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mkplummer - construct a Plummer model
mkplummer [parameters=values...]
mkplummer constructs an N-body realization of a Plummer model,
with a spatial or mass based cut-off, after which it (optionally) performs
a coordinate transformation to the center-of-mass coordinate system. The data
are then written into a file snap-file, in a standard N-body snapshot(5NEMO)
format. The model is constructed in VIRIAL or NBODY 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. The distribution
function of a Plummer model is spherically symmetric and isotropic, and
is a polytrope of index n = 5. See also Aarseth et al. (1974) and Plummer
(1911).
There is also an implementation in Dehnen’s falcON suite: mkplum(1falcON)
For more advanced Plummer models, see mcluster(1NEMO)
.
The following
parameters are recognized in order; they may be given in any order if the
keyword is also given. Use --help to confirm this man page is up to date.
- out=snapfile
- Output data is written into snapfile, in standard snapshot(5NEMO)
format.
No default
- nbody=integer
- Number of particles in the model.
No default.
- mlow=real
- inner core mass fraction within which no stars will
be populated.
[Default: 0]
- mfrac=real
- mass fraction of the (otherwise infinitely extended)
Plummer model; see rfrac immediately below Note that the total mass is
still normalized to 1.
[Default: rfrac=22.8042468]
- rfrac=real
- radius fraction of the (otherwise
infinitely extended) Plummer model. If mfrac = 1.0 then particles will be
sprinkled in all over space. If mfrac < 1.0 or rfrac > 0.0 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. Note: specifying either value may have no effect if the default
value of the other parameter is still the limiting factor; Beware! (Default:
mfrac=0.999; rfrac=22.8042468 , chosen so that the cumulative mass at rfrac
is mfrac).
Default: ....
- seed=integer
- seed for the random number generator. A value of
0 (the default) will be converted into a unique new value using UNIX’s clock
time, in seconds since 1970.0). See also xrandom(1NEMO)
for more options.
[Default: 0]
- time=time
- Time at which the snapshot applies
[Default: 0.0]
- zerocm=t|f
- Reset center of mass to zero? If not centered,
the (0,0,0) is the mathematical origin of the Plummer model, but due to
finite-N noise not at the center of mass.
[Default: t].
- scale=scale_factor
- A scale factor or scale to virial units
(M=G=-4E=1). Use -1 for virial units (see also UNITS below), and 1 to get
a model in structural (natural) units. Note: large scale factors means small
systems with large velocity disperson.
[Default: -1].
- quiet=level
- Level of quit start. 0 is noisy, 1=somewhat quiet,
2=more quiet. See "QUIET START" below
[Default: 0].
- massname=name
- Identification of the mass spectrum. It is normally
only a function of mass, so n(m) will suffice. If nothing specified, all
stars will have the same mass (total mass M=1).
[Default: not used].
- massexpr=expr
- Expression for the mass-spectrum. In addition
to the mass m from the massname it may contain any variables contained
in the masspars to be specified next.
[Default: pow(m,p)].
- masspars=pars
- List of parameters and their values. They
can be used by name in the massexpr specified before.
[Default: p,0.0].
- massrange=mlow,mhigh
- Valid massrange. A lower and higher
cutoff must be supplied. The massrange has arbitrary units, since all masses
will be rescaled to set the total mass M=1.
[Default: 1,1].
- headline=string
- Optional headline, which is written as the
first item in the snapshot file, the next item being the snapshot itself.
[Default: not used].
- nmodel=integer
- Number of models to generate. All models
will be different here. Although mostly meant for benchmarks, generating
more then 1 model can be useful to process very large snapshots (that normally
won’t fit in memory) in a serialized fashion. See also snapsplit. Most NEMO
programs will only read the first snapshot. See also mkgrid nmodel= for
a faster way to benchmark.
[Default: 1]
- mode=0|1|2
- The processing mode, purely for debugging benchmarks.
0=no data written. 1=data written, but no extra analysis. 2=data written,
and extra analysis done.
[Default: 1]
The scale length of a Plummer sphere in virial units
is 3.pi/16 ~ 0.589. As an example the following two commands should plot
the same "rotation" curve:
mkplummer - 10000 | radprof - tab=t | tabplot
- 1 3 0 2 0 1 yapp=1/xs
rotcurves plummer ’0,1,3*pi/16’ xrange=0,2 yrange=0,1 yapp=2/xs
For small N-body systems it can easily happen that small
random fluctuations cause a unacceptabel large deviation from an ideal
Plummer sphere. One way to achieve more "quiet" initial conditions is by
positioning the particles more "uniformly" in their 1/N mass shells, instead
of uniformly filling the space between 0 and 1. This is controlled by the
quiet=1 setting. An even more quiet start can be achieved by placing the
particles on exactly the radius compatible with its mass fraction, this
is achieved with the the quiet=2 setting.
In this example you can clearly
see the difference between the radii selected:
mkplummer - 10 quiet=0
zerocm=f | snapsort - - r | snapprint - r | tabplot - 0 1 line=1,1 point=2,0.1
mkplummer - 10 quiet=1 zerocm=f | snapsort - - r | snapprint - r | tabplot -
0 1 line=1,1 point=2,0.1
mkplummer - 10 quiet=2 zerocm=f | snapsort - - r | snapprint - r | tabplot -
0 1 line=1,1 point=2,0.1
Important to note that with zerocm=f the center of mass will drift,
while the "mathematical center" was placed at the origin. This will counter
the quietness, if you will.
A non-delta function mass-spectrum will
not create a properly virialized system yet. See snapvirial(1NEMO)
For very
large (>1000) ratio in the mass ranges the spline interpolation, used in
frandom(3NEMO)
, can fail using a valid [0,1] range.
mkplummer can
also be used to create a plummer sphere with a mass spectrum, e.g. a Salpeter
mass spectrum with
mkplummer salpeter.dat 10000 massname=’n(m)’ massexpr=’pow(m,p)’
masspars=p,-2.35 massrange=0.1,10
Another method to create a Plummer sphere is by using the Osipkov-Merritt
tables in NEMO, e.g.
plummer plum.dat ntab=1024
mkommod plum.dat plum.snap nbody=10000
or in ZENO their new General Spherical Profile:
plumsnap plum1.snap
plumgsp plum.gsp
gsprealize plum.gsp plum.snap zerocm=true
snapcopy plum.snap plum2.snap
with a note that ZENO files may need an extra snapcopy(1NEMO)
to be
compatible with NEMO snapshot(5NEMO)
files.
The default benchmark
(see Benchfile) creates a 10,000,000 snapshot in double precision, with
and without writing to a local file:
cd $NEMO/nemo/src/nbody/init/
make -f Benchfile bench0 bench1
or
/usr/bin/time mkplummer . 10000000
/usr/bin/time mkplummer bench1.snap 10000000
with some sample CPU for bench0: xps13 3.1s or 171 MB/s
t480 4.9s or 72 MB/s
the time difference betweeen bench0 and bench1 can be interpreted as
the time needed to write 535MB (for 10M particles)
NEMO/src/nbody/init/mkplummer.c
mkpolytrope(1NEMO)
, snapvirial(1NEMO)
, mkplummer(3NEMO)
, snapmass(1NEMO)
,
snapsplit(1NEM0)
, mkgrid(1NEMO)
, mkplum(1NEMO)
, mcluster(1NEMO)
, xrandom(3NEMO)
H.C.Plummer (1911), MNRAS, 71, 460.
S.J. Aarseth, M. Henon and R. Wielen (1974),
Astron. and Astrophys. 37, p. 183.
A.H.W. Kuepper, Th. Maschberger, P. Kroupa and
H. Baumgardt, 2011, MNRAS, 417, 2300 (McLuster)
Arnold et al. (2022) - https://arxiv.org/abs/2207.10681
- https://github.com/r-j-arnold/gen_fractal_star_clusters
@ads 1974A&A....37..183A
Piet Hut (Peter Teuben)
~/src/nbody/init mkplummer.c
23-Apr-87 Version 1.0: created PIET
10-Jun-88 Version 1.1: created PIET
xx-xxx-88 V1.2: zerocm keyword added PJT
xx-Mar-89 V2.0: full new snapshot version+doc PJT
15-nov-90 V2.3: mass-spectrum and cleanup for NEMO 2.x PJT
6-jun-96 V2.5d: report total mass before scaling PJT
21-mar-04 V2.7: added mlow= PJT+NCM
11-apr-05 V2.8: added nmodel= PJT
15-sep-10 V2.9: clarified rfrac and allow rfrac<0 PJT
2-dec-2017 documented mcluster PJT
29-mar-2021 benchmark PJT
25-sep-2023 describe quiet starts PJT
1-apr-2024 experimenting with how to place defaults PJT
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