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1. Superhalogens Among 3 d -Metal Compounds: M F ₄ , M F ₆ , M F ₁₂ , and M F ₁₈ ( M = Sc–Zn)

   https://doi.org/10.1021/acs.jpca.1c02884  

   Gutsev, Gennady L.; Tibbetts, Katharine M.; Gutsev, Lavrenty G.; Ramachandran, Bala R. (May 2021, The Journal of Physical Chemistry A)
2. Investigating the residuals in the M _• – M _* relation using the SIMBA cosmological simulation

   https://doi.org/10.1051/0004-6361/202555571  

   Ma, Wenlin; Cui, Weiguang; Davé, Romeel; Anglés-Alcázar, Daniel; Guo, Hong (October 2025, Astronomy & Astrophysics)

   We investigate the scaling relation between black hole (BH) and stellar mass (M_• − M_*), diagnosing the residual Δlog(M_•/M_⊙) (Δ) in this relation to understand the coevolution of galaxies and BHs in the cosmological hydrodynamic simulation SIMBA. We show that SIMBAreproduces the observedM_• − M_*relation well, with little difference between central and satellite galaxies. By using the median value to determine the residuals, we find that the residual correlates with galaxy cold gas content, star formation rate, colour, and BH accretion properties. Both torque and Bondi models implemented in SIMBAcontribute to this residual, with torque accretion playing a major role in high-redshift and low-mass galaxies, while Bondi (including BH mergers) dominates at low redshift and massive galaxies. By dividing the sample into two populations (Δ > 0 and Δ < 0), we compare their evolutionary paths by following the main progenitors. From this evolutionary tracking, we propose a simple picture for BH-galaxy coevolution: early-formed galaxies seed BHs earlier, with stellar mass increasing rapidly to reach the point of triggering ‘jet mode’ feedback. This process reduces the cold gas content and halts the growth ofM_*, effectively quenching galaxies. Meanwhile, during the initial phase of torque accretion growth, the BH mass is comparable between galaxies formed early and those formed later. However, galaxies that formed earlier appear to attain a marginally greater BH mass when transitioning to Bondi accretion, aligning with the galaxy transition time. As the early-formed galaxies reach this point earlier – leaving a longer period for Bondi accretion and mergers – their residuals become positive, i.e. having more massive BHs atz = 0 compared to these late-formed galaxies at the sameM_*. This picture is further supported by the strong positive correlation between the residuals and the galaxy age, which we propose as a validation with observation data of the scenario suggested by SIMBA. 

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3. Inferring M _BH – M _bulge Evolution from the Gravitational-wave Background

   https://doi.org/10.3847/1538-4357/ae2480  

   Matt, Cayenne; Gültekin, Kayhan; Kelley, Luke Zoltan; Blecha, Laura; Simon, Joseph; Agazie, Gabriella; Anumarlapudi, Akash; Archibald, Anne M; Arzoumanian, Zaven; Baier, Jeremy G; et al (January 2026, The Astrophysical Journal)

   Abstract We test the impact of an evolving supermassive black hole mass scaling relation (M_BH–M_bulge) on the predictions for the gravitational-wave background (GWB). The observed GWB amplitude is 2–3 times higher than predicted by astrophysically informed models, which suggests the need to revise the assumptions in those models. We compare a semi-analytic model’s ability to reproduce the observed GWB spectrum with a static versus evolving-amplitudeM_BH–M_bulgerelation. We additionally consider the influence of the choice of galaxy stellar mass function (GSMF) on the modeled GWB spectra. Our models are able to reproduce the GWB amplitude with either a large number density of massive galaxies or a positively evolvingM_BH–M_bulgeamplitude (i.e., theM_BH/M_bulgeratio was higher in the past). If we assume that theM_BH–M_bulgeamplitude does not evolve, our models require a GSMF that implies an undetected population of massive galaxies (M_⋆≥ 10¹¹M_⊙atz> 1). When theM_BH–M_bulgeamplitude is allowed to evolve, we can model the GWB spectrum with all fiducial values and anM_BH–M_bulgeamplitude that evolves asα(z) =α₀(1 +z)^1.04±0.5. 

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4. VOA[ M ₄ ]

   https://doi.org/10.1063/1.5100059  

   Feigin, Boris; Gukov, Sergei (January 2020, Journal of Mathematical Physics)
5. Gravitational-wave Measurement of the M _BH – M _bulge Intrinsic Scatter at High Redshift

   https://doi.org/10.3847/1538-4357/ae801e  

   Matt, Cayenne; Gültekin, Kayhan; Agazie, Gabriella; Agarwal, Nikita; Anumarlapudi, Akash; Archibald, Anne M; Arzoumanian, Zaven; Baier, Jeremy G; Baker, Paul T; Bécsy, Bence; et al (July 2026, The Astrophysical Journal)

   Abstract The observed gravitational-wave background (GWB) spectrum is higher in amplitude than model predictions by a factor of 2–3. Using a semi-analytic model, we evaluate the effect of a high-scatter supermassive black hole (SMBH) scaling relation (M_BH–M_bulge) on models of the nanohertz GWB. By implementing an intrinsic scatter of theM_BH–M_bulgerelation, which is larger at higher redshift, but matches local observations, we find that the amplitude of GWB models increases to be consistent with the low-frequency end of the GWB spectrum. This amplitude increase is not uniform across frequencies, a strongly evolving scatter preferentially increases the number density of the most massive SMBHs which, in the GWB spectrum, minimizes the strength of the low-frequency turnover. Our models with positively evolving intrinsic scatter can reproduce the electromagnetically observed overmassive SMBHs at 4 < z < 6 without changing theM_BH–M_bulgenormalization though we find that including moderate normalization evolution marginally improves fits to the GWB data. We conclude that theM_BH–M_bulgerelation which best describes the available GWB and electromagnetic data sets has intrinsic scatter that evolves as $\epsilon \left(z\right)={\epsilon }_0+(0.56\pm 0.4){\log }_{10}(1+z)$ and normalization that evolves asα(z) = α₀(1 + z)^0.84±0.35. The results of this work imply that theM_BH–M_bulgerelation we see today is not universal throughout cosmic time and that a diversity of seeding models and growth mechanisms may be at play in the early stages of SMBH–galaxy evolution. 

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