# [Users] Resolving two BH

Ian Hinder ian.hinder at aei.mpg.de
Wed Jun 8 10:55:50 CDT 2016

```On 8 Jun 2016, at 17:22, Peter Diener <diener at cct.lsu.edu> wrote:

> 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.

par_m_plus and par_m_minus are always the bare masses.  give_bare_mass = yes means that they are used as the bare masses.  give_bare_mass = no mean that TwoPunctures will iterate to find them .  You need to set give_bare_mass = no, so that they are ignored, and then set

TwoPunctures::target_M_plus             = 0.09090909090909
TwoPunctures::target_M_minus            = 0.9090909090909

These are the target masses that you want, and TwoPunctures will then iterate to find the bare masses needed to get these target masses.

>> 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?

If you want a circular orbit, then you need to work out the correct tangential momentum for the separation you are using, otherwise you will in general get an eccentric orbit.  Note that these are momenta, not velocities.  This can be done using PN, though for mass ratios of 1:20 I doubt that will be accurate.  Typically, you need to evolve with an initial guess, measure the eccentricity, then update your initial parameters to reduce that eccentricity.  It's a pain.

>> 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.

And finally, please note that q = 20 is well beyond what most experienced NR groups are comfortable evolving.  q=10 is also very challenging.

--
Ian Hinder
http://members.aei.mpg.de/ianhin

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