Computational modeling of hydrodynamic astrophysical systems is a ground-up approach to understanding the
fundamental nature of fluids and the
inherent behavior of astrophysical systems such as protostellar and protoplanetary disks.
Theoretical research in this area began in the 1980’s with modeling of very simple systems.
It was predicted that gravitational instabilities would produce internal structure in star-disk systems.
Today, we have very highly evolved computational systems which allow us to carry out high-powered
simulations of hydrodynamic structures. It is only in the last few years that observation of
star-disk systems has borne out the work of the theorists in this regime. Recent advances in
observational techniques have, for the first time, allowed us to see that protostellar disks
contain internal structure, reminiscent of spiral arms seen in spiral galaxies.
Our modeling method for star-disk systems involves using an equilibrium model
as an initial condition for the time-evolving model.
We calculate the equilibrium disk structure by solving conservation equations
on a computational grid, using an initial guess for the mass density and
angular momentum structure. We use an independent relationship between
enthalpy and density to compare the result to a previously defined tolerance.
If the tolerance is not met, we improve the guess and reiterate until the
tolerance is met. We then linearly perturb the equations and solve them on a
cylindrical grid. Each solution of the equations serves as the initial
condition for the next time step. We monitor the growth of the perturbed
density until it has either settled into exponential growth (unstable) or a
sufficient amount of time has elapsed to declare the model stable.
We have developed an array of analysis tools useful in determining the
properties of the unstable models. We see that the geometry of the disk and
the relative mass of the central star to the disk produces various kinds of
modes in the disk. For systems where the disk mass is much greater than the
mass of the star, and inner edge of the disk is far removed from the star,
the self-gravity of the disk is the dominating mechanism and J modes arise in
the disk (named after the Jeans instability). In systems where the star mass
dominated, we see P modes and edge modes, depending on how far the inner edge
of the disk lies from the star. Intermediate I modes arise where the
self-gravity of the disk and the pressure support are comparable.
Our nonlinear approach uses the same equilibrium models as initial conditions,
but solves the system of equations by fluxing mass and angular momentum in the
grid. This approach is much more computationally expensive than the linear
modeling, and it gives more information about the development of the systems,
as it includes higher order coupling between the modes and evolves all of the
modes simultaneously. The nonlinear code we employ is an adaptation of the
Chymera code, which is fully parallelized and includes several subroutines
devoted to realistic equations of state and radiative cooling. Chymera is
second-order in space and time and includes artificial viscosity, enabling the
correct handling of hydrodynamic shocks. The richness of the dual approach of
combining linear and nonlinear calculations is that the linear models allow an
extensive sampling of parameter space, indicating regions of interest in which
to focus nonlinear investigation. Linear models also give a check for early
behavior of the nonlinear models. The linear results allow us to perform a
quasi-linear analysis, which is predictive of the nonlinear development.
Understanding the underlying reasons for the behavior of these systems
is fundamental to this research. One of the main issues we address is
how the bulk of the available mass in the system ends up in the star,
while the early central object is relatively low in mass, compared to
the disk. We focus on understanding how mechanisms of angular momentum
transport arise, and how various kinds of modes inherent in the disks are
driven. We are working on advancing the physics of the models by including
radiative cooling and complicated equations of state, including molecular
hydrogen and dust. Our recent progress has been very promising,
seeing that the formation of clumps of material can arise as a result of
radiative cooling. Clumps like these may precede the formation of Jovian planets.
Typical models in this field include the star as a point mass.
Very little work has been done where the star is included as a resolved
object in the grid. Our recent work has shown that inclusion of the star
in this manner is important. Modes of oscillation in the star itself can
gravitationally couple to the disk, changing the evolution of the system.
I am currently conducting simulations in both the linear and nonlinear
regimes of systems including a resolved star. Nonlinear models are very
computationally expensive in that very high resolution of the grid must be
maintained in order to correctly model the modes internal to the star.
My work is fundamental at the moment, excluding cooling. I intend to add
more complicated equations of state and radiative cooling to my models.
This methodology will shed light on many systems, such as first stars
(those formed early in the universe) and protostellar and protoplanetary
systems. Another application of this method would be to model star-disk
systems where the star is a white dwarf or a neutron star. Equations of
state for systems like this are readily available, and can be included
in our intact code in tabular form.