A model for GN-z11: top-heavy stellar initial mass functions in forming galactic nuclei and ultra-compact dwarfs

A significant fraction of dwarf and late-type spiral galaxies in various environments are observed to contain stellar galactic nuclei or “nuclear star clusters” (e.g., Sandage & Binggeli 1984; Böker et al. 2002; Côte et al. 2006). The physical origin of the stellar nuclei and their evolutionary links to massive black holes (MBHs) dominating the central regions of massive early-type galaxies are yet to be fully understood (e.g., Graham & Spitler 2008; Antonini et al. 2015). The observed very small half-light radii ($R_{\rm h}<100$ pc) and large stellar masses ($10^{6}\leq M_{\rm s}/{\rm M}_{\odot}\leq 10^{8}$) in ultra-compact dwarf (UCD) galaxies (e.g., Drinkwater et al. 2003; Mieske et al. 2008) have been extensively discussed in the context of their transformation from massive nucleated dwarf galaxies (e.g., Bekki et al. 2001; Pfeffer et al. 2014). Recent spectroscopic studies of a few UCDs (e.g., M60-UCD1 and UCD3) have confirmed the possible presence of MBHs (Seth et al. 2014; Afanasiev et al. 2018), which implies that there is a link between UCD and MBH formation. The nitrogen abundance of M60-UCD1 is observed to be strongly enhanced with [N/Fe]$=0.61\pm 0.04$ (Strader et al. 2013).

Recent JWST observations of the $z=10.6$ galaxy GN-z11 first identified by Bouwens et al. (2010) have revealed (i) an intriguing morphology with a central point source and an outer diffuse stellar envelope, (ii) very compact $R_{\rm h}$ ($=64\pm 20$ pc), (iii) large stellar mass ($\log(M_{\rm s}/M_{\odot})=9.1^{+0.3}_{-0.4}$) for its size, and (iv) unusually large gas-phase nitrogen abundance with $\log{\rm(N/O)}>-0.24$ (e.g., Bunker et al., 2023; Tacchella et al. 2023; Cameron et al. 2023). A number of authors have already discussed the origin of the high nitrogen abundance in the context of ejection of nitrogen-rich gas from tidal destruction of massive stars in a star cluster (Cameron et al. 2023), the possible presence of supermassive stars (Charbonnel et al. 2023), chemical enrichment by Wolf-Rayet (WR) stars (Watanabe et al. 2023), and globular clusters (GCs) at their birth (Senchyna et al. 2023; S23). Given that the observed morphology and structure of GN-z11 are reminiscent of massive nucleated dwarf galaxies or UCDs, it is quite reasonable to discuss the high $\log{\rm(N/O)}$ in the context of stellar nucleus/UCD formation at high $z$.

Jeřábková et al. (2017) pointed out that forming $z=9$ UCDs with $M_{\rm s}=10^{8}{\rm M}_{\odot}$ and a top-heavy stellar initial mass function (IMF) with the slope ($\alpha$) as flat as 1.1 (2.35 for the Salpeter type) can be detected by the JWST NIRcam (e.g., F115W) with $S/N>7$ for a $\approx 3$ hour exposure time. GC formation models by Bekki & Chiba (2007) show that if the IMF is top-heavy with $\alpha\approx 1.5$, gas-phase nitrogen abundance can be rather high ([N/Fe]$>0.5$) for a large mass fraction of the intra-cluster gas due to pollution by massive stars. Although the models by Bekki & Chiba (2007) would be relevant to a star cluster with $M_{\rm s}\approx 10^{7}{\rm M}_{\odot}$ and $\log{\rm(N/O)}\approx-0.21$ found in the Sunburst Arc (Pascale et al. 2023), they need to be revised to discuss the origin of GN-Z11 that is much more massive than GCs.

The purpose of this paper is to show that the observed high gas-phase $\log{\rm(N/O})$ of GN-z11 can be consistent with the formation of massive stellar nuclei or UCDs with top-heavy IMFs. Using one-zone chemical evolution models for GN-z11, we investigate in what physical conditions the observed high log(N/O) and log(C/O) can be reproduced self-consistently by our models. We particularly investigate how (i) the IMF, (ii) gas consumption/infall timescales, and (iii) mixing process of stellar winds and CCSNe determine the chemical abundance patters of gas and stars in our models.

We investigate the chemical abundances of gas and stars in GN-z11 using one-zone chemical evolution models adopted in our previous studies (e.g., Bekki & Tsujimoto 2012, BT12). Since the basic equations and the details of the models are already given in BT12, we here briefly describe the models. One major difference in the present model is that chemical yields of massive stars and CCSNe predicted from Limongi & Chieffi (2018, LC18) rather than those from Tsujimoto et al. (1995) used in BT12 are newly adopted in the present study. Accordingly, massive stars with $m\geq 25{\rm M}_{\odot}$ cannot explode as CCSNe in LC18, because they become stellar mass black holes through direct gravitational collapse. Such a small upper bound on the mass of CCSN progenitor stars is supported by various aspects including the observations (e.g., Smartt 2015), theoretical modeling of supernovae (e.g., Sukhbold et al. 2016), and Galactic chemical evolution (Tsujimoto 2023). Thus, chemical pollution by CCSNe can occur only after massive stars with $m<25{\rm M}_{\odot}$ die away so that stellar winds of massive stars can pollute gas longer in the present models.

The present study with yields from LC18 assumes that stellar winds from massive stars with $8\leq m/{\rm M}_{\odot}\leq 120$ and ejecta from CCSNe with $m<25{\rm M}_{\odot}$ can chemically enrich gas. Therefore, interstellar medium can be enriched by stellar winds of massive OB and WR stars for a significantly longer timescale (until stars with $m=25{\rm M}_{\odot}$ explode as CCSNe) so that the nitrogen abundance can become rather high for a range of IMFs. If we assume that CCSNe from stars with $8\leq m/{\rm M}_{\odot}\leq 120$ can all contribute to chemical enrichment, as in BT12, then the timescale for GN-z11 to have a high nitrogen abundance becomes very short ($\approx 10^{6}$ yr), because CCSNe can rapidly lower the nitrogen abundance (e.g., Watanabe et al. 2023). Gas from winds and CCSNe is recycled into interstellar medium just after the gas ejection. Since the best-fit age to observational data is $\log_{10}{\rm(age/yr)}=6.57^{+0.09}_{-0.2}$ (S23), we stop the calculations at $T=10^{7}$ yr for all models except the “dwarf” model M10 (later described).

The following IMF is adopted in the present study:

where $m$ is the mass of each individual star and $\alpha$ is the IMF slope: $\alpha=2.35$ corresponds to the canonical Salpeter IMF (Salpeter 1955). The normalization factor $C_{0}$ is a function of $\alpha$, the lower mass cut-off (fixed at $0.1{\rm M}_{\odot}$), and the upper mass cut-off ($120{\rm M}_{\odot}$). IMF-averaged yields for stellar winds and CCSNe are separately calculated for a given $\alpha$ using “rotating” models with rotational velocities of 300 km s^-1 and metallicities ($Z$) of $0.01Z_{\odot}$ by LC18.

The total masses of gas ($M_{\rm g}$) and stars ($M_{\rm s}$) evolve with time due to gas accretion and gas consumption by star formation. The gas infall time scale ($t_{\rm inf}$) is a parameter ranging from 1 Myr to 1 Gyr (BT12), and the star formation rate SFR ($\psi(t)$) is assumed to be proportional to the gas fraction ($f_{\rm g}$) as follows:

where $C_{\rm sf}$ controls the timescale of star formation ($t_{\rm sf}$), which is derived by dividing $M_{\rm g}$ by SFR at the final time step. Although ejecta from all CCSNe is assumed to be retained within massive dwarf galaxies ($M_{\rm s}\approx 3\times 10^{9}{\rm M}_{\odot}$) in BT12, we consider that GN-z11 with the assumed $M_{\rm s}\approx 3\times 10^{8}{\rm M}_{\odot}$ can retain only a fraction of the ejecta. Accordingly, the mass fraction of ejecta from CCSNe is assumed to be a parameter represented by $f_{\rm r}$ whereas all gas from stellar winds is assumed to be retained. Initial [Fe/H] in infalling gas is set to be $-2.5$ dex and the initial [N/O] and [C/O] are consistent with the observed $\log{\rm(N/O)}$ and $\log{\rm(C/O)}$ in low-metallicity extragalactic HII regions.

It is found that the observed gas-phase abundances and SFR can be best reproduced by the model with $\alpha=1.55$, $t_{\rm sf}=6.6\times 10^{6}$ yr (corresponding to $C_{\rm sf}=15$), and $t_{\rm inf}=10^{6}$ yr, which predicts the final SFR, $M_{\rm s}$, and $M_{\rm g}$ at $T=10$ Myr are $20{\rm M}_{\odot}$ yr^-1, $3.0\times 10^{8}{\rm M}_{\odot}$, and $1.3\times 10^{8}{\rm M}_{\odot}$, respectively. We therefore focus on this “fiducial” model (M1) with these parameter values. We consider that the smaller $M_{\rm s}$ compared to $\log(M_{\rm s}/{\rm M}_{\odot})=9.1^{+0.3}_{-0.4}$ in Tacchella et al. (2023) is an outcome of the adopted top-heavy IMF (and star formation history) instead of the canonical one that is used for estimating the observed $M_{\rm s}$. Table 1 summarizes the parameter values for all of the ten models.

Fig. 1 clearly demonstrates that the observed location of GN-z11 on the $12+\log{\rm(O/H)}$-$\log{\rm(N/O)}$ plane can be reproduced well by the models with $\alpha=1.15$ and 1.55 (but not by the model with the Salpeter IMF), which suggests a top-heavy IMF is required for the high $\log{\rm(N/O)}$ of GN-z11. This is essentially because the mass fractions of nitrogen-rich ejecta from OB and WR stars in the models with top-heavy IMFs can be significant so that the mean gas-phase nitrogen abundances can be rather high even after mixing (dilution) of the ejecta with infalling gas. Fig. 1 also shows that the three models with different $\alpha$ can have $\log{\rm(C/O)}$ higher than the observed fiducial value (Cameron et al. 2023), which means that the observed lower limit of $\log{\rm(C/O)}$ cannot be a strong constraint on the model parameters. The derived high $\log{\rm(C/O)}$ is due to the high carbon yields of stellar winds in LC18. The model M1 shows $\log{\rm(N/O)}\approx-0.24$ at $T\approx 5$ Myr (to T=10 Myr), which means that the timescale of such a high N/O phase is not short. This model shows a significant increase of [Fe/H] from $-2.5$ to $-2.4$ during its 10 Myr evolution, which means a larger [Fe/H] spread in the stars.

The dwarf model with $\alpha=2.35$ and $t_{\rm inf}=300$ Myr, which represents the early star formation histories of massive dwarf galaxies like the Large Magellanic Cloud (LMC), does not show a high $\log{\rm(N/O)}$ even after $10^{8}$ yr evolution. This result indicates that $\log{\rm(N/O)}$ of GN-z11 is quite distinct from those of extragalactic HII regions due to the combination of its very short gas infall/star formation timescales and the top-heavy IMF. It should be stressed here that all of the present models show higher $\log{\rm(C/O)}$ ($>-0.4$), which means that the present model is unable to explain lower $\log{\rm(C/O)}$ ($<-0.4$) observed in some of the HII regions. It should be also noted that S23 suggested a low $\log{\rm(C/O)}$ ($\approx-0.5$) for GN-z11. The adoption of significantly lower carbon yields for models of massive stars in LC18 would alleviate these problems of high $\log{\rm(C/O)}$ in the models. We will discuss how this problem can be solved in our forthcoming papers based on different models for stellar yields from massive stars with different rotational velocities.

Fig. 2 shows that the model with longer $t_{\rm sf}$ ($6.6\times 10^{7}$ yr) cannot reproduce the observed high $\log{\rm(N/O)}$, which suggests that $t_{\rm sf}$ is one of key parameters for high $\log{\rm(N/O)}$ of GN-z11. The physical reason for this $t_{\rm sf}$-dependence is as follows. If $t_{\rm sf}$ is very short, then a large number of massive stars can be formed within a short time scale so that the mass fraction of nitrogen-rich gaseous ejecta from stellar winds of the OB and WR stars in all gas can be significant. As a result of this, gas-phase $\log{\rm(N/O)}$ can rapidly increase before gaseous ejecta with lower nitrogen abundances from CCSNe can start to pollute the gas. In the models with longer $t_{\rm sf}$, on the other hand, a larger amount of gas can be accreted and subsequently consumed very slowly by star formation. Consequently, the mass fraction of nitrogen-rich ejecta from stellar winds cannot be so high due to the dilution of the ejecta by the infalling gas. Thus, $\log{\rm(N/O)}$ can be rather high only in the models with short $t_{\rm sf}$.

As shown in Fig. 2, the models with $f_{\rm r}>0.2$ cannot have $\log{\rm(N/O)}\approx-0.49$, which corresponds to the “conservative” lower limit of the observed $\log{\rm(N/O)}$ (Cameron et al. 2023): the model with $f_{\rm r}=0.2$ can show $\log{\rm(N/O)}\approx-0.49$. Accordingly, we can conclude that at least 80% of ejecta from CCSNe needs to be expelled from GN-z11 to keep its high gas-phase nitrogen abundance. Fig. 3 shows that the number fraction of nitrogen-rich stars with [N/Fe]$>0.5$ depends strongly on $\alpha$ such that it is larger for more top-heavy IMFs (i.e., smaller $\alpha$). This is firstly because gas-phase nitrogen abundances can become higher for more top-heavy IMFs (due to more mass of winds), and secondly because the nitrogen abundances of new stars at a given time are the same as those of gas at that time. The large fraction ($\approx 0.6$) of N-rich stars for $\alpha=1.55$ implies that even the integrated spectra of GN-z11 can possibly show [N/Fe]$>0.5$.

The present study has demonstrated that (i) the observed high log(N/O) of GN-z11 can be reproduced in the model with yields from LC18 in which OB and WR stars and CCSNe with $m<25{\rm M}_{\odot}$ can chemically enrich the interstellar medium and (ii) both top-heavy IMFs ($\alpha$ as flat as $1.5$) and very short $t_{\rm sf}$ ($\approx 10^{7}$ yr) are required to explain the observation. Recent theoretical models for integrated galaxy-wide IMFs (“IGIMF”) predict that IMFs can be more top-heavy for higher SFRs (e.g., Yan et al. 2017). Therefore, the required top-heavy IMFs are consistent with the IGIMF theory for GN-z11 with a rather high SFR of $\approx 20{\rm M}_{\odot}$ yr^-1, at least qualitatively. However, it is yet unclear why the required short $t_{\rm sf}$ is possible in GN-z11 at $z=10.6$. S23 pointed out that the emission line properties of GN-z11 are strikingly similar to those of the blue compact dwarf (BCD) galaxy Mrk 996. Given that BCDs can be formed from dwarf-dwarf merging (e.g., Bekki 2008; Chhatkuli et al. 2023), high-$z$ merging of low-mass dwarfs might be responsible for the required short $t_{\rm sf}$: it should be noted here that a candidate of such high-$z$ ($z$=10.17) merging has been recently identified by Hsiao et al. (2023) with JWST. The “Haze” observed around GN-z11 (Tacchella et al. 2023) might be possible evidence for such a merger event.

If the IMF of GNz11 is indeed top-heavy, $M_{\rm s}$ of GN-z11 estimated in previous studies based on the canonical IMF (Tacchella et al. 2023) could be an overestimation. The much larger numbers of CCSNe and prompt SNIa for top-heavy IMFs imply very efficient energetic feedback effects of supernovae (SNe) that can truncate star formation very rapidly. It is therefore likely that GN-z11 can evolve into a poststarburst system after its SNe expel the remaining gas almost completely, if no further gas supply/accretion is possible. Recently, Strait et al. (2023) have discovered a very compact ($R_{\rm h}\approx 30$pc) post-starburst galaxy at $z=5.2$ (MACS0417-z5PSB): there could be an evolutionary link between very compact post-starburst galaxies like MACS0417-z5PSB and very compact star-forming ones with high nitrogen abundances like GN-z11 in the high-$z$ universe.

If GN-z11 with $M_{\rm s}=3\times 10^{8}{\rm M}_{\odot}$ ($10^{9}{\rm M}_{\odot}$) at z=10.6 is formed with $\alpha=1.55$ and if it stops its ongoing star formation due to feedback effects of numerous CCSNe and consequently evolves passively until now, then its present-day total mass of low-mass stars ($m<0.8{\rm M}_{\odot}$) is only $2.0\times 10^{7}{\rm M}_{\odot}$ ($6.6\times 10^{7}{\rm M}_{\odot}$). These masses are more consistent with those of UCDs and stellar nuclei in massive dwarfs (e.g., Côte et al. 2006) than those of GCs ($\approx 2\times 10^{5}{\rm M}_{\odot}$). If UCDs with $M_{\rm s}$ at $z=0$ larger than $2\times 10^{7}{\rm M}_{\odot}$ like M60-UCD1 are formed at $z>10$, they should be significantly brighter than GN-z11 in the rest-frame UV wavelength: they will be able to be detected in JWST observations. Given that the number fractions of nucleated dwarfs are higher in dense cluster environments (e.g., Côte et al. 2006), the discovery of such nitrogen-rich compact objects like GN-z11 can indicate the central regions of proto clusters of galaxies (see Tacchella et al. 2023 for such possible evidence).

If a significant number of high-$z$ objects with high $\log{\rm(N/O)}$ and $M_{\rm s}=[10^{6}-10^{7}]{\rm M}_{\odot}$ are discovered, their physical properties can be discussed in the context of (i) self-enrichment of forming GCs with multiple stellar populations through stellar winds of massive stars (e.g., Prantzos & Charbonnel 2006) and (ii) the Galaxy formation (e.g., Belokurov & Kravtsov 2023). It should be stressed here that stellar populations of GN-z11 can have large [Fe/H] spreads ($>0.05$ dex) due to the chemical enrichment by low-mass ($m<25{\rm M}_{\odot}$) CCSNe: GN-z11 could differ from normal GCs with small [Fe/H] spreads ($<0.05$ dex: Carretta et al. 2019). GN-z11 also might have (i) no O-Na and Mg-Al anti-correlations observed in GCs (e.g., Carretta et al. 2019) and (ii) smaller [Na/O] in its integrated spectra (compared to GCs) if it was chemically enriched both by OB and WR stars and by low-mass CCSNe.

The Galaxy is observed to have a significant fraction of “N-rich” stars with [N/Fe]$>0.5$ (e.g., Schiavon et al. 2017), the physical origin of which is yet to be fully understood in theoretical models of galaxy formation (e.g., Bekki 2019). Given that even the integrated spectra of elliptical galaxies show moderately high [N/Fe] (up to $\approx 0.2$; Schiavon 2007), they should contain a significant fraction of N-rich stars. Large fractions of N-rich stars derived in the present models with top-heavy IMFs suggest that if some of the low-mass building blocks of the Galaxy and elliptical galaxies are like GN-z11, the galaxies should be able to contain N-rich stars after the tidal destruction of the building blocks.

The present model predicts a large number ($>10^{6}$) of stellar mass BHs within the central $\approx 60$pc of GZ-z11, where there should be a plenty of cold gas to fuel ongoing star formation: the possible presence of active galactic nucleus (Maiolino et al. 2023) might be physically related to such a BH cluster. The retention probability of stellar mass BHs in massive stellar systems with $M_{\rm s}>10^{7}{\rm M}_{\odot}$ is almost 100% (Jeřábková et al. 2017). Therefore, dynamical evolution of such a dense cluster of BHs within a massive gas-rich environment is a new dynamical problem, because both two-body BH-BH interaction and hydrodynamical interaction between gas and BHs are quite important for the evolution of the self-gravitating system. Our future studies on the dynamical evolution of BH clusters in gas-rich environments will be able to address whether or not there is a physical link between dense clusters of BHs in forming compact galaxies at high $z$ and MBHs in the present-day UCDs and stellar nuclei.

The data used in this paper (outputs from one-zone models) will be shared on reasonable request to the corresponding author.

We are grateful to the referee for constructive and useful comments that improved this paper. T. T. acknowledges the support by JSPS KAKENHI Grant Nos. 18H01258, 19H05811, and 23H00132.