Yongyun Chen, Qiusheng Gu, Junhui Fan, Xiaoling Yu, Dingrong Xiong, Nan Ding, Xiaotong Guo, and Xue Ge

1 College of Physics and Electronic Engineering, Qujing Normal University, Qujing 655011, China; ynkmcyy@yeah.net

2 School of Astronomy and Space Science, Nanjing University, Nanjing 210093, China; qsgu@nju.edu.cn

3 Collaborative Innovation Center of Modern Astronomy and Space Exploration, Nanjing 210093, China

4 Center for Astrophysics, Guangzhou University, Guangzhou 510006, China

5 Yunnan Observatories, Chinese Academy of Sciences, Kunming 650011, China

6 School of Physical Science and Technology, Kunming University, Kunming 650214, China

7 Anqing Normal University, Anqing 246133, China

8 School of Physics and Electronic Engineering, Jiangsu Second Normal University, Nanjing 211200, China

Abstract We use a large sample of gamma-ray narrow-line Seyfert 1 galaxies (γ-NLS1s) to study the jet formation mechanisms.We find that the jet power of γ-NLS1s is lower than the maximum jet power of the Blandford–Payne(BP)mechanism.At the same time,we find that there is a significant correlation between jet power and accretion disk luminosity.Moreover,the contribution rates of the accretion to the jet power are larger than that of black hole mass to jet power.These results further suggest that the jet of γ NLS1s is mainly produced by the BP mechanism.

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

1. Introduction

Narrow-line Seyfert 1 galaxies(NLS1s)are a special class of active galactic nuclei (AGNs) identified by Osterbrock &Pogge (1985), which show narrow Balmer lines (FWHM(Hβ) ＜2000 km s-1), weak [O III], strong Fe II emission lines and steep soft X-ray spectra (e.g., Boller et al. 1996; Wang et al. 1996; Leighly 1999). NLS1s are generally regarded as radio-quiet (e.g., Ulvestad et al. 1995; Moran 2000; Boroson 2002). Therefore, discovering the radio-loud narrow-line Seyfert 1 galaxies (RLNLS1s) seems entirely unexpected. In particular,these RLNLS1s were detected by Fermi-Large Area Telescope (Fermi-LAT),which further confirms that they have strong relativistic jets (Abdo et al. 2009). Many authors restudied the properties of these γ-NLS1s.Some authors found that γ-NLS1s have similar properties to flat spectra radio quasars (FSRQs) (e.g., Berton et al. 2019; Paliya et al. 2019).Chen et al.(2021)found that the γ-NLS1s belong to the Fermi blazars sequence. However, it is not clear what is the jet formation mechanism of these γ-NLS1s?

Jet formation has always been a hot topic in astrophysics.At present, there are two most popular jet formation mechanisms.The first is the Blandford–Znajek (BZ) mechanism (Blandford& Znajek 1977): the jets extract rotational energy from a rotating black hole.The jet power mainly depends on the black hole mass. The second is the Blandford–Payne (BP) mechanism (Blandford & Payne 1982): the jets extract rotational energy from the accretion disk.The power extracted in this way is proportional to the disks magnetic field. If the squared magnetic field is proportional to the accretion rate, then there will be a correlation between jet power and accretion disk luminosity (Ghisellini et al. 2014). Many authors have found that jet and accretion are closely related (e.g., Rawlings &Saunders 1991; Celotti et al. 1997; Cao & Jiang 1999;Ghisellini et al. 2014; Chen et al. 2015). Livio et al. (1999)suggested that the BP mechanism dominates over the BZ mechanism. However, some authors put forward the opposite view. Chai et al. (2012) found that the BZ mechanism may dominate over the BP mechanism for blazars.

In this paper, we investigate the jet formation in γ-NLS1s.The cosmological parameters H0=70 km s-1Mpc-1,Ωm=0.3, and ΩΛ=0.7 are adopted in this work. Section 2 presents the samples; Section 3 describes the jet formation mechanisms; Section 4 describes the results and discussions;Section 5 presents the conclusions.

2. The Sample

We try to collect a large sample of γ-NLS1s. We consider the sample of Paliya et al. (2019). Paliya et al. (2019) studied the physical properties of 16 γ-NLS1s. The accretion disk luminosity, X-ray luminosity in 0.3–10 keV, and black hole mass come from their work.The accretion disk luminosity and black hole mass are obtained by using the SED modeling (see Paliya et al. 2019). Conventionally, optical spectral line and continuum measurements are used to derive them (see Shaw et al. 2012). It is found that parameters derived from both methods reasonably agree with each other (e.g., Paliya et al.

Table 1 The Sample of γ-NLS1s

where the factor of 2 indicates two jets, f=16/5 for the external Compton (EC). Paliya et al. (2019) suggested that the bolometric output of γ-NLS1s radiates from the X-ray to γ-ray bands dominated by EC.The Pradis radiative jet power. The δ and Γ are Doppler and bulk Lorentz factors, respectively. The radiative jet power, Doppler factor, and bulk Lorentz factors come from the work of Paliya et al. (2019). Thus, we use Equation (1) to get jet bolometric luminosity.

Komossa et al.(2018)used the following formula to estimate the jet kinetic power of RLNLS1s (B?rzan et al. 2008),

3. Jet Formation Mechanisms

Some authors have calculated the jet power of the BZ and BP mechanisms(e.g.,Ghosh&Abramowicz 1997;Livio et al.1999; Meier 2001; Cao 2003). We use similar methods to derive the maximal jet power of BP and BZ mechanisms.

3.1. The BP Mechanism

The maximal jet power of the BP mechanism is

The strength of the dynamo magnetic field is calculated by the following formula (Cao 2003)

where a is the spin of black hole.

Using Equations (3)–(9) the maximal jet power of the BP mechanism can be obtained through integral Equation(3)when some parameters (m,m˙,a) are given.

3.2. The BZ Mechanism

The maximal jet power of the BZ mechanism is given by the following formula (e.g., Ghosh & Abramowicz 1997; MacDonald & Thorne 1982),

4. Results and Discussion

In Figure 1, we show the relation between logPjetLboland logLbolLEdd.The jet kinetic power is estimated from the lowfrequency radio luminosity by using Equation (2). The maximal jet power of the BP mechanism is calculated by using Equations (3),(4)and(7).Similarly, the maximal jet power of the BZ mechanism is estimated by using Equations(4),(7)and(10).From Figure 1,we find that the jet power of all sources in our sample is lower than the maximum jet power extracted from a magnetized accretion disk(see Figure 1,below the solid line). These results imply that jet power of all sources can be powered by the BP mechanism.At the same time,we also find that the jet power of about 40%of sources with high accretion rates is lower than the maximum jet power extracted from the rapidly rotating black hole (see Figure 1, below dashed lines).These 40%sources with a high accretion rate can be explained by the BZ mechanism.

Figure 1. The Lbol/LEdd vs.Pjet/Lbol.The solid line is maximal jet power PBPmax extracted from a accretion disk. The dashed line is maximal jet power PBZmax extracted from a rapidly spinning black hole a=0.99.The black filled circle is γ-NLS1s.

At low accretion rates, the accretion disks may be truncated by the evaporation and become advection-dominated accretion flows (e.g., Yuan & Narayan 2014). The condensation of corona gas provides fuel for a small inner accretion disk (e.g.,Liu et al. 2007). With the increase in accretion rate, the contribution of the inner disk increases.The inner thin disk for γ-NLS1s may extend to around the innermost stable circular orbit (ISCO), and thus their jets may be produced via the BP and/or BZ mechanisms (e.g., Sun et al. 2015). At the same time,an increase in accretion rate may also result in insufficient evaporation to completely remove the disk, then the IC scattering of the soft photons on the disk condenses the corona(e.g., Liu et al. 2007). In this case, a complete thin disk with a weak corona exists. The thin disk also extends around the ISCO, and the jets may be mainly produced by the BZ mechanism.

However, we also note that there are some uncertainties in black hole mass,accretion disk luminosity, jet radiation power and jet kinetic power.The uncertainty of black hole mass is 0.4 dex (Ghisellini & Tavecchio 2015); the uncertainty of 0.3 dex in logLdiskand 0.23 dex in logPrad(Ghisellini et al. 2014); the uncertainty of jet kinetic power is 0.85 dex(B?rzan et al.2008).We calculate the uncertainty in Lbolpropagating the error associated with logLdiskand logPrad. The uncertainties of a

Figure 3.Relation between accretion disk luminosity and jet power.The solid lines correspond to the best-fit linear models obtained with the symmetric leastsquares fit. The dashed lines indicate 2σ confidence band.

Figure 2. Relation between black hole mass and jet power. The solid lines correspond to the best-fit linear models obtained with the symmetric leastsquares fit. The dashed lines indicate 2σ confidence band.

The relation between jet power and black hole mass is shown in Figure 2. The Pearson analysis shows that there is a weak correlation between jet power and black hole mass (r=0.46,P=0.07, significant correlation P ＜0.05 confidence level).The Spearman correlation coefficient and significance level are r=0.41 and P=0.11. The Kendalltau correlation coefficient and significance level are r=0.28 and P=0.14. These two tests also show a weak correlation.It is generally believed that there may be a strong correlation between jet power and black hole mass. However, we find a weak correlation between jet power and black hole mass for γ-NLS1s.The possible reason is that we use small samples,and our results should be tested with large samples in the future.

Figure 3 shows the relation between jet power and accretion disk luminosity. The Pearson analysis shows that there is a significant correlation between jet power and accretion disk luminosity (r=0.56, P=0.02). The Spearman correlation coefficient and significance level are r=0.55 and P=0.03.The Kendalltau correlation coefficient and significance level are r=0.36 and P=0.04. These two tests also show a significant correlation between jet power and accretion disk luminosity. These results support a close connection between jet and accretion.

Figure 4. Relation between jet power and both accretion disk luminosity and black hole mass. The solid lines correspond to the best-fit linear models obtained with the symmetric least-squares fit. The dashed lines indicate 2σ confidence band.

We use multiple linear regression analysis to obtain the relation between jet power and both accretion disk luminosity and black hole mass for whole sample with 99 per cent confidence level and r=0.57 (Figure 4):

We define the contribution rates of the accretion and black hole mass to the jet power as ξaccretion=0.18/(0.18+0.03)×100%=85.7% and ξmass=0.03/(0.18+0.03)×100%=14.3%. The contribution rate of the accretion to jet power is larger than that of black hole mass to jet power.From the above results,we find that the jet power mainly depends on accretion,namely the BP mechanism.

5. Conclusions

We use a large sample of γ-NLS1s to study the formation mechanism of the jets. Our main results are as follows:

1. We find that the jet power of all γ-NLS1s is lower than the maximum jet power of the BP mechanism. The jet power of about 40%γ-NLS1s is lower than the maximum jet power of the BZ mechanism.

2. We find that there is a significant correlation between jet power and accretion disk luminosity. At the same time,the contribution rates of the accretion to the jet power are larger than that of black hole mass to jet power. These results further suggest that the jet of γNLS1s is mainly produced by the BP mechanism.

Acknowledgments

We are very grateful to Foschini,L and Cao,Xinwu for their suggestion.This work is supported from the research project of Qujing Normal University (Grant No. 2105098001/094). This work is supported by the youth of Yunnan Provincial Science and Technology Department (Grant Nos. 202101AU070146 and 2103010006). This work is supported by the National Natural Science Foundation of China (NSFC, Grant Nos.11733001, 11733002 and 11773013). This work is supported by the National Key Research and Development Program of China (Grant No. 2017YFA0402703). Nan Ding gives thanks for the financial support from the National Natural Science Foundation of China (NSFC, Grant No. 12103022) and the Special Basic Cooperative Research Programs of Yunnan Provincial Undergraduate Universities Association (No.202101BA070001-043).