increasing largely the cosmological distance of target is important to use super-Eddington accreting NLS1s as candidates of cosmological candle.PMN J0948+0022 may be used as a target for the next step of reverberation mapping monitoring project of SEAMBHs.

5. Conclusions

We have monitored the γ-ray emitting NLS1 galaxy PMN J0948+0022 in the B and R bands from 2020 to 2021.We have also performed the spectral observation on 2022 February 11.Our main conclusions are as follows.

(i) The RWB chromatic trend in PMN J0948+0022 is dominant on intra-day and long timescales, resembles those in FSRQs, and is dominated by the accretion disk and jet radiation. When considering the data brighter than R=17 5,no color change trend appears.The optical IDV was detected in two nights. Our results of variability indicate the presence of relativistic jets with a small angle of view, which is similar to blazars.

(ii) Based on spectral observation, we get M?=1.61×107M⊙andM˙=93for the SMBH in PMN J0948+0022,and identify that PMN J0948+0022 is a super-Eddington accreting AGN.PMN J0948+0022 expands the redshifts of those known super-Eddington accreting NLS1s by almost an order of magnitude up to above 0.5.Some of those NLS1s were adopted as candidates of cosmological candle.It may be used as a target for the next step of reverberation mapping monitoring project of SEAMBHs.

(iii) The magnitude fades by ΔR=0 65 in about 4 days,which is the shortest timescale of variations with such a large magnitude change(ΔR>0 5)during our observation epochs.When considering all the observed data, the average magnitudes are 〈mR〉=17.72±0.01 and 〈mB〉=17.88±0.01, and the average optical spectral index is 〈αBR〉=0.32±0.01.

(iv) On 2020 May 11, the target fades by ΔR=0 14 in 40.32 minutes and then brightens by ΔR=0 3 in 120 minutes corresponding to Amp=29.9%. The DC value is 29% with Amp > 12.9% in the R band. On long timescale, the object displays significant variability in the B and R bands.

(v) The variability amplitude is 73.67% for the B band and 79.96%for the R band when considering all the observed data.For many obvious flares, the amplitude of magnitude changes in the B band is much smaller than that in the R band.The Amp in the R band is larger than that in the B band for the two nights detected as IDV, i.e., variability in higher frequencies detects lower amplitude.

Acknowledgments

We are very grateful to the anonymous referee for constructive comments leading to significant improvement of this paper. We think very much to Yang Huang for his help with photometric data reduction. This work is supported by the National Key R&D Program of China with No.2021YFA1600404, the National Natural Science Foundation of China (NSFC, grant Nos. 11991051, Y911080201,12073068, 11673062, 11703077, 11703078), the CAS “Light of West China” Program, the Yunnan Province Foundation(2019FB004,202001AT070069),Yunnan Province Youth Top Talent Project (YNWR-QNBJ-2020-116), and the science research grants from the China Manned Space Project with NO. CMS-CSST-2021-A06 and CMS-CSST2021-A05. This research has made use of NASA’s Astrophysics Data System Bibliographic Services and the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory,California Institute of Technology,under contract with the National Aeronautics and Space Administration. We acknowledge the use of the Lijiang 2.4 m telescope and its technical operation and maintenance team. This research uses data obtained through the Lijiang 2.4 m Telescope, which is funded by the Chinese Academy of Sciences, the People’s Government of Yunnan Province and the National Natural Science Foundation of China.

ORCID iDs

Yu-Xin Xin https://orcid.org/0000-0003-1991-776X

Kai-Xing Lu https://orcid.org/0000-0002-2310-0982