I am pleased to announce that Cayenne Matt’s latest paper—Inferring MBH​–Mbulge​ Evolution from the Gravitational-Wave Background—has been officially published in The Astrophysical Journal. This work addresses a major question in modern multi-messenger astronomy: why is the observed gravitational-wave background (GWB) amplitude significantly higher than standard astrophysical models predict?

By comparing semi-analytic models with the observed GWB spectrum, Cayenne’s results suggest that to reproduce the GWB amplitude seen by pulsar timing arrays, one must either assume a significantly higher number density of massive galaxies at high redshift than previously thought, or allow for a positively evolving MBH​–Mbulge​ relation. Specifically, the study finds evidence that the MBH​/Mbulge​ ratio may have been higher in the past, evolving as  α(z) = α0​(1+z)1.04±0.5.

A scientific line plot showing the posterior probability density for the parameter alpha-z, which represents the redshift evolution of the black hole-bulge mass relation. Four colored curves (red, blue, gold, and green) represent different model configurations. Most models show a peak in probability at positive values between 0.5 and 1.5, indicating that the ratio of black hole mass to bulge mass was likely higher in the early universe. Horizontal error bars indicate 68 percent confidence regions, and a gray dashed line represents the uniform prior.
This plot displays the posterior distributions for αz​ across the various models tested in the paper. The distributions fall into two categories based on how the Galaxy Stellar Mass Function (GSMF) parameters were handled. Models with fewer degrees of freedom converged to higher values of αz​ with higher confidence, providing strong evidence for a positive evolution in the MBH​–Mbulge​ amplitude.

Full Citation: Matt, C. et al. 2026, ApJ, 997, 188. 
DOI:10.3847/1538-4357/ae2480
NASA ADS:2026ApJ…997..188M

A professional headshot of CJ Harris, a person with dark curly hair and glasses, wearing a grey button-down shirt and smiling in front of a bright blue background.
CJ Harris, astrophysicist

I am thrilled to highlight the exceptional work of CJ Harris, who has just submitted a significant new paper to AAS Journals. CJ is currently a PhD candidate at the University of Michigan and is officially on the postdoc market (see their CV). Their latest research provides a critical analysis of how stellar scattering is likely to be insufficient on its own to explain how supermassive black hole binaries harden.

Breaking the “Final Parsec” Bottleneck

Although we are now reasonably certain that supermassive black holes form binaries that harden sufficiently to coalesce through gravitational wave emission, the exact solution to the “Final Parsec Problem” is unknown to us, if not to nature.

In their new paper, “Core Scouring Dynamics and Gravitational Wave Consequences: Constraints on Supermassive Black Hole Binary Hardening,” CJ and collaborators (Laura Blecha and I) use a multi-messenger approach to tackle this. By making use of merger trees from the IllustrisTNG cosmological simulations with physically motivated models of core scouring, they were able to see how efficient stellar scattering is in hardening binaries. They were able to reproduce the relationship between mass deficit and galaxy total stellar mass, but only if scattering is more efficient than previously expected. But they were not able to reproduce the nanohertz gravitational wave background with the same efficiency. Meaning that there must be some other source of hardening, most likely gas hardening. If gas hardening plays a dominant role, then we can be far more optimistic about finding binary AGN.

Scientific scatter plot on logarithmic scales. The x-axis represents galaxy log stellar mass ranging from 10 to 13.5 in solar units. The y-axis represents log stellar mass deficit ranging from 6 to 11 in solar units. The plot features numerous colored data points with error bars: green diamonds (Brightest Cluster Galaxies), blue circles (Ellipticals), purple triangles (Lenticulars), a maroon square (Early Type Spirals), and a single yellow circle highlighting M87. These observational points sit atop a underlying density of small black dots and gray contour lines labeled 'TNG Cores,' showing that the simulated merger models closely track the observed trend of increasing mass deficit with increasing galaxy mass.
The figure shows stellar mass deficit as a function of stellar mass for both the observed set of core galaxies and a sample generated using our core scouring model with Ĥ = 1.64. Synthetic data-points are shown in black with the corresponding KDE and are in agreement with the observed data. We reproduce the slope and amplitude of the mass deficit–stellar mass relation, and recover some of the flattening seen in the BCG population at the high mass end. (Fig. 7 from Harris et al. 2026)

Key takeaways from the work:

A double-logarithmic line plot showing gravitational wave strain versus frequency. Three colored curves with shaded confidence intervals are compared against vertical gray violin plots of observational data. The curves show varying degrees of "turnover" at lower frequencies.
Shown on the y-axis is the characteristic strain amplitude of the GWB, with frequency in Hz on the x-axis. The gray violins show the GW spectrum derived from the NANOGrav HD-w/MP+DP+CURN models (G. Agazie et al. 2023a; W. G. Lamb et al. 2023). The colored curves are GW spectra resulting from SBHB populations generated by the holodeck semi-analytic modeling submodule (SAMs) over 1000 realizations. Shown in green is the spectrum expected if the hardening mechanism that drove all binaries to coalescence was GW emission alone. The orange spectrum is the G. Agazie et al. (2023b) fit to the GWB data. The pink hybrid model is comprised of the phenomenological model where the parameters in equation (24) are set by the results of our model. Shaded regions indicate the 68% confidence intervals. The phenomenological and hybrid models are in agreement in the high frequency regime, but diverge at low frequencies. The discrepancy implies that the attenuation of the GWB at low frequencies is not caused by energy being transferred into the environment through loss-cone scattering alone. Because the attenuation occurs at such low binary separations the effect is most likely caused by gas dynamics.

The “Bright” Side: This strongly suggests that gas dynamics must play a dominant role in bringing these giants together—providing a reason to be optimistic about finding electromagnetically visible binary AGN.

Community Leadership & Presence

Beyond the data, CJ continues to be a leader in the broader physics community. This past November, they presented these findings at the National Society of Black Physicists (NSBP) 2025 Annual Meeting. Their talk, “Multimessenger Constraints on the Supermassive Black Hole Binary Hardening Timescale,” was a deep dive into these results and showcased their ability to bridge complex theory with observational reality.

I am thrilled to announce that CJ Harris has been voted in as a full member of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). As a dedicated and innovative researcher in our astronomy and astrophysics program, CJ has significantly contributed to advancing our understanding of binary supermassive black holes through a multimessenger approach. Their hard work and collaborative spirit have not gone unnoticed, and this membership is a testament to their commitment and potential within the gravitational wave science community. Congratulations, CJ, on this well-deserved achievement!

This week has been NANOGrav week at U-M! We are hosted the NANOGrav 2024 Fall Collaboration Meeting at Palmer Commons. This week’s Astronomy Colloquium will be given by Joe Simon (U. Colorado) talking about the astrophysics of gravitational wave background. Monday’s High Energy / Astrophysics Seminar in the Physics Department was given by Jeff Hazboun (Oregon St. U.) talking about pulsar timing array detector characterization and optimization.

Over the weekend there was a student workshop. The meeting proper saw roughly 90 people in-person coming through Ann Arbor and many talks. In particular, Cayenne Matt gave a talk titled “Insights into SMBH-Galaxy Co-Evolution From the GravitationalWave Background” and CJ Harris gave a talk titled “Echoes from the Core: Constraints on the Supermassive Black Hole BinaryPopulation from Core Galaxy Properties”.

Illustration of pulsar with text reading "NANOGrav Physics Frontiers Center" at the top and "2024 Fall Meeting Ann Arbor, Michigan" at the bottom

A huge congratulations to former undergraduate group member Dr. Erica Hammerstein, who successfully defended her dissertation, titled “Population Studies of Tidal Disruption Events and Their Hosts: Understanding Host Galaxy Preferences and the Origin of the Ultraviolet and Optical Emission”.

screenshot of zoom presentation of dissertation defense. Left-hand panel shows powerpoint slide with amazing M-sigma plot. Right-hand panel shows room where defense is happening.
Erica Hammerstein defends her dissertation with a great M–σ figure.

The NANOGrav results keep on coming out! The following papers were officially published in the past few weeks.

I forgot to mention that I am now a full NANOGrav member! (As of several months ago now.)

I am very excited to to say that the first NANOGrav paper I am on is out, and it’s a great one! It was led by Caitlin Witt and concerns the search for continuous wave (individually resolved long-lived) gravitational wave sources in the 12.5-year data.

Key figures:

Aitoff projection of the whole sky with colorscale showing upper limit to gravitational wave sources between 0.3e-14 and 1.0e-14. Stars show positions of pulsars clustered to one hemisphere.
Sky map of 12.5-year NANOGrav dataset upper limits to continuous wave sources. Map of CW strain 95% upper limits at f_GW = 7.65 × 10^{−9} Hz, the most sensitive frequency searched, for the 12.5-year data set. Pulsar locations are shown as white stars, with new pulsars added from the 12.5-year data set outlined in red. The most sensitive pixel is marked with a red dot, and is located at an RA of 19h07m30s and a Dec of −30◦00′00′′. In this region, where the our best-timed pulsars lie, our upper limits are nearly an order of magnitude more sensitive than the least sensitive pixel.
Plot of Gravitational wave strain upper limit as a function of frequency. The limit gets as low as 8e-15 at 7e-9 Hz.
All-sky CW strain 95% upper limits and associated error regions, with (red) and without (purple) a CRN included in the model. At low frequencies, modeling the CRN is necessary to avoid over-estimating our strain upper limits. We are the least sensitive to CWs at fGW =1/(1 year) due to the Earth’s orbit, creating the large feature seen in this and other figures.