I believe the best place to have mass and temperature units set is in the equation of state thorns and to have the magnetic field units set by the code implementing the particular implementation of the Maxwell equations.
This goes into one of your original questions about whether there were other dimensions left to specify, but in principle one could measure temperature using a completely different unit system--for instance taking c=MeV=k_b=1 and using MeV to measure temperature. Since this would only affect the equation of state thorn (the hydro equations don't see temperature directly) it wouldn't introduce any inconsistency if one was measuring the density in units where c=G=M_sun=1. The equation of state thorn would need to do some internal bookkeeping on the two different unit systems, is all. This would be useful if one was working internally with some statistical physics expressions directly so that you would not need to continuously convert the temperature.
As I see it now, when using the ideal fluid equation of state (or polytrope), one is free to interpret the units. Always. This is really unavoidable: there is no microphysical interpretation of kappa or gamma. This changes when you use a realistic (or a fit) equation of state, the units would then be specified by the particular thorn which is implementing the functions needed by EOS_Base.
In short: I believe the units to be best specified in the particular equation of state thorns.
Cheers,
Aaryn
-----Original Message----- From: Roland Haas [mailto:roland.haas@physics.gatech.edu] Sent: Tuesday, April 27, 2010 4:16 PM To: Aaryn Tonita Subject: Re: [Users] HydroBase description
Hello all,
Actually, the units of "Whisky" is a myth I have been trying to dispel
from
some of the people at the AEI for a while now. In the hydro equations, the only place that a mass scale enters is through the equation of state. So HydroBase will work with any choice of mass unit (defined through the equation of state) so long as G=c=1 is used consistently. I have run quite successfully using polytropic units and kilometres.
Well it should certainly possible to remove these statements from documentation and interface.ccl. I agree that in particular fixing the mass unit is awkward (Tanja Bode here has simulations where the natural mass unit is 10^8 M_sun) for some simulations. Is there a strong preference for fixing all (or only G=c=eps0=mu0=1, maybe k_B=1?) units or should they be left unspecified?
As for the ideal magnetohydrodynamic equations, Whisky_Exp chooses div(Faraday) = 4-current without any constant of nature, so this is equivalent to choosing the permeability of free space (\mu_0) to be unity.
Hmm, mostly I was curious about factors of \sqrt{4\pi} in B^i. I believe that B^i as defined in HydroBase is Anton's et. al. (astro-ph/0506063v1) b^\mu after the rescaling by \sqrt{4\pi} in Eq (29).
However, this would not be defined by HydroBase unless HydroBase sets the stress energy tensor.
HydroBase does not set Tmunu. Fully determining the units might be useful for some analysis thorns. Another option might be to add parameters defining the units/describing the fluid to HydroBase or EOS_Base, though this did not seem to be very popular when it was suggested before. Eg. the unit mass in gramms, unit length in cm etc.
Yours, Roland