.help gallist Feb90 noao.artdata
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TASK
gallist -- make an artificial galaxies list
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USAGE
gallist gallist ngals
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PARAMETERS
.ls gallist
The name of the output text file for the x and y coordinates,
magnitudes, profile types, half-flux radii, axial ratios, and position
angles of the artificial galaxies.  Output will be appended to this
file if it exists.
.le
.ls ngals = 100
The number of galaxies in the output galaxies list.
.le
.ls interactive = no
Examine plots and change the parameters of the spatial, luminosity, and
morphology distributions interactively.
.le

			SPATIAL DISTRIBUTION
.ls spatial = "uniform"
Type of spatial distribution for the galaxies.  The types are:
.ls uniform
The galaxies are uniformly distributed between \fIxmin\fR, \fIxmax\fR,
\fIymin\fR, and \fIymax\fR.
.le
.ls hubble
The galaxies are distributed around the center of symmetry \fIxcenter\fR and
\fIycenter\fR according to a Hubble density law of core radius
\fIcore_radius\fR and background density \fIbase\fR.
.le
.ls file
The radial density function is contained in the text file \fIsfile\fR.
.le
.le
.ls xmin = 1., xmax = 512., ymin = 1., ymax = 512.
The range of the output coordinates in pixels.
.le
.ls xcenter = INDEF, ycenter = INDEF
The coordinate of the center of symmetry for the "hubble"
and "file" radial density functions. The default is the
midpoint of the coordinate limits.
.le
.ls core_radius = 50
The core radius of the Hubble density distribution in pixels.
.le
.ls base = 0.0
The background density relative to the central density of the Hubble
density distribution.
.le
.ls sseed = 2
The initial value supplied to the random number generator used to
generate the output x and y coordinates.
If a value of "INDEF" is given then the clock
time (integer seconds since 1980) is used as the seed yielding
different random numbers for each execution.
.le

			MAGNITUDE DISTRIBUTION
.ls luminosity = "powlaw"
Type of luminosity distribution for the galaxies.  The types are:
.ls uniform
The galaxies are uniformly distributed between \fIminmag\fR and
\fImaxmag\fR.
.le
.ls powlaw
The galaxies are distributed according to a power law with coefficient
\fIpower\fR.
.le
.ls schecter
The galaxies are distributed according to a Schecter luminosity
function with characteristic magnitude \fImstar\fR and power law exponent
\fIalpha\fR between \fIminmag\fR and \fImaxmag\fR.
.le
.ls file
The luminosity function is contained in the text file \fIlfile\fR.
.le
.le
.ls minmag = -7., maxmag = 0.
The range of output relative magnitudes.
.le
.ls mzero = 15.
Magnitude zero point for Schecter luminosity function.
.le
.ls power = 0.6
Coefficient for the power law magnitude distribution The default value
of 0.6 is the Euclidean value.
.le
.ls alpha = -1.24
The power law exponent of the Schecter luminosity function.
The default value is that determined by Schecter from nearby galaxies.
.le
.ls mstar = -21.41
The characteristic magnitude of the Schecter luminosity function.
.le
.ls lseed = 2
The initial value supplied to the random number generator used to
generate the output magnitudes.
If a value of "INDEF" is given then the clock
time (integer seconds since 1980) is used as the seed yielding
different random numbers for each execution.
.le

			MORPHOLOGY DISTRIBUTION
.ls egalmix = 0.4
The fraction of the galaxies that are "ellipticals" represented
by a de Vaucouleurs surface brightness law as opposed to "spirals"
represented by an exponential disk surface brightness law.
.le
.ls ar = 0.3
Minimum elliptical galaxy axial ratio (major/minor ratio).
.le
.ls eradius = 20.0
The maximum elliptical galaxy half-flux semi-major scale radius.  This is
the radius of an elliptical galaxy with magnitude \fIminmag\fR
before a random factor is added.  Spiral galaxies and fainter galaxies
are scaled from this value.
.le
.ls sradius = 1.0
Ratio between half-flux scale radii of spiral and elliptical models at the
same magnitude.  For example an elliptical galaxy with magnitude
\fIminmag\fR will have radius \fIeradius\fR while a spiral galaxy
of the same magnitude with have radius \fIsradius\fR * \fIeradius\fR.
.le
.ls absorption = 1.2
Absorption correction for edge on spirals in magnitudes.
.le
.ls z = 0.05
Minimum redshift for power law distributed galaxies.  This is the
redshift assigned galaxies of magnitude \fIminmag\fR.  The redshifts
are assumed proportional to the square root of the apparent luminosity;
i.e the luminosity distance proportional to redshift.  The redshift is used
for computing the mean apparent sizes of the galaxies
according to (1+z)**2 / z.
.le

			USER FUNCTIONS
.ls sfile = ""
The name of the input text file containing the sampled spatial radial
density
function, one sample point per line, with the radius and relative probability
in columns one and two respectively. The sample points need not be
uniformly spaced or normalized.
.le
.ls nssample = 100
The number of points at which the spatial density function is 
sampled. If the spatial density function is analytic or approximated
analytically (the "hubble" option) the function is sampled
directly. If the function is read from a file  (the "file" option) an
initial smoothing step is performed before sampling.
.le
.ls sorder = 10
The order of the spline fits used to evaluate the integrated spatial
density function.
.le
.ls lfile = ""
The name of the input text file containing the sampled luminosity
function, one sample point per line, with the magnitude and relative
probability in columns one and two respectively. The sample points need
not be uniformly spaced or normalized.
.le
.ls nlsample = 100
The number of points at which the luminosity function is 
sampled. If the luminosity function is analytic or approximated
analytically (the "uniform", "powlaw" and "schecter" options) the
function is sampled directly.  If it is read from a file
(the "file" option) an initial smoothing step is performed before sampling.
.le
.ls lorder = 10
The order of the spline fits used to evaluate the integrated
luminosity function.
.le

			INTERACTIVE PARAMETERS
.ls rbinsize = 10.
The bin size in pixels of the plotted histogram of the radial density
distribution.
.le
.ls mbinsize = 0.5
The bin size in magnitudes of the plotted histogram of the luminosity function.
.le
.ls dbinsize = 0.5
The bin size in pixels of the plotted histogram of the half-power semi-major
axis distribution.
.le
.ls ebinsize = 0.1
The bin size of the plotted histogram of the axial ratio distribution.
.le
.ls pbinsize = 20.
The bin size in degrees of the plotted histogram of the position angle
distribution.
.le
.ls graphics = stdgraph
The default graphics device.
.le
.ls cursor = ""
The graphics cursor.
.le
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DESCRIPTION
\fBGallist\fR generates a list of x and y coordinates, magnitudes,
morphological types, half-power radii, axial ratios, and position
angles for a sample of \fIngals\fR galaxies based on a user selected
spatial density function \fIspatial\fR  and luminosity function
\fIluminosity\fR and writes (appends) the results to the text file
\fIgallist\fR. If the \fIinteractive\fR parameter is "yes" the user can
interactively examine plots of the spatial density function, the
radial density function,  the luminosity function, radii, axial ratios,
and position angle distributions and alter the parameters of the task
until a satisfactory artificial field is generated.

The spatial density function generates x and y values around a center
of symmetry defined by \fIxcenter\fR and \fIycenter\fR within the x and
y limits \fIxmin\fR, \fIxmax\fR, \fIymin\fR and \fIymax\fR according to
the spatial density function specified by \fIspatial\fR.  The three
supported spatial density functions are listed below where R is the
radial distance in pixels, P is the relative spatial density, C is a
constant, and f is the best fitting cubic spline function to the spatial
density function R(user), P(user) supplied by the user in the text file
\fIsfile\fR.

.nf
  uniform:  P = C
  hubble:   P = 1.0 / (1 + R / core_radius) ** 2 + base
  file:     P = f (R(user), P(user))
.fi

The Hubble and user spatial density functions are sampled at
\fInssample\fR equally spaced points, and integrated to give the
spatial density probability function at each sampled point. The
integrated probability function is normalized and approximated by a
cubic spline of order \fIsorder\fR.  The x and y coordinates are
computed by randomly sampling the integrated probability function until
\fIngals\fR galaxies which satisfy the x and y coordinate limits
\fIxmin\fR, \fIxmax\fR, \fIymin\fR and \fIymax\fR are generated.

The luminosity function generates relative magnitude values between
\fIminmag\fR and \fImaxmag\fR (before absorption effects are added)
according to the luminosity function specified by \fIluminosity\fR.
The four supported luminosity functions are listed below where M is the
magnitude, P is the relative luminosity function, C is a constant and f
is the best fitting cubic spline function to the luminosity function
M(user), P(user) supplied by the user in the text file \fIlfile\fR.

.nf
  uniform:   P = C
  powlaw:    P = C * 10. ** (power * M)
  schecter:  P = C * 10. ** (alpha * dM) * exp (-10. ** dM)
  file:      P = f (M(user), P(user))

  where      dM = 0.4 * (mstar - M + mzero)
.fi

The uniform distribution is not very physical but may be useful for
testing.  The power law distribution is that expected for a homogeneous
and isotropic distribution of galaxies.  The default value of 0.6 is
that which can be calculated simply from Euclidean geometry.  Observations
of faint galaxies generally show a smaller value.  The Schecter
function provides a good approximation to a galaxy cluster when
used in conjunction with the Hubble spatial distribution (though there
is no mass segregation applied).  The "best fit" values for the
parameters \fImstar\fR and \fIalpha\fR are taken from the paper by
Schecter (Ap.J 203, 297, 1976).  The \fImzero\fR parameter is used
to convert to absolute magnitudes.  Note that it is equivalent to
set \fImzero\fR to zero and adjust the characteristic magnitude
to the same relative magnitude scale or to use absolute magnitudes
directly.

The Schecter and user file distributions are sampled at \fInlsample\fR
equally spaced points, and integrated to give the luminosity
probability function at each sampled point. The probability function is
normalized and approximated by a cubic spline of order \fIlorder\fR.
The magnitudes are computed by randomly sampling the integrated
probability function until \fIngals\fR objects which satisfy the
magnitude limits \fIminmag\fR and \fImaxmag\fR are generated.

The artificial galaxies have one of two morphological types,
"ellipticals" with a de Vaucouleurs surface brightness law and
"spirals" with an exponential surface brightness law. The fraction
of elliptical galaxies is set by the parameter \fIegalmix\fR.  The
position angles of the major axis are distributed uniformly between 0.0
and 360.0 degrees.  The axial ratio (major to minor) of the elliptical
models is allowed to range uniformly between 1 and \fIar\fR
(that is E0 - E7).

The spiral models have inclinations, i, ranging uniformly between 0 and
90 degrees.  The axial ratio is then given by

	a/b = sqrt (sin(i)**2 * .99 + .01)

which is taken from Holmberg in Galaxies and the Universe (which
references the work of Hubble).  Note the axial ratio is limited to
0.1 by this formula.  An internal absorption correction is then
made based on the inclination using the relation

	dM = A * (min (10, cosecant (i)) - 1) / 9

where is the absorption of an edge on galaxy relative to face on and
the cosecant is limited to 10.  Note that this correction changes
allows galaxies with magnitudes less than \fImaxmag\fR and alters
the luminosity function somewhat.  Or in other words, the luminosity
function is based on absorption corrected magnitudes.

The sizes of the galaxy images are scaled from the maximum half-flux
radius of an elliptical galaxy given by the parameter \fIeradius\fR.
This is the radius given to an elliptical galaxy of magnitude
\fIminmag\fR (prior to adding a random factor described below).  The
ratio between the half-flux radii of the exponential disk and de
Vaucouleurs models at a given total magnitude is set by the parameter
\fIsradius\fR (note this is a fraction of \fIeradius\fR and not an
actual radius).  This allows adjusting the relative surface brightness
of elliptical and spiral models.

The distribution of sizes is based on the apparent
magnitude of the galaxies.  For the power law magnitude distribution
the cosmological redshift factor for angular diameters is used.  The
redshift/magnitude relation is assumed to be such that the redshift is
proportional to the luminosity distance (the square root of the
apparent luminosity).  Thus,


.nf
                Z = z * 10. ** (0.2 * (M - minmag))
                Zfactor = ((1+Z)**2 / Z) / ((1+z)**2 / z)
  ellipticals:  r = eradisus * Zfactor
  spirals:      r = sradius * eradius * Zfactor
.fi

where z is the reference redshift at the minimum magnitude, and Z is the
redshift at magnitude M.  For very small z the size varies as the
luminosity distance but at larger z the images appear more extended with
lower surface brightness.  For very deep simulations a pure luminosity
distance relation gives faint galaxies which are too small and compact
compared to actual observations.

For the other magnitude distributions, the Schecter cluster function
in particular where all galaxies are at the same distance, the scale radius
obeys the following relation.

.nf
  ellipticals:  r = eradius * 10. ** ((minmag - M) / 6)
  spirals:      r = sradius * eradius * 10. ** ((minmag - M) / 6)
.fi

This relation gives the size decreasing slightly less rapidly than that
giving a constant surface brightness.  This relation is taken from
Holmberg (Galaxies and the Universe).

A uniform random factor of 50% is added to the sizes computed for
the power law magnitude distribution and 20% for the other distributions.

The interactive spatial plot shows the positions of the galaxies, the
galaxy type (circles are de Vaucouleurs profiles and other types are
diamonds), and rough size.
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CURSORS
The following interactive keystroke commands are available from within the
GALLIST task.

.nf
	Gallist Keystroke Commands

?	Print options
f	Fit one or more of following 
	    Spatial density function (SDF)
            Luminosity  function (LF)
	    Distribution of morphological type
	    Diameter distribution
	    Roundness distribution
	    Position angle distribution 
x	Plot the x-y spatial density function
r	Plot the histogram of the radial density function
m	Plot the histogram of the luminosity function
d	Plot the histogram of the diameter values
e	Plot the histogram of the roundness values 
p	Plot the histogram of the position angle values
:	Colon escape commands (see below)
q	Exit program
.fi

The following parameters can be shown or set from within the GALLIST task.

.nf
		Gallist Colon Commands

:show			Show gallist parameters
:ngal       [value]	Number of galaxies

:spatial    [string]	Spatial density function (SDF) (uniform|hubble|file) 
:xmin       [value]	Minimum X value
:xmax       [value]	Maximum X value
:ymin       [value]	Minimum Y value
:ymax       [value]	Maximum Y value
:xcenter    [value]	X center for SDF
:ycenter    [value]	Y center for SDF
:core       [value]	Core radius for Hubble density function
:base       [value]	Background density for Hubble density function

:luminosity [string]	Luminosity function (LF)
			(uniform|powlaw|schecter|file)
:minmag     [value]	Minimum magnitude
:maxmag     [value]	Maximum magnitude
:mzero      [value]	Magnitude zero-point of schecter LF
:power      [value]     Power law coefficient for powlaw LF
:alpha      [value]	Schecter parameter
:mstar      [value]	Characteristic mag for Schecter LF

:egalmix    [value]	Elliptical/Spiral galaxy ratio
:ar         [value]     Minimum elliptical galaxy axial ratio
:eradius    [value]     Maximum elliptical half flux radius
:sradius    [value]     Spiral/elliptical radius at same magnitude
:z          [value]     Minimum redshift
:absorption [value]     Absorption correction for spirals

:lfile      [string]    Name of the LF file
:sfile	    [string]    Name of the SDF file
:nlsample   [value]	Number of LF sample points 
:lorder	    [value]	Order of spline approximation to the integrated LF
:nssample   [value]	Number of SDF sample points
:sorder	    [value]	Order of spline approximation to the integrated SDF

:rbinsize   [value]	Resolution of radial SDF histogram in pixels
:mbinsize   [value]	Resolution of magnitude histogram in magnitudes
:dbinsize   [value]	Resolution of diameter histogram in pixels
:ebinsize   [value]	Resolution of roundness histogram in pixels
:pbinsize   [value]     Resolution of position angle histogram in degrees
.fi
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EXAMPLES
1. Create a galaxy cluster with a power law distribution of field galaxies
and stars as background/foreground.

.nf
    ar> gallist galaxies.dat 100 spatial=hubble lum=schecter egal=.8
    ar> gallist galaxies.dat 500
    ar> starlist galaxies.dat 100
    ar> mkobjects galaxies obj=galaxies.dat gain=3 rdnoise=10 poisson+
.fi

Note that the objects are appended to the same file.  Actually making
the image with \fBmkobjects\fR takes about 5 minutes (2.5 min cpu) on a
SPARCstation 1.

2. Examine the distributions for a uniform spatial distribution
and power law magnitude distribution using 1000 galaxies without
creating a data file.

.nf
    ar> gallist dev$null 1000 inter+
	    ... an x-y plot will appear on the screen
	    ... type r to examine the radial density function
	    ... type m to examine the luminosity function
	    ... type d to examine the half-flux radii distribution
	    ... type e to examine the axial ratio distribution
	    ... type = to make a copy of any of the plots
	    ... type q to quit
.fi
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REVISIONS
.ls GALLIST V2.11+
The random number seeds can be set from the clock time by using the value
"INDEF" to yield different random numbers for each execution.
.le
.ls GALLIST V2.11
The default value for the minimum elliptical galaxy axial ratio was
change to 0.3 to cover the range E0-E7 uniformly.
.le
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BUGS
This is a first version and is not intended to produce a full model
of galaxy fields.  Some of the relations used are empirical and
simple minded with the aim being to produce reasonably realistic images.

The spline approximation to the spatial density and luminosity
probability functions can cause wiggles in the output spatial density
and luminosity functions. Users can examine the results interactively
and experiment with the spline order and number of sample points if
they are not satisfied with the results of GALLIST. The default setup
of 10 sample points per spline piece is generally satisfactory for the
spatial density and luminosity functions supplied here.
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SEE ALSO
starlist mkobjects
.endhelp