gallist: Make an artificial galaxies list

Package: artdata

Task

gallist -- make an artificial galaxies list

Usage

gallist gallist ngals

Parameters

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.

ngals = 100: The number of galaxies in the output galaxies list.

interactive = no: Examine plots and change the parameters of the spatial, luminosity, and morphology distributions interactively.

SPATIAL DISTRIBUTION

spatial = "uniform"

Type of spatial distribution for the galaxies. The types are:

uniform: The galaxies are uniformly distributed between xmin, xmax, ymin, and ymax.

hubble: The galaxies are distributed around the center of symmetry xcenter and ycenter according to a Hubble density law of core radius core_radius and background density base.

file: The radial density function is contained in the text file sfile.

xmin = 1., xmax = 512., ymin = 1., ymax = 512.: The range of the output coordinates in pixels.

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.

core_radius = 50: The core radius of the Hubble density distribution in pixels.

base = 0.0: The background density relative to the central density of the Hubble density distribution.

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.

MAGNITUDE DISTRIBUTION

luminosity = "powlaw"

Type of luminosity distribution for the galaxies. The types are:

uniform: The galaxies are uniformly distributed between minmag and maxmag.

powlaw: The galaxies are distributed according to a power law with coefficient power.

schecter: The galaxies are distributed according to a Schecter luminosity function with characteristic magnitude mstar and power law exponent alpha between minmag and maxmag.

file: The luminosity function is contained in the text file lfile.

minmag = -7., maxmag = 0.: The range of output relative magnitudes.

mzero = 15.: Magnitude zero point for Schecter luminosity function.

power = 0.6: Coefficient for the power law magnitude distribution The default value of 0.6 is the Euclidean value.

alpha = -1.24: The power law exponent of the Schecter luminosity function. The default value is that determined by Schecter from nearby galaxies.

mstar = -21.41: The characteristic magnitude of the Schecter luminosity function.

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.

MORPHOLOGY DISTRIBUTION

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.

ar = 0.3: Minimum elliptical galaxy axial ratio (major/minor ratio).

eradius = 20.0: The maximum elliptical galaxy half-flux semi-major scale radius. This is the radius of an elliptical galaxy with magnitude minmag before a random factor is added. Spiral galaxies and fainter galaxies are scaled from this value.

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 minmag will have radius eradius while a spiral galaxy of the same magnitude with have radius sradius * eradius.

absorption = 1.2: Absorption correction for edge on spirals in magnitudes.

z = 0.05: Minimum redshift for power law distributed galaxies. This is the redshift assigned galaxies of magnitude minmag. 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.

USER FUNCTIONS

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.

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.

sorder = 10: The order of the spline fits used to evaluate the integrated spatial density function.

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.

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.

lorder = 10: The order of the spline fits used to evaluate the integrated luminosity function.

INTERACTIVE PARAMETERS

rbinsize = 10.: The bin size in pixels of the plotted histogram of the radial density distribution.

mbinsize = 0.5: The bin size in magnitudes of the plotted histogram of the luminosity function.

dbinsize = 0.5: The bin size in pixels of the plotted histogram of the half-power semi-major axis distribution.

ebinsize = 0.1: The bin size of the plotted histogram of the axial ratio distribution.

pbinsize = 20.: The bin size in degrees of the plotted histogram of the position angle distribution.

graphics = stdgraph: The default graphics device.

cursor = "": The graphics cursor.

Description

Gallist generates a list of x and y coordinates, magnitudes, morphological types, half-power radii, axial ratios, and position angles for a sample of ngals galaxies based on a user selected spatial density function spatial and luminosity function luminosity and writes (appends) the results to the text file gallist. If the interactive 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 xcenter and ycenter within the x and y limits xmin, xmax, ymin and ymax according to the spatial density function specified by spatial. 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 sfile.

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

The Hubble and user spatial density functions are sampled at nssample 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 sorder. The x and y coordinates are computed by randomly sampling the integrated probability function until ngals galaxies which satisfy the x and y coordinate limits xmin, xmax, ymin and ymax are generated.

The luminosity function generates relative magnitude values between minmag and maxmag (before absorption effects are added) according to the luminosity function specified by luminosity. 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 lfile.

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)

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 mstar and alpha are taken from the paper by Schecter (Ap.J 203, 297, 1976). The mzero parameter is used to convert to absolute magnitudes. Note that it is equivalent to set mzero 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 nlsample 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 lorder. The magnitudes are computed by randomly sampling the integrated probability function until ngals objects which satisfy the magnitude limits minmag and maxmag 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 egalmix. 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 ar (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 maxmag 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 eradius. This is the radius given to an elliptical galaxy of magnitude minmag (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 sradius (note this is a fraction of eradius 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,

              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

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.

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

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.

Cursors

The following interactive keystroke commands are available from within the GALLIST task.

        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

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

                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

Examples

1. Create a galaxy cluster with a power law distribution of field galaxies and stars as background/foreground.

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+

Note that the objects are appended to the same file. Actually making the image with mkobjects 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.

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

Revisions

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.

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.

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.