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units - various units used in simulations


Most NEMO programs use the "virial" (sometimes also called "N-Body") units as described by Heggie & Mathieu (1986). We also list a few other common units, and the value of the gravitational constant in these. Notably some of the potential(5NEMO) descriptors use other unit systems.

The gravitational constant is often set to unity in N-body codes, since it saves a precious floating point operation! However, for sake of completeness, here are a few common values of G in some other ’common’ unit systems, recalling that G*m/(r*v*v) is dimensionless:

  mass    length    velocity    G           1/G         time    "system"
     g    cm        cm/s        6.6732e-8      1.49853e+07      s       (cgs)
    kg    m     m/s         6.6732e-11     1.49853e+10       s        (SI)
     M    pc       km/s        .               2.32385e2         1e6.yr    (starcluster)
     M    kpc       km/s        .              2.32385e5         1e9.yr    .
1e10.M    10.kpc    .                 2.32385           1e8.yr    (galaxy)
1e10 M    1.kpc        43007.1        .        1e9.yr    [gadget] 
~2e4.M    kpc    1              1                 1e6.yr    (galaxy)
1e11.M    10.kpc    4.497           0.22237           1e8.yr    (galaxy)


For the purpose of comparison of results obtained by different authors, it is very convenient if they share a common system of units. The following system of units seems to find quite wide (if not universal) favor. The units are such that:
            G = 1
            M = 1
            E = -1/4
where G is the gravitational constant, M the total initial mass, and E
initial energy. The corresponding units of mass, length and time are then
            U_m = M
            U_l = - G M^2 / (4E)
            U_t = G M^2.5 / (-4E)^1.5
(cf. Henon, 1972).
The choice for E looks odd, but corresponds to a virial radius R (harmonic mean particles separation) equal to unity for a system in virial equilibrium. In N-body work a somewhat different, actually N-dependant, system is often used (cf. Aarseth 1972), but leads to a crossing time scale proportional to N^(-1/2). This system is also unsuitable for galaxy simulations, where neither the number of stars nor the number of particles in the simulation is relevant to the imortant dynamical timescales. There are of course stellar dynamical calculations for which the above described units are unsuitable, e.g. unbound systems or cosmological simulations.

See Also

units(1NEMO) , nemoinp(1NEMO)
Heggie, D.C. and Mathieu, R.D. 
Standardized Units and Time Scales, in:
The Use of Supercomputers in Stellar Dynamics, ed. P. Hut and
S. McMillan. (1986, Spinger Verlag)
NPL’s United of Measurement webpage: AstroTables:


Peter Teuben

Update History

7-may-96    Created      PJT

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