15 research outputs found
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
-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 to . 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 . 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
scaling rather than the Kolmogorov/Kraichnan expectation of
, 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 -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 -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