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mkplummer - construct a Plummer model
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 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).
is also an implementation in Dehnen’s falcON suite: mkplum(1NEMO)
advanced Plummer models, see mcluster(1NEMO)
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.
The scale length of a Plummer sphere
in virial units is 3.pi/16 ~ 0.589. As an example this should plot the same
- Output data is written into snapfile, in standard snapshot(5NEMO)
- Number of particles nobj in N-body snapshot realization
of the Plummer model.
- inner core mass fraction within which no
stars will be populated. (Default: 0)
- 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).
- 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).
for the random number generator (default: 0, which will be converted into
a unique new value using UNIX’s clock time, in seconds since 1970.0). See
- Time at which the snapshot applies (default:
- Reset center of mass to zero? [default: t].
- A scale factor or scale to virial units (M=G=-4E=1). Use -1 for virial units
(see also VIRIAL 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].
- Level of quit start. 0 is noisy, 1=somewhat
quiet, 2=more quiet. See "QUIET START" below [default: 0].
- 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].
- 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:
- List of parameters and their values. They can be
used by name in the massexpr specified before. [default: p,0.0].
- 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].
- Optional headline, which is written
as the first item in the snapshot file, the next item being the snapshot
itself. [default: not used].
- Number of models to generate.
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 Default:
- 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].
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
% mkplummer salpeter.dat 10000 massname=’n(m)’ massexpr=’pow(m,p)’ masspars=p,-2.35
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 the new General Spherical Profile in ZENO:
% 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)
The default benchmark (see Benchfile)
creates a 10,000,000 snapshot in double precision, with and without writing
to a local file:
make -f Benchfile bench0 bench1
/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)
(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
Piet Hut (Peter Teuben)
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
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