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We present extensive proper motion measurements of the Crab Nebula made from Canada-France-Hawaii Telescope MegaPrime/MegaCam images taken in 2007, 2016, and 2019. A total of 19974 proper motion vectors with uncertainty < 10 mas yr−1 located over the majority of the Crab Nebula are used to map the supernova remnant’s two-dimensional expansion properties that reflect the dynamics of the original explosion, acceleration of ejecta imparted by spin-down energy from the pulsar, and interaction between the ejecta and surrounding circumstellar material (CSM). The average convergence date we derive is 1105.5 ± 0.5 CE, which is 15-35 years earlier compared to most previous estimates. We find that it varies as a function of position angle around the nebula, with the earliest date and smallest proper motions measured along the equator defined by the east and west bays. The lower acceleration of material along the equatorial plane may be indicative of the supernova’s interaction with a disk-like CSM geometry. Comparing our measurements to previous analytical solutions of the Crab’s expansion and our own numerical simulation using the moving mesh hydrodynamics code Sprout, we conclude that the ejecta have relaxed closer to homologous expansion than expected for the commonly adopted pulsar spindown age of τ ∼ 700 yr and a pulsar wind nebula (PWN) still evolving inside the flat part of the ejecta density profile. These findings provide further evidence that the PWN has broken out of the inner flat part of the supernova ejecta density profile and has experienced “blowout”. 

Abstract Among the potential milliHz gravitational wave (GW) sources for the upcoming space-based interferometer LISA are extreme- or intermediate-mass ratio inspirals (EMRI/IMRIs). These events involve the coalescence of supermassive black holes in the mass range 105M⊙ ≲ M ≲ 107M⊙ with companion BHs of much lower masses. A subset of E/IMRIs are expected to occur in the accretion discs of active galactic nuclei (AGN), where torques exerted by the disc can interfere with the inspiral and cause a phase shift in the GW waveform. Here we use a suite of two-dimensional hydrodynamical simulations with the moving-mesh code DISCO to present a systematic study of disc torques. We measure torques on an inspiraling BH and compute the corresponding waveform deviations as a function of the binary mass ratio q ≡ M2/M1, the disc viscosity (α), and gas temperature (or equivalently Mach number; $$\mathcal {M}$$). We find that the absolute value of the gas torques is within an order of magnitude of previously determined planetary migration torques, but their precise value and sign depends non-trivially on the combination of these parameters. The gas imprint is detectable by LISA for binaries embedded in AGN discs with surface densities above $$\Sigma _0\ge 10^{4-6} \rm \, g cm^{-2}$$, depending on q, α and $$\mathcal {M}$$. Deviations are most pronounced in discs with higher viscosities, and for E/IMRIs detected at frequencies where LISA is most sensitive. Torques in colder discs exhibit a noticeable dependence on the GW-driven inspiral rate as well as strong fluctuations at late stages of the inspiral. Our results further suggest that LISA may be able to place constraints on AGN disc parameters and the physics of disc-satellite interaction.