A Bayesian Hurdle Model Approach to the Relationship Between Supermassive Black Hole Mass and Host Galaxy Stellar Velocity Dispersion

Core Concepts

This research introduces a novel Bayesian hurdle model to analyze the relationship between supermassive black hole mass and host galaxy stellar velocity dispersion, revealing a steeper relation than previously found and predicting populations of under-massive and over-massive black holes.

Abstract

• Bibliographic Information: Sasseville, G., Hlavacek-Larrondo, J., Berek, S. C., Eadie, G. M., Rhea, C. L., Springford, A., ... & Haggard, D. (2024). A novel approach to understanding the link between supermassive black holes and host galaxies. arXiv preprint arXiv:2411.07242.

• Research Objective: This study aims to re-evaluate the relationship between supermassive black hole (BH) mass (M•) and host galaxy stellar velocity dispersion (σ) using a novel Bayesian hurdle model, addressing limitations of previous studies in handling upper limits and potential absence of BHs in some galaxies.

• Methodology: The authors utilize a Bayesian hurdle model, combining logistic regression to model the probability of a galaxy hosting a BH and linear regression to model the M• − σ relation for galaxies containing BHs. The model incorporates uncertainties in BH mass measurements and distinguishes between precise measurements and upper limits, employing a mixture model for the latter. The analysis is based on a dataset of 244 galaxies with dynamically measured or temporally resolved BH masses.

• Key Findings:

  • The hurdle model reveals a steeper M• − σ relation (M• ∝ σ^5.8) compared to previous studies.
  • Galaxies with velocity dispersions greater than 11 km/s, 34 km/s, and 126 km/s show 50%, 90%, and 99% probabilities of hosting a BH, respectively.
  • The model predicts populations of under-massive BHs (M• = 10 − 10^5 M⊙) in galaxies with σ ≲ 127 km/s and over-massive BHs (M• ≥ 1.8 × 10^7 M⊙) above this threshold.

• Main Conclusions: The steeper M• − σ relation suggests a stronger link between BH growth and host galaxy evolution than previously thought. The predicted populations of under-massive and over-massive BHs challenge existing assumptions and provide targets for future observations with telescopes like the Extremely Large Telescope.

• Significance: This research advances our understanding of the co-evolution of BHs and their host galaxies, particularly in the low-mass regime. The findings have implications for models of BH feedback and galaxy formation.

• Limitations and Future Research: The study acknowledges limitations due to selection effects inherent in the dataset. Future research incorporating selection effects and expanding the dataset with observations from next-generation telescopes will further refine the M• − σ relation and its implications.

Stats

The study uses a sample of 244 galaxies.
14 out of 24 BHs with masses ≤ 10^6 M⊙ are upper limits.
Zero upper limits comprise ~2% (5/244) of the sample.
Nonzero upper limits represent ~18% (44/244) of the dataset.
Precise measurements constitute ~80% (195/244) of the sample.
The 50%, 90%, and 99% probability of hosting a central BH is attained at σ values greater than 11 km/s, 34 km/s, and 126 km/s, respectively.

Quotes

"Although the scatter in the M•−σ relation is low (0.40 dex) for high-mass BHs with M• ≥ 10^6 M⊙, it does not succeed in fitting the data at the low-mass end, where it rather follows M• ∝ σ^3.32 (e.g. Xiao et al. 2011)."
"Here, we introduce a novel approach using a Bayesian hurdle model to analyze the M• − σ relation across 244 galaxies."
"Our model also predicts a population of under-massive black holes (M• = 10 − 10^5 M⊙) in galaxies with σ ≲ 127 km/s and over-massive black holes (M• ≥ 1.8 × 10^7) above this threshold."

Key Insights Distilled From

A novel approach to understanding the link between supermassive black holes and host galaxies

by Gabriel Sass... at arxiv.org 11-12-2024

https://arxiv.org/pdf/2411.07242.pdf

Deeper Inquiries

How might future observations with next-generation telescopes like the James Webb Space Telescope contribute to refining the M• − σ relation and our understanding of BH-galaxy co-evolution?

Next-generation telescopes like the James Webb Space Telescope (JWST), with its unprecedented sensitivity and resolution, are poised to revolutionize our understanding of the M• − σ relation and BH-galaxy co-evolution in several ways:

Probing the Low-Mass End: JWST's infrared capabilities will be crucial in observing the faint signatures of low-mass black holes (BHs) in dwarf galaxies, which are often obscured by dust in optical wavelengths. This will allow for more accurate measurements of BH masses and velocity dispersions in these low-mass systems, providing crucial data points to constrain the faint end of the M• − σ relation. This will help determine if the relation continues to hold in this regime or deviates, offering insights into the processes governing BH growth in dwarf galaxies.

Characterizing High-Redshift Galaxies: JWST can observe galaxies at high redshifts, providing a glimpse into the early Universe when BHs and galaxies were still forming and evolving. By studying the M• − σ relation at these early epochs, we can gain insights into the co-evolution of BHs and galaxies over cosmic time. This will help determine if the relation has evolved significantly since the early Universe and shed light on the mechanisms that drive this evolution.

Resolving Stellar Kinematics: JWST's high resolution will enable us to resolve stellar kinematics in greater detail, even in distant galaxies. This will lead to more precise measurements of stellar velocity dispersions, reducing uncertainties in the M• − σ relation. Improved measurements will help disentangle the intrinsic scatter in the relation from observational uncertainties, revealing a clearer picture of the underlying physics.

Studying Gas Dynamics: JWST can study the gas dynamics in and around galaxies, providing insights into the processes of gas accretion onto BHs and the impact of BH feedback on the host galaxy. This will help us understand how BHs influence the growth and evolution of their host galaxies and vice versa.

Detecting Obscured BHs: JWST's infrared sensitivity will allow us to peer through dust and gas, revealing previously hidden BHs. This is particularly important for studying active galactic nuclei (AGN), where the central BH is obscured by a torus of dust. By studying obscured BHs, we can obtain a more complete census of BHs in the Universe and refine our understanding of the M• − σ relation.

By combining these capabilities, JWST will provide invaluable data to refine the M• − σ relation, test theoretical models of BH-galaxy co-evolution, and advance our understanding of the intricate relationship between these fascinating objects.

Could alternative mechanisms beyond BH feedback, such as galaxy mergers or interactions, play a significant role in shaping the observed M• − σ relation, particularly in the low-mass regime?

While BH feedback is widely considered a key player in shaping the M• − σ relation, alternative mechanisms, particularly galaxy mergers and interactions, could also play a significant role, especially in the low-mass regime:

Galaxy Mergers: When galaxies merge, their central BHs sink to the center of the newly formed galaxy and eventually coalesce. This process can significantly influence the final BH mass and the stellar velocity dispersion of the merger remnant. Major mergers, where galaxies of comparable mass merge, can lead to a rapid increase in both BH mass and velocity dispersion, potentially scattering galaxies off the M• − σ relation. Minor mergers, involving a larger galaxy and a smaller satellite, can also affect the relation, potentially increasing the scatter at the low-mass end.

Galaxy Interactions: Even without merging, gravitational interactions between galaxies can perturb their gas and stellar distributions. These perturbations can trigger gas inflows towards the central regions, fueling BH growth and potentially leading to an increase in velocity dispersion. In the low-mass regime, where galaxies are more susceptible to tidal forces, interactions could play a more prominent role in shaping the M• − σ relation.

Secular Processes: Internal processes within galaxies, such as bar instabilities or spiral arm formation, can also drive gas inflows towards the center, fueling BH growth and potentially affecting the velocity dispersion. While these processes might not be as dramatic as mergers or interactions, they could contribute to the scatter in the M• − σ relation, particularly in the low-mass regime where BHs are less massive and their feedback might be less efficient.

Combined Effects: It's important to note that these mechanisms are not mutually exclusive and likely operate in conjunction with BH feedback. Disentangling their individual contributions to the observed M• − σ relation is a complex task that requires sophisticated simulations and detailed observations.

In the low-mass regime, where BH feedback might be less efficient, alternative mechanisms like mergers, interactions, and secular processes could play a more dominant role in shaping the M• − σ relation. Future observations and simulations will be crucial in quantifying their relative importance and understanding their interplay with BH feedback in driving the co-evolution of BHs and galaxies.

If the predicted populations of under-massive and over-massive BHs are confirmed, what implications might this have for our understanding of the formation and growth of the very first BHs in the early Universe?

The confirmation of under-massive and over-massive BH populations, deviating from the established M• − σ relation, would have profound implications for our understanding of BH formation and growth in the early Universe:

Diverse Formation Channels: The existence of under-massive BHs could suggest alternative formation pathways besides the direct collapse of massive gas clouds, which is thought to produce more massive seeds. These alternative channels might involve the mergers of smaller seed BHs or the growth of stellar-mass BHs through accretion. This would imply a more complex and diverse picture of early BH formation than previously thought.

Early Growth Mechanisms: Over-massive BHs, on the other hand, would challenge our understanding of BH growth limitations. Their presence could indicate that BHs in the early Universe could grow more efficiently than predicted by standard accretion models. This might point towards super-Eddington accretion, where BHs accrete matter at rates exceeding the Eddington limit, or mergers with other BHs as significant contributors to their early growth.

Impact on Early Galaxy Evolution: The presence of under-massive or over-massive BHs would also affect our understanding of early galaxy evolution. Under-massive BHs might have had a reduced impact on their host galaxies, while over-massive BHs could have exerted stronger feedback, potentially influencing star formation and galaxy morphology in the early Universe.

Constraints on Cosmological Models: The properties of these outlier BH populations could provide valuable constraints on cosmological models, particularly those describing the conditions in the early Universe. For instance, the abundance of under-massive BHs could constrain the nature of dark matter or the properties of the first stars, while the existence of over-massive BHs could test models of early structure formation.

Revised Co-evolution Paradigm: The confirmation of these populations would necessitate a revision of our current paradigm of BH-galaxy co-evolution. It would suggest that the relationship between BHs and their host galaxies in the early Universe was more complex and less tightly regulated than previously thought.

The discovery of under-massive and over-massive BHs would open up new avenues of research, prompting us to re-evaluate our understanding of BH formation, growth, and their role in shaping the early Universe. It would highlight the need for more sophisticated models and observations to unravel the complexities of BH-galaxy co-evolution across cosmic time.