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) ~ cs2 or h = cs2 * r2 / GM

This would essentially give a disk where the height is a quadratic and would be comparable to the radius at r=GM/cs2 (or at the thermal radius)

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

Comments

1. martinhe -- 13 years ago

Simulation parameters:

rdisk=1 (equivalent to 10AU)

cs=sound speed=1 (equivalent to 2.9km/s)

densdisk= 100 (100 part cm-3); densdisk/densamb=100

tempdisk= 1 (1000K); tempdisk/tempamb=0.01

presdisk=presamb

veldisk(r=rdisk)=vKepler(r=rdisk)=2 (equivalent to 5.7km/s)

Machdisk(r=rdisk)=2

timeorbit=3.1416 (~51 yr)

final simulation time = 10 orbits (~500yr)

Ldomain=8 (800AU)

baseRefinement=16 cells

Parameter space in computational units:

rthermal=GM/cs2 = {2,4,8,16}rdisk

will be adjusted by changing the particle's mass (which takes values of order 0.5Msun). Note that Jonathan and I discussed on how to change the thermal radius and thought that doing so via the temperature scale was good. However, a change in tempScale affects the sounds speed too, i.e. it modifies both the disk and ambient characteristics. So I've decided to adjust the thermal radius vi the mass of the particle which only affects the disk.

rgrav-soft={½,¼,1/8,1/16}rdisk=4dx

will be adjusted by increasing the resolution: dx={.125,.0625,.03125,.01563}

2. Jonathan -- 13 years ago

The disk support equation should be or

3. martinhe -- 13 years ago

I've started running the first set of simulations using gamma=1.001 given that we're interested in such gamma. I plan to ask bin to run the same set of sims but with gamma=5/3

4. martinhe -- 13 years ago

Cylindrical disks, gamma=1.001

rsoft=1/8rd rth=2rd rsoft=1/8rd rth=8rd
http://www.pas.rochester.edu/~martinhe/2011/disk/soft8-therm2-17.pnghttp://www.pas.rochester.edu/~martinhe/2011/disk/soft8-therm8-7.png
6. martinhe -- 13 years ago

We're satisfied with these disk simulations. I'll now work towards using a setup which is a similar as possible but for the binar simulations. For the latter, the important radii should be rs (again) and the Hill radius:

rh=d [msec / (3 mpri ) ]1/3

where d, msec and mpri are the distance between the stars, the mass of the secondary and the mass of the primary, respectively. I've used d=25AU, msec=1Mo and mpri=1.5Mo, however I may need to change this values. Also, I'm not sure how important rh is for the wind capture process; the wind gas does not feel the gravitational pull of the primary at all.

7. martinhe -- 13 years ago

… and by this values I meant these values :P

8. martinhe -- 13 years ago

Because in the binary simulations the primary's wind is isothermal, i.e. there is no temperature difference between the ambient and the disk, I decided to run the keplarian disk simulation with rs=rd/8 and rthe=8rd (see ​https://clover.pas.rochester.edu/trac/astrobear/blog/martinhe12092011, bottom set of panels, column 6) but for tempd=tempamb, instead of pressd=pressamb. I did not change any of the other parameters. Such setup yields a disk, the central part of which collapses very fast (.5 orbit). The central dense part of the disk seems to tilt,

http://www.pas.rochester.edu/~martinhe/2011/disk/soft8-therm8-f5-iso.png

just as we see in the binary setup.

9. Jonathan -- 13 years ago

Martin,

Just a couple of questions:

  • So the setup is identical to the upper set of panels - column 6 - except that the ambient is cooler?
  • Why is the density so much higher in the center (40x) then in the corresponding 2 temperature run?
  • The 2 temperature run also seems to have some asymmetry at .7 orbits though perhaps not to the same degree - but it evens out by 10 orbits? What does this run look like at 10 orbits?
  • Does the same tilting happen if you start with a flared disk?
10. martinhe -- 13 years ago

Jonathan:

I will now try 3 more tests which should give us more answers:

  1. exactly this run (comment 8, i.e. isothermal gas) but with a plummer gravity soft function (instead of a spline function)
  1. exactly this run (comment 8, i.e. isothermal gas, spline soft function), but gamma=5/3 (instead of gamma=1.001)
  1. exactly this run (comment 8, i.e. isothermal gas, spline soft function, gamma=1.001), but 4 times more central refinement in order to see if the tilt effect is related to numerical dissipation.
11. martinhe -- 13 years ago

Jonathan:

I will now try 3 more tests which should give us more answers:

  1. exactly this run (comment 8, i.e. isothermal gas) but with a plummer gravity soft function (instead of a spline function)
  1. exactly this run (comment 8, i.e. isothermal gas, spline soft function), but gamma=5/3 (instead of gamma=1.001)
  1. exactly this run (comment 8, i.e. isothermal gas, spline soft function, gamma=1.001), but 4 times more central refinement in order to see if the tilt effect is related to numerical dissipation.