mkplummer|-n#| |-s # (seed)| |-m #| |-r #| |-i| |-o| |-c "..."|


mkplummer - constructs a Plummer model, with a spatial or mass cut-off


mkplummer -n # [options]


Mkplummer builds a nbody system according to a Plummer model, in virial units (M=G=-4E=1, with E the total energy), and finite spatial extent which can be regulated by specifying mfrac or rfrac or using their default values.

litt: S.J. Aarseth, M. Henon and R. Wielen (1974), Astron. and Astrophys. 37, p. 183.

Calculating the coordinates is easiest in STRUCTURAL units; conversion to VIRIAL units will be performed below.

Recipe for scaling to the proper system of units:

Since G = M = 1, if we switch from a coordinate system with length unit r_old to a coordinate system with length unit r_new , the length units simply scale by a factor C = r_new / r_old . Consequently, the coordinate values of physical quantities such as positions should transform inversely to maintain the same coordinate-invariant meaning. Similarly, the square of the velocities should transform inversely proportional to the positions, since GM = 1 (cf. a relation such as v*v = G*M/r ).

  To summarize: If
                       r_unit(new) = C * r_unit(old)  ,
                       pos(new) = (1/C) * pos(old)
                       vel(new) = sqrt(C) * vel(old)  .

the position coordinates are determined by inverting the cumulative mass-radius relation, with the cumulative mass drawn randomly from [0, mfrac]; cf. Aarseth et al. (1974), eq. (A2).

the velocity coordinates are determined using von Neumann's rejection technique, cf. Aarseth et al. (1974), eq. (A4,5). First we take initial values for x, the ratio of velocity and escape velocity (q in Aarseth et al.), and y, as a trick to enter the body of the while loop.



where # is the number of bodies in the Nbody system. There is no default, this is a required parameter.

-s # (seed)

where # stands for an integer either in the range [1,2147483647], or # = 0 which causes a seed to be chosen as the value of the UNIX clock in seconds; this guarantees that no two calls will give the same value for the seed if they are more than 2.0 seconds apart.

-m #

mass fraction of the (infinitely extended) Plummer model

-r #

radius fraction of the (infinitely extended) Plummer model

If the mass fraction and radius fraction are both 1.0 then particles will be sprinkled in all over space. If mfrac < 1.0 or rfrac < 1.0 then each particle is constrained to lie within both the radial and (cumulative) mass bound. For example, if rfrac( mfrac ) > rfrac then rfrac is the limiting factor, but if rfrac( mfrac ) < rfrac then mfrac limits the extent of the Plummer realization.



-c "..."






after sprinkling in particles according to a Plummer distribution, the whole system is shifted in position and velocity so as to put the center of mass at rest at the coordinate center.


this should be moved elsewhere, of course. Included here just to get it to work quickly (Piet, 921210).




Piet Hut - 11-feb-95