Central Massive Black Holes Are Not Ubiquitous in Local Low-Mass Galaxies

TL;DR

This study robustly constrains how often local galaxies host central massive black holes and how these MBHs accrete at low rates. By analyzing ~1,600 galaxies within 50 Mpc with Chandra X-ray data through a flexible Bayesian framework, the authors jointly infer the MBH occupation fraction $f_\text{occ}(M_\star)$ and the specific accretion-rate distribution $p(\lambda)$, finding a peak near $\log\lambda\approx 28$ and a mass-independent shape, while $f_\text{occ}$ declines sharply for lower stellar masses, reaching ~33% in the dwarf regime. They show that a Box-Cox form for $p(\lambda)$ provides a better fit than normal or simple power-law models and demonstrate consistency with a plateau in the low-$\lambda$ regime. These results imply a high occupation fraction in massive galaxies but significantly fewer MBHs in dwarfs, with important consequences for the local MBH mass function and the seeding scenarios in galaxy evolution.

Abstract

The black-hole occupation fraction ($f_\mathrm{occ}$) defines the fraction of galaxies that harbor central massive black holes (MBHs), irrespective of their accretion activity level. While it is widely accepted that $f_\mathrm{occ}$ is nearly 100% in local massive galaxies with stellar masses $M_\star \gtrsim 10^{10}~M_\odot$, it is not yet clear whether MBHs are ubiquitous in less-massive galaxies. In this work, we present new constraints on $f_\mathrm{occ}$ based on over 20 years of Chandra imaging data for 1606 galaxies within 50 Mpc. We employ a Bayesian model to simultaneously constrain $f_\mathrm{occ}$ and the specific accretion-rate distribution function, $p(λ)$, where the specific accretion rate is defined as $λ=L_\mathrm{X}/M_\star$, and $L_\mathrm{X}$ is the MBH accretion luminosity in the 2-10 keV range. Notably, we find that $p(λ)$ peaks around $10^{28}~\mathrm{erg~s^{-1}}~M_\odot^{-1}$; above this value, $p(λ)$ decreases with increasing $λ$, following a power-law that smoothly connects with the probability distribution of bona-fide active galactic nuclei. We also find that the occupation fraction decreases dramatically with decreasing $M_\star$: in high mass galaxies ($M_\star \approx 10^{11-12}M_\odot$), the occupation fraction is $>93\%$ (a $2σ$ lower limit), and then declines to $66_{-7}^{+8}\%$ ($1σ$ errors) between $M_\star\approx10^{9-10}M_\odot$, and to $33_{-9}^{+13}\%$ in the dwarf galaxy regime between $M_\star\approx10^{8-9}~M_\odot$. Our results have significant implications for the normalization of the MBH mass function over the mass range most relevant for tidal disruption events, extreme mass ratio inspirals, and MBH merger rates that upcoming facilities are poised to explore.

Figures (12)

• Figure 1: $M_\star$ vs. distance for the target sample of 1,606 galaxies. Blue and orange points represent X-ray-detected and undetected galaxies, respectively. There are points visually "piling up" at a distance of 16.5 Mpc because they are from the Virgo Cluster (see Section 3.3 in Ohlson24).
• Figure 2: Nuclear X-ray luminosity vs. $M_\star$. Blue points represent sources with compact X-ray nuclei, with increased color transparency reflecting an increasing likelihood of XRB contamination to the signal. Most of the blue points are not transparent because most sources have low $P_\mathrm{XRB}$. Downward orange triangles represent upper limits, which include both non detections as well as (few) extended sources. The solid red and violet lines are nonparametric, Akritas-Theil-Sen (ATS) regression lines for massive galaxies (with $M_\star>10^{10}~M_\odot$) and all the galaxies, respectively. The solid black line represents the best-fit $\log L_\mathrm{X}=\log M_\star+\log\lambda=\log M_\star+\alpha+\beta(\log M_\star-10)$ relation (Equation \ref{['eq: mu']}). The shaded region, dashed lines, and dotted lines represent the $1\sigma$, $2\sigma$, and $3\sigma$ uncertainties, respectively.
• Figure 3: Visual illustration of the chosen parameterization for $f_\mathrm{occ}$ (left; Equation \ref{['eq: focc']}) and $p(\lambda)$ (right; Equation \ref{['eq: plambda']}). Left: In this plot, $\log M_0=9.5$. The black horizontal line represents the limiting $f_\mathrm{occ}$ as $\delta \to 0$ for any $\theta$. The other black curves correspond to $\delta \to +\infty$ at different $\theta$ values, reaching $f_\mathrm{occ}=1$ at $\log M_\star=\log M_0$. The colored curves show how $f_\mathrm{occ}$ evolves with $\delta$ when $\theta=1$. As $\delta$ increases, the curve becomes less flat and approaches the corresponding limiting black curve for $\theta=1$. Right: The plot illustrates $p(\lambda)$ for different $(\mu, \sigma, \xi)$ values, as indicated in the legend. When $\xi=1$, $p(\lambda)$ is a normal distribution, shown by the black curve. The blue and orange curves have different $\xi$ values, resulting in heavier tails: on the left when $\xi>1$ and on the right when $\xi<1$. The green curve, compared to the orange curve, demonstrates that $\sigma$ controls the width of $p(\lambda)$. The red curve shows that our $p(\lambda)$ can mimic a power-law distribution over the plotted $\log\lambda$ range when both $\mu$ and $\xi$ are small.
• Figure 4: Example comparison among the likelihood ignoring measurement uncertainties (blue), the likelihood accurately accounting for measurement uncertainties (red), and our adopted approximation (black). All likelihoods are normalized to a maximum value of one. Here, $\beta$ is varied while all other parameters are fixed at their median posterior values. The near-complete overlap of the black and red curves indicates that our adopted likelihood closely approximates the fully accurate likelihood.
• Figure 5: Sampling results. Contours represent 68% and 95% levels; grayscale pixels represent probabilities, and the rasterized points outside the 95% contours are individual sampling points. The first three parameters, $(\log M_0, \delta, \theta)$, represent the dependence of $f_\mathrm{occ}$ on $M_\star$ (Equation \ref{['eq: focc']}), as illustrated in the left panel of Figure \ref{['fig: illustration']}. $\alpha$ represents the typical $\log\lambda$ of galaxies with $M_\star=10^{10}~M_\odot$, and $\beta$ is the slope of the mass dependence of the sARDF (Equation \ref{['eq: mu']}). $\xi$ and $\sigma$ control the shape of $p(\lambda)$ (Equation \ref{['eq: plambda']}), as shown in the right panel of Figure \ref{['fig: illustration']}. The fitted $\beta$ is consistent with zero, indicating that $p(\lambda)$ has little dependence on $M_\star$. The fitted $\xi$ is $\ll1$, suggesting that $p(\lambda)$ is highly right-skewed compared to normal distributions.