Dynamical Thin Disks

Thin disk accretion is often modeled in highly dynamical settings using the two-dimensional equations of viscous hydrodynamics, with viscosity representing unresolved turbulence. These equations are supposed to arise after vertical integration of the full three-dimensional equations of hydrodynamics, under the assumption of a geometrically thin disk with mirror symmetry about the midplane. But in the dynamical context, vertical dynamics are neglected by incorrectly assuming instantaneous vertical hydrostatic equilibrium. The resulting errors in the local disk height couple to the horizontal dynamics through some viscosity prescriptions and gravitational softening models. Furthermore, the viscous terms in the horizontal equations are only complete if they are inserted after vertical integration, as if the system is actually two-dimensional. Since turbulence breaks mirror symmetry, it is more physically correct to insert a turbulence model at the three-dimensional level, and impose mirror symmetry only on average. Thus, some viscous terms are usually missing. We revisit the vertical integration procedure, restricting to the regime of a Newtonian, non-self-gravitating disk. We obtain six evolution equations with only horizontal dependence, which determine the local vertical position and velocity of the disk surface, in addition to the usual fluid variables. This "2.5-dimensional" formulation opens the door to efficiently study vertical oscillations of thin disks in dynamical settings, and to improve the treatment of unresolved turbulence. As a demonstration, by including viscous stress at the three-dimensional level, we recover missing viscous terms which involve the vertical variables. We also propose a resummation of the vertically integrated gravitational force, which has a strikingly similar form to a gravitational softening model advocated for in protoplanetary disk studies.Comment: Accepted to Physical Review

Consistent perturbative modeling of pseudo-Newtonian core-collapse supernova simulations

We write down and apply the linearized fluid and gravitational equations consistent with pseudo-Newtonian simulations, whereby Newtonian hydrodynamics is used with a pseudo-Newtonian monopole and standard Newtonian gravity for higher multipoles. We thereby eliminate the need to use mode function matching to identify the active non-radial modes in pseudo-Newtonian core-collapse supernova simulations, in favor of the less complex and less costly mode frequency matching method. In doing so, we are able to measure appropriate boundary conditions for a mode calculation.Comment: 11 pages, 9 figures, 2 tables. Journal submission will be delayed to allow for comments. v2: Added acknowledgement. v3: Published version, aside from style changes made during proofs. More complete context is given with respect to existing literatur

Numerical Measurements of Scaling Relations in Two-Dimensional Conformal Fluid Turbulence

We present measurements of relativistic scaling relations in $(2+1)$-dimensional conformal fluid turbulence from direct numerical simulations, in the weakly compressible regime. These relations were analytically derived previously in Westernacher-Schneider, Lehner, Oz (2015) for a relativistic fluid; this work is a continuation of that study, providing further analytical insights together with numerical experiments to test the scaling relations and extract other important features characterizing the turbulent behavior. We first explicitly demonstrate that the non-relativistic limit of these scaling relations reduce to known results from the statistical theory of incompressible Navier-Stokes turbulence. In simulations of the inverse-cascade range, we find the relevant relativistic scaling relation is satisfied to a high degree of accuracy. We observe that the non-relativistic versions of this scaling relation underperform the relativistic one in both an absolute and relative sense, with a progressive degradation as the rms Mach number increases from $0.14$ to $0.19$. In the direct-cascade range, the two relevant relativistic scaling relations are satisfied with a lower degree of accuracy in a simulation with rms Mach number $0.11$. We elucidate the poorer agreement with further simulations of an incompressible Navier-Stokes fluid. Finally, as has been observed in the incompressible Navier-Stokes case, we show that the energy spectrum in the inverse-cascade of the conformal fluid exhibits $k^{-2}$ scaling rather than the Kolmogorov/Kraichnan expectation of $k^{-5/3}$, and that it is not necessarily associated with compressive effects. We comment on the implications for a recent calculation of the fractal dimension of a turbulent $(3+1)$-dimensional AdS black brane.Comment: 18 pages, 10 figures, 1 table. To be submitted to JHEP - comments welcome. V2 contains a technical edit for the JHEP compiler, as well as minor grammatical correction

Self-lensing flares from black hole binaries III: general-relativistic ray tracing of circumbinary accretion simulations

Self-lensing flares (SLFs) are expected to be produced once or twice per orbit by an accreting massive black hole binary (MBHB), if the eclipsing MBHBs are observed close to edge-on. SLFs can provide valuable electromagnetic (EM) signatures to accompany the gravitational waves (GWs) detectable by the upcoming Laser Interferometer Space Antenna (LISA). EM follow-ups are crucial for, e.g., sky-localization, and constraining the Hubble constant and the graviton mass. We use high-resolution two-dimensional viscous hydrodynamical simulations of a circumbinary disk (CBD) embedding a MBHB. We then use very high-cadence output of these hydrodynamical simulation inputs for a general-relativistic ray-tracing code to produce synthetic spectra and phase-folded light curves. Our main results show a significant periodic amplification of the flux with the characteristic shape of a sharp flare with a central dip, as the foreground black hole (BH) transits across the minidisk and shadow of the background BH, respectively. These corroborate previous conclusions based on the microlensing approximation and analytical toy models of the emission geometry. We also find that at lower inclinations, without some occlusion of the minidisk emission by the CBD, shocks from quasi-periodic mass-trading between the minidisks can produce bright flares which can mimic SLFs and could hinder their identification.Comment: 14 pages, 11 figures, submitted to journal, split Fig. 1 by frequency, fixed some typo

Disappearing thermal X-ray emission as a tell-tale signature of merging massive black hole binaries

The upcoming Laser Interferometer Space Antenna (LISA) is expected to detect gravitational waves (GWs) from massive black hole binaries (MBHB). Finding the electromagnetic (EM) counterparts for these GW events will be crucial for understanding how and where MBHBs merge, measuring their redshifts, constraining the Hubble constant and the graviton mass, and for other novel science applications. However, due to poor GW sky localisation, multi-wavelength, time-dependent electromagnetic (EM) models are needed to identify the right host galaxy among many candidates. We studied merging MBHBs embedded in a circumbinary disc using high-resolution two-dimensional simulations, with a $\Gamma$-law equation of state, incorporating viscous heating, shock heating, and radiative cooling. We simulate the binary from large separation until after merger, allowing us to model the decoupling of the binary from the circumbinary disc (CBD). We compute the EM signatures and identify distinct features before, during, and after the merger. Our main result is a multi-band EM signature: we find that the MBHB produces strong thermal X-ray emission until 1-2 days prior to the merger. However, as the binary decouples from the CBD, the X-ray-bright minidiscs rapidly shrink in size, become disrupted, and the accretion rate drops precipitously. As a result, the thermal X-ray luminosity drops by orders of magnitude, and the source remains X-ray dark for several days after the merger, regardless of any post-merger effects such as GW recoil or mass loss. Looking for the abrupt spectral change where the thermal X-ray disappears is a tell-tale EM signature of LISA mergers that does not require extensive pre-merger monitoring.Comment: 14 pages, 16 figures, 1 table, submitted to journa