A Hidden Population of Massive Black Holes in Simulated Dwarf Galaxies

Stars in Romulus25 form according to a star formation efficiency when cold gas has a density that exceeds a threshold for star formation:

• 1.  
  star formation efficiency c_* = 0.15;
• 2.  
  gas density threshold n_* ≥ 0.2 m_p cm⁻³;
• 3.  
  gas temperature T < 10⁴ K.

Additionally, 0.75 × 10⁵¹ erg of thermal energy is deposited in the ISM by Type II SNe following the "blast wave" mechanism (Stinson et al. 2006). Cooling is shut off in the gas particles that receive Type II SN energy for a time period representing the adiabatic expansion phase of a blast wave SN remnant.

These star formation parameters were tuned using a set of 80 zoom-in simulations of four halos with halo masses M_vir = 10^10.5–10¹² M_⊙. A set of parameters were chosen by their ability to reproduce z = 0 scaling relationships between stellar mass, halo mass, H i gas mass, and angular momentum (Cannon et al. 2011; Haynes et al. 2011; Moster et al. 2013; Obreschkow & Glazebrook 2014).

Prescriptions for metal diffusion (Shen et al. 2010), thermal diffusion (Wadsley et al. 2017), and low-temperature radiative cooling (Guedes et al. 2011) are also included in Romulus25, with a Kroupa (2001) initial mass function for stars. Romulus25 does not include high-temperature metal cooling, which should not have an effect in low-mass halos with typically low-metallicity gas (see Tremmel et al. 2019 for a more detailed discussion).

MBHs in Romulus25 are seeded according to local, precollapse gas properties with thresholds and seed mass similar to a direct-collapse model (Wiklind et al. 2013; Greene et al. 2020). A star-forming gas particle is instead marked to form an MBH if it meets the following criteria:

• 1.  
  low metallicity, Z < 3 × 10⁻⁴;
• 2.  
  gas density threshold, n_*,BH > 3m_p cm⁻³;
• 3.  
  temperature, T = 9500−10⁴ K,

effectively restricting BH creation to high-density regions in the early universe. If these criteria are met, the gas particle forms an MBH with mass M_BH = 10⁶ M_⊙, accreting mass from nearby gas particles. This seed mass is somewhat higher than theoretical estimates (e.g., Volonteri 2012). The high seed mass for MBHs allows us to well resolve their dynamics over cosmic time (Tremmel et al. 2015; see below). Additionally, the early growth onto MBH progenitors may exceed 0.1 M_⊙ yr⁻¹ and is governed by processes below the resolution limits of the simulation (Hosokawa et al. 2013; Schleicher et al. 2013). In Romulus25, 95% of MBHs form within the first Gyr of the simulation (Tremmel et al. 2017).

Romulus25 employs prescriptions for MBH dynamical friction that produce realistic MBH sinking timescales (Tremmel et al. 2015). This subgrid model allows MBHs in large halos to stay centered (Kazantzidis et al. 2005; Pfister et al. 2017) but also allows some MBHs to "wander" within sufficiently shallow potentials, as has been discovered in recent observations (Reines et al. 2020) and simulations (e.g., Tremmel et al. 2018; Bellovary et al. 2019; Ricarte et al. 2021a, 2021b; Bellovary et al. 2021). The dynamical friction prescriptions, along with the "oversampling" of dark matter particles, the high seed mass, and high resolution of Romulus25, together help avoid unrealistic numerical heating of MBHs and help ensure accurate MBH dynamics.

MBH feedback takes the form of thermal energy injection into the surrounding environment. Thermal energy from the MBH, E_BH, is isotropically injected into the 32 nearest gas particles in some time, dt, following

$$\begin{eqnarray}&&{E}_{\mathrm{BH}}={\epsilon }_{r}{\epsilon }_{f}\dot{M}{c}^{2}{dt},\end{eqnarray} \tag{ 1 }$$

where _r = 0.1 is the radiative efficiency, _f = 0.02 is the energy injection efficiency, and $\dot{M}$ is the MBH accretion rate.

Accretion itself follows a modified Bondi–Hoyle prescription to incorporate angular momentum on unresolved spatial scales. The "instantaneous" accretion is averaged over the smallest simulation time element, typically 10⁴–10⁵ yr, and remains Eddington limited at all times. We can write the accretion rate depending on whether the dominant gas motion is rotational, v_θ , or bulk flow, v_bulk:

$$\begin{eqnarray}\dot{M}=\alpha \times \left\{\begin{array}{cc}\displaystyle \frac{\pi {G}^{2}{M}_{\mathrm{BH}}^{2}\rho }{{\left({v}_{\mathrm{bulk}}^{2}+{c}_{s}^{2}\right)}^{3/2}} & \mathrm{if}\ {v}_{\mathrm{bulk}}\gt {v}_{\theta }\\ \displaystyle \frac{\pi {G}^{2}{M}_{\mathrm{BH}}^{2}\rho {c}_{s}}{{\left({v}_{\theta }^{2}+{c}_{s}^{2}\right)}^{2}} & \mathrm{if}\ {v}_{\mathrm{bulk}}\lt {v}_{\theta },\end{array}\right.\end{eqnarray} \tag{ 2 }$$

where

$$\begin{eqnarray*}\alpha =\left\{\begin{array}{cc}{\left(\frac{{n}_{\mathrm{gas}}}{{n}_{* }}\right)}^{\beta } & \mathrm{if}\ {n}_{\mathrm{gas}}\geqslant {n}_{* }\\ 1 & \mathrm{if}\ {n}_{\mathrm{gas}}\leqslant {n}_{* }\end{array}\right.\end{eqnarray*}$$

is the density-dependent boost factor that corrects for underestimated accretion rates due to resolution limitations (Booth & Schaye 2009), β = 2 is the corresponding boost coefficient, n_gas is the number density of the surrounding gas, n_* is the star formation density threshold, ρ is the mass density of the surrounding gas, c_s is the local sound speed, v_θ is the rotational velocity of the surrounding gas at the smallest resolved scales, and v_bulk is the bulk velocity of the surrounding gas. This calculation is performed over the 32 nearest particles. Free parameters related to accretion and feedback were optimized to reproduce various empirical scaling relations for low-mass halos $\left({M}_{\mathrm{vir}}\lesssim {10}^{12}\,{M}_{\odot }\right)$ at z = 0 (Tremmel et al. 2017), including the observed relationship between MBH mass and stellar mass (Schramm & Silverman 2013).

Figure 1 illustrates the evolution of the MBH occupation fraction in Romulus25, where the occupation fraction is defined as the fraction of halos of a given stellar/halo mass containing at least one MBH within the inner 10 kpc. We do not include MBHs within the substructure of the primary halo. The high-redshift MBH occupation fraction is determined by the seeding mechanism, while the time evolution is primarily driven by structure growth. We show the occupation fraction as a function of both stellar mass and halo mass. At z = 0.05, the MBH occupation fraction drops below unity at M_star = 3 × 10¹⁰ M_⊙, M₂₀₀ = 3 × 10¹¹ M_⊙.

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The local z = 0.05 occupation fraction is consistent with constraints from observations and empirical modeling. Dynamical MBH mass estimates (Nguyen et al. 2019) place the occupation fraction between 50% and 80% for dwarf galaxies between 10⁹ M_⊙ < M_star < 10¹⁰ M_⊙. X-ray-selected AGN (Miller et al. 2015) provide lower limits on the occupation fraction as a function of stellar mass. Greene (2012) estimates the occupation fraction using X-ray observations of eight optically selected AGN with M_BH > 3 × 10⁵ M_⊙, as estimated from the M_BH–σ relation (Desroches et al. 2009). Baldassare et al. (2020; not shown) use variability of optical light curves from the NASA-Sloan Atlas with Palomar Transient Factory coverage to identify local, low-mass AGN. They find that AGN variability fractions are approximately constant down to stellar masses M_star = 10⁹ M_⊙, suggesting that the MBH occupation fraction does not change much between M_star > 10⁹ and 10¹⁰ M_⊙, consistent with our estimates. The local occupation fraction also agrees with occupation fractions from Buchner et al. (2019; closeup $p=0.3,\mathrm{log}{M}_{c}=10$), who use empirical models to explore valid regions of the parameter space of critical halo mass versus MBH seed probability.

We use the Amiga Halo Finder (AHF; Knollmann & Knebe 2009) to extract gravitationally bound dark matter halos, as well as subhalos, and the baryonic content associated with these structures. AHF utilizes a spherical top-hat collapse technique to define the virial radius (R_vir) and mass (M_vir) of each halo and subhalo. AHF uses a spherical top-hat collapse technique to define the virial radius and total mass of each halo. The center of each halo/galaxy is calculated using a shrinking spheres approach (Power et al. 2003).

Dwarf galaxies have been found to exhibit relationships between MBH X-ray luminosity, stellar mass, and SFR similar to those found in massive galaxies (e.g., Aird et al. 2017, 2018). These relationships may illuminate any connection between MBH activity and star formation, as well as provide insight into how readily dwarf AGN at each mass scale may be observed.

Figure 2 shows the relationships between ${L}_{{\rm{X}}}^{\mathrm{AGN}}$, M_star, and SFR for dwarf galaxies at z = 0.05 that host an MBH in the central 10 kpc. Each point that satisfies the contamination threshold ${L}_{{\rm{X}}}^{\mathrm{AGN}}\gt 2{L}_{{\rm{X}}}^{\mathrm{XRB}+\mathrm{Gas}}$ is colored according to the instantaneous Eddington fraction. Dwarfs that fail the contamination threshold are marked in gray. Arrows mark dwarfs with extremely low luminosities or zero star formation, with SFRs averaged over the past 100 Myr.

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We compare our results with X-ray-selected dwarf AGN from Mezcua et al. (2018), who identify 40 dwarf AGN between 10⁷ M_⊙ < M_star < 3 × 10⁹ M_⊙ from the Chandra-COSMOS-Legacy survey out to z < 2.4, in the full 0.5–10 keV band. We only show their sample up to z < 0.25 for better comparison with our local dwarfs. We also include results from Birchall et al. (2020), who provide 61 X-ray-selected dwarf AGN that fall within both the optical MPA-JHU footprint and X-ray 3XMM footprint. Birchall et al. (2020) identify dwarfs with M_star < 3 × 10⁹ M_⊙ out to z < 0.25 in the harder 2–12 keV band. Both observational sets calculate the AGN X-ray luminosity by subtracting off contributions to the total X-ray luminosity from XRBs and the hot ISM.

Overall, the scaling relationships between our uncontaminated luminous dwarfs are consistent with observed relations of local dwarf AGN. Simulated dwarfs tend not to reach the highest luminosities found in the observations, ${L}_{{\rm{X}}}^{\mathrm{AGN}}\gt {10}^{42}$ erg s⁻¹, though these observed luminous dwarfs are typically at slightly higher redshifts, z ≳ 0.1. Our dwarfs strike a middle ground between the higher luminosities found in Mezcua et al. (2018) and the lower luminosities found in Birchall et al. (2020), which are at least partially due to the harder X-ray band in which Birchall et al. (2020) observe.

There exists a large population of dwarfs at low luminosities and high contamination (${L}_{{\rm{X}}}^{\mathrm{AGN}}\lt 2{L}_{{\rm{X}}}^{\mathrm{XRB}+\mathrm{Gas}}$) that are not found in observations. These contaminated dwarfs make up 70% of dwarfs with MBHs at z = 0.05. This hidden population that is missed by observations suggests that typical relationships between ${L}_{{\rm{X}}}^{\mathrm{AGN}}$ and both M_star and SFR are dramatically impacted by a survey's ability to detect low luminosities and distinguish contaminated AGN. Indeed, the largest scatters in these relationships are found at dwarf galaxy masses, suggesting that the relationships found in massive galaxies may break down for dwarf galaxies. We further explore the role of detection threshold and X-ray contaminants in Section 3.3.

Many simulated dwarfs also exhibit quenched star formation. Since MBH accretion is, on average, correlated with SFR among star-forming main-sequence galaxies in Romulus25 (Ricarte et al. 2019), it is unsurprising that many low-luminosity MBHs are found in galaxies with little star formation. However, a surprising number of quenched dwarfs exhibit an actively accreting MBH, in line with X-ray observations from Aird et al. (2019) and Carraro et al. (2020), which both find elevated AGN activity among quiescent galaxies relative to star-forming galaxies at the same SFR. This phenomenon suggests that the mechanism that fuels star formation is, at least in some dwarfs, separate from that which fuels MBH activity. It may also indicate a connection between active accretion and the suppression of star formation in some dwarfs.

It is worth noting that 20% of quenched (zero SFR) dwarf galaxies in Romulus25 are isolated, meaning that they are (i) outside the virial radius of a larger halo and (ii) farther than >1.5 Mpc from any neighboring galaxy with M_star > 2.5 × 10¹⁰ M_⊙ (Geha et al. 2012). The high number of quenched, isolated dwarf galaxies in Romulus25 is in tension with observations of local field dwarfs (Geha et al. 2012), where the quenched fraction in isolated dwarf galaxies is f _q ∼ 0.01–0.1. Dickey et al. (2021) find that many other cosmological simulations similarly overproduce quenched, isolated dwarfs. Future work will explore the dwarf quenching mechanism in Romulus25, including the possible ties to AGN activity.

Next, we examine the evolution of AGN prevalence across cosmic time. The active fraction is defined here as the fraction of all galaxies emitting above a given 0.5–10 keV X-ray luminosity threshold. Figure 3 shows the active fraction for all galaxies in Romulus25 above M_star > 10⁸ M_⊙ as a function of stellar mass, in bins of redshift. We define activity using three X-ray luminosity thresholds and include observational constraints from X-ray observations (Mezcua et al. 2018; Birchall et al. 2020). We set a cut on acceptable contamination such that ${L}_{{\rm{X}}}^{\mathrm{AGN}}\gt 2{L}_{{\rm{X}}}^{\mathrm{XRB}+\mathrm{Gas}}$. Setting this cut on contamination impacts the active fractions in lower-luminosity AGN but does not change fractions among the two highest AGN luminosities shown here.

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In addition to expressing a lower occupation fraction than massive galaxies, low-mass galaxies are overall less luminous and hence exhibit a lower active fraction. While the most massive galaxies consistently emit well above ${L}_{{\rm{X}}}^{\mathrm{AGN}}\gt {10}^{41.5}$ erg s⁻¹, only the higher-mass dwarf galaxies between 10⁹ M_⊙ < M_star < 10¹⁰ M_⊙ reach such high luminosities, and most prominently around z = 2. Dwarf galaxies peak in activity around z = 2 and drop off in luminosity with time, steeply dropping around z = 0.05. By z = 0.05, approximately 2% of galaxies between 10⁸ M_⊙ < M_star < 10⁹ M_⊙ and 8% of galaxies between 10⁹ M_⊙ < M_star < 10¹⁰ M_⊙ host an X-ray-detectable MBH brighter than ${L}_{{\rm{X}}}^{\mathrm{AGN}}\gt {10}^{40.5}$ erg s⁻¹. For reference, this luminosity threshold is similar to the detection threshold for the 4.6 Ms Chandra-COSMOS-Legacy observations at z = 0.05 in the full X-ray band (Suh et al. 2017). Despite the steep drops in luminosity, dwarf galaxies at z = 0.05 in Romulus25 exhibit a factor of a few higher active fractions than found in X-ray observations.

There may be a few reasons why our dwarf active fractions are higher than the observed ones: (1) The high seed mass in Romulus25 may ultimately drive unrealistically high accretion rates onto dwarf AGN at the wrong times. Although our dwarf AGN follow observed local scaling relations, including the M_BH–M_star relation for more massive galaxies, dwarfs in reality may follow a different M_BH–M_star relation from massive galaxies (Reines & Volonteri 2015). Further, it is possible to correctly predict the empirical relationships while still overpredicting the AGN fraction if the timing of the simulated MBH accretion history is wrong. Indeed, Ricarte et al. (2019) find that the luminosity density of AGN in Romulus25 is high relative to observations at z = 0. (2) MBHs in Romulus25 accrete on timescales greater than ≳10⁴ yr. A duty cycle of order 10³ yr may account for factor ∼10 differences in observed fraction. (3) Although our occupation fractions are consistent with observations, changing the MBH seeding model to be more restrictive may alleviate the AGN fraction discrepancy while maintaining agreement with observational constraints on the occupation fraction. This change is largely equivalent to changing the seeding model of the simulation. (4) As with other cosmological simulations, we do not directly measure AGN luminosities but instead assume a radiative efficiency to convert MBH accretion rates. We convert accretion rates using a two-mode accretion model where radiative efficiency depends on Eddington fraction (Churazov et al. 2005). However, there is no consensus on the Eddington fraction distributions that underlie accretion models for low-luminosity AGN, and hence the precise dependence on Eddington fraction is unclear (Trump et al. 2011; Weigel et al. 2017; Pesce et al. 2021). Further, we do not take into account AGN obscuration. Although the obscuration fraction among AGN is still uncertain, population synthesis models from Tasnim Ananna et al. (2019) indicate that 50% of AGN within z ∼ 0.1 may be Compton-thick. (5) Similarly, we rely on existing bolometric corrections from Shen et al. (2020) to calculate X-ray luminosities, but these corrections are calibrated for more massive galaxies. As with radiative efficiency, there is evidence that X-ray bolometric corrections depend on Eddington fraction (Lusso et al. 2012). Radiative efficiency and bolometric corrections are closely linked quantities and together form a free parameter that is not well constrained within dwarf galaxies (Baldassare et al. 2017). Indeed, Latimer et al. (2021) find evidence that IR-selected dwarf AGN are comparatively underluminous in the X-ray regime, suggesting a breakdown in typical luminosity scaling relations at dwarf masses, as we have found. Moreover, Molina et al. (2021b) identify 81 AGN candidates using coronal line emission in the optical regime and find that 49% cannot be correctly identified using other AGN-detection techniques, including X-ray detection.

Figure 4 illustrates how the active fraction differs when switching from a two-mode accretion model to a single-mode model in which ${L}_{\mathrm{bol}}={\epsilon }_{r}{\dot{M}}_{\mathrm{BH}}{c}^{2}$. We calculate the active fraction for the two-mode model using a flat bolometric correction, ${k}_{\mathrm{bol},{\rm{X}}}={L}_{\mathrm{bol}}\,/{L}_{{\rm{X}}}^{\mathrm{AGN}}=25$. We also explore the luminosity-dependent bolometric corrections obtained from X-ray-selected AGN by Lusso et al. (2012), applying them to the two-mode accretion model. For the low luminosities found among Romulus25 dwarfs, the extrapolated luminosity-dependent corrections are approximately k_bol,X ∼ 10. Lusso et al. (2012) provide Eddington fraction bolometric corrections for hard X-rays, but we do not use those corrections since their AGN do not extend down to the Eddington fractions found in Romulus25.

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Single-mode accretion, wherein even MBHs with low Eddington fractions radiate equally efficiently, produces luminosities that are significantly higher than in two-mode accretion. Active fractions for single-mode accretion at a given stellar mass are approximately 1 dex higher than observations from Birchall et al. (2020). On the other hand, applying a flat bolometric correction of k_bol,X = 25 (∼5× larger than corrections from Shen et al. 2020) to the two-mode model yields even closer consensus with observations. The luminosity-dependent corrections derived from X-ray AGN yield even lower active fractions, despite having k_bol,X ∼ 10 (only ∼2× larger than corrections from Shen et al. 2020). It is worth noting that among massive galaxies, high bolometric corrections of order k_bol ∼ 100 are typically only found in Compton-thick AGN and/or AGN with particularly high Eddington fraction (Vasudevan & Fabian 2007; Lusso et al. 2012; Brightman et al. 2017), while the dwarfs in Romulus25 typically exhibit Eddington fractions f_Edd < 10⁻².

Next, we illuminate a population of MBHs within Romulus25 that may be hidden from current X-ray surveys. We explore the impact of current X-ray detection limits, contamination of low-luminosity AGN by XRBs and the hot ISM, and off-center (outside 2 kpc of the galaxy center) versus central (within 2 kpc of the galaxy center) MBHs within dwarf galaxies on the detected population of dwarf AGN.

Using semianalytic models of MBH growth in low-mass galaxies, Pacucci et al. (2018) find that the tight scaling relationship between MBH mass and bulge stellar velocity dispersion, σ_⋆, found in high-mass galaxies tends to overpredict M_BH in low-mass galaxies.

Observations indicate that the tight scaling relationships between M_BH and M_star (or velocity dispersion, σ_⋆) found among massive galaxies tend to overpredict M_BH in low-mass galaxies (Reines & Volonteri 2015). Using semianalytic models, Pacucci et al. (2018) find that MBHs that are undermassive relative to the expected M_BH–σ_⋆ or M_BH–M_star relations tend to have grown from weakly accreting low-mass seeds, which may fall below typical survey detection thresholds. This trend suggests that the observed M_BH–σ_⋆ (and similarly the M_BH–M_star) relation in massive galaxies only appears to extend to low-mass galaxies because those MBHs are detectable, when there may in fact be many undetected, low-luminosity MBHs that fall below the relation (Baldassare et al. 2020).

Figure 5 illustrates how varying the X-ray detection limit alters the detected distribution of M_BH / M_star for dwarf galaxies at z = 0.05. As a baseline, we show the underlying distribution of M_BH / M_star without cuts on X-ray luminosity for dwarfs in each stellar mass bin. In each stellar mass bin, setting luminosity thresholds as low as ${L}_{{\rm{X}}}^{\mathrm{AGN}}\gt {10}^{39}$ erg s⁻¹ removes the majority of MBHs from detection, including many of the most undermassive MBHs. Setting a threshold at ${L}_{{\rm{X}}}^{\mathrm{AGN}}\gt {10}^{39}$ erg s⁻¹ misses 78% of MBHs in dwarfs between 10⁸ M_⊙ < M_star < 10^8.5 M_⊙ and 38% of MBHs in dwarfs between 10^9.5 M_⊙ < M_star < 10¹⁰ M_⊙. Increasing the threshold to ${L}_{{\rm{X}}}^{\mathrm{AGN}}\gt {10}^{41.5}$ erg s⁻¹ samples a strongly biased sample of MBHs, keeping only those few with $\mathrm{log}\left({M}_{\mathrm{BH}}^{\mathrm{acc}}\,/\,{M}_{\mathrm{star}}\right)\sim -3$. However, the median of the distribution changes little regardless of detection threshold, different from what is found by Pacucci et al. (2018).

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Figure 6 further shows how varying the acceptable contamination from XRBs and hot gas impacts the detected distribution of ${M}_{\mathrm{BH}}^{\mathrm{acc}}\,/\,{M}_{\mathrm{star}}$, where we define ${f}_{\mathrm{cont}}={L}_{{\rm{X}}}^{\mathrm{AGN}}\,/\,{L}_{{\rm{X}}}^{\mathrm{XRB}+\mathrm{Gas}}$. Throughout this work we have adopted f_cont = 2 as the standard contamination threshold. Setting a contamination threshold as low as f_cont = 1 similarly misses the most undermassive MBHs. A threshold set at f_cont = 1 misses 77% of MBHs in dwarfs between 10⁸ M_⊙ < M_star < 10^8.5 M_⊙ and 60% of MBHs in dwarfs between 10^9.5 M_⊙ < M_star < 10¹⁰ M_⊙. As with setting luminosity thresholds, the median of the distribution changes little when setting contamination thresholds.

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Another complicating factor in MBH detection is distance from the galaxy center. Both simulations (Bellovary et al. 2019, 2021) and observations (Mezcua & Domínguez Sánchez 2020; Reines et al. 2020; Greene et al. 2021) have found MBHs at large radii from the centers of dwarf galaxies. Galaxies in Romulus25 have also been found to frequently host off-center MBHs at radii >2 kpc from the halo center (Ricarte et al. 2021a, 2021b). Off-center MBHs frequently exhibit low luminosities (Mezcua & Domínguez Sánchez 2020) and low accretion efficiencies (Ricarte et al. 2021b), implying that the detection of off-center MBHs is intrinsically tied to luminosity thresholds and contamination. When selecting our initial sample of MBH hosts, we search for the brightest MBH within 10 kpc of the halo center, which includes the majority of off-center MBHs. At z = 2, 20% of dwarfs with MBHs have their brightest MBH outside of 2 kpc. Over time, bright off-center MBHs become even less common, as the percentage drops to 11% by z = 0.05. Regardless of redshift, approximately 98% of MBHs in dwarf galaxies are found within 10 kpc of the halo center.

To further quantify the combined impact of off-center MBHs, X-ray luminosity limits, and contamination on the detection of MBHs, Figure 7 shows the ${M}_{\mathrm{BH}}^{\mathrm{acc}}-{M}_{\mathrm{star}}$ relation up to M_star < 10¹¹ M_⊙ with the same set of X-ray luminosity thresholds and acceptable contamination fractions. We distinguish between galaxies with central (within 2 kpc of the galaxy center) and off-center (outside 2 kpc of the galaxy center) MBHs. In cases where there are multiple central or multiple off-center MBHs, we choose the brightest one. For reference, we overplot observed relations for massive galaxies from Schramm & Silverman (2013) and Kormendy & Ho (2013). There exists a "hidden" population of MBHs at both low luminosities $\left({L}_{{\rm{X}}}^{\mathrm{AGN}}\lt {10}^{39}\,\mathrm{erg}\ {{\rm{s}}}^{-1}\right)$ and high contamination $\left({L}_{{\rm{X}}}^{\mathrm{AGN}}\lt {L}_{{\rm{X}}}^{\mathrm{XRB}+\mathrm{Gas}}\right)$ that are undetectable by current instruments. Approximately 74% of central MBHs in dwarf galaxies are hidden by these criteria. While the majority of hidden central MBHs lie directly along the observed relation, a significant number are found well below the relation. On the other hand, 88% of off-center MBHs in dwarf galaxies are further hidden by low luminosities and/or contamination, and the majority are significantly undermassive. These results indicate that increasing the detection sensitivity alone would not allow hidden MBHs to be reliably detected since they are often heavily contaminated and sometimes exist at large distances from the galaxy center. Detecting these hidden MBHs with X-rays, especially MBHs that are far off-center, would require higher instrument sensitivity in addition to (i) a better understanding of XRBs + hot ISM emission in dwarf galaxies (e.g., in the low-metallicity, low-SFR regimes as discussed in Lehmer et al. 2021) and/or (ii) multiwavelength imaging of the AGN.

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Although we predict that sensitivity limits will cause surveys to miss many undermassive MBHs, common detection limits only slightly impact the fit relation. Fits to the total (central + off-center) ${M}_{\mathrm{BH}}^{\mathrm{acc}}-{M}_{\mathrm{star}}$ relation below M_star < 10¹⁰ M_⊙ at z = 0.05 reveal that setting a ${L}_{{\rm{X}}}^{\mathrm{AGN}}\gt {10}^{39}\,\mathrm{erg}\ {{\rm{s}}}^{-1}$ detection limit simply shifts the relation up by 0.1 dex while keeping the slope intact. The small change in predicted M_BH is not large enough to explain the 1 dex difference found in Pacucci et al. (2018). Their abundant undermassive MBHs are likely the result of their mixed seeding mechanism that generates both high-mass $\left({M}_{\mathrm{seed}} \tilde {10}^{4}\,{M}_{\odot }\right)$ and weakly accreting low-mass $\left({M}_{\mathrm{seed}} \tilde {10}^{2}\,{M}_{\odot }\right)$ seeds.

Finally, we report on the spatial number density of hidden MBHs and AGN relative to the total number density of MBHs in Romulus25. The initial number of MBHs within Romulus25 is set by the seeding prescription, while the evolution with time is determined by the merger rates. In particular, the seeding prescription determines where and with what frequency MBHs can form. Since the majority of MBHs in Romulus25 form prior to z = 5 (Tremmel et al. 2017), the evolution of the number density from z = 2 to z = 0.05 is driven by MBH mergers. Although we do not directly report on MBH merger rates, it is worth noting that Volonteri et al. (2020) find that MBH merger rates tend to increase among low-mass galaxies when moving to higher-resolution simulations. Lower-resolution simulations tend to miss mergers of low-mass galaxies and hence underpredict the MBH merger fraction. It is likely that moving to higher resolutions than Romulus25 would lead to differing results for the evolution of the MBH number density.

Figure 8 tracks the comoving number density of MBHs as a function of redshift. We include lines for all MBHs in well-resolved halos, "detectable" MBHs in dwarf galaxies (${L}_{{\rm{X}}}^{\mathrm{AGN}}\gt {10}^{39}$ erg s⁻¹ and ${L}_{{\rm{X}}}^{\mathrm{AGN}}\gt 2\,{L}_{{\rm{X}}}^{\mathrm{XRB}+\mathrm{Gas}}$), and hidden MBHs in dwarf galaxies (${L}_{{\rm{X}}}^{\mathrm{AGN}}\lt {10}^{39}$ erg s⁻¹ and/or ${L}_{{\rm{X}}}^{\mathrm{AGN}}\lt 2\,{L}_{{\rm{X}}}^{\mathrm{XRB}+\mathrm{Gas}}$). We also show the evolution of the AGN number density from Romulus25 alongside X-ray observations (Ueda et al. 2014; Aird et al. 2015; Buchner et al. 2015) and EAGLE (Rosas-Guevara et al. 2016) in the hard X-ray band with L_X,hard > 10⁴² erg s⁻¹.

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The total number density of MBHs decreases over time, from n_BH = 8 × 10⁻² cMpc⁻³ at z = 2 down to n_BH = 5 × 10⁻² cMpc⁻³ at z = 0.05. These number densities are within a factor of a few of estimates from Volonteri (2010), who estimate n_BH = 0.02–0.1 cMpc⁻³ at z = 0; slightly lower than those from Buchner et al. (2019), who find n_BH ≳ 0.01 cMpc⁻³ at z = 0 for their seed-independent empirical model; and in line with those from EAGLE (Rosas-Guevara et al. 2016), which finds n_BH = 7.2 × 10⁻² cMpc⁻³ at z = 0.1 with MBH seed mass M_seed = 1.48 × 10⁵ M_⊙. Among dwarf galaxies, visible and hidden MBHs are found in equal amounts at z = 2, approximately with densities 2 × 10⁻² cMpc⁻³, but at z = 0.05 hidden dwarfs are more common by a factor of 3, around 2 × 10⁻² cMpc⁻³.

AGN follow a slightly different shape and evolution than the full population of MBHs. The number densities of AGN are instead determined by the accretion history of the underlying population of MBHs. As explored in Section 3.2, AGN have decreased in both luminosity and prevalence since z = 2 within the simulation. The number of AGN above L_X,hard > 10⁴² erg s⁻¹ peaks at z = 2 around n_AGN = 1.2 × 10⁻³ cMpc⁻³. AGN are most rare at z = 0.05, at n_AGN = 4.2 × 10⁻⁴. These estimates are slightly higher than observations and EAGLE results in the same band (Ueda et al. 2014; Aird et al. 2015; Buchner et al. 2015; Rosas-Guevara et al. 2016) at z ∼ 0. This difference is likely tied to our overprediction of the AGN fraction.