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Binary neutron star mergers are thought to produce hot, rapidly rotating neutron stars with masses that can far exceed their Tolman─Oppenheimer─Volkoff mass. The gravitational-wave emission from such remnants provides a unique opportunity to measure the nuclear equation of state at densities and temperatures not available to terrestrial experiments. Current detector design is informed by gravitational-wave signals from general relativistic hydrodynamics simulations of neutron star mergers, typically with hybrid thermal treatments for the equation of state, where a cold equation of state is modified by adding a thermal component. We use realistic equations of state based on the relativistic mean field model with consistent treatment of thermal effects to compute the distribution of expected peak gravitational-wave frequencies. Marginalizing over equation of state and progenitor neutron star masses, we show the peak frequency of emission ranges from <inline-formula><tex-math>${\sim} 2.5$</tex-math></inline-formula> to 4 kHz. The width of this distribution suggests the need for broad-band observatories with kHz sensitivity, and calls into question some of the so-called post-merger optimized configurations. We show the proposed KAGRA high-frequency design is well-suited to measuring post-merger remnants when compared to the KAGRA broad-band design.

We investigate the origins of quasiperiodic eruptions (QPEs) in galactic nuclei using global three-dimensional meshless finite-mass (MFM) simulations. By modeling stellar and black hole impactors traversing accretion disks under various inclinations and surface densities, we evaluate their consistency with the observed properties of QPEs. Stellar impacts produce highly asymmetric bipolar ejecta with forward outbursts dominating by over an order of magnitude in energy and luminosity due to the star blocking downstream flow and creating a low-density wake. This shock-compression mechanism often renders backward events unobservable, implying one detectable burst per orbit, and challenging the standard assumption of two bursts. It also fails to explain alternating long─short recurrence patterns and places several sources near or within twice the tidal disruption radius for solar-mass stars, raising severe stability concerns. Whereas a stellar-mass black hole (sBH) gravitationally focuses and heats disk gas over an effective interaction scale that extends beyond its Bondi radius R<SUB>B</SUB> and is naturally bounded by its Hill radius R<SUB>H</SUB> during an impact, yielding nearly symmetric ejecta with mild contrasts. This gravitational drag mechanism generates higher energy budgets at low inclinations due to enhanced mass accumulation. We suggest an ad hoc effective interaction radius <inline-formula> <mml:math><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>eff</mml:mi></mml:mrow></mml:msub><mml:mo>≃</mml:mo><mml:mn>0.5</mml:mn><mml:mspace></mml:mspace><mml:msubsup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:msubsup><mml:msubsup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>/</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:msubsup></mml:math> </inline-formula> to quantify this trend. Incorporating this effective radius substantially increases the energy that sBH-disk collisions can produce compared to previous Bondi-only estimates, improving the viability of sBHs as the impactors for a wide range of observed QPE energies and properties.