Black Hole Scaling Relations in the Dwarf-galaxy Regime
with Gaia-Sausage/Enceladus and $\omega$Centauri

The main takeaway from Figure 1 is that the IMBH of $\omega{\rm Cen}$/GSE resides on top of the ${\rm M_{\rm BH}}$–${\rm M_{\star}}$ scaling relations from Greene et al. (2020); see text below for possible variations. Since GSE analogs in cosmological hydrodynamical simulations are found to be ubiquitously star-forming systems leading to gas-rich mergers with their MW-like hosts (e.g., Bignone et al., 2019; Grand et al., 2020), we consider ${\rm M_{\rm BH}}$–${\rm M_{\star}}$ relations for both all galaxies and late-type only samples. Different possible ${\rm M_{\star}}$ and/or ${\rm M_{\rm BH}}$ values for $\omega{\rm Cen}$/GSE would not change this qualitative conclusion given the scatters (shaded areas around the black and blue relation lines). The consequence is that S/LMC-mass galaxies ($10^{8}<{\rm M_{\star}}/{\rm M_{\odot}}\lesssim 10^{9}$, similar to GSE) might follow a natural extension of high-mass systems (${\rm M_{\star}}\gtrsim 10^{10}\,{\rm M_{\odot}}$) in the ${\rm M_{\rm BH}}$–${\rm M_{\star}}$ relation; note the claimed IMBHs in NGC 205 (Nguyen et al., 2019) and NGC 4395 (Woo et al., 2019) also plotted in Figure 1. Therefore, other MW and/or M31 satellites and stripped NSCs could be promising targets to further expand IMBH demographics in the dwarf-galaxy regime. Observational challenges are many (see Reines, 2022), but this approach would allow us to further contextualize IMBHs within the broader picture of galaxy-BH coevolution.

JWST has revealed a surprising excess of overmassive BHs in faint AGNs at $z\gtrsim 4$ (red symbols in Figures 1 and 3), far exceeding the number density expected from canonical quasar luminosity functions (e.g., Kokorev et al., 2024). These AGNs host central BHs where ${\rm M_{\rm BH}}/{\rm M_{\star}}\gtrsim 0.01$, well above the expected from the local ${\rm M_{\rm BH}}$–${\rm M_{\star}}$ relation (see Pacucci et al., 2023). Many of these high-$z$ AGNs have similar ${\rm M_{\star}}$ to GSE, but central BHs of order 100–1000$\times$ more massive than $\omega{\rm Cen}$’s IMBH. To reconcile the fast growth of these overmassive BHs in the early universe with the IMBH of $\omega{\rm Cen}$/GSE, similar host ${\rm M_{\star}}$ at different $z$, might be challenging for BH–galaxy coevolution theory, but useful for supermassive BH growth and seeding models (Section 3.3).

Many previous works, including some aforementioned ones, have derived the ${\rm M_{\rm BH}}$–${\rm M_{\star}}$ scaling relation from various samples and found discrepant shapes for it (Kormendy & Ho, 2013; Reines & Volonteri, 2015; Greene et al., 2020, and Pacucci et al. 2023 for very high $z$ only). These empirical relations basically all converge in the high-mass regime ($10^{10}<{\rm M_{\star}}/{\rm M_{\odot}}\lesssim 10^{12}$), which is expected given that all of them are derived from data for massive galaxies. However, their slopes can be dramatically different, ranging from ${\sim}{\rm M_{\rm BH}}\propto{\rm M_{\star}}$ to ${\rm M_{\rm BH}}\propto{\rm M_{\star}}^{3}$ (see Shankar et al., 2016). Hence, when approaching the IMBH/dwarf-galaxy regime, some of these fits severally under predict, by factors of $\sim$1000$\times$, the ${\rm M_{\rm BH}}$ of $\omega{\rm Cen}$/GSE. These might simply mean that these relations should not be extrapolated below ${\rm M_{\star}}\approx 10^{10}\,{\rm M_{\odot}}$. Having said that, we basically have constraints neither on the scatter around ${\rm M_{\rm BH}}$ nor on the BH occupation fraction for GSE-mass (S/LMC-mass) galaxies with so few IMBH detections: NGC 205 (Nguyen et al., 2019), NGC 4395 (Woo et al., 2019), and now $\omega{\rm Cen}$/GSE (Häberle et al., 2024). Therefore, although the exact choice of ${\rm M_{\rm BH}}$–${\rm M_{\star}}$ relation might change the exact statement that $\omega{\rm Cen}$/GSE follows an extrapolation from massive galaxies, we can now extend it to the IMBH/dwarf-galaxy regime.

Apart from the broader implications to the ${\rm M_{\rm BH}}$–${\rm M_{\star}}$ relation for dwarf galaxies, the formation/evolution of a GSE-mass system with its central IMBH is also interesting to explore. It would be important to understand how the central dynamics of dwarf galaxies and star formation in them respond to the presence of an IMBH within the specific ${\rm M_{\rm BH}}/{\rm M_{\star}}$ ratios allowed for $\omega{\rm Cen}$/GSE (e.g., Koudmani et al., 2021). Likewise, the evolutionary pathway of GSE-mass galaxies with central (IM)BHs could be useful for refining feedback models since AGN activity is expected to regulate the ${\rm M_{\rm BH}}$–${\rm M_{\star}}$ relation itself (Di Matteo et al., 2005), although that might not be the case for dwarf galaxies (Sharma et al., 2020). The accretion history of the IMBH in $\omega{\rm Cen}$/GSE could even tell us about how stellar feedback regulates the early growth of central BHs in dwarf galaxies (Anglés-Alcázar et al., 2017; Habouzit et al., 2017). Moreover, $\omega{\rm Cen}$/GSE’s IMBH might hold clues to the role of environment (isolated versus satellite dwarf) since merger activity could play a role in providing the necessary conditions for BH growth (Volonteri et al., 2008). $\omega{\rm Cen}$/GSE could even be explored as a laboratory for IMBH “incubation” in NSCs, where the host would provide the necessary gas supply for a stellar mass BHs to grow to the intermediate-mass status (Natarajan, 2021).

I also explore the location of $\omega{\rm Cen}$/GSE’s IMBH in the ${\rm M_{\rm BH}}$–$\sigma_{\star}$ relation (Figure 2). Previous works have attempted to constraint the slope of this relation toward the low-mass regime, in particular leveraging dwarf AGNs (Xiao et al., 2011; Schutte et al., 2019; Baldassare et al., 2020). The ${\rm M_{\rm BH}}$–$\sigma_{\star}$ relations derived by Greene et al. (2020), and adopted here, also extend to dwarf galaxies/IMBHs by incorporating constraining ${\rm M_{\rm BH}}$ upper limits in their fits, mostly from Neumayer & Walcher (2012) and including Fornax dSph (Jardel & Gebhardt, 2012). For $\omega{\rm Cen}$, we take the recent $\sigma_{\star}$ value from Pechetti et al. (2024). We refer the reader to the ${\rm M_{\rm BH}}$–$\sigma_{\star}$ relation plot by Barth et al. (2009, their figure 10) for an earlier version of this exercise, including both $\omega{\rm Cen}$ (data from Noyola et al., 2008) and G1 (Gebhardt et al., 2002), another stellar cluster with an IMBH candidate known at the time (see Section 3.4).

$\omega{\rm Cen}$ and its IMBH reside on top of the Greene et al.’s (2020) ${\rm M_{\rm BH}}$–$\sigma_{\star}$ relation for all galaxies (within scatter for late-type only; Figure 2). I verify that M31 stellar clusters with candidate IMBHs, the aforementioned G1 (Gebhardt et al., 2002) and B023-G078 (Pechetti et al., 2022), also closely follow the relation. Another class of stellar systems related to NSCs with detected central massive BHs (Seth et al., 2014; Afanasiev et al., 2018; Ahn et al., 2018) are the so-called “ultracompact” dwarf galaxies (UCDs, $10^{6}\lesssim{\rm M_{\star}}/{\rm M_{\odot}}\leq 10^{8}$, Drinkwater et al., 2003). Akin to $\omega{\rm Cen}$, these UCDs are thought to be remnants of stripped NSCs (Wang et al., 2023), and are usually found in dense environments such as galaxy clusters (e.g., Liu et al., 2020, and references therein). Figure 2 shows that UCDs also appear to follow the ${\rm M_{\rm BH}}$–$\sigma_{\star}$ relation, perhaps reinforcing their evolutionary connection to NSCs. Although samples are still quite small, the emerging broad picture takeaway might be that, since both NSCs and UCDs alike follow the ${\rm M_{\rm BH}}$–$\sigma_{\star}$ relation, the $\sigma_{\star}$ in these low-mass systems can be compared to those in the bulges of local massive galaxies.

The main classes of BH seeding prescriptions are “light seeds” (Population III supernovae remnants) and “heavy seeds” (direct collapse); see Volonteri (2010). The latter might be favored by the high-$z$ population of overmassive BHs discovered by JWST. For example, galaxy GN-z11 (Oesch et al., 2016), similar $\log{({\rm M_{\star}}/{\rm M_{\odot}})}=8.9$ to GSE, has a central BH of ${\rm M_{\rm BH}}=1.5\times 10^{6}\,{\rm M_{\odot}}$ already at $z=10.6$ (Maiolino et al., 2024). On the other hand, the IMBH of $\omega{\rm Cen}$/GSE has an estimated ${\rm M_{\rm BH}}$ quite close to the minimum value expected by heavy seeding models (e.g., Volonteri et al., 2008, ${\approx}10^{4}\,{\rm M_{\odot}}$). Hence, the IMBH in $\omega{\rm Cen}$/GSE could, in principle, establish a lower limit to the mass distribution of heavy seeds (Reines, 2022).

The IMBH in $\omega{\rm Cen}$ must have stopped accretion at the time of the merger due to gas removal by the MW via ram-pressure and/or tidal stripping, as evidenced by the fast quenching of GSE analogs in simulations (Bignone et al., 2019; Grand et al., 2020), hence being “frozen” at $z\sim 2$. Indeed, this scenario could be consistent with $\omega{\rm Cen}$’s IMBH exquisitely weak accretion rate implied by upper limits in X-ray luminosity (Haggard et al., 2013; Tremou et al., 2018). I consider this fact to estimate possible BH growth trajectories for $\omega{\rm Cen}$/GSE (similar to Pacucci et al. 2023 for high-$z$ galaxies). For this exercise, I use the same formalism as Fan et al. (2023, their equations 7 through 9). Under the hypothesis of heavy seeding, one potentially important implication is that the IMBH of $\omega{\rm Cen}$/GSE must have experienced extremely low accretion rate throughout its entire $\sim$3 Gyr lifetime. Assuming an 8000 ${\rm M_{\odot}}$ initial mass at $z=18$ and a constant accretion rate, the IMBH of $\omega{\rm Cen}$/GSE should have grown at only $\sim$1% of the Eddington luminosity. If I adopt a light seed of 30 ${\rm M_{\odot}}$ (similar to the ${\rm M_{\rm BH}}$ of the recently discovered Gaia BH3; Gaia Collaboration et al. 2024), the ${\rm M_{\rm BH}}$ of $\omega{\rm Cen}$/GSE’s IMBH can be achieved at a fixed 10% Eddington rate (Figure 3).

This analysis of BH growth tracks should be regarded as initial exploration, but it points to a scenario where the IMBH of $\omega{\rm Cen}$/GSE could represent the complete opposite extreme from GN-z11 and its high-$z$ counterparts (Harikane et al., 2023; Maiolino et al., 2023) in terms of possible BH growth histories with heavy seeding. These very high-$z$ AGNs with overmassive central BHs likely require a combination of both high initial ${\rm M_{\rm BH}}$ and accretion rate (sometimes $\sim$50,000 ${\rm M_{\odot}}$ and $\gtrsim$80% Eddington, Pacucci et al. 2023), perhaps including super-Eddington episodes (Maiolino et al., 2024); see the recent detection by Suh et al. 2024. On the other hand, $\omega{\rm Cen}$/GSE’s IMBH would have a low initial mass and experience almost no accretion.

If Population III supernovae seeding is allowed, one interpretation could be that both mechanisms are at play, light and heavy seeding simultaneously, hence creating a true physical distinction between supermassive and intermediate-mass central BHs. This reinforces the need to hunt for additional IMBHs to constrain both their properties and their host dwarf galaxies’. Sagittarius dSph might be interesting for testing that hypothesis since the local ${\rm M_{\rm BH}}$–${\rm M_{\star}}$ relation predicts that the mass of a central BH in that dwarf galaxy would be of $\lesssim$1000 ${\rm M_{\odot}}$ (Greene et al., 2020, Figure 1).

If the discovery of an IMBH in $\omega{\rm Cen}$ is confirmed, the next step would be to extend the search to other NSCs with the obvious candidate being NGC 6751 (M54), the NSC of Sagittarius dSph galaxy (Bellazzini et al., 2008). However, M54 is ${\sim}5\times$ farther from the Sun than $\omega{\rm Cen}$ and is located behind the Galactic bulge, so stars are fainter, more difficult to resolve, and the field is plagued with MW foreground. Moreover, M54 still resides within the dark-matter halo of Sagittarius and this galaxy is undergoing severe tidal stripping by the MW (Majewski et al., 2003), which might affect its central dynamics.

There are other candidate NSCs in the MW. NGC 6273 (M19) and NGC 6934 have been proposed to be NSCs of Kraken/Heracles (Kruijssen et al., 2020; Horta et al., 2021) and Helmi streams (Helmi et al., 1999) disrupted dwarfs, respectively, by Pfeffer et al. (2021). However, unlike $\omega{\rm Cen}$/GSE and M54/Sagittarius, both NGC 6273 and NGC 6934 would be significant outliers in the ${\rm M_{\rm NSC}}$–${\rm M_{\star}}$ relation if really related to these satellites (Figure 4). These associations could be incorrect, but these candidate NSCs might have also experienced substantial mass loss through tides. Future studies on the stripping history of NSCs in dwarf galaxies merging with massive hosts would be of interest to test if these systems would really be expected to be outliers in the ${\rm M_{\rm NSC}}$–${\rm M_{\star}}$ relation.

With respect to the NSC candidates themselves, there is strong evidence from high-resolution stellar spectroscopy that NGC 6273 is a genuine NSC (Johnson et al., 2017). Hence, there might be a low-mass (${\rm M_{\star}}\lesssim 10^{7}\,{\rm M_{\odot}}$) dwarf-galaxy host for NGC 6273 still undiscovered in the MW. On the other hand, confirmation of NGC 6934 as a true NSC is still needed; the best spectroscopic sample available is from Marino et al. (2021) with only 13 stars. Other aforementioned candidate stripped NSCs in M31 with claims of IMBHs are G1 (Gebhardt et al., 2002, ${\rm M_{\rm BH}}\sim 20{,}000\,{\rm M_{\odot}}$) and B023-G078 (Pechetti et al., 2022, ${\rm M_{\rm BH}}\sim 100{,}000\,{\rm M_{\odot}}$). In Figure 1, I only provide lower limits on ${\rm M_{\star}}$ for these clusters since their original hosts are unknown.