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We investigate the detectability of subdominant spin effects in merging black-hole binaries using current gravitational-wave data. Using a phenomenological model that separates the spin dynamics into precession (azimuthal motion) and nutation (polar motion), we present constraints on the resulting amplitudes and frequencies. We also explore current constraints on the spin morphologies, indicating if binaries are trapped near spin-orbit resonances. We dissect such weak effects from the signals using a sequential prior conditioning approach, where parameters are progressively re-sampled from their posterior distribution. This allows us to investigate whether the data contain additional information beyond what is already provided by quantities that are better measured, namely the masses and the effective spin. For the current catalog of events, we find no significant measurements of weak spin effects such as nutation and spin-orbit locking. We synthesize a source with a high nutational amplitude and show that near-future detections will allow us to place powerful constraints, hinting that we may be at the cusp of detecting spin nutations in gravitational-wave data. 

Binary black holes with misaligned spins will generically induce both precession and nutation of the orbital angular momentum 𝐋 about the total angular momentum 𝐉. These phenomena modulate the phase and amplitude of the gravitational waves emitted as the binary inspirals to merger. We introduce a “taxonomy” of binary black-hole spin precession that encompasses all the known phenomenology, then present five new phenomenological parameters that describe generic precession and constitute potential building blocks for future gravitational waveform models. These are the precession amplitude ⟨𝜃𝐿⟩, the precession frequency ⟨Ω𝐿⟩, the nutation amplitude Δ⁢𝜃𝐿, the nutation frequency 𝜔, and the precession-frequency variation Δ⁢Ω𝐿. We investigate the evolution of these five parameters during the inspiral and explore their statistical properties for sources with isotropic spins. In particular, we find that nutation of 𝐋 is most prominent for binaries with high spins (𝜒≳0.5) and moderate mass ratios (𝑞∼0.6). 

ABSTRACT Massive black hole (MBH) binary inspiral time-scales are uncertain, and their spins are even more poorly constrained. Spin misalignment introduces asymmetry in the gravitational radiation, which imparts a recoil kick to the merged MBH. Understanding how MBH binary spins evolve is crucial for determining their recoil velocities, their gravitational wave (GW) waveforms detectable with Laser Interferometer Space Antenna, and their retention rate in galaxies. Here, we introduce a sub-resolution model for gas- and gravitational wave (GW)-driven MBH binary spin evolution using accreting MBHs from the Illustris cosmological hydrodynamic simulations. We also model binary inspiral via dynamical friction, stellar scattering, viscous gas drag, and GW emission. Our model assumes that the circumbinary disc always removes angular momentum from the binary. It also assumes differential accretion, which causes greater alignment of the secondary MBH spin in unequal-mass mergers. We find that 47 per cent of the MBHs in our population merge by z = 0. Of these, 19 per cent have misaligned primaries and 10 per cent have misaligned secondaries at the time of merger in our fiducial model with initial eccentricity of 0.6 and accretion rates from Illustris. The MBH misalignment fraction depends strongly on the accretion disc parameters, however. Reducing accretion rates by a factor of 100, in a thicker disc, yields 79 and 42 per cent misalignment for primaries and secondaries, respectively. Even in the more conservative fiducial model, more than 12 per cent of binaries experience recoils of >500 km s−1, which could displace them at least temporarily from galactic nuclei. We additionally find that a significant number of systems experience strong precession. 

A usability study evaluated the ease with which users interacted with an author-designed modeling and simulation program called STEPP (Scaffolded Training Environment for Physics Programming). STEPP is a series of educational modules for introductory algebra-based physics classes that allow students to model the motion of an object using Finite State Machines (FSMs). STEPP was designed to teach students to decompose physical systems into a few key variables such as time, position, and velocity and then encourages them to use these variables to define states (such as running a marathon) and transitions between these states (such as crossing the finish line). We report the results of a usability study on high school physics teachers that was part of a summer training institute. To examine this, 8 high school physics teachers (6 women, 2 men) were taught how to use our simulation software. Data from qualitative and quantitative measures revealed that our tool generally exceeded teacher’s expectations across questions assessing: (1) User Experience, (2) STEM-C Relevance, and (3) Classroom Applicability. Implications of this research for STEM education and the use of modeling and simulation to enhance sustainability in learning will be discussed.