Hi all,
Could you guys please point me to the reference where I can see how units are defined for a binary black hole simulation?
(Or possibly simply answer):
I just want to know what the units of space and time (M) are. What is M? is it the ADM mass at initial time? the addition of the two black hole masses?... or so...
I apologize in advance in case my question is terribly dummy.
Thanks, Francisco
Francisco
Without hydrodynamics, nothing fundamental sets the mass scale. If you assume that c = G = 1, then there is a rescaling freedom for M, the black hole mass. Apart from this, it is up to the designer of the parameter file what they call M. I think that the ADM mass is a good choice, but others might use a different convention. In practice, one examines the black hole masses and the ADM mass in a simulation, which is then returned in terms of the grid spacing, which is related to the time step size, thus you see what M is used in this particular case.
For example, in http://einsteintoolkit.org/gallery/bbh/index.html I assume that M_ADM = 1, but I don't know whether this is taken from the initial conditions or whether this is measured after the initial junk radiation has left.
I hope my answer isn't too trivial.
-erik
On Wed, Apr 12, 2017 at 3:30 PM, Francisco Guzman guzman@ifm.umich.mx wrote:
Hi all,
Could you guys please point me to the reference where I can see how units are defined for a binary black hole simulation?
(Or possibly simply answer):
I just want to know what the units of space and time (M) are. What is M? is it the ADM mass at initial time? the addition of the two black hole masses?... or so...
I apologize in advance in case my question is terribly dummy.
Thanks, Francisco
Users mailing list Users@einsteintoolkit.org http://lists.einsteintoolkit.org/mailman/listinfo/users
On 12 Apr 2017, at 22:12, Erik Schnetter schnetter@cct.lsu.edu wrote:
Francisco
Without hydrodynamics, nothing fundamental sets the mass scale. If you assume that c = G = 1, then there is a rescaling freedom for M, the black hole mass. Apart from this, it is up to the designer of the parameter file what they call M. I think that the ADM mass is a good choice, but others might use a different convention.
Hi Erik,
If you want the units of the simulation to be the ADM mass, then you need a mechanism to iterate the bare mass parameters of the punctures to make this the case. We don't have that in TwoPunctures; we iterate until we get the puncture masses equal to the targets. I think it is useful to compare two BBH systems where the BHs have the same total mass. This would be natural also if you were comparing with PN. I'm not sure it is so useful to compare systems with the same ADM mass; the ADM mass will consist of the BH masses, plus the energy content in the junk radiation, and the orbital energy. The junk radiation isn't very interesting, which is why I am rarely interested in M_ADM.
For example, in http://einsteintoolkit.org/gallery/bbh/index.html I assume that M_ADM = 1, but I don't know whether this is taken from the initial conditions or whether this is measured after the initial junk radiation has left.
No, M_ADM is not 1 for that parameter file. It's
initial-ADM-energy = 0.9899366929086094169
In the parameter file, we have q = 36.0/29.0 # Mass ratio: q = mp/mm >= 1 M = 1.0 # Total mass mp = M * q/(1+q) # Heavier, larger BH, AH1, SS 0 mm = M * 1/(1+q) # Lighter, smaller BH, AH2, SS 1 TwoPunctures::target_M_plus = $mp TwoPunctures::target_M_minus = $mm
so the sum of the puncture masses is 1 in the units of the simulation, so the units of the simulation are the sum of the puncture masses.
Hi Francisco,
To add a little more detail to what Ian and Erik already said, you might find it helpful to look at the Waveforms SimulationTools tutorial [ http://simulationtools.org/examples/Waveforms.cdf] from the BBH gallery example page. This gives a short explanation of the units in that simulation along with demonstrations of how to interpret the data from the simulation in terms of those units.
Regards, Barry
On 12 April 2017 at 21:21, Ian Hinder ian.hinder@aei.mpg.de wrote:
On 12 Apr 2017, at 22:12, Erik Schnetter schnetter@cct.lsu.edu wrote:
Francisco
Without hydrodynamics, nothing fundamental sets the mass scale. If you assume that c = G = 1, then there is a rescaling freedom for M, the black hole mass. Apart from this, it is up to the designer of the parameter file what they call M. I think that the ADM mass is a good choice, but others might use a different convention.
Hi Erik,
If you want the units of the simulation to be the ADM mass, then you need a mechanism to iterate the bare mass parameters of the punctures to make this the case. We don't have that in TwoPunctures; we iterate until we get the puncture masses equal to the targets. I think it is useful to compare two BBH systems where the BHs have the same total mass. This would be natural also if you were comparing with PN. I'm not sure it is so useful to compare systems with the same ADM mass; the ADM mass will consist of the BH masses, plus the energy content in the junk radiation, and the orbital energy. The junk radiation isn't very interesting, which is why I am rarely interested in M_ADM.
For example, in http://einsteintoolkit.org/gallery/bbh/index.html I assume that M_ADM = 1, but I don't know whether this is taken from the initial conditions or whether this is measured after the initial junk radiation has left.
No, M_ADM is not 1 for that parameter file. It's
initial-ADM-energy = 0.9899366929086094169
In the parameter file, we have
q = 36.0/29.0 # Mass ratio: q = mp/mm >= 1 M = 1.0 # Total mass
mp = M * q/(1+q) # Heavier, larger BH, AH1, SS 0 mm = M * 1/(1+q) # Lighter, smaller BH, AH2, SS 1
TwoPunctures::target_M_plus = $mp TwoPunctures::target_M_minus = $mm
so the sum of the puncture masses is 1 in the units of the simulation, so the units of the simulation are the sum of the puncture masses.
-- Ian Hinder http://members.aei.mpg.de/ianhin
Users mailing list Users@einsteintoolkit.org http://lists.einsteintoolkit.org/mailman/listinfo/users
Thanks for the help Barry, Ian and Erik.
Cheers, Francisco
From: "Barry Wardell" barry.wardell@gmail.com To: "Ian Hinder" ian.hinder@aei.mpg.de Cc: "Einstein Toolkit Users" users@einsteintoolkit.org Sent: Wednesday, April 12, 2017 3:58:07 PM Subject: Re: [Users] units
Hi Francisco, To add a little more detail to what Ian and Erik already said, you might find it helpful to look at the Waveforms SimulationTools tutorial [ http://simulationtools.org/examples/Waveforms.cdf ] from the BBH gallery example page. This gives a short explanation of the units in that simulation along with demonstrations of how to interpret the data from the simulation in terms of those units.
Regards, Barry
On 12 April 2017 at 21:21, Ian Hinder < ian.hinder@aei.mpg.de > wrote:
On 12 Apr 2017, at 22:12, Erik Schnetter < schnetter@cct.lsu.edu > wrote:
BQ_BEGIN
Francisco Without hydrodynamics, nothing fundamental sets the mass scale. If you assume that c = G = 1, then there is a rescaling freedom for M, the black hole mass. Apart from this, it is up to the designer of the parameter file what they call M. I think that the ADM mass is a good choice, but others might use a different convention.
Hi Erik,
If you want the units of the simulation to be the ADM mass, then you need a mechanism to iterate the bare mass parameters of the punctures to make this the case. We don't have that in TwoPunctures; we iterate until we get the puncture masses equal to the targets. I think it is useful to compare two BBH systems where the BHs have the same total mass. This would be natural also if you were comparing with PN. I'm not sure it is so useful to compare systems with the same ADM mass; the ADM mass will consist of the BH masses, plus the energy content in the junk radiation, and the orbital energy. The junk radiation isn't very interesting, which is why I am rarely interested in M_ADM.
BQ_BEGIN
For example, in < http://einsteintoolkit.org/gallery/bbh/index.html > I assume that M_ADM = 1, but I don't know whether this is taken from the initial conditions or whether this is measured after the initial junk radiation has left.
BQ_END
No, M_ADM is not 1 for that parameter file. It's
initial-ADM-energy = 0.9899366929086094169
In the parameter file, we have q = 36.0/29.0 # Mass ratio: q = mp/mm >= 1 M = 1.0 # Total mass mp = M * q/(1+q) # Heavier, larger BH, AH1, SS 0 mm = M * 1/(1+q) # Lighter, smaller BH, AH2, SS 1 TwoPunctures::target_M_plus = $mp TwoPunctures::target_M_minus = $mm
so the sum of the puncture masses is 1 in the units of the simulation, so the units of the simulation are the sum of the puncture masses.
On 12 Apr 2017, at 21:30, Francisco Guzman guzman@ifm.umich.mx wrote:
Hi all,
Could you guys please point me to the reference where I can see how units are defined for a binary black hole simulation?
(Or possibly simply answer):
I just want to know what the units of space and time (M) are. What is M? is it the ADM mass at initial time? the addition of the two black hole masses?... or so...
I apologize in advance in case my question is terribly dummy.
Hi Francisco,
I made a document a long time ago with my understanding of the situation. I always refer back to it, so I attach it here in case it is useful. I might not explain some of the aspects in quite the same way now though.
The upshot is that there is a single unit in the simulation, which we can call M. Lengths, times and masses can be measured in this unit. It is *conventional* to arrange for the sum of the masses of the BHs to sum to 1 in these units, so that M = m1+m2. This makes it easy to quickly compare two BBH simulations without having to rescale the units of each. Note that this could be the masses of the punctures, the initial horizon masses, or the horizon masses after a short amount of evolution, to account for absorption of junk energy.
If you want to rigorously compare different simulations, it's best to compare dimensionless numbers from each simulation, e.g. by dividing e.g. a time by the *measured* masses of the BHs, e.g. t_merger / (m1+m2). Then it doesn't matter what the original unit of the simulation was.
users@lists.einsteintoolkit.org
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Barry Wardell -
Erik Schnetter -
Francisco Guzman -
Ian Hinder