DENMAX(1.1) DENMAX DENMAX(1.1)
NAME
denmax - Find gravitationally bound groups in N-body simula-
tions.
SYNOPSIS
denmax -e <fEpsilon> [-s <nSmooth>]
[-d <fMinDensity>] [-t <fMaxTemperature>]
[-z <fRedShift>] [-G <fGravConst>]
[-O <fOmega>] [-H <fHubble>] [-m <nMinMembers>]
[-p <xyzPeriod>]
[-px <xPeriod>] [-py <yPeriod>] [-pz <zPeriod>]
[-c <xyzCenter>]
[-cx <xCenter>] [-cy <yCenter>] [-cz <zCenter>]
[-r] [-nu] [-o <Output Name>]
Reads particles from stdin in the tipsy binary format.
OPTIONS
-e <fEpsilon>: No Default fEpsilon value!
This parameter should be set to the length scale of interest
for the groups. For example in a gas simulation it might be
set to the rough size of galaxies. This parameter also sets
the resolution limit of the simulation and thus the resolu-
tion of the density gradients used for sliding the parti-
cles. For more information of this parameter's signifigance
see the discussion below.
[-s <nSmooth>]: Default nSmooth = 64
Specifies the number of neighbors to smooth over when find-
ing densities.
[-d <fMinDensity>]: Default fMinDensity = 0.0
This sets the minimum density for dark matter or gas parti-
cles which are considered for grouping.
[-t <fMaxTemperature>]: Default fMaxTemperature = HUGE
This sets the maximum temperature for gas particles which
are considered for grouping.
[-z <fRedShift>]: Default fRedShift = 0.0
The redshift of the input file. This is used to determine
physical coordinates from comoving ones. The default of 0.0
specifies that the input file is the state of the simulation
at our (the current) epoch.
[-G <fGravConst>]: Default fGravConst = 1.0
The relevant gravitational constant in the units of the
simulation. Most N-body simulations have their units set
such that this constant is 1.0.
[-O <fOmega>]: Default fOmega = 1.0
Stadel Release 1.1 Last change: May 28 1994 1
DENMAX(1.1) DENMAX DENMAX(1.1)
This sets the Omega parameter for the simulation in ques-
tion. The default value of 1.0 specifies a flat universe.
[-H <fHubble>]: Default fHubble = 0.0
Sets the Hubble constant for the simulation. If the simula-
tion was not performed in comoving coordinates then this can
be left at zero. Note that this must be set in the units of
the simulation.
[-m <nMinMembers>]: Default nMinMembers = 4
This argument allows the user to specify what the minimum
number of members (particles) per group should be. All
groups with less than this value will be dicarded.
[-px <xPeriod>]: Default non-periodic in x dimension
Specifies that denmax take into account periodicity in the
x-dimension given by the period <xPeriod>.
[-py <yPeriod>] [-pz <zPeriod>]: As above.
[-p <xyzPeriod>]: Default non-periodic in x,y and z dimen-
sions
Specifies that denmax take into account periodicity in all
three dimension given by the period <xyzPeriod>. This can be
used in place of the above as a shorthand.
[-cx <xCenter>]: Default box center is 0.0 in x dimension
Specifies the center of the periodic box when denmax takes
into account periodicity in the x-dimension. This arguement
can be ignored for a non-periodic simulation.
[-cy <yCenter>] [-cz <zCenter>]: As above for y and z dimen-
sions.
[-c <xyzCenter>]: Default box center is 0.0 in x,y and z
dimensions
For periodic simulations specifies the center of the box in
all three dimensions. This is a shorthand to the above.
[-r]: Causes the denmax.ray output file to be produced.
By default denmax does not produce the denmax.ray output
file. With this argument present it will produce this (tipsy
vector format) file.
[-nu]: Disables Unbinding (No Unbinding).
When this flag is specified denmax will bypass the unbinding
procedure but still output all the normal group information.
This is useful if special unbinding methods are required for
a simulation or if unbinding is completely undesired. The
user can write a special unbinding program which would read
the denmax.grp file.
Stadel Release 1.1 Last change: May 28 1994 2
DENMAX(1.1) DENMAX DENMAX(1.1)
[-o <Output Name>]: Default Output Name = "denmax".
This allows the user to specify an alternate name for the
output files. For example, if the user specifies -o sim5 on
the command line, then denmax will by default produce the
files sim5.grp and sim5.gtp (and if requested sim5.ray).
DESCRIPTION
Denmax finds gravitationally bound groups in N-body simula-
tions. The general procedure is first to decide which parti-
cles should be grouped, these are called the "moving" parti-
cles. The particles considered may be of a certain type
(there are three types in the tipsy format, dark matter, gas
and stars). They may have to satisfy a minimum density cri-
terion and may also (in the case of gas) need to satisfy a
maximum temperature criterion. This choice of particles is
affected by the type of input file and the users settings
for the minimum density and maximum temperature. There are
seven possible types of tipsy input files and here is how
each is handled.
Dark matter only: density and density gradients are calcu-
lated from all the particles (dark), and the moving parti-
cles are those meeting the minimum density criterion.
Gas only: density and density gradients are calculated from
all the particles (gas), and the moving particles are those
meeting both the minimum density and maximum temperature
criteria.
Stars only: density gradients are calculated from all the
particles (stars), and all the particles are moved.
Gas and dark matter: density and density gradients are cal-
culated from the gas particles only, and the moving parti-
cles are the gas particles which meet the density and tem-
perature criteria.
Stars and gas: density gradients are calculated from the
star particles only, and the moving particles are all the
star particles.
Stars and dark matter: Same as stars and gas case.
Stars and gas and dark matter: density and density gradients
are calculated from all the star particles and all the gas
particles. The moving particles are then the gas particles
meeting the density and temperature criteria and all the
star particles.
Once the moving particles have been found they are then
moved along the initial density gradients toward regions of
Stadel Release 1.1 Last change: May 28 1994 3
DENMAX(1.1) DENMAX DENMAX(1.1)
higher density. The particles are successively stepped a
distance of fEpsilon/4.0 in this manner until they stay
within a distance of fEpsilon over 5 steps. This mean that
they are oscillating in a local high density region. We
then group all the particles in each high density region
together using the friends-of-friends method with a linking
length of fEpsilon. Note that this also links together high
density regions seperated by less than fEpsilon. Once all
particles are localized in this way, we proceed to "squish"
them together even more to find the high density center.
Lastly we discard groups with less than nMinMembers number
of particles.
The next stage (if the user has not specified -nu) is to
remove particles from a group which are not gravitationally
bound to it. We call this phase unbinding and the initial
positions are considered here, not the moved positions.
There are cases for unbinding, one for dark matter only or
star particle only inputs (case I unbinding) and one for the
other input types (case II unbinding).
Case I unbinding:
1. Calculate the potential energies of all the particles in
the group taking into account the redshift of the simulation
to get physical distances (redshift zero applies also to a
simulation in physical coordinates).
2. The center of mass and center of mass velocity for the
group is found. The velocity relative to the center of mass
velocity if found for all the particles in the group. This
relative velocity is converted to a physical velocity by
taking into account the redshift and adding a term to
include the Hubble flow. For a simulation in physical coor-
dinates fHubble must be 0.0. (Note that this is the
default!) From this the kinetic energy with respect to the
center of mass is found for all particles in the group.
3. The least bound particle is found. If this particle is
bound then all particles are bound and we have finished
unbinding for this group. Otherwise we must remove it from
the group, adjusting the potential energies and kinetic
energies (the center of mass changes) of the remaining par-
ticles and return to step 3.
Case II unbinding:
Here we include some of the group's environment to the
potential. For example a galaxy depends on its dark matter
halo in order to stay together.
1. Calculate the potential energies as per case I, step 1.
Stadel Release 1.1 Last change: May 28 1994 4
DENMAX(1.1) DENMAX DENMAX(1.1)
1a. Include the potential contribution of all non-grouped
mass within a 2*fEpsilon ball about the center of the high
density region of the group. In otherwords we want to
include some of the mass about the density maximum.
2. Calculate the kinetic energies as per case I, step 2.
3. The least bound particle is found. If this particle is
bound then again we are finished with the group. Otherwise
we remove it from the group, adjusting the kinetic energies
as in case I. Then we go back to step 3. Note that this time
we do not subtract the potential energy contribution of this
particle from the others in the group. The potential ener-
gies remain fixed as any removed particle is still con-
sidered to be part of the groups environment.
After unbinding we check once more that all groups have at
least nMinMembers number of particles. We discard those that
don't and output the group information.
OUTPUT FILES
Denmax produces three different output files, by default a
denmax.grp file, and a denmax.gtp file. Optionally also a
denmax.ray file.
denmax.grp: This ASCII file is in TIPSY ARRAY format and
contains the group number to which each particle in the
input file belongs. Group number zero means this particle
was not grouped (could have been removed by unbinding). This
file can be read in by tipsy or any other analysis tool able
to read this format.
denmax.gtp: This file is in TIPSY BINARY format (same as the
input file) and contains one star particle to represent each
group that denmax finds. Each particle in this file has as
its position, the position of the group's density maximum.
As its velocity, the center of mass velocity of the group.
Each star particle's mass is the mass of the entire group
and the star_particle.eps field contains the radial size of
the group. (The time stamp of the input file is also stored
in each star_particle.tform field.) This file can also be
read in by tipsy or any tool accepting TIPSY BINARY format.
denmax.ray: This ASCII file is in TIPSY VECTOR format and
contains a vector pointing from the initial position of each
particle to the localized (moved and squished) position of
that particle. For particles not moved the vector stored is
null. This file can be read in by tipsy and used to analyse
the actions of denmax.
Stadel Release 1.1 Last change: May 28 1994 5
DENMAX(1.1) DENMAX DENMAX(1.1)
EXAMPLES
> denmax -e 9e-4 -H 2.8944 -d 170 -p 1 -o dark < dark.bin
This example groups dark matter particles in the file
dark.bin. The simulation is periodic with period length of
1.0 in each dimension and box centered on (0,0,0). The Hub-
ble constant in system units in this case is 2.8944
(sqrt(8*Pi/3)) and the redshift defaults to 0 (current
epoch). The density cut is made at a density of 170 (mean
density is 1 in these units). The files dark.grp and
dark.gtp are produced.
> denmax -e 9e-4 -H 2.8944 -d 170 -t 30000 -z 1 -p 1 <
all.bin
Here we suppose that dark matter, gas and stars are in the
input file. A cut in the gas is made at a density minimum of
170 and temperature maximum of 30000 (cold dense gas) and
groups of this gas and all the stars are formed at a red-
shift of 1. The files denmax.grp and denmax.gtp are created.
> denmax -e 0.5 -d 100 -m 8 -r -nu -o phys < phys.bin
Here denmax processes a dark matter file in physical coordi-
nates which is non-periodic. It makes a density cut at 100
and finds the groups, but does not try to unbind any parti-
cles. It does remove groups with less than 8 members. The
output files phys.grp, phys.gtp and phys.ray (-r) are pro-
duced.
WARNINGS
1. Make sure you set fEpsilon to a reasonable size for your
simulation. If too small it can take a long time to converge
and may not give reasonable groups do to the limited resolu-
tion of objects in the simulation. If too large, it will
miss the smaller scale objects and may group together many
smaller objects to form large associations. For example the
desired groups could be galaxies in a gas and dark matter
simulation, epsilon should reflect this fact.
2. Do not run denmax with an nSmooth of less than 64 when
finding groups in a dark matter only input file. For gas
simulations an nSmooth of 32 is acceptable.
3. The unbinding procedure is O(Ngroup^2), this means that
for very large simulations and specifically situations where
groups larger than a couple of thousand members are found
the unbinding procedure could be prohibitive. So far this
has not been a real problem, even in a 2.1 million particle
simulation, however, future versions of denmax may need to
use a tree code for the group pootential energies. (The
Stadel Release 1.1 Last change: May 28 1994 6
DENMAX(1.1) DENMAX DENMAX(1.1)
friends-of-friends is actually also O(Ngroup^2) but this is
not such a big problem)
BUGS
Please report any!
SEE ALSO
tipsy(1), smooth(1), fof(1)
Stadel Release 1.1 Last change: May 28 1994 7
