# Stable Keplerian disks

We want to simulate stable Keplerian disks, here I'll keep record of the tests I'l be doing in this context.

Jonathan: So as I see it, fundamentally there are 8 different parameters that fully define the problem - at least for a fixed grid run

softening length disk height disk radius thermal radius cell size density contrast box size/boundary conditions equation of state (gamma)

I think it makes sense to fix chi >> 1 (like 100) and gamma=5/3 and to set the box length ≥ 4 disk radii to avoid boundary effects and then use periodic bc's (or reflecting)

That leaves only five parameters: softening length disk height disk radius thermal radius cell size

I think we want to keep the softening length small but not too small … Because of numerical diffusion - gravitational energy that is converted into rotational energy inside of a few cells will get converted into heat resulting in jets etc… Keeping the softening length at 4 cells will reduce this effect.

That leaves 4 free parameters disk height disk_radius thermal_radius softening length

Since there is no cooling the problem can be arbitrarily scaled so the disk radius can be fixed without loss of generality and will make setting up the data files easier.

This just leaves 3 more parameters or ratios

disk height / disk radius thermal radius / disk radius softening length / disk radius

With the disk setup - there is no pressure support in the z-direction so it might make sense to have a disk that is not a hockey puck but a rotated wedge where at any given radius, the disk mass can be balanced by thermal support.. GM/r*(h/r) ~ cs^{2 or h = cs}2 * r^{2 / GM
}

This would essentially give a disk where the height is a quadratic and would be comparable to the radius at r=GM/cs^{2 (or at the thermal radius)
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This would essentially remove the disk height as a free parameter and would limit it to physically consistent values… We then just have

thermal radius / disk radius softening length / disk radius

Having the thermal radius > disk radius will prevent us from having super puffy disks and having the softening length << disk radius will allow for physically consistent disk regions…

I would suggest doing a set of runs where the thermal radius = 2, 4, 8 disk radii and the softening length = 1/16, 1/8, ¼, and ½ of the disk radius*
*

# Binary wind capture and accretion diks formation

This page is continuation of http://www.pas.rochester.edu/~martinhe/2011/binary/binary.html.

**Sep 27**

Find movie of the disk density at http://www.pas.rochester.edu/~martinhe/2011/binary/27sep.gif. Top - logarithmic density maps of the orbital plane. Bottom - 3-D logarithmic density iso-contours viewed edge-on (left); y (vetical) - z (horizontal) plane -perpendicular to the orbital plane- showing linear maps of the Vz velocity component (right). The bottom right panel maintains its blue-red colors close to the left and right boundaries, hence no inflow.

**The disk tilts** (see bottom left panel). And the tilt angle sem to increase in time. Could this be torques from the AGB wind on the disk?

Angles plot: http://www.pas.rochester.edu/~martinhe/2011/binary/27sep-angles.png

**Sep 23**

Case with V_{AGB}=5km/s. This is slightly less than the scape velocity from the secondary which, thus, dominates the wind dynamics after a few orbital periods after its gravity is switched on.

**Sep 22**

a=25AU, V_{AGB}=10km/s (twice as fast as in old sims), l_{grid}=200AU (twice as long as the old sims), outflow_only BC. I do not see inflow from the boundaries. I see a **varying** tilt angle (10^{o}-45^{o}) between the disk and the orbital angular momentum vectors.
http://www.pas.rochester.edu/~martinhe/2011/binary/22sep.png

Angular momentum projection angles plot is coming soon.

**Sep 14**

Some corrections to the bear2fix angular momentum projection routines. The still plots in the two links below have been updated accordingly. Mild changes. I've resumed the simulation that corresponds to the links below (a=25 AU, v_{AGB}=5km/s), it's running in bluehive and should go three times further.

**Sep 13**

Plot of the mean angular momentum direction as a function of radius and time: http://www.pas.rochester.edu/~martinhe/2011/binary/plot.pdf

Plot of the mean angular momentum direction as a function of time: http://www.pas.rochester.edu/~martinhe/2011/binary/13sep.html

**Aug**

a=25AU, Vagb=5km/s, "sandwich grid" (-5:5,-5:5,-2.5:2.5) AU. This simulation has two phases. During the 1st one, the binaries orbit each other twice, the AGB primary has its slow wind and the secondary **only affects the orbit of the primary, but not the gas**. This allows the grid to be filled with the AGB wind condition before the disk formation begins. The 2nd simulation phase begins next, when I turn on the gravity between the secondary and the gas. The system orbits 4 times.

2D pole-one logarithmic density map:

http://www.pas.rochester.edu/~martinhe/2011/binary/25-5-fullAGB-2Ddens.gif

3D, 2 panels: pole-on and edge-on views. The disk that forms is not significantly tilted.

http://www.pas.rochester.edu/~martinhe/2011/binary/25-5-fullAGB-2panels-3Ddens.gif

Also ran the same simulation but in a cubic grid. I see significant differences in the disks:

http://www.pas.rochester.edu/~martinhe/2011/binary/25-5-2panels-3Ddens-sandwichVScubicGRIDS.gif

Here's a good still shot too:

http://www.pas.rochester.edu/~martinhe/2011/binary/2panels-3Ddens-sandwichVScubicGRIDS-0180.png

A cubic grid version also with an AGB wind which has filled the grid and a=25AU, but with Vagb=30km/s, is running now. Should have the movie in a few days (before my trip).

Next simulation: a=25AU, Vagb=5km/s. The initial conditions for the disk should be an AGB wind which has expanded beyond the grid boundaries.

The simulation of a=25AU and Vagb=5km/s has run up to 5.7 orbits. Here's a number density [cm^{-3}] logarithmic grayscale map, and an opaque dark-blue map of the grid:

http://www.pas.rochester.edu/~martinhe/2011/binary/25-5-2Ddens.gif (A)

The grid in this simulation is [-5:5,-5:5,-2.5:2.5], "a sandwich", and each computational length unit=10AU. This makes the simulation faster without compromising disk formation dynamics. I see complex flow patterns. The rotation of the diks is synchronous with the orbital one.

Here a 3D view of the number density of this simulation:

http://www.pas.rochester.edu/~martinhe/2011/binary/25-5-2panels-3Ddens.gif (B)

The left panel is a perspective view. The AGB primary is the red particle. The orbital plane is opaque, in the middle of the figures. This is a viewing angle of about 10 degrees. Disk material below the orbital plane is shaded. The right panel shows the same simulations but normal to the orbital plane and** from bottom to top relative to the left panel**.

Newest runs (as fas as they've gotten). a=binary separation [AU] , v=AGB [km/s] wind velocity.

a=5, v=5. http://www.pas.rochester.edu/~martinhe/2011/binary/summer/18jul-densISOCONTOURS-a.gif

a=5, v=30. http://www.pas.rochester.edu/~martinhe/2011/binary/summer/18jul-densISOCONTOURS-b.gif

a=25, v=5. Tired to run with lScale=10AU and the same grid size as the tow simulations above (just at the post of 13 june, http://www.pas.rochester.edu/~martinhe/2011/binary/binary.html). This setup, however, produced wrongly high v, because the code's velocity scale only depends on tempScale (i.e. velscale \propto tempscale and not to lscale). Easy solution would be to reduce tempscale and rerun. Yet, I decided to change as little parameters as possible between different runs (a=5 and a=25), so I'm now running this case (a=25 v=5) with lscale =1AU and a 4 times larger grid than in the a=5 case. **Progress**, about .5 orbit.

a=25, v=30. Very problematic run. Need to adjust AR to follow the wind while it travels between the stars. Currently running in bluehive with the above described setup. **Progress**, I only have 3 chombos, ~ ¼ of the 1st orbit.

**Difficult to get much further before the Tenerife conference.**