In-situ star formation in accretion disk and explanation for correlation between black hole mass and metallicity in AGNs

Most galaxies harbor a supermassive black hole (SMBH) at their nuclei, where the BH mass is around $10^{5-10}M_{\odot}$ from dwarf galaxies to massive elliptical galaxies. The active galactic nuclei (AGNs) are the most luminous persistent sources in the universe and have been detected at redshift up to $z=7.64$, which are powerful tools to study the evolution of SMBHs and galaxies (Wang et al., 2021a; Mortlock et al., 2011; Bañados et al., 2018; Matsuoka et al., 2019; Yang et al., 2020). The big blue bump as observed in many luminous AGNs provides a strong evidence for mass accretion onto SMBHs (e.g., Shakura & Sunyaev, 1973; Ho, 2008). A large fraction of AGNs show both broad emission lines (BELs) with full width at half maximum (FWHM) of a few thousands $\rm{km\ s^{-1}}$ and narrow lines with FWHM of a few hundreds $\rm{km\ s^{-1}}$ (see the reviews by Osterbrock & Mathews, 1986; Netzer, 1990; Sulentic et al., 2000; Czerny, 2019). The BEL is radiated from the fast moving clouds surrounding the SMBHs (e.g., broad line region, BLR), and therefore, it provides fundamental clues for the kinematics, metallicity, ionization, and structure of the nuclear regions in AGNs (e.g., Netzer & Laor, 1993; Alexander & Netzer, 1997; Collin & Huré, 2001; Wang et al., 2012, 2017; Czerny et al., 2015, 2016, 2017).

The chemical evolution of AGNs and galaxies across cosmic time contains crucial information about the star formation history and galaxy evolution (see a recent review by Maiolino & Mannucci, 2019). Photoionization calculations suggest that ratio of some metal emission lines or helium recombination lines (e.g., (SiIV+OIV])/CIV, SiIII/CIV, AlIII/CIV, NV/CIV, and NV/HeII) can be used to infer the metallicity of BLR (Hamann & Ferland, 1993; Hamann et al., 2002; Nagao et al., 2006; Tang et al., 2019; Wang et al., 2022). One of the most important results is that the BLR metallicity is generally supersolar (e.g., several $Z_{\odot}$ and up to $15Z_{\odot}$) and approximately redshift-independent (Hamann & Ferland, 1999; Warner et al., 2004; Nagao et al., 2006; Jiang et al., 2007; Xu et al., 2018; Onoue et al., 2020; Śniegowska et al., 2021; Wang et al., 2022), which is much higher than the metallicity of narrow line regions (NLRs) and host galaxies (Tremonti et al., 2004; Erb et al., 2006; Zahid et al., 2014, 2017; Thomas et al., 2019; Curti et al., 2020). It is found that BLR metallicity is positively correlated with the BH mass (so-called mass-metallicity relation, or $M_{\rm BH}-Z_{\rm BLR}$ relation) or luminosity (Shemmer et al., 2004; Warner et al., 2004; Nagao et al., 2006; Matsuoka et al., 2011; Xu et al., 2018; Lai et al., 2022). Matsuoka et al. (2011) suggested $M_{\rm BH}-Z_{\rm BLR}$ relation may be more fundamental if considering line ratios that not including nitrogen. Xu et al. (2018) found that the BLR metallicity is significantly larger than the metallicity of host galaxies, which can not be explained by observational uncertainties. This is also a similar case even for a quasar at redshift of $z\sim 7.5$ that the metallicity of BLR is very high but the metallicity of the host galaxy is still near solar value (Novak et al., 2019). Simon & Hamann (2010) found that the BLR metallicity does not correlate with star formation rates (SFRs) of host galaxies as constrained from far-infrared emission, which indicates that the chemical enrichment should be associated with the rapid and intense star formation in the compact nuclear region rather than transporting from the host galaxy.

The accretion disk is optically thick and geometrically thin in bright AGNs (i.e., SSD, Shakura & Sunyaev, 1973). It is well-known that SSD is gravitationally unstable and prone to be self-gravitated at distances larger than several thousand Schwarzschild radii (Toomre, 1964; Paczynski, 1978; Shlosman & Begelman, 1987; Goodman, 2003; Thompson et al., 2005). Fragmentations due to the gravitational instability have been proposed as a mechanism for star formation in AGNs (Cheng & Wang, 1999; Collin & Zahn, 1999; Nayakshin, 2006; Collin & Zahn, 2008; Wang et al., 2010, 2011, 2012; Kawakatu & Wada, 2008; Wada et al., 2009), e.g., to explain the stars in the Galactic center (Levin & Beloborodov, 2003; Nayakshin & Sunyaev, 2005; Levin, 2007; Davies & Lin, 2020; Mapelli et al., 2012). The evolution of massive stars may lead to heavy-element enrichment near Sgr A*, which has indeed been detected in the spectra of some stars within 0.5 pc of the Galactic center (Do et al., 2018). Based on SNe in the accretion disk, Wang et al. (2010) found that it can roughly reproduce the observed positive metallicity–luminosity correlation. The stellar evolution in the disk environments may be much different from that in host galaxies (e.g., so-called “accretion-modified stars(AMS)” in Wang et al., 2021b) and potentially increase supernova rate and the number of compact objects in the nuclei of galaxies (Cantiello et al., 2021; Dittmann et al., 2021; Jermyn et al., 2021, 2022).

The BH mass-metallicity correlation may be more fundamental in AGNs (Warner et al., 2004; Matsuoka et al., 2011), the main goal of this work is to explore the possible metal enrichment based on the model of in-situ star formation in the outer region of the SSD. We introduce our sample to revisit the $M_{\rm BH}-Z_{\rm BLR}$ relation in Section 2. In Section 3, we describe the metal enrichment model. The main results are presented in section 4. Discussions and conclusions are presented in Section 5. Throughou this paper, we adopt flat $\Lambda$CDM cosmology with $H_{0}=70{\rm km\ s^{-1}}$, $\Omega_{\Lambda}=0.7$ and $\Omega_{\rm m}=0.3$.

The flux ratios of high-ionization lines are commonly assumed to indicate the metallicity of the BLR in luminous AGNs. Hamann et al. (2002) and Nagao et al. (2006) adopted the locally optimally emitting clouds model (Baldwin et al., 1995) and used the photoionization code CLOUDY (Ferland, 2000) to simulate emission line fluxes at different metallicities. A handful of diagnostic ratios in the UV and optical wavebands have been tested to constrain the metal contents of BLRs, such as NV/CIV, (SiIV+OIV)/CIV, AlIII/CIV, NV/HeII, and FeII/MgII. In this work, we adopt NV/CIV as the metallicity indicator, which is also wildly used in the literature (Hamann & Ferland, 1993; Shemmer et al., 2004; Shin et al., 2013; Du et al., 2014; Shin et al., 2019; Wang et al., 2022; Lai et al., 2022), since that NV and CIV emission lines are normally prominent in the AGN spectrum. The metallicity of selected sources is estimated from the ratio of NV/CIV based on the simulations of Nagao et al. (2006).

It should be noted that there are two definitions to describe the metallicity in the literature, which are metal mass fraction ($Z$) and elemental abundance ratio by number relative to solar value ($A$). The ratio of $Z/Z_{\odot}$ is roughly the same as the value of $A$ if the abundance is around solar or sub-solar, while they differ a lot when $A>3$ (e.g., $\sim$30% for $A=10$, see Appendix A and Hamann et al. 2002 for more details). The difference between $A$ and $Z$ comes from the fact that metal elements are produced by the fusion of hydrogen. The number of metal atoms will increase as that of hydrogen atoms decreases, where the number ratio of metal atoms to hydrogen ($A$) will not increase with $Z$ linearly. The widely adopted emission line flux ratios normally give the elemental abundance ratio rather than the metal mass fraction based on the CLOUDY code (e.g., Hamann et al., 2002; Nagao et al., 2006; Wang et al., 2022). In this paper, we adopt the commonly used definitions of $Z$ and/or $A$ to denote metallicity, the correlation between them is shown in Appendix A.

The BLR metallicity has been widely explored in the literature, where the metallicity is positively correlated with BH mass when $M_{\rm{BH}}\gtrsim 10^{8}M_{\odot}$ (Warner et al., 2004; Matsuoka et al., 2011; Xu et al., 2018; Wang et al., 2022; Lai et al., 2022). But it is still unknown whether this correlation can extend to low-mass BH sources (e.g., narrow-line Seyfert 1, NLS1). To explore the possible physical mechanism behind the $M_{\rm BH}-Z_{\rm BLR}$ correlation, we assemble a sample containing 174 AGNs from six published AGN samples, including quasars, Seyferts, and NLS1s. Among the 174 sources, 98 are low-redshift PG quasars and Seyfert 1 galaxies (${z}<0.5$) observed by International Ultraviolet Explorer or Hubble Space Telescope (Shin et al., 2013; Du et al., 2014). The other 41 sources with $z\sim 3$ (Shemmer et al., 2004; Shin et al., 2019) and 35 sources with ${z}\sim 6$ (Lai et al., 2022; Wang et al., 2022) are also included in our sample. Redshift, BH mass, NV flux, CIV flux, and bolometric luminosity of these sources are all available in the literature and listed in Table 1. In our sample, the BH mass roughly spans five orders of magnitude from $10^{6}M_{\odot}$ to $10^{11}M_{\odot}$ and the redshift range from 0 to 6. It should be noted that our sample is not complete, but it will not affect our main conclusion since there is roughly no metallicity evolution with redshift in BLRs (Jiang et al., 2007; Onoue et al., 2020; Wang et al., 2022).

The gravitational instability in the outer part of the AGN disk can trigger star formation, where is also a candidate region for producing the metals (e.g., Wang et al., 2010, 2011, 2012; Śniegowska et al., 2021). We explore metal enrichment by considering the contribution of stars and SNe in the outer part of the SSD. We assume that the disk with Toomre’s stability parameter, $Q\equiv c_{\rm{s}}\Omega/\pi G\Sigma<1$, is gravitationally unstable (Toomre, 1964) and the self-gravitating clouds will collapse to form stars. In Figure 1, we present the sketch map of our model. As shown in the top panel, the region within the critical self-gravity radius ($R_{\rm sg}$, defined as the radius where $Q=1$) is the accretion disk while the outer part is the star disk. The stars embedded in the disk will grow through accretion, and some of them will explode as SNe. The SN ejecta mix with disk material and enrich the gas metallicity of the disk. If the SN explosions have very high kinetic energy, part of the gas will break out the disk directly (Moranchel-Basurto et al., 2021; Grishin et al., 2021; Zhu et al., 2021). In the standard disk model, heavier SMBHs predict a smaller critical self-gravity radius at the given accretion rate (e.g., the dashed line in bottom panel of Figure 1). Therefore, the heavier SMBH in AGNs with more intense star formation will possibly lead to higher metallicity. We calculate the metal enrichment in more detail as follows, where the BLR gas from the wind of enriched disk and some fraction of gas pushed out by energetic SN explosions are considered.

The BLR metallicity of AGNs is generally super-solar, positively correlates with $M_{\rm BH}$, and is roughly independent of the redshift. These observations suggested that the metal elements are most possibly produced in the nuclear region close to SMBHs. The stars that formed in the outer region of SSD or are captured by accretion disks will evolve quickly in these gas-rich environments and disk stars will provide considerable metal elements through SNe. In this work, we revisit the possible correlation between the metallicity of BLR and BH mass with more AGNs with $M_{\rm BH}\sim 10^{6-8}M_{\odot}$ based on NV/CIV as a metallicity indicator and find that positive $M_{\rm BH}-Z_{\rm BLR}$ correlation become flat at low-mass range. Based on the assumption of star formation in the self-gravitating disk, we calculate the metal enrichment and find that the positive $M_{\rm BH}-Z_{\rm BLR}$ correlation can be reproduced if the stellar mass distribution of disk stars is “top-heavy”. We find that the size of BLR is roughly consistent with the self-gravity radius, where the embedded stars grow most rapidly and the probability of producing SNe is highest.

The positive $M_{\rm BH}-Z_{\rm BLR}$ correlation has been reported in several former works (Shemmer et al., 2004; Xu et al., 2018; Wang et al., 2022; Lai et al., 2022), where the $Z_{\rm BLR}$ depends much more significantly on $M_{\rm BH}$ rather than $L/L_{\rm Edd}$ (see Warner et al., 2004; Matsuoka et al., 2011, for more details). Some works also proposed that this correlation may be not strong (Shin et al., 2013; Du et al., 2014). In this work, we find that the different conclusions are mainly caused by the sources in different BH mass range, where this relation is indeed weak in low mass regime ($M_{\rm BH}\sim 10^{6-8}M_{\odot}$) but show a positive correlation when $M_{\rm BH}\gtrsim 10^{8}M_{\odot}$. The estimation of metallicity for more sources with $M_{\rm BH}\sim 10^{6-7}M_{\odot}$ and $M_{\rm BH}\sim 10^{9-10}M_{\odot}$ are wished to be further explored.

In this work, the BLR metallicity is estimated from the line ratio of NV/CIV, while the ratio of NV/HeII, (SiIV+OIV])/CIV, and AlIII/CIV are also widely adopted in the literature (e.g., Hamann et al., 2002; Nagao et al., 2006; Matsuoka et al., 2011). Matsuoka et al. (2011) found that there is a significant correlation between $M_{\rm BH}$ and $Z_{\rm{BLR}}$ as inferred from all above four metallicity-sensitive emission-line flux ratios. It should be noted that the line flux ratios of (SiIV+OIV)/CIV, and AlIII/CIV are better served as a metallicity indicator since that they are not correlated with the Eddington ratios. However, the lines of NV and CIV are normally stronger than other lines, and we adopt these two lines to estimate the BLR metallicity, even though it may be affected by the possible ionization parameter or the shape of the ionizing continuum (Hamann et al., 2002; Nagao et al., 2006). The metallicity estimation based on different line ratios will not affect our main results since that they are all calibrated.

The physical origin of $M_{\rm BH}-Z_{\rm BLR}$ correlation and no redshift evolution of elemental abundance ratios in AGNs are unclear. The higher metallicity in BLRs than that in NLRs and host galaxies suggest that the metal enrichment is most likely to happen in the compact nuclear region (e.g., pc or even smaller scales). The high densities and large amounts of gas in the central region of AGN likely trigger rapid star formation and enrich the metallicity of environments quickly due to SNe. We explore the possible metal enrichment process based on the model of in-situ star formation in gravitationally unstable regions in the outer accretion disk. More massive SMBHs have larger star formation regions, and more disk stars will lead to higher metallicities (see the cartoon picture of Figure 1). The sound speed of the disk is lower for AGNs with smaller SMBHs, where the SN explosion can break out of the disk much easier than that of more massive BHs (Moranchel-Basurto et al., 2021; Grishin et al., 2021). The SNe will contribute metals to the BLR directly, which will lead to a shallower $M_{\rm BH}-Z_{\rm BLR}$ correlation. Based on the well-known Kennicutt–Schmidt law (Kennicutt, 1998), we calculate the SFR in the outer accretion disk and estimate the metal enrichment through SNe by assuming stellar mass distribution. We find that the standard IMF with $\Gamma=2.35$ predicts a much shallower $M_{\rm BH}-Z_{\rm BLR}$ correlation, which can not explain the observed correlation (e.g., the green dashed line in the bottom panel of Figure 3). Our results imply a “top-heavy” stellar mass distribution, i.e., $\Gamma<1$ is needed to reproduce the average $M_{\rm BH}-Z_{\rm BLR}$ relation, which is roughly consistent with the results of Toyouchi et al. (2022); Qi et al. (2022). The direct observational constraints on the stellar mass distribution in the galaxy center are difficult due to the limited telescope resolutions. The high-resolution observations of the stars near Sgr A* indicate an extremely “top-heavy” stellar mass distribution in the galactic center (e.g., $\sim 1{{}^{\prime\prime}}-10^{{}^{\prime\prime}}$, Bartko et al. 2010), where hundreds of massive, young OB stars and Wolf-Rayet stars have been detected in the central nuclear region (e.g., within $\sim$0.5 pc, Krabbe et al. 1995; Genzel et al. 2003; Ghez et al. 2003. Based on the fragment masses of pre-stellar clumps caused by gravitational instability in the AGN disc, Derdzinski & Mayer (2022) also suggested that the stellar mass distribution in the nuclear region of AGNs should be “top-heavy” with $\Gamma\sim 0.7$, which is roughly consistent with our results. The typical timescale for metallicity to approach the saturation value is 0.1 Gyr, which can roughly explain the non-redshift evolution up to $z\sim 7$.

Some metallicity-sensitive emission-line flux ratios strongly support a tight correlation between $Z_{\rm{BLR}}$ and $M_{\rm BH}$, while $Z_{\rm{BLR}}$ does not correlate with the Eddington ratios and redshift (e.g., Warner et al., 2004; Matsuoka et al., 2011). It should be also noted that the line ratios related to NV and FeII are possibly correlated with the Eddington ratio. Matsuoka et al. (2011) proposed that the possible correlation between NV/CIV and Eddington ratios may be caused by a delay of the black hole accretion rate relative to the onset of nuclear star formation of about $10^{8}$ years, which is the timescale required for the nitrogen enrichment. The FeII/MgII line flux ratio, the first-order proxy of Fe/$\alpha$ elemental abundance ratio, is another indicator of AGN metallicity (Shin et al., 2019; Sameshima et al., 2017; Shin et al., 2021), which acts like a clock of star formation history since that the iron element is mainly ejected by the type Ia SN that is delayed by $10^{8}$ years relative to $\alpha$ elements from core-collapse SNe (Type II and Type Ib/Ic SNe). The star formation and stellar evolution in the nuclear region close to SMBH are still highly uncertain (Cantiello et al., 2021; Dittmann et al., 2021; Jermyn et al., 2021, 2022; Li et al., 2022). The simultaneous measurements of different line ratios can provide a chance to constrain the possible stellar evolution for the stars embedded in accretion disk. We estimate the star formation rate from the KS law with an observational index of 1.14 as constrained from nuclear regions of AGNs ($\sim$ 100 pc, Casasola et al. 2015), and high-resolution constraints are wished to further explore the stellar properties in these special environments.

It should be noted that the origin of materials in the BLR clouds is still unclear, which may originate from the winds/envelopes of bloated stars (Alexander & Netzer, 1997), inflow from large-scale gas (e.g., torus clumps), the gas of SNe from the stars embedded in accretion disk and/or winds of the accretion disk (see Wang et al., 2012, 2017; Galianni & Horne, 2013; Czerny et al., 2016, 2017; Czerny, 2019). Theoretical studies have suggested that stars embedded in the self-gravitating regimes of AGN disks will suffer strong evolution after their formation. The SNe from massive stars can support a geometrically thick, turbulent gas disk where the turbulent viscosity excited by SNe transports the angular momentum of the metal-rich gas efficiently (e.g., Wada & Norman, 2002; Kawakatu & Wada, 2008). The ejected material from the SNe that happened in the outer gravitationally unstable disk also enrich the metallicity of the AGN disk (e.g., Wang et al., 2012), which may be the physical reason for the high metallicity of BLR if considering the BLR clouds are related to the underlying AGN disk. The evolution of AGN stars should be much different from the classical star evolution with quite low density surroundings (or low accretion rate, e.g., Cantiello et al. 2021; Dittmann et al. 2021; Wang et al. 2021b; Jermyn et al. 2022). With the assumption of Bondi-like accretion, we calculate the accretion rate of the stars at different disk radii and find that the accretion rates always peak at $\sim R_{\rm{sg}}$ (see Figure 4). We proposed that the stars should most possibly undergo a runaway accretion and explode as SNe in the region from $\sim 10R_{\rm sg}$ to $\sim 0.1R_{\rm sg}$, where the stars can increase up to several tens to several hundred solar masses by assuming the typical migration timescale of $\sim 10^{6}$ yr for type I migration (Derdzinski & Mayer, 2022). Therefore, the metallicity in this region should be highest in the accretion disk. The BLR clouds formed from the disk winds and/or SN-ejected materials will have quite high metallicity. In Figure 5, we compare the observed BLR size with the size of $R_{\rm{sg}}$ as predicted from the disk model, which is roughly consistent with each other. It should be noted that above correlation itself cannot give the physical origin of BLR, which just suggests that the BLR clouds may be closely correlated with the underlying disk. More detailed investigations considering the stellar evolution, accretion, and migration are needed to further test this issue, which will be our future work.

We thank our referee for constructive comments and suggestions that help us to improve this paper. We appreciate Jianmin Wang, Bozena Czerny, Luis C. Ho and the members in our BH group for very useful discussions and suggestions. This work is supported by the NSFC (grants U1931203,12233007), the science research grants from the China Manned Space Project (No. CMS-CSST-2021-A06). The authors acknowledge Beijng PARATERA Tech CO.,Ltd. for providing HPC resources that have contributed to the results reported within this paper.