22 research outputs found
Potential Vorticity Evolution of a Protoplanetary Disk with An Embedded Protoplanet
We present two-dimensional inviscid hydrodynamic simulations of a
protoplanetary disk with an embedded planet, emphasizing the evolution of
potential vorticity (the ratio of vorticity to density) and its dependence on
numerical resolutions. By analyzing the structure of spiral shocks made by the
planet, we show that progressive changes of the potential vorticity caused by
spiral shocks ultimately lead to the excitation of a secondary instability. We
also demonstrate that very high numerical resolution is required to both follow
the potential vorticity changes and identify the location where the secondary
instability is first excited. Low-resolution results are shown to give the
wrong location. We establish the robustness of a secondary instability and its
impact on the torque onto the planet. After the saturation of the instability,
the disk shows large-scale non-axisymmetry, causing the torque on the planet to
oscillate with large amplitude. The impact of the oscillating torque on the
protoplanet's migration remains to be investigated.Comment: 17 pages total with 9 figures (Fig.4,5,9 are in .jpg), accepted to
Ap
Keeping It Real: Revisiting a Real-Space Approach to Running Ensembles of Cosmological N-body Simulations
In setting up initial conditions for ensembles of cosmological N-body
simulations there are, fundamentally, two choices: either maximizing the
correspondence of the initial density field to the assumed fourier-space
clustering or, instead, matching to real-space statistics and allowing the DC
mode (i.e. overdensity) to vary from box to box as it would in the real
universe. As a stringent test of both approaches, I perform ensembles of
simulations using power law and a "powerlaw times a bump" model inspired by
baryon acoustic oscillations (BAO), exploiting the self-similarity of these
initial conditions to quantify the accuracy of the matter-matter two-point
correlation results. The real-space method, which was originally proposed by
Pen 1997 and implemented by Sirko 2005, performed well in producing the
expected self-similar behavior and corroborated the non-linear evolution of the
BAO feature observed in conventional simulations, even in the
strongly-clustered regime (sigma8 >= 1). In revisiting the real-space method
championed by Sirko 2005, it was also noticed that this earlier study
overlooked an important integral constraint correction to the correlation
function in results from the conventional approach that can be important in
LambdaCDM simulations with Lbox == Lbox / 10.
Rectifying this shows that the fourier space and real space methods are about
equally accurate and efficient for modeling the evolution and growth of the
correlation function, contrary to previous claims. An appendix provides a
useful independent-of-epoch analytic formula for estimating the importance of
the integral constraint bias on correlation function measurements in LambdaCDM
simulations.Comment: 28 pages, 7 figures, substantial improvements throughou