The Extreme Super-Eddington NLS1 RX J0134.2-4258 – II. A Weak-Line Seyfert Linking to the Weak-Line Quasar

Active galactic nuclei (AGN) are powered by accretion onto a super-massive black hole (SMBH). This converts some fraction of the gravitational potential energy into radiation, powering the observed activity. The multi-wavelength properties of AGN are mainly determined by three parameters, namely the black hole mass, black hole spin and mass accretion rate. The inclination angle also plays a significant role in observations (e.g. Luo et al. 2015; Jin et al. 2017b). Narrow-line Seyfert 1 (NLS1) galaxies are a subtype of AGN characterized by relatively narrow broad lines such as H$\beta$ and relatively weak narrow lines such as [O iii]$\lambda$5007 (Osterbrock & Pogge 1985; Boroson 2002). Comparing with the entire AGN population, NLS1s tend to have small black hole masses of $10^{6-7}~{}M_{\odot}$ and high mass accretion rates (e.g. Pounds, Done & Osborne 1995; Mathur, Kuraszkiewicz & Czerny 2001; Boroson 2002; Jin et al. 2012a).

In the X-ray band, it is common to observe a strong soft X-ray excess in NLS1s (e.g. Boller, Brandt & Fink 1996; Brandt, Mathur & Elvis 1997), which can often be modelled with an ionized disc reflection component (e.g. Miniutti & Fabian 2004; Ross & Fabian 2005; Crummy et al. 2006; Fabian et al. 2013), and/or a separate warm Comptonisation component (e.g. Laor et al. 1997; Magdziarz et al. 1998; Done et al. 2012; Jin et al. 2013; Jin, Done & Ward 2016, 2017a, 2021). Complex absorption (partially ionised material partially covering the source) can also shape the soft X-ray emission in some AGN (e.g. Miller et al. 2007; Turner et al. 2007; Tatum et al. 2012).

NLS1s themselves form two subtypes, including the X-ray simple NLS1s and X-ray complex NLS1s (Gallo 2006). The X-ray simple NLS1s have smooth and steep X-ray spectra, while the X-ray complex NLS1s show more complicated absorption and emission features. Meanwhile, NLS1s with high mass accretion rates, especially super-Eddington, are likely to have a geometrically-thick (i.e. puffed-up) inner disc structure and disc wind (Ohsuga & Mineshige 2011; Takeuchi, Ohsuga & Mineshige 2014; Jiang, Davis & Stone 2016), which can obscure the intrinsic X-ray emission and introduce additional spectral complexities and variability (e.g. Hagino et al. 2016; Done & Jin 2016; Jin et al. 2017b; Parker et al. 2021). Therefore, the difference between X-ray simple and complex NLS1s can be explained by their different inclination angles, which lead to different line-of-sight to the X-ray corona (Done & Jin 2016; Jin et al. 2017b). Supporting evidence for these subtypes being intrinsically the same is that their optical/UV emission is the same, suggesting that their intrinsic disc properties should indeed be similar (Done & Jin 2016).

A similar physical scenario of a puffed-up inner disc with significant winds is proposed to explain the properties of weak-line quasars (WLQs, e.g. Fan et al. 1999; Plotkin et al. 2010; Wu et al. 2011, 2012; Luo et al. 2015; Ni et al. 2018). WLQs are characterized by their weak UV high-ionization emission lines, e.g. rest-frame equivalent width (REW) of C iv $\lesssim 10$ Å, and/or REW of Ly $\alpha~{}+$ N v is $\lesssim 15$ Å (e.g. Ni et al. 2018). Winds are clearly indicated as the peak of the weak C iv lines is often highly blue-shifted (Richards et al. 2011; Rankine et al. 2020). WLQs have high black hole masses of $10^{8-9}M_{\odot}$, and also fairly high but not extreme mass accretion rates of $L_{\rm bol}/L_{\rm Edd}\sim 1$ (e.g. Luo et al. 2015). The empirical $\alpha_{\rm ox}-L_{\rm 2500\text{\AA}}$ relation (e.g. Lusso & Risaliti 2016) implies that these are somewhat X-ray weak compared to less luminous quasars, but $\sim$35% of the WLQ population show X-ray emission which is at least a factor 6 below this expectation (Pu et al. 2020). This fraction of X-ray weakness is significantly higher than in the non-WLQ AGN population. A plausible explanation is that the high Eddington ratio causes the inner accretion disc of a WLQ to puff up, which partially shields the X-ray emission from near the black hole. Then the observed X-ray emission will depend on the viewing angle, in which case an X-ray weak WLQ will have a higher inclination angle, so that the line-of-sight to the X-ray corona is obscured by the geometrically thick inner disc (e.g. Wu et al. 2011; Luo et al. 2015; Ni et al. 2018).

Therefore, WLQs and super-Eddington NLS1s share some similar properties (Leighly et al. 2007b; Jin et al. 2017b), yet they do also differ significantly in black hole masses and, more importantly, in Eddington ratios, so the disc structure and geometry need not be the same. A more detailed comparison between these two AGN populations would allow us to better understand the evolution of super-Eddington accretion flows with black hole mass and mass accretion rate.

We conduct a new multi-wavelength campaign from radio to hard X-rays to observe one of the most extreme super-Eddington NLS1s, namely RX J0134.2-4258 in order to deepen our understanding about super-Eddington accretion. This campaign involves new observations with XMM-Newton, NuSTAR, Swift, ATCA and the 2.3-m telescope in the Sliding Spring Observatory (SSO), as well as a large set of archival multi-wavelength data (see Section 2 and Jin et al. 2022, here after: Paper-I).

RX J0134.2-4258 was discovered by Voges et al. (1999) in the ROSAT all sky survey. Its key properties are summarized below, while a more detailed introduction can be found in Paper-I. This NLS1 lies at the redshift of 0.237, and it appears as an unresolved source in optical. It has a black hole mass of $M_{\rm BH}\simeq 1.5\times 10^{7}M_{\odot}$ and an extremely high Eddington ratio of $L_{\rm bol}/L_{\rm Edd}\simeq 10.0$ (Grupe et al. 2010). It has a steep hard X-ray slope ($\Gamma\simeq 2.2$, Paper-I), typical of NLS1, but has only an extremely weak soft X-ray excess, which is both peculiar and puzzling. In addition, it also exhibits drastic X-ray variability in terms of both spectral shape and flux (Paper-I). Its optical/UV properties such as the extremely weak [O iii] $\lambda$5007 and blue-shifted C iv were shown to be similar to the WLQ PHL 1811 by Leighly et al. (2007b).

The latest simultaneous XMM-Newton and NuSTAR observations in our campaign caught RX J0134.2-4258 in its one of the lowest X-ray flux states in history, thus we conducted a detailed X-ray spectral-timing analysis. As shown in Paper-I, we found that the time-average X-ray spectra in the low-flux state has excess flux above 4 keV, which is lagged by $\sim$4 ks behind the soft X-rays. The spectral-timing properties in both low and high-flux states can be well modelled under the warm Comptonisation plus a distant neutral reflection scenario, or by a partial covering absorption scenario. Both scenarios require a clumpy disc wind in this super-Eddington accretion system.

Here we perform a detailed multi-wavelength study from infrared, through optical/UV and then to X-rays to provide independent constraints on the global properties of the accretion flow. For example, the optical/UV continuum can be used to measure the mass accretion rate through the outer disc (e.g. Davis & Laor 2011; Done & Jin 2016). The optical/UV emission/absorption lines can provide information about the broad-line region and outflows (e.g. Bottorff et al. 1997; Pancoast, Brewer & Treu 2011; Pancoast et al. 2014; Grier et al. 2017; Li et al. 2018), and can also be used to measure virial black hole mass (e.g. Peterson et al. 2004; Vestergaard & Peterson 2006; Peterson 2014; Du & Wang 2019). The infrared emission can be used to constrain the properties of the dusty torus (e.g. Fuller et al. 2016; Collinson et al. 2017; Martínez-Paredes et al. 2017; Landt et al. 2019). The broadband spectral energy distribution (SED) can be used to estimate the black hole mass and Eddington ratio (e.g. Jin et al. 2012a; Jin, Done & Ward 2016; Jin et al. 2017b), which can then be used to measure the global radiative efficiency ($\mu$, e.g. Davis & Laor 2011). In this work, we collate a large multi-wavelength dataset to study RX J0134.2-4258.

This paper presents a detailed study on the optical/UV and broadband SED properties of RX J0134.2-4258, as well as a detailed comparison with some representative super-Eddington NLS1s and WLQs. We will suggest a new category of weak-line Seyfert (WLS) galaxies, and demonstrate that RX J0134.2-4258 is an archetypal WLS.

The structure of this paper is as follows. Firstly, we describe the multi-wavelength datasets used in this work, and then briefly describe the data reduction procedures. Then we present a detailed estimate of the black hole mass of RX J0134.2-4258 because it is a key parameter. Section 4 presents a detailed multi-component broadband SED modelling, in order to derive key parameters such as the bolometric luminosity, mass accretion rate and Eddington ratio. In Section 5, we first compare RX J0134.2-4258 with WLQs, and propose it as an archetypal WLS, i.e. a new category of AGN. Then we use a small sample to conduct a more general comparison between the super-Eddington NLS1 population and the more typically Eddington WLQ population. In Section 6, we propose a picture for super-Eddington accretion flows with different parameters. We show how the disc properties, such as the disc structure, wind and global radiative efficiency, may depend on the black hole mass and mass accretion rate. Section 7 summarizes the main results of this paper. A detailed optical/UV spectral analysis is presented in the appendix.

We adopt a flat universe model throughout this work, with the Hubble constant H${}_{0}=72$ km s^-1 Mpc^-1, $\Omega_{\Lambda}=0.73$ and $\Omega_{\rm M}=0.27$.

There are two XMM-Newton (Jansen et al. 2001) observations for RX J0134.2-4258, whose observation dates differ by 11 years. The first observation in 2008 is referred to as Obs-1, and the second in 2019 is Obs-2. These observations also have simultaneous optical/UV data from various filters with the optical monitor (OM). We summarize the data reduction procedures below. The data are downloaded from the XMM-Newton Science Archive (XSA), and reprocessed with the epproc and empproc tasks in the XMM-Newton Science Analysis System (SAS v18.0.0). The source extraction region was chosen to be a circle of 35 arcsec radius, and no pile-up effect was detected during the two observations. The source and background spectra were extracted with the evselect task, and the response and auxiliary files were produced by the rmfgen and arfgen tasks. The data obtained by the optical monitor (OM) were reprocessed with the omichain task.

The NuSTAR (Harrison et al. 2013) observation of RX J0134.2-4258 was conducted simultaneously with the XMM-Newton observation in 2019. The nupipline task inside the HEASoft package (v6.27.2, Blackburn 1995) was used to reprocess the data. The source extraction region was chosen to be a circle with 1 arcmin radius, and the background was extracted from a nearby circular source-free region with the same radius. The nuproducts task was used to extract the spectra.

There are 51 Swift (Gehrels et al. 2004) observations on RX J0134.2-4258 from 2019-12-19 to 2021-08-22. In this work we only use the observation conducted on 2019-12-31, because it is simultaneous with the XMM-Newton and NuSTAR observations. A complete analysis of all the Swift observations will be present in a following paper (Panessa et al. in preparation, hereafter: Paper-III). Six filters were used in the Swift Ultra-violet Optical Telescope (UVOT) during this Swift observation (i.e. UVW2, UVM2, UVW1, U, B and V). The HEASsoft (v6.27.2) package was used to reduce the data. The Swift X-ray Telescope (XRT) data were reprocessed with the xrtpipeline. The source spectrum was extracted from a circular region of 30 arcsec radius. For the UVOT photometric data, a circular aperture of 5 arcsec radius was adopted. Background was chosen from nearby source-free regions with larger areas. We also ran the standard sensitivity check for UVOT, in order to ensure that the data are not affected by the regions on the detector where the throughputs are degraded due to the contamination of dust/debris (Edelson et al. 2015).

Hubble Space Telescope (HST) observed RX J0134.2-4258 in 1996 with the Faint Object Spectrograph (FOS), which covered the spectral range of 970 – 5500 Å in the AGN rest-frame. The calibrated data were downloaded from the Mikulski Archive for Space Telescopes (MAST), from which the spectra were extracted with the IRAF/STSDAS tasks following the standard procedure¹¹1https://www.stsci.edu/instruments/wfpc2/Wfpc2_dhb/intro_ch36.html. We obtained a new optical spectrum of RX J0134.2-4258 with the SSO 2.3-m telescope on 2019-12-19. Infrared photometry from WISE (band: 1 – 4) and 2MASS (band: J, H, K) were downloaded from the NASA/IPAC Infrared Science Archive (IRSA).

Then we analyze the SSO optical and HST UV spectra, fitting for the lines and continuum components. Details are given in Appendix A, with spectra shown in Figure 1a, de-reddened with $E(B-V)=0.0144$ for the Fitzpatrick & Massa (2007) reddening curve for $R_{\rm V}$ = 3.1, and de-redshifted for $z=0.237$. These data are separated by 23 years but the overall difference of normalization is only 7%. Below 4000Å, the two spectra match almost perfectly after removing this 7% difference, while above 4000Å the HST spectrum is weaker by another 5%. Therefore, we can connect the HST spectrum (scaled up by 1.07) and the SSO spectrum at 4000Å to derive a broad optical/UV spectrum, which is shown in Figure 1b.

The optical spectrum of RX J0134.2-4258 resembles a typical NLS1 galaxy. According to the empirical eigenvector 1 of AGN (e.g. Boroson 2002; Jin, Ward & Done 2012c), the strong Fe ii and weak [O iii]$\lambda$5007 lines imply that RX J0134.2-4258 should have a very high mass accretion rate. Another key property of RX J0134.2-4258 is that its UV spectrum has very weak and blue-shifted C iv and Ly$\alpha$+Nv emission lines, like WLQs. We performed a detailed multiple Gaussian+Lorentzian profile decomposition for different emission lines. The methods and results are described in Appendix A. The optical/UV line decomposition and best-fit parameters can be found in Figures 6, 7 and Tables 6, 7.

Based on the above datasets and model configurations, we obtain the best-fit broadband SED for RX J0134.2-4258. Figure 2a shows this SED model, where both model and data are corrected for the Galactic and intrinsic extinction/absorption, and shown in the AGN rest-frame. The best-fit parameters are listed in Table 3.

It is clear that the near-IR emission is dominated by the hot dust components, while the UV continuum is well-fitted by the accretion disc component. There is a small ($\sim 10$ per cent) contribution from host galaxy star light between these two in the optical/near-IR band. At higher energies, the soft X-ray emission observed by ROSAT below 0.3 keV is dominated by the emission from the inner disc. The hard X-rays above 2 keV are dominated by a hot corona with photon index of 2.22${}^{+0.05}_{-0.04}$. There is some evidence for a warm Comptonisation component, with electron temperature of 0.22${}^{+0.37}_{-0.08}$ keV and photon index 2.84${}^{+1.46}_{-1.62}$. All these Comptonisation parameters are typical for X-ray simple super-Eddington NLS1s (e.g. Jin et al. 2013; Jin, Done & Ward 2016, 2017a), apart from the soft X-ray excess being much weaker relative to the disc and hot corona as discussed in Paper-I (see also the explicit comparison to RX04 in Section 5.1).

The mass accretion rate through the outer disc ($\dot{m}_{\rm out}$) is completely determined by the observed optical/UV emission for the fixed black hole mass and spin, giving $\dot{m}_{\rm out}=20.6^{+0.3}_{-0.6}$, confirming that the accretion flow is highly super-Eddington. A higher value of black hole spin will only increase this. The only way to significantly reduce $\dot{m}_{\rm out}$ is to go to higher black hole mass, as the monochromatic luminosity on the Rayleigh-Jeans part of the standard (multi-temperature blackbody) disc continuum has $L_{\rm\nu}\propto(M_{\rm BH}~{}\dot{M})^{2/3}\propto(M_{\rm BH}^{2}~{}\dot{m}_{\rm out})^{2/3}$, where $\dot{m}_{\rm out}=\dot{M}/\dot{M}_{\rm Edd}$ (e.g. Shakura & Sunyaev 1973; Davis & Laor 2011; Kubota & Done 2019). Increasing the mass by a factor of 2 (i.e. $4\times 10^{7}M_{\odot}$) then reduces $\dot{m}_{\rm out}$ by a factor of 4, but then $\dot{m}_{\rm out}$ is still $\sim 5$, so the disc is still super-Eddington even a factor of 2 away from our preferred black hole mass.

The observed bolometric luminosity is derived by integrating the best fit model, and gives $L_{\rm bol}=1.63\times 10^{46}$ ergs s^-1. Thus $L_{\rm bol}/L_{\rm Edd}=6.3$, substantially below the $\dot{m}_{\rm out}=20.6$ derived for the accretion flow itself. This is clear evidence for a loss of power through advection and/or winds, as expected for a strongly super-Eddington flow.

The weak UV lines of RX01 resemble those from WLQs, defined as Ly$\alpha$ + N v REW $\leq$ 15 Å, and C iv REW $\leq$ 10 Å (Fan et al. 1999; Diamond-Stanic et al. 2009; Plotkin et al. 2010; Wu et al. 2011, 2012; Luo et al. 2015; Ni et al. 2018). In this section, we compare RX01 with some typical WLQs and NLS1s (see Table 5)³³3Note that the estimates of the mass, mass accretion rate and bolometric luminosity are all subject to various systematic uncertainties, so we only show their typical values and do not provide their uncertainties in Table 5., in order to obtain a full understanding of their similarities and differences.

The global radiative efficiency ($\mu$) is a key parameter of the accretion flow around SMBHs, which indicates the fraction of accreted energy that is converted into radiation. $\mu$ can be estimated by measuring the difference between the observed Eddington ratio and mass accretion rate (Davis & Laor 2011). In Table 5 we have estimated the radiative efficiency for RX01 from its best-fit SEDs, which is found to be $\sim$ 30 per cent of the theoretical efficiency $\mu_{0}=0.057$ of a standard thin disc for $M_{\rm BH}=2\times 10^{7}~{}M_{\odot}$ and zero spin. Likewise, we measure $\mu$ for the other AGN mentioned in this work based on their best-fit SEDs, which are shown in Table 5.

We find that as $\dot{m}_{\rm out}$ increases, $\mu$ decreases significantly. This is qualitatively consistent with theoretical expectation that as the accretion flow becomes more super-Eddington, its properties deviate from the standard thin disc more significantly, the advection and wind may carry away a larger fraction of accretion energy, thus the global radiative efficiency becomes smaller. For instance, Poutanen et al. (2007) derived a simple equation, $L_{\rm bol}/L_{\rm Edd}=1+x\cdot$ln$(\dot{m}_{\rm out})$, to describe the relation between the Eddington ratio and mass accretion rate for super-Eddington accretion flows. The $x$ factor is directly related to $\mu$. For a super-Eddington disc with advection but without outflow, the $x$ factor is 1.0; while for a disc with outflow but without advection, the $x$ factor is 0.6. In Figure 5 we plot our small AGN sample on the parameter space of $\dot{m}_{\rm out}$ and $L_{\rm bol}/L_{\rm Edd}$, and compare them with various theoretical relations. We find that for a fixed $\dot{m}_{\rm out}$, the observed Eddington ratio is a factor of few higher than the disc+advection and disc+outflow model, and the deviation increases as AGN becomes more and more super-Eddington. This suggests that while the actual radiative efficiency of a super-Eddington accretion flow is significantly lower than that of a standard thin disc (Shakura & Sunyaev 1973), it remains higher than those predicted by previous super-Eddington disc models.

Based on the six AGN in Figure 5, we perform second-order polynomial model fit to derive an empirical relation between $\dot{m}_{\rm out}$ and $L_{\rm bol}/L_{\rm Edd}$,

where $a_{0}=-0.234^{+0.237}_{-0.136}$, $a_{1}=0.919^{+0.170}_{-0.189}$, and $a_{2}=0.044^{+0.009}_{-0.104}$ are derived from the parameter values and inferred uncertainties. This equation can be used to infer the radiative efficiency for an AGN with $1.7\leq\dot{m}_{\rm out}\lesssim 50$, but it is limited by the small sample size, and so it should be refined by future large sample studies.

Figure 5 also shows the inferred uncertainty region for every source. The uncertainty of $\mu$ is mainly caused by the measurement accuracies of the black hole mass $M_{\rm BH}$, spin $a_{*}$ (we assumed spin 0 in this work as a conservative limit) and bolometric luminosity $L_{\rm bol}$. The typical measurement uncertainty of $L_{\rm bol}$ is a few tens of per cent for a well defined SED of an unobscured super-Eddington AGN with high-quality optical/UV and soft/hard X-ray data (e.g. Jin, Ward & Done 2012c; Jin et al. 2013, 2017b; Jin, Done & Ward 2021). The black hole spin is largely unknown, but Davis & Laor (2011) showed that spin can introduce a few tens of per cent uncertainty on $\dot{m}_{\rm out}$. However, this can be easily overwhelmed by the uncertainty of black hole mass estimate, because this uncertainty can be a factor of few, and we have $\dot{m}_{\rm out}\propto M_{\rm BH}^{-2}$ for an observed optical/UV luminosity, so the uncertainty propagated from $M_{\rm BH}$ to $\dot{m}_{\rm out}$ is square-amplified. The uncertainty regions in Figure 5 are based on these black hole mass ranges and $\pm$ 50 per cent uncertainty of $L_{\rm bol}$, and we have also assumed that $L_{\rm bol}/L_{\rm Edd}$ cannot exceed $\dot{m}_{\rm out}$. We find that except RE10 and PH10 whose $\dot{m}_{\rm out}$ values are only 1.7 and 2.3, all the other uncertainty regions lie between the standard thin disc model and the disc+advection/outflow models. Therefore, considering various measurement uncertainties, it appears robust that the observed radiative efficiencies of our super-Eddington AGN sample are indeed lower than the prediction of standard thin disc model, but significantly higher than predictions of theoretical super-Eddington disc models.

It is also useful to compare our results with numerical simulations of super-Eddington accretion flows. For example, Jiang, Stone & Davis (2014) performed three-dimensional (3D) radiation magneto-hydrodynamical (MHD) simulations for an AGN with $M_{\rm BH}=4.2\times 10^{6}~{}M_{\odot}$ and $\dot{m}_{\rm out}=12.5$. These parameters are comparable with those of RX04. Jiang, Stone & Davis (2014) reported $L_{\rm bol}/L_{\rm Edd}\sim 10$, which then leads to $\mu=0.045$, as shown by the star symbol in Figure 5. This radiative efficiency is significantly higher than those predicted by most theoretical models. It is caused by the inclusion of magnetic buoyancy in the simulation, which enhances the vertical advection of radiation, thereby increasing the global radiative efficiency. The efficiency we found for RX04 is 0.029, which is also much higher than previous theoretical models, but is $\sim$ 55 per cent lower than the 3D MHD simulation.

The observed correlation in Figure 5 for the extreme super-Eddington regime is broadly consistent with the moderate correlation reported by Davis & Laor (2011) using a much larger sample of both sub and super-Eddington Palomar-Green quasars. Davis & Laor (2011) also reported a significant correlation between the radiative efficiency and the black hole mass, which can be explained by the mass-spin correlation predicted by the cosmic evolution of SMBH (Fanidakis et al. 2011). We do not find such a relation in our small sample, which is probably because these six AGN only cover a narrow mass range, and so the effect of mass-spin correlation is negligible.

Super-Eddington NLS1s and WLQs are both characterized by their high mass accretion rates, but their black hole masses differ by more than one order of magnitude, thus comparing these two types of AGN can bring new insights on the super-Eddington accretion flow of SMBH. Based on their different multi-wavelength properties, a puffed-up inner disc scenario was proposed for both types of SMBH accretion systems (e.g. Luo et al. 2015 for WLQs and Jin et al. 2017b for NLS1s). This was discussed even in the original paper of Shakura & Sunyaev (1973), where they show that the flow forms a quasi-spherical funnel when the disc reaches the local Eddington limit, within the spherization radius $r_{\rm sp}~{}=~{}R_{\rm sp}/R_{\rm in}~{}\sim~{}\dot{m}_{\rm out}$ where $R_{\rm in}$ is the inner radius (see also Poutanen et al. 2007, Kubota & Done 2019). We can derive a rough estimate of this radius for each object. Such an inner disc structure will produce a geometric collimation of the inner disc/soft X-ray/hard X-ray emission. This inclination dependence will be enhanced by any wind from the super-Eddington flow, and strong evidence for a wind is seen in the rapid and complex X-ray variability. However, both the funnel and the super-Eddington wind might be expected to depend only on $\dot{m}_{\rm out}$ rather than on mass, yet we showed examples in the previous section where sources at similar high Eddington fractions have weaker/more blue-shifted UV lines at higher masses, so there should be another intrinsic factor at work as well.

One possibility is that there is an additional wind from the disc due to UV line driving. This is already implicated in the WLQ by the fact that the UV lines (C iv and Ly$\alpha$+N v) are blue-shifted. UV line driving is sensitively dependent on the disc temperature which depends on $M_{\rm BH}$ as well as $\dot{m}_{\rm out}$. A continuum SED which peaks in the UV (as in the mildly super-Eddington high mass AGN) is much more efficient in UV line driving than one that peaks in the EUV/soft X-rays (as in the strongly super-Eddington low-mass NLS1s). Hence this gives a component which depends on mass as well as $\dot{m}_{\rm out}$. Based on the above ideas, we compare the inferred structure of super-Eddington accretion discs for different black hole masses and mass accretion rates, which is shown in Figure 6.

The first row is the puffed-up disc scenario proposed for WLQs such as PH18 and PH10 (e.g. Wu et al. 2012; Luo et al. 2015; Ni et al. 2018). Since their mass accretion rates are close to or slightly above the Eddington limit, the puffed up region is quite small (a few tens of $R_{\rm g}$), and the Eddington wind is not very powerful. However, these structures shield the rest of the disc from the hottest emission (inner funnel and X-ray corona). The maximum outer disc temperature is given at the radius where the puffed up region starts. To infer the SED shape outside the spherization radius, we adopt the optxagnf model (Done et al. 2012) and take the best-fit $M_{\rm BH}$ and $\dot{m}_{\rm out}$ listed in Table 5 as inputs⁴⁴4As a rough comparison, we take the average $\dot{m}_{\rm out}$ of 25 for 1H07, and 20.6 for RX01., and then truncate the SED at $R_{\rm sp}$. As shown in Figure 7, for WLQs with masses of $\sim 10^{8}$, this outer disc emits in the UV, and is just below Eddington. This should power an extremely strong UV line-driven disc wind. This shields the standard BLR from the outer disc from the inner UV/X-ray emission, so the standard BLR which makes the core of the lines is weak, so the UV lines are dominated by the wind emission, giving the characteristic blueshift of the BLR line profile. In Figure 6, we also show the failed dust-driven wind from the model of Czerny & Hryniewicz (2011), where it is suggested that the BLR is itself a (failed) wind, but driven by dust rather than by the UV⁵⁵5This disc scenario may also be applicable for another famous AGN called PDS 456. It is a low-redshift AGN located at $z=0.184$ with $M_{\rm BH}\sim\times 10^{9}~{}M_{\odot}$ and $L_{\rm bol}/L_{\rm Edd}\sim 1.0$ (Simpson et al. 1999; Reeves et al. 2000). It is famous for showing extreme X-ray variability and X-ray absorption features indicating ultra-fast outflows (Reeves et al. 2020 and references therein). Besides, it is known to show weak [O iii] $\lambda 5007$ line with REW $<$ 2 Å (Simpson et al. 1999), as well as weak UV high-ionization lines such as C iv REW $=14.7$ Å and broad UV absorption lines (Hamann et al. 2018). These multi-wavelength properties are similar to RX01 and PH18, although its C iv is still stronger than the definition of WLQ. PDS 456 also shows a low level of radio emission, although it can be classified as a radio-quiet AGN (Vignali et al. 2000; Yang et al. 2021)..

The second row of Figure 6 shows the disc scenario for the archetypal super-Eddington NLS1 RX04 (Jin et al. 2017b). Comparing to PH18, its black hole mass is one order of magnitude lower, and its mass accretion rate is one order of magnitude higher, thus we expect the disc to be much hotter ($T_{\rm eff}^{4}\propto M_{\rm BH}^{-1}~{}\dot{m}$) and the puffed-up disc region to be larger ($\sim$ 50 $R_{\rm g}$), and so the super-Eddington disc wind may be more powerful. This again shields the outer disc from the hottest parts of the disc, but the disc temperature just outside of the funnel region is somewhat hotter than seen in WLQs (see Figure 7). This stronger emission below 200Å could be enough to over-ionise the disk wind, so the UV line driving is not efficient. The UV wind then does not shield the core of BLR as efficiently, so the core of the UV lines (e.g. C iv) are stronger, as well as the blue-wing of the lines being weaker (due to the weaker UV wind), so these line profiles do not meet the criteria for a WLQ.

The above picture is further supported by the multi-wavelength properties of the WLS RX01, whose black hole mass and mass accretion rates are both higher than RX04, as shown in the third row of Figure 6. In this case, higher mass accretion rate means that the disc can begin to puff up at an even larger radius of $\sim$ 100 $R_{\rm g}$, and so an even stronger super-Eddington wind is expected. This clumpy wind absorbs the soft X-rays of RX01 and causes its drastic X-ray variability, similar to those observed in PH10 and PDS 456. But the emission from the disk outside of the funnel is now similar to that of the WLQ (see Figure 7), so this can have a similarly strong UV line driven wind, and so weak core lines from the BLR, and UV lines dominated by the UV line driven disc wind. Then the UV line-driving mechanism still works efficiently at outer/cooler disc region, making RX01 the so far unique WLS. This also explains why RX01 and PH18 show similar infrared luminosity from hot torus relative to their optical luminosity.

A jet is also drawn in this picture, because the radio-loudness of RE10 was reported to be $\sim~{}17$, and so it was a marginally radio-loud NLS1 more than one decade ago (Gelbord, Mullaney & Ward 2009). But our latest observation campaign shows that now it becomes a radio-quiet source, and so its jet emission may be episodic (see more details in Paper-III).

The last row of Figure 6 shows the disc scenario for 1H07, whose $\dot{m}_{\rm out}$ is similar to RX01, but with one order-of-magnitude lower black hole mass. In this case, the accretion disc is the hottest among all the AGN mentioned above, and so the super-Eddington wind is also the strongest, which leads to drastic X-ray variability (e.g. Hagino et al. 2016; Done & Jin 2016; Boller et al. 2021; Parker et al. 2021). The disc emission outside of the funnel region is now similar to RX04 (see Figure 7), just a little too high for the UV line driving to be efficient, so the blue-shifted line from the wind is not strong and the core BLR is not shielded. This explains why 1H07 does not turn out to be a WLS.

Finally, we emphasize that our study of the similarities and differences between super-Eddington NLS1s and WLQs is just at the beginning. More similarities/differences may be found by future studies, including detailed photoionization analyses of the BLRs of super-Eddington NLS1s and WLQs assuming different illuminating SEDs. If the above scenarios are generally correct, we speculate that further studies may find more WLS, as well as more WLQs showing drastic X-ray variability.