# [Users] Resolving two BH

Peter Diener diener at cct.lsu.edu
Wed Jun 8 10:22:20 CDT 2016

```Hi Maria,

On Tuesday 2016-06-07 10:02, Hamilton, Maria wrote:

>Date: Tue, 7 Jun 2016 10:02:36
>From: "Hamilton, Maria" <babiuc at marshall.edu>
>To: Peter Diener <diener at cct.lsu.edu>, Frank Loeffler <knarf at cct.lsu.edu>
>Cc: Einstein Toolkit Users <users at einsteintoolkit.org>
>Subject: Re: [Users] Resolving two BH
>
> Hello,
>
> Does this paper come with access to a par file that will show how to
> set the dynamic shift?

No it doesn't. That paper was based on the Jena groups BAM code and
these features have not yet been implemented in McLachlan.

> I need some help as well in setting up a run with two unequal mass
> black holes, for an undergraduate visualization project. My
> understanding is that the initial conditions are set with the
> parameters given in the TwoPunctures thorn. For example, if I want the
> first black hole to be equal with the mass of the sun, and the second,
> 10 times the mass of the sun, I do something like this?
>
> TwoPunctures::par_m_plus                = 1.5
> TwoPunctures::par_m_minus            = 15

The code uses units so G=c=1 so you can get mass you want. But yes, this
will give you a mass ratio of 10. Note however, that if you want this to
be the physical masses, you have to set

TwoPunctures::give_bare_mass = no

as well. Otherwise these will be the bare mass parameters given as input
to the elliptical solve, and the actual physical masses after the solve
might be a little bit different. One comment: I usually preferred to
have the total mass be 1.0 in order to make grid setup as well
as analysis simpler between runs with different mass ratio. So I would
use

TwoPunctures::par_m_plus                = 0.09090909090909
TwoPunctures::par_m_minus            = 0.9090909090909

But That is a matter of taste of course.

> The last thing I need to set is the velocity for each hole, If I want
> each of them to move at 1/3 c tangential velocity? I’m assuming I need
> to set:
>
> TwoPunctures::par_P_plus [1] = +0.45
> TwoPunctures::par_P_minus[1] = -4.5

You most likely want to do the simulation in the rest frame, where the
total momentum is 0. Otherwise your black hole system will drift away
from the system. So the larger black hole will move 10 times slower than
the small black hole. How big a velocity you want depends on exactly
what kind of system you want to evolve. Do you want a hyperbolic flyby,
an elliptical orbit or a quasi-circular orbit?

> Is this correct? And one more important thing: if I want the distance
> between them to be for example 150, how do I set this? I see a
> parameter par_b which gives the x coordinate of the m+ puncture, but
> I’m not clear if this is what I need to set, and how.

Yes, par_b gives the x-coordinate of the m+ puncture. By default the m-
puncture will then be at -par_b (on the x-axis). So par_b is 1/2 the
coordinate separation of the punctures. There is in addition a parameter
center_offset that allow you to add an offset to the initial position.
Again the choice of the separation and of the momenta goes hand in hand
to determine what kind of orbit you'll get.

> All the other parameters I am assuming are to be kept the way they
> are. In Rahul’s parameter file I do not see the PunctureTracker thorn
> activated. I do want to know the position of the back holes on the
> grid, and the distance between them at each step of the evolution. Do
> I need to activate PunctureTracker? What output do I need for this?

As far as I remember you just need to activate PunctureTracker and then
set a few parameters to activate tracking as well as setting the initial
puncture positions consistently with the TwoPuncture parameters.

And as far as I remember PunctureTracker keeps track of the punctures in
Cactus grid scalars and you'd just need to request output for those.

> Thank you,
> Maria

Cheers,

Peter

> On 6/7/16, 10:13 AM, "users-bounces at einsteintoolkit.org on behalf of Peter Diener" <users-bounces at einsteintoolkit.org on behalf of diener at cct.lsu.edu> wrote:
>
>> Hi,
>>
>> This issue is discussed for example in
>>
>> http://arxiv.org/abs/1003.4681
>>
>> where a non-constant damping in the gamma driver shift is presented to
>> handle unequal mass binaries. As far as I remember there may also be
>> later papers with further improvements to the method.
>>
>> Cheers,
>>
>>   Peter
>>
>> On Tuesday 2016-06-07 01:00, Frank Loeffler wrote:
>>
>>> Date: Tue, 7 Jun 2016 01:00:59
>>> From: Frank Loeffler <knarf at cct.lsu.edu>
>>> To: rahul kashyap <rahulkashyap411 at gmail.com>
>>> Cc: Einstein Toolkit Users <users at einsteintoolkit.org>
>>> Subject: Re: [Users] Resolving two BH
>>>
>>> On Mon, Jun 06, 2016 at 06:50:04PM -0400, rahul kashyap wrote:
>>>> Thanks for the reply. My apologies that I'm not completely familiar many of
>>>> the physical and numerical issues while simulating bbh. I have experience
>>>> in AMR astrophysical simulations.
>>>
>>> No need to apologize.
>>>
>>>> When I do the bbh simulation of ratio around 1, it evolves perfectly fine.
>>>> With higher mass ratio, the smaller BH just becomes bigger and blows up.
>>>> I'm assuming this as a problem of refinement.
>>>
>>> It is not. It looks like what I described earlier: your gauge
>>> conditions, in particular the shift condition, isn't well suited for the
>>> small black hole. Grid points are "falling in", making it appear growing
>>> on the computational grid. You may try to play with the values such that
>>> the small black hole evolves fine (you can try that with a simulation of
>>> only a small black hole of that size), but then you might find that the
>>> large black hole "vanishes from the grid" because grid points there are
>>> pushed out too much. If this is the case, you might need
>>> position-dependent values.
>>>
>>> Frank
>>>
>>>
>>
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>
```