Authors: Seungjae Lee, Hyung Mok Lee, Ji-Hoon Kim, Rainer Spurzem, Jongsuk Hong, Eunwoo Chung
First Author’s Institution: Center for Theoretical Physics, Department of Physics and Astronomy, Seoul National University
Status: Available on ArXiv
A delicate dance goes on in astronomy between theory and observation. Most astronomy research, by and large, fits into one of two categories. In one category, you start with a theory, model, or simulation, and attempt to figure out what observations you might expect given those initial assumptions. The other approach begins with raw data and attempts to determine what kinds of theories, models, and fundamental astrophysical assumptions might give rise to it. Accepted knowledge usually happens when these two approaches agree and reinforce each other, but a lot of the actual science occurs when one side dances ahead of the other – either we have theories and models that make predictions that cannot yet be observationally tested, or we have data that defies attempts at fitting underlying models.
Another dynamical dance goes on in globular clusters between binary black holes. Today’s paper investigates IMBHs, or intermediate mass black holes, a pristine example of an astronomical topic in which theory has danced ahead of observations. IMBHs fill the gap between stellar mass and supermassive black holes. We can observe black holes in multiple ways, usually from the electromagnetic radiation of the gas disks surrounding some black holes (either stellar or supermassive), or the gravitational waves of two orbiting merging black holes. Unfortunately, each method requires some extra component – either gas to accrete or a companion to orbit – and IMBHs are far more challenging to observe through these methods. Hence, we have a lot of ideas about how they might form, and scarce observational evidence for their existence.
That hasn’t stopped many researchers from trying to make better models and predictions. One of the most commonly proposed mechanisms for forming IMBH’s is in dense globular or nuclear star clusters (up to a million times denser than our region of the Milky Way). In these dense environments, stars and the black holes they produce might have a chance to find and run into each other often enough to reach the masses of the IMBH regime through mergers. Today’s authors use a series of n-body simulations to study these dense stellar clusters, into which they embed IMBHs. Their study investigates the gravitational waves’ detectability from IMRIs, or intermediate-mass ratio inspirals. Because so many mergers occur in dense clusters, it allows for more mergers between objects with greater mass differences. The mass ratio between the two objects (usually denoted as ‘q’) is one of the most important parameters for characterizing a merger, and a high q value creates a gravitational wave signature that is different from a low q, even if the total mass of the system is the same.
To investigate the formation and detectability of IMRIs, the authors conducted a suite of direct N-body simulations of star clusters with total masses between 5×10⁴ and 10⁵ solar masses, containing ~10⁵ particles. They include initial conditions for how densely the particles should be separated, given how far they are from the cluster’s center (called a Plummer profile). They also include a rule for how the initial masses of the stars are distributed (called a Kroupa IMF). Then, they use a code called SEVN (Stellar EVolution for N-body) to follow the evolution of the stars in the system for one hundred million years.
In that time, massive stars in the simulation can evolve into neutron stars and stellar mass black holes. In addition to simulating the clusters, the authors embed an IMBH of 300–5000 solar masses into the clusters. The key to this paper is that some of the stellar mass binary black holes will interact with the intermediate mass black hole, creating an IMRI, which gives off gravitational waves. This paper’s primary goal is to characterize these IMRIs and to test how well current and future gravitational wave detectors will measure them.
In the simulation, when a stellar mass binary black hole and an IMBH come close, the authors must create a “merger criteria” – essentially, how it is decided whether the two objects merge, and what the subsequent “gravitational wave” would look like. Once they model the wave itself, they turn to five current or future detectors to see how well they will measure those waves if they were at particular astronomical distances from Earth.
One of the primary relationships the authors look at in the cluster is the half-mass radius velocity dispersion of the cluster and the number of IMRI encounters between the IMBH and stellar mass objects. One can think of the velocity dispersion as a more complicated “average velocity” of the stars in the cluster (a high velocity dispersion means, on average, the stars are moving faster, the half mass radius is the distance from center that separates the inner half of the stars and outer half of the stars, and we use it because it is more representative of stellar motion in the overall cluster than the packed center or the mellow edge). Figure 1 shows the relationship between the number of IMRI events (y-axis) vs. the velocity dispersion (x-axis) of the cluster where the IMBH sits. Note that the y-axis is in log-space, so a small increase in velocity dispersion actually results in a large increase in the number of IMRIs. This tells us that the number of events is much more highly dependent on the properties of the larger cluster than the IMBH itself.
Figure 1: IMRI event rate as a function of cluster half-mass velocity dispersion (σ_hm) for 1000 solar mass IMBHs in the simulations. The IMRI merger rate is highly sensitive to the velocity dispersion of the cluster as a whole, making it a key observable of how efficiently IMRIs can form and merge in a given cluster. Figure 11 in the paper.
In addition to analyzing the dynamics of the clusters and the mergers within them, the authors go further and attempt to characterize what specific detectors will see. They chose five detectors. The first is aLIGO (advanced LIGO), the current incarnation of the LIGO detector network. Next is ET (Einstein Telescope), a future proposed European ground-based detector. Following that is LISA (the Laser Interferometer Space Antenna), a future space-based detector set to launch in the 2030’s designed to observe supermassive black hole mergers. Next are two detectors that are less established, aSOGRO, and DECIGO. aSOGRO (advanced Superconducting Omni-directional Gravitational Radiation Observatory) is a proposed Earth-based detector that could theoretically measure gravitational waves in lower frequencies than the current LIGO-Virgo-KAGRA (LVK) detectors, and DECIGO (the Deci-hertz Interferometer Gravitational Wave Observatory) is a proposed space-based detector designed to observe gravitational waves in the frequencies between the LVK network and LISA.
How do the authors translate the gravitational wave signal from the IMRI into what might be observed on Earth? First, they must pick an SNR threshold, which is the ratio of the gravitational wave signal to the background noise in the detector. In this case, they chose an SNR of 8, a commonly chosen threshold in the gravitational wave literature. From the SNR, the authors can calculate a horizon distance. The horizon distance is the distance that a detector can measure a specific gravitational wave event with a given set of properties at or above the SNR threshold chosen. Figure 2 shows the horizon distances (y-axis) for each detector for sets of gravitational wave sources with different properties vs. the mass of the IMBH generating the gravitational wave (x-axis). The solid vs. dotted lines represent two chosen masses of the IMBH’s stellar mass companion. The figures show that aLIGO (blue and blue-dotted circle) can detect only low-mass IMBHs (≲ 300 solar masses) at z ≲ 0.05. ET (red and red-dotted triangles) is sensitive to lower-mass IMBHs, LISA excels at higher mass IMBHs. aSORGO (purple and purple-dotted triangles) covers a broad mass range but at lower redshifts. DECIGO (yellow and yellow dotted ‘x’s) offers the broadest mass range at the highest redshift.
Figure 2 – Horizon redshift vs IMBH mass for several GW observatories (aLIGo represented by blue circles, ET by red triangles, LISA by green diamonds, aSOGRO by purple triangles, and DECIGO by yellow ‘x’s). Solid vs dotted lines represent the mass of the stellar mass black hole interacting with the IMBH, with the dashed line representing a 10 solar mass companion and the solid lines representing a 60 solar mass companion. Figure 15 in the paper.
Today’s authors offer a glimpse into globular clusters as dynamic environments where we might see IMRIs. They also predict how those signals might be received by our current, future, and proposed gravitational wave detectors. As next-generation observatories prepare to listen for these cosmic mergers, this work helps chart a path for where and how we might first detect the elusive intermediate-mass black hole.
Edited by: Kasper Zoellner
Image Credit: NASA
