Reading the tea leaves in the $M_{\rm bh}$-$M_{\rm*,sph}$ and $M_{\rm bh}$-$R_{\rm e,sph}$ diagrams: dry and gaseous mergers with remnant angular momentum

Two contributions we have strived to make over the years are improved measurements of the spheroid mass coupled with a better recognition of the host galaxy morphology. This has been achieved through several advancements in galaxy image analysis, such as the introduction of the core-Sérsic model (Graham et al., 2003), which unites a spheroid’s inner and outer structure. King & Minkowski (1966) and King & Minkowski (1972) had reported that massive ETGs have cores which flatten relative to the outer de Vaucouleurs (1948) $R^{1/4}$ light profile. Begelman et al. (1980) and Ebisuzaki et al. (1991) explained how binary black holes from galaxy merger events could create such cores, with massive dense infalling star systems creating larger cores (e.g., El-Zant et al., 2001; Goerdt et al., 2010; Bonfini & Graham, 2016). Building on the ‘core-Hubble’ model of Crane et al. (1993), and the double power-law models of Ferrarese et al. (1994) and Grillmair et al. (1994), application of the core-Sérsic model revealed that roughly 1-in-5 past allegations of a partially depleted core — when based on the Nuker model⁷⁷7The Nuker model is mathematically equivalent to the double power-law introduced by Hernquist (1990, his Equation 43). (Grillmair et al., 1994; Kormendy et al., 1994), — were not correct (see Dullo & Graham, 2012, 2013, their Appendix A.2).⁸⁸8This was in part due to the measured Nuker model parameters depending on the fitted radial range (Graham et al., 2003), but also because low-mass spheroids with low Sérsic indices have shallow inner light profiles but no depleted core Graham & Guzmán (2003, their Fig. 8). The presence of additional nuclear discs can also flatten the inner light profile, creating the illusion of a central deficit Dullo & Graham (2013). Fitting a Sérsic model to a spheroid containing a core-Sérsic light profile can result in a misleadingly low Sérsic index and erroneously faint spheroid luminosity. The core-Sérsic model is available in Profiler (Ciambur, 2016) and was implemented into Galfit (Peng et al., 2010) by Bonfini (2014) and can be found in Imfit (Erwin, 2015).

Coupled with the above has been the realisation that the less luminous ($M_{B}\gtrsim-20.5\pm 0.75$, or $M_{V}\gtrsim-21.4\pm 0.75$ Vega mag) galaxies often extra lighave ‘extra light’, such as a nuclear star cluster, rather than a central deficit of light. Furthermore, the nuclear star cluster mass has been discovered to scale with the host spheroid mass (Balcells et al., 2003; Graham & Guzmán, 2003), and nuclear discs are also a common feature (e.g., Nieto et al., 1991; Jaffe et al., 1994; Balcells et al., 2007). While nuclear star clusters are typically only a fraction of one per cent of the host spheroid’s stellar mass (e.g., Ferrarese et al., 2006; Wehner & Harris, 2006; Scott & Graham, 2013), if they are overlooked in the modelling of the galaxy light, then they can have a disproportionate influence on the galaxy decomposition by, for example, inflating both the fitted Sérsic index and luminosity of the spheroid.⁹⁹9This situation arises when sufficiently high spatial resolution reveals an excess in the image capable of biasing the galaxy decomposition. As such, accounting for these additional components in the image analysis can be important for acquiring an unbiased spheroid magnitude, and also for better understanding the nature of, and connections between, galaxies.

For example, Faber et al. (1997, p. 1783) partly advocated against a division among ETGs at $M_{B}\sim-20.5$ mag by arguing that the additional brightness of the nuclear star clusters yields a continuous and unifying galaxy luminosity-(central surface brightness) relation for ETGs brighter than $M_{B}\sim-18$ mag (Faber et al., 1997, their Fig.4c and 6). This followed Kormendy (1985), which concluded that ETGs brighter and fainter than $M_{B}\sim-18$ mag formed in very different ways. Why that interpretation of ETGs was misleading is explained in Graham & Guzmán (2003) and detailed further in Graham (2019a), both of which advocated for a divide at $M_{B}\sim-20.5$ mag, in agreement with other arguments in (Faber et al., 1997). This divide is mirrored by the (cold gas)-poor S0 versus E galaxy separation at $\log(M_{*,sph}/M_{\odot})\approx 10.9\pm 0.2$, seen in Figure 1. It arises from the (large scale disc)-eroding, spheroid-building, core-depleting mergers of disc galaxies with massive black holes (Negroponte & White, 1983; Nieto & Bender, 1989; Ebisuzaki et al., 1991).

An additional breakthrough of sorts has been the rediscovery of ES galaxies (Savorgnan & Graham, 2016b). Introduced by Liller (1966) and reviewed by Graham (2019b), they contain intermediate-scale discs having sizes greater than nuclear discs ($\sim$20 pc to a few hundred parsecs) and smaller than the large-scale discs of S0 galaxies (with typical disc scalelengths of a few kpc). Some of these ES galaxies are also known as ‘disc ellipticals’ (Nieto et al., 1988). In Section 3.2.2, we have introduced the ES,e and ES,b subtypes. Failing to identify such discs during the decomposition of the galaxy light can result in an erroneous luminosity for the spheroid.

Another advance has stemmed from the realisation that the ELLIPSE task (Jedrzejewski, 1987) in the IRAF software suite is flawed, failing to properly capture the isophotal deviations from pure ellipses observed at least since Oort (1940) in the case of NGC 3115, and described using Fourier harmonics by Carter (1978), see also Carter (1987) and Bender & Moellenhoff (1987). Ciambur (2015) revealed how the size of the error in the ELLIPSE task grows with the ellipticity of the isophote, which means it is particularly prominent when a bar is present, or a disc is approaching an edge-on orientation. Correcting this, Ciambur & Graham (2016) were, for the first time, able to detect and quantify the radial variation in the amplitude of the sixth order Fourier Harmonic term, which does well with capturing (peanut shell)-shaped structures (e.g., de Vaucouleurs, 1974; Jarvis, 1986; Shaw, 1987) associated with buckled bars (Combes et al., 1990; Athanassoula, 2005). As dramatically illustrated by Ciambur (2015), in the case of NGC 128, the superposition of the bar and (peanut shell)/box/X-shaped ‘bulge’ results in isophotes which are not boxy, i.e., neither described by nor captured with the fourth-order Fourier Harmonic term but instead requiring the sixth order Fourier Harmonic term. Collectively, this has enabled progress in dissecting and understanding the $M_{\rm bh}$-$M_{\rm*,sph}$ diagram.

In this work, we provide some further notes on individual galaxies, which are common to us and KH13, but for which we disagree on the spheroid mass. Finally, it is noted that there is of course room for further improvement, which could include application of galaxy-component-specific stellar mass-to-light ratios for calculation of galaxy component masses, and also for the derivation of black hole masses, taking into account the nuclear star clusters. Nguyen et al. (2017) represents a good example where the nuclear stellar populations in NGC 404 were modelled and a spatially-varying colour-dependent $\Upsilon_{*}$ used.¹⁰¹⁰10Davis et al. (2020) subsequently updated the measured black hole mass in NGC 404, which we have used. Working with images taken at 3.6 $\mu$m, the influence of hot young stars is small given that their blackbody radiation curves peak in the blue to UV region of the electromagnetic spectrum. Instead, older stars, and to a lesser degree thermally-glowing dust (Querejeta et al., 2015), contribute to the light seen at 3.6 $\mu$m. An analysis of Hubble Space Telescope (HST) images, coupled with stellar mass-to-light ratios for the nuclear star clusters, plus the refined galaxy morphologies used here, would enable advances with the $M_{\rm nsc}$-$M_{*}$ relation for LTGs (Balcells et al., 2003) and ETGs (Graham & Guzmán, 2003), and with the $(M_{\rm nsc}+M_{\rm bh})$-$M_{*}$ relation (Graham & Spitler, 2009) and the $(M_{\rm nsc}+M_{\rm bh})$-$\sigma$ relation (Graham, 2012a). To date, these discoveries have taken a back seat to the $M_{\rm bh}$-$M_{*}$ and $M_{\rm bh}$-$\sigma$ relations (Magorrian et al., 1998; Ferrarese & Merritt, 2000; Gebhardt et al., 2000), yet such mass-mass-morphology (m³) and mass-sigma–morphology (msm) diagrams involving nuclear star clusters will enable a better understanding of massive compact objects at the centres of galaxies, as will the $M_{\rm bh}$-$M_{\rm nsc}$ relation (Graham, 2016). HST-resolved images, coupled with the galaxy morphologies, will also enable an exploration of the depleted cores built by merging black hole binaries (Begelman et al., 1980; Merritt & Milosavljević, 2005), and the prior destruction of the nuclear star clusters (Bekki & Graham, 2010).

KH13 had a subsection titled “Mergers in progress have abnormally small BH masses”. They were referring to the known result that, relative to the original near-linear $M_{\rm bh}$-$M_{\rm sph}$ relation, the $M_{\rm bh}/M_{\rm sph}$ ratio is low in the mergers they mentioned. Here, we explain that these system’s black hole masses are not abnormal but instead as expected, given their origin from a wet galaxy merger likely involving one or two spiral galaxies.

KH13 advocated excluding five merger products (NGC 1316, NGC 2960, NGC 4382, NGC 5128 and IC 1481) from the black hole scaling diagrams (see their Table 2). These galaxies contain merger-built ‘classical bulges’ whose inclusion, as we shall see, provides a more complete understanding of galaxy/(black hole) coevolution. KH13 regarded these systems as elliptical galaxies; see the final paragraph of their Section 5, and in their $M_{\rm bh}$-$M_{\rm sph}$ diagram (their Fig. 14), they appear as notable outliers. However, their offset location is somewhat exaggerated because the galaxy rather than the bulge luminosity was used for these (three S0,pec plus two S?) galaxies.

While still perturbed at varying levels, these are recognised disc galaxies whose light profiles display an unmistakable bulge plus outer exponential structure (Savorgnan & Graham, 2016a; Sahu et al., 2019a) and for which rotation has been measured. Indeed, in the case of NGC 5128, it has long been known to rotate (Burbidge & Burbidge, 1959; Hui et al., 1995). As noted in the Introduction, wet mergers involving spiral galaxies can lead to disc galaxies with more prominent bulges (e.g., Barnes & Hernquist, 1996). NGC 5128 (aka Centaurus A) is a recognised merger involving at least one spiral galaxy (Tubbs, 1980; Bekki et al., 2003; Wang et al., 2020), as is NGC 1316 (Vagshette et al., 2021), which underwent a major gas-rich merger 3 Gyr ago (e.g., Goudfrooij et al., 2004). NGC 2960 (Mrk 1419) is an optically disturbed S0–Sa LINER with no nearby companions (Kuo et al., 2008) and labelled a merger product by KH13. NGC 2960 may represent an advanced stage of the suspected spiral-spiral merger NGC 7252 (Whitmore et al., 1993).

In passing, we note that pushing observations into the low surface brightness regime around the outskirts of galaxies (e.g., Martínez-Delgado et al., 2001; Bennert et al., 2008; Hood et al., 2018; Martin et al., 2022), may be insightful if tidal streams, debris tails, shells and ripples (e.g., NGC3923: Fort et al., 1986) can distinguish between accretion versus more substantial mergers. As such, deep observations of the sample of galaxies with directly measured black hole masses, coupled with their location in the $M_{\rm bh}$-$M_{\rm sph}$ diagram, may reveal further tell-tale clues as to the origin and evolution of galaxies more generally. For example, Morales et al. (2018) have flagged the dusty spiral galaxy NGC 3227 as a possible major merger remnant, somewhat akin to NGC 2960 but with $M_{\rm bh}$ eight times larger. Future gains in this exciting area are expected from ESA’s new ARRAKIHS (Analysis of Resolved Remnants of Accreted galaxies as a Key Instrument for Halo Surveys) F-class mission, comprised of a dedicated satellite providing incredibly deep optical and near-infrared images of $\sim$100 nearby galaxies and their outskirts (P.I. R.Guzmán).

While NGC 4382 and IC 1481 are not in our Spitzer sample, Sahu et al. (2019b) reported an additional two S0 merger remnants among our Spitzer sample of galaxies with directly measured black hole masses. These are NGC 1194 and NGC 5018, an S0 galaxy whose black hole mass was only recently acquired by Saglia et al. (2016). Sahu et al. (2019b) commented on a faint debris tail in NGC 1194, a galaxy which displays a prominent dust lane somewhat reminiscent of that seen in NGC 1316 and NGC 5128. Fedorova et al. (2016) explored but could not confirm the presence of two BHs in this galaxy. In NGC 5018, the brightest galaxy within the NGC 5018 Group, there are multiple dust lanes in addition to stellar shells and tidal debris (Buson et al., 2004; Kim et al., 2012; Spavone et al., 2018, and references therein).

We noticed that all five of the clearly merger-built galaxies in our sample (NGC 1194, NGC 1316, NGC 2960, NGC 5018, and NGC 5128) reside close to each other in the $M_{\rm bh}$-$M_{\rm e,sph,eq}$ diagram and the $M_{\rm bh}$-$M_{\rm*,sph}$ diagram, where they sit at the low-mass end of the elliptical galaxy sequence (Fig. 1). They have spheroid masses larger than the other (less gas-rich) S0 galaxies hosting a similar mass black hole. While not on the $M_{\rm bh}$-$R_{\rm e,sph}$ relation for elliptical galaxies, they have larger sizes than the spheroidal component of the other (relatively gas-poor) S0 galaxies hosting a similar mass black hole (Fig. 1, left-hand panel).

The red coloured track in the middle of Fig. 1 shows how an equal-mass spiral$+$spiral galaxy merger could explain the location and movement of the above five bulges in the $M_{\rm bh}$-$M_{\rm*,sph}$ diagram. The associated shift in the $M_{\rm bh}$-$R_{\rm e,sph}$ diagram stems from the expected movement along the tight $M_{\rm*,sph}$-$R_{\rm e,sph}$ relation (Graham & Sahu, 2022, their Fig. 7). While the black hole mass in this example merger (red track) has roughly doubled, the spheroid mass has increased four-fold. The spheroid mass can more than double depending on how much of the pre-existing disc stars contribute to the new galaxy’s bulge. The current example could represent the merger of two spiral galaxies with bulge-to-total, $B/T$, stellar mass ratios equal to 1 to create an S0 with $B/T=1/4$. That is, half of the stars in the new bulge came from what was disc material, and the other half came from what was pre-existing bulge material. Of course, other scenarios are possible, such as a collision involving an S and an S0 galaxy with different $B/T$ ratios and fractions of discs stars making it into the merger product’s bulge.

Wet mergers are expected to be accompanied by star formation and AGN fueling (e.g., Joseph & Wright, 1985; Di Matteo et al., 2007), which the ‘quasar mode’ of galaxy/(black hole) coevolution tries to capture (Kauffmann & Haehnelt, 2000; Di Matteo et al., 2005; Croton et al., 2006; Silk, 2013). In Fig. 1, we only show the jump (punctuated equilibrium) in growth from the (dissipationless component of the) merger and not the movement arising from star formation and AGN feeding. However, ‘quasar mode’ activity may ultimately progress the systems further along the $M_{\rm bh}$-$M_{\rm*,sph}$ distribution for either S galaxies or perhaps the relatively (cold gas)-poor S0 galaxies. Here, we recast this term (quasar mode) to encapsulate black hole growth from (i) the subsequent binary black hole merger and (ii) accretion — as per the original definition — and for spheroid growth from (i) the merger of the pre-existing spheroids, (ii) the fraction of pre-existing disc stars converted into the new spheroid, and (iii) the fraction of cold gas that underwent star formation to create new spheroid stars. Collectively, this is more complicated than the simple prescriptions given to date (e.g., Graham & Scott, 2013, their Equation 6). One also needs to resolve where these wet mergers ultimately end up, that is, do they remain on the E sequence or evolve to the S or S0 sequence depicted in Fig. 1.

The above type of merger event introduces a deviation to the general picture presented in Graham & Sahu (2022), in which, at a given spheroid stellar mass, the bulges of S0 galaxies have an $M_{\rm bh}/M_{\rm*,sph}$ ratio that is an order of magnitude greater than that in E galaxies. We now have a situation where, at a given spheroid stellar mass, the relatively (cold gas)-poor S0 galaxies have an $M_{\rm bh}/M_{\rm*,sph}$ ratio roughly an order of magnitude greater than that in S0 galaxies built by wet mergers. The presence/absence of hot gas versus cool gas and dust in these S0 galaxies helps discriminate their origin. For example, the core-Sérsic S0 NGC 5813 is immersed in a hot gas halo (Randall et al., 2015) that keeps star formation at bay, while the Sérsic S0 NGC 5128 is rich in cool gas and dust (e.g., Hawarden et al., 1993). The latter is clearly formed from a gas-rich merger, and the partially-depleted core in the former is thought to suggest a relatively dry merger origin.

Like the merger-built elliptical galaxies, these (wet merger)-built bulges roughly follow the same $M_{\rm bh}$-$M_{\rm*,sph}$ relation as the elliptical galaxies. However, as noted above, we have not yet incorporated any black hole or bulge growth due to gaseous processes. Conceivably, the AGN may be about to experience a Seyfert/quasar growth spurt and return the system to the $M_{\rm bh}$-$M_{\rm*,sph}$ relation traced by the relatively (cold gas)-poor S0 galaxies, in accord with trends seen in some simulations (e.g., Anglés-Alcázar et al., 2017; Bower et al., 2017; McAlpine et al., 2018; Tillman et al., 2022). As with tidal interactions which disturb the HI gas reservoir and ignite AGN (Kuo et al., 2008), minor and major mergers can also liberate HI and HII gas from their Keplerian merry-go-round (Hernquist, 1989; Hernquist & Mihos, 1995). For an S galaxy with $M_{\rm bh}/M_{\rm*,sph}\sim 10^{-3}$ and $M_{\rm bh}/M_{\rm*,gal}\sim 10^{-4}$ (e.g., Graham & Sahu, 2022), it does not take an unrealistic amount of cold gas to boost $M_{\rm bh}$ and thus $M_{\rm bh}/M_{\rm*,sph}$. For example, if gas amounting to 0.1 per cent of the galaxy’s stellar mass were accreted onto the black hole, it would boost $M_{\rm bh}$ by an order of magnitude.

Tillman et al. (2022, their Fig. 1 and references therein) present a scenario which may reveal the fate of the S0 galaxies built from wet mergers. Having exceeded a critical (galaxy stellar) mass threshold, where supernova also becomes less effective at clearing away potential fuel for the AGN, the mergers may experience a rapid burst of AGN accretion capable of growing the black hole by a couple of orders of magnitude. Even if star-formation were to double the spheroid’s stellar mass, this AGN spurt would more than compensate for the observed disparity between the (cold gas)-rich and the relatively (cold gas)-poor S0 galaxies in the $M_{\rm bh}$-$M_{\rm*,sph}$ diagram. Although, as alluded to by Kauffmann & Haehnelt (2000), in an evolving Universe in which galaxies are less (cold gas)-rich, the uptick in the $M_{\rm bh}$-$M_{\rm*,sph}$ diagram today may not be as pronounced as it perhaps was in the younger Universe. As lower-mass spiral galaxies dry up over time, perhaps due to ram-pressure stripping from their environment or strong supernova feedback which inhibits the growth of the spheroid, they too may evolve along a more upward trajectory in the $M_{\rm bh}$-$M_{\rm*,sph}$ diagram, bringing them onto the distribution seen for the relatively (cold gas)-poor S0 galaxies.

While the above wet mergers reveal that not all S0 galaxies are faded spiral galaxies, some may be if (cold gas)-rich disc galaxies evolve (and fade) in a primarily upward direction in the $M_{\rm bh}$-$M_{\rm*,sph}$ diagram. Of course, this would also mean that some S0 galaxies may be faded, merger-built S0 galaxies. This could mesh with the observation that while massive S0 galaxies consist of old stars — and as we will see in the following section, some of these have likely been built by dry mergers — the less massive S0 galaxies can have a broader range of stellar ages (Barway et al., 2013; Bait et al., 2017; Rathore et al., 2022).

We note that the $M_{\rm bh}$-$M_{\rm*}$ diagram from the SIMBA simulation (Davé et al., 2019, their Fig. 13), when coloured according to the (galaxy) specific star formation rate, shows a promising correlation with what is expected given the galaxy types shown in Figures 2 and 3. This agreement, at least at $M_{\rm bh}/M_{\odot}\gtrsim 10^{7}$, is even more evident in Fig. 4 from Habouzit et al. (2021). The merger-induced jump, explained in Graham & Sahu (2022), from the non-(star-forming) S0 galaxies defining the left-hand envelope of points across to the E galaxies is even more pronounced in the $M_{\rm bh}$-$M_{\rm e,sph}$ diagram (Fig. 2, left-hand side).

If not for the ES,b and S0 galaxies (the green and cyan squares in Fig. 3), there would be a notably tighter $M_{\rm bh}$-$M_{\rm*,gal}$ relation.¹¹¹¹11Removal of the ES,b and S0 galaxies also reduces the scatter in the $M_{\rm bh}$-$M_{\rm*,sph}$ and $M_{\rm bh}$-$M_{\rm e,sph}$ diagrams (Figure 2. If the ES,b galaxies were to acquire a large-scale disc and thus have a higher disc-to-bulge stellar mass ratio more typical of S0 galaxies, they would reside closer to the E galaxies. This makes us wonder if some of the S0 galaxies, specifically the cyan points on the left-hand side of the distribution in Fig. 3, may have reduced disc-to-bulge ratios. Might they perhaps reside in clusters, where S0 galaxy disc scalelengths are known to be smaller (e.g., Gutiérrez et al., 2004), perhaps due to cluster-hindered growth from ram pressure stripping of gas (e.g., Gunn & Gott, 1972; Yagi et al., 2010; Merluzzi et al., 2013) or tidal stripping of disc stars (Moore et al., 1996) which build the intracluster light (ICL). The BCGs aside, the high galaxy velocities in clusters will act to hinder collisions, thereby preventing some systems from moving across to the right in the $M_{\rm bh}$-$M_{\rm*,gal}$ diagram. Supernovae and stellar winds (e.g., De Loore et al., 1977; Björklund et al., 2022) may also reduce the stellar mass, while a final burst of quasar fuelling might drive the systems up in the $M_{\rm bh}$-$M_{\rm*,gal}$ diagram before they ‘dry out’. In future work, the S0 galaxies will be studied in more detail, as will the addition of intermediate mass black hole (IMBH) candidates (e.g., Chilingarian et al., 2018; Graham et al., 2019; Mezcua & Domínguez Sánchez, 2020).

With an eye to collisions involving supermassive black holes, Fig. 4 may offer some guidance for simulations and predictions for the stochastic background of long-wavelength gravitational radiation. Due to the clutter in Fig. 4, it was felt that a less adulterated version (Fig. 3) should be included. Although the number of data points is still low, it appears that the merger-built lenticular galaxies broadly partake in the same distribution as the elliptical galaxies.¹²¹²12Curiously, one can also see how removing the cyan points, i.e., the possibly (non-merger)-built S0 galaxies, will result in a notably tighter $M_{\rm bh}$-$M_{\rm*,gal}$ relation. This will be pursued in a future paper. This observation may be of practical use if (i) all (major merger)-built galaxies in the $M_{\rm bh}$-$M_{\rm*,gal}$ diagram follow the same relation and (ii) no bulge/disc/etc. decomposition is required. To date, obvious mergers have been excluded from the scaling relations, and it has frequently been emphasised that black holes correlate with spheroid mass rather than galaxy mass (e.g., KH13). However, a merger-built galaxy relation represents the ‘end product’ of major mergers generating nanohertz gravitational waves (e.g., Burke-Spolaor et al., 2019). Fig. 4 may reveal how elliptical galaxies are built from dry mergers involving lenticular galaxies on the (cold gas)-poor S0 ‘sequence’¹³¹³13This ‘sequence’ is perhaps more of an elongated cloud until lower mass S0 galaxies are included. while relatively (cold gas)-rich S0,pec galaxies are built from wet mergers. This broad merger-built galaxy relation has not been presented before and has a steeper slope than 1.69$\pm$0.17 defined by just the E galaxies in Graham & Sahu (2022). It is instead roughly such that

with $\upsilon=1$ when using stellar mass-to-light ratios $\Upsilon_{*}$ that are consistent with Graham & Sahu (2022, their Equation 4), which is based on the models of Into & Portinari (2013) and a Kroupa (2002) initial mass function. Equation 1 is shown by the grey line in Fig. 4.

As discussed in Graham & Sahu (2022), massive compact spheroids from ‘relic galaxies’ — largely unevolved, compact massive galaxies, aka ‘red nuggets’ from $z\sim 2.0\pm 0.5$ with $M_{*}\gtrsim 10^{11}$ M_⊙, $R_{\rm e}\lesssim 2$ kpc, and a red colour characteristic of a quiescent non-starforming stellar population (Daddi et al., 2005; Damjanov et al., 2009; Hon et al., 2022a, and references therein) — tend to reside near the top of the bulge sequence in the $M_{\rm bh}$-$M_{\rm*,sph}$ diagram. Examples are the ES,b galaxies NGC 1332 and NGC 5845 listed in Table 1. Other examples, albeit without our uniform analysis of a Spitzer image, include Mrk 1216 ($\log(M_{\rm bh}/M_{\odot})\leq 9.69\pm 0.16$, D=40.7 Mpc, Yıldırım et al., 2015) with ($\log(M_{\rm*,sph}/M_{\odot})=11.34\pm 0.20$, Savorgnan & Graham, 2016b), NGC 1271 ($\log(M_{\rm bh}/M_{\odot})=9.48\pm 0.16$, Walsh et al., 2015) with ($\log(M_{\rm*,sph}/M_{\odot})=10.95\pm 0.10$, Graham et al., 2016c), and NGC 1277 with $\log(M_{\rm*,sph}/M_{\odot})=11.43\pm 0.10$ (central $M_{*}/L_{V}=11.65$, Martín-Navarro et al., 2015) and a likely upper limit to the black hole mass of $1.2\times 10^{9}$ M_⊙ based on high spatial resolution (adaptive optics)-assisted Keck/osiris data (Graham et al., 2016b). Looking at Fig. 2, the spheroid mass for NGC 1277 seems some three times higher than expected from the distribution of the other ES,b galaxies. Although Martín-Navarro et al. (2015, their Fig. 6) suggest a lower $M_{*}/L_{V}\approx 8$ from 0.7 to 1.4 $R_{\rm e,gal}$, this would only reduce the spheroid mass by one-third. It would require $M_{*}/L_{V}\approx 4$ to yield a two-third reduction giving the speculated factor of three shift.

NGC 5252 ($\log(M_{\rm bh}/M_{\odot})=9.03\pm 0.40$, Capetti et al., 2005), with $\log(M_{\rm*,sph}/M_{\odot})=10.97\pm 0.27$ (Sahu et al., 2019a), is thought to represent a (possible relic) compact massive spheroid that has acquired a large-scale disc rather than an intermediate-scale disc (see Graham et al., 2015, and references therein). It is the S0 galaxy with the highest black hole mass among the S0 galaxies in our sample and is thought to represent a good example of the two-step scenario introduced¹⁴¹⁴14First posted on arxiv.org in 2011. by Graham (2013) in which discs grow in and around pre-existing ‘red nuggets’. The potential binary black hole in this galaxy would be further evidence of a past accretion event (Yang et al., 2017).

NGC 6861 is an ES,b galaxy likely to cause some confusion, assuming we have assigned the correct designation. While it appears to have grown/accreted an intermediate-scale disc (Sahu et al., 2019a), there is still a dusty disc in this galaxy, at odds with what the term ‘relic’ might conjure for some. It is. however, a galaxy that may have been left behind in an evolutionary sense, having not acquired a substantial disc mass.

We already have key insight into the morphogenesis and ontogeny of spheroids. For example, S0$+$S0 unions may create E galaxies, branching off from the $M_{\rm bh}$-$M_{*,bulge}$ relation. Indeed, major dry mergers in which the large-scale angular momentum is erased will produce elliptical galaxies (Naab et al., 2006b). Graham & Sahu (2022) noted that a single S0 merger is sufficient to explain the average offset of the elliptical galaxies in the $M_{\rm bh}$-$M_{\rm*,sph}$ diagram (Sahu et al., 2019a). Some BCGs have likely formed from the merger of E galaxies. Such an equal mass merger would roughly double both the black hole and spheroid mass, thereby forming an offshoot in the scaling diagram following a trajectory with a slope of 1.

Some massive E galaxies may have suffered such extensive erosion by infalling perturbers (Goerdt et al., 2010) and supermassive black holes (Merritt & Milosavljević, 2005) that it has fundamentally re-shaped the remnant galaxy to yield a system well described by a low-$n$ Sérsic profile. Indeed, some cD galaxies at the centres of clusters are likely built by multiple mergers, evidenced by multiple bright nuclei in the same system. They are sometimes seen to consist of a low-$n$ spheroid surrounded by intracluster light with a tendency to have an exponential light profile (Seigar et al., 2007). Systems involving such a halo are referred to as cD galaxies.

As Graham & Sahu (2022) illustrated, in terms of $M_{\rm bh}/M_{\rm*,sph}$ ratios, the E galaxies represent a population built by mergers. The super-linear $M_{\rm bh}$-$M_{\rm*,sph}$ relation observed for brightest group galaxies (BGGs) and BCGs by Bogdán et al. (2018) is understood here in terms of mergers which built the offset E galaxy sequence (Sahu et al., 2019a). By definition, they do not contain substantial discs or significant rotation. With BCGs and BGGs representing systems that may have experienced the highest number of mergers, here we check if they occupy a distinct region of the $M_{\rm bh}$-$M_{\rm*,sph}$ and $M_{\rm bh}$-$R_{\rm e,sph}$ diagram.

In Table 2, we identify the BCGs and BGGs in our sample. If they are a known cD galaxy, this is also reported. Our imaging data may not have always been deep/extended enough to capture the contribution from the ICL. For four of the six cD galaxies, we did not detect the presence of the ICL. This non-detection is only a problem if there is an ICL component that has influenced a portion of the outer-light profile included in the galaxy decomposition work. Within the $M_{\rm bh}$-$M_{\rm*,sph}$ diagram, we do not detect a separation of BCG/BGG from the non-(BCG/BGG) elliptical galaxies. While there is likely benefit to be had by acquiring and investigating new deep images of the cD galaxies in our sample, such an undertaking is beyond the intended scope of the present research project.

The galaxy with the largest directly measured black hole is Holm 15A, with an adopted distance modulus of 37.02 mag. Holm 15A is an intriguing galaxy which was initially reported to have a vast 4.57$\pm$0.06 kpc depleted core (López-Cruz et al., 2014) which was later queried by Bonfini et al. (2015) and Madrid & Donzelli (2016). Although lacking a noticeable downward break in its light profile, it is conceivable that this galaxy has been so heavily eroded that what may have once been a high Sérsic index galaxy now resembles a low Sérsic index system with no discernable break in its light profile. To distinguish this potential scenario from the less severe core depletion seen in many big spheroids, we coin a new phrase and refer to such dramatic reshaping as ‘galforming’, in a somewhat similar vein to the term terraforming. Other brightest cluster galaxies, such as NGC 5419 (Table 2), NGC 4874 in the Coma cluster and UGC 9799 (not in our sample), are also known to display this behaviour of an unusually low Sérsic index for their luminosity, embedded in a halo of intracluster light (Seigar et al., 2007). NGC 4472 (M49), the brightest galaxy in the Virgo B subcluster, has also been reported to have an unexpectedly low Sérsic index (Dullo & Graham, 2014, their Appendix C).¹⁷¹⁷17According to Sandage & Tammann (1981), NGC 4472 is an S0 galaxy. From photometry, Laurikainen et al. (2011) fit a large-scale exponential function which dominates the light beyond $\sim$ 100$\arcsec$, although we wonder (but have not explored) if this might be a halo of ICL given that other works regard NGC 4472 as an E galaxy.

Mehrgan et al. (2019) report $M_{\rm bh}=(4.0\pm 0.8)\times 10^{10}M_{\odot}$ for Holm 15A. Presumably, when measuring the brightness of BCGs, one needs to exclude the ICL, which belongs to the cluster, rather than the BCG. This was done by Bonfini et al. (2015), who reported a CFHT $r$-band magnitude of $\sim$13.8 mag (AB system). Using $M_{\odot,r}=4.64$ mag, and adopting an $M_{*}/L_{r}$ ratio of 3$\pm$1, gives a stellar mass $M_{*,sph}=4.2^{+1.4}_{-1.0}\times 10^{11}\,M_{\odot}$. On the other hand, Mehrgan et al. (2019) include the ICL and adopt an $M_{*}/L_{i}$ ratio of 4.5$\pm$0.19 to report a galaxy+ICL stellar mass of $(25.0\pm 6.4)\times 10^{11}\,M_{\odot}$, six times larger than the galaxy stellar mass reported by Bonfini et al. (2015). While this places it smack on the super-linear $M_{\rm bh}$-$M_{\rm*,sph}$ relation for elliptical galaxies, the inclusion of the ICL appears questionable.

Finally, we note that KH13 excluded NGC 4889 (Coma) and NGC 3842 (Leo) due to these galaxies’ high black hole masses relative to the near-linear $M_{\rm bh}$-$M_{\rm*,sph}$ relation in KH13. However, these galaxies do not have an over-massive black hole relative to the morphology-dependent, super-linear $M_{\rm bh}$-$M_{\rm*,sph}$ relations from Graham & Sahu (2022), and we do not exclude them. KH13 also excluded NGC 1316, NGC 3607, NGC 4261 and IC 4296 (Abell 3565-BCG) from their regression. They also did not have NGC 1275 and NGC 5419 in their sample. As such, they only used 6 of the 14 galaxies listed in Table 2.

Soon after William Parsons¹⁸¹⁸18William Parsons was the 3^rd Earl of Rosse, Ireland, and is often referred to as Lord Rosse. discovered the first spiral nebulae (Rosse, 1850a, b), the tidal theory of Roche (1850) explained how a massive galaxy could gravitationally strip stars from a neighbouring galaxy. Alexander (1852) reasoned that the relatively stronger (weaker) gravitational force on the facing (opposing) sides of the galaxy would lead to two protrusions which would be drawn out into spiral-like arms if the galaxy rotated. Indeed, tidal arms and tails have since been modelled (e.g., Toomre & Toomre, 1972), and are well known (e.g., Brüns et al., 2000; Jarrett et al., 2006). It is the ongoing tidal-stripping which is thought to eventually pare away a galaxy’s disc, rather than the outskirts of a large E galaxy, to create a more dominant bulge (Bekki et al., 2001b), as seen in the ‘compact elliptical’ (cE) galaxies. If the bulge is not stripped, ignoring any black hole growth or spheroid mass loss due to stellar winds, the system will remain on the S0 $M_{\rm bh}$-$M_{\rm*,sph}$ relation shown in Fig. 1. Ongoing stripping may pare away the bulge, leaving the more resilient nuclear star cluster to become a UCD galaxy, in a process referred to as threshing (e.g., Bekki et al., 2001a; Graham, 2020, and references therein). The migration from these processes is illustrated in Fig. 6, including the compact elliptical galaxies M32 and NGC 4486B, the stripped galaxy NGC 4342, and several UCDs. This pattern has been seen before, for example, Ferré-Mateu et al. (2021, their Fig. 7).

van den Bosch & de Zeeuw (2010) report $M_{\rm bh}=(2.4\pm 1.0)\times 10^{6}\,M_{\odot}$ for M32. Saglia et al. (2016, their Table 1) report $\log\,M_{\rm*,sph}=8.627\pm 0.022$ based on $\log(L_{V,M32}/L_{V,\odot})=8.572$ from Magorrian et al. (1998), along with a $V$-band Galactic extinction of 0.206 mag, and the use of $M_{*}/L_{V}=1M_{\odot}/L_{\odot}$ rather than $M_{*}/L_{V}=2.18M_{\odot}/L_{\odot}$ as reported by Magorrian et al. (1998). We depart from this mass estimate in two ways. First, the adopted mass-to-light ratio is probably too small for the ancient stellar population in M32 (Coelho et al., 2009), which has $B-V\approx 0.95$ (de Vaucouleurs et al., 1991). The models of Schombert et al. (2022) suggest $M_{*}/L_{V}=5.0$ $M_{\odot}/L_{\odot}$, which we reduce by $10^{-0.1}$, i.e., 0.1 dex, to give $M_{*}/L_{V}=4.0$ $M_{\odot}/L_{\odot}$ for a Kroupa (2002) initial mass function. Second, M32 is known to have a three-component structure (Graham & Spitler, 2009), including a weak disc (Graham, 2002) that was likely eroded by tidal-stripping (King, 1962; King & Kiser, 1973; Rood, 1965; Faber, 1973; Bekki et al., 2001b). As such, we reduce the galaxy luminosity by a factor of 0.62 (Graham, 2002) to obtain the spheroid luminosity. In so doing, we obtain a Galactic extinction corrected ($A_{V}=0.17$: Schlafly & Finkbeiner, 2011) stellar mass for the spheroidal component of M32 equal to $1.08\times 10^{9}\,M_{\odot}$. This is just 35 per cent higher than the preferred derivation provided in Graham & Sahu (2022), which we use here.

Another well known cE galaxy is NGC 4486B, for which Magorrian et al. (1998) report $\log(L_{V,gal}/L_{V,\odot})=8.960$ and $M_{*}/L_{V}=3.6\pm 0.4$, giving $\log(M_{\rm*,gal}/M_{\odot})=9.516$. Saglia et al. (2016) report a higher value of $\log(M_{\rm*,gal}/M_{\odot})=9.847\pm 0.027$, and $\log(M_{\rm bh}/M_{\odot})=8.602\pm 0.024$, which we plot in Fig. 6 along with M32. While M32 may be the result of stripping much of the disc from an S0 galaxy while leaving the spheroidal component largely intact, NGC 4486B may have additionally had some of the spheroidal component removed.¹⁹¹⁹19As revealed in Graham & Soria (2019, their Fig. 11), IC 3653 (not in our sample) is another galaxy which might be expected to have an elevated $M_{\rm bh}/M_{\rm*,sph}$ ratio due to tidal stripping if its bulge component has been depleted. However, confirming this would require further investigation. For example, while the S0 galaxy NGC 2787 appears to the left of the (cold gas)-poor S0 sequence in the $M_{\rm bh}$-$M_{\rm*,sph}$ diagram, similar to NGC 4486B, it is not regarded as a tidally-stripped galaxy.

Although not a cE galaxy, the S0 galaxy NGC 404 also resides at the low-mass end of our scaling relations. NGC 404 is marginally consistent with the black hole scaling relations for the predominantly non-(star-forming) S0 galaxies, as seen in the lower left of the panels in Fig. 1. While most of the stars in NGC 404 are old, it does contain cold gas in its disc but only displays a declining tail of star formation in its outer disc (Williams et al., 2010; Bresolin, 2013). If NGC 404, or the dwarf ETG Pox 52 (Thornton et al., 2008)²⁰²⁰20Pox 52 appears to have an AGN plus a two-component stellar structure. It may be a dwarf S0 galaxy with a disc and bulge, with the unsubtracted portion of the bulge visible in the residual image of Kim et al. (2017, their Fig. 11.50)., were to merge with a larger bulgeless LTG, the remnant might resemble the post-merger spiral galaxy NGC 4424 (Graham et al., 2021), which can be appreciated from Fig. 3. Although, we do caution that more, and reliable, data is needed at low masses before a secure picture can be established in the low-mass regime. Silk (2017) has argued that the presence of IMBHs may be a common feature of old dwarf galaxies. Unlike in low-mass LTGs, IMBHs may be hard to spot due to their expectedly lower Eddington ratios, possibly explaining the lower detection rates in ETGs than LTGs (Graham & Soria, 2019; Graham et al., 2019).