Using GLens

The configuration of the lens and observed multiple images is easy and intuitive. Since the diameter distances of the lenses and sources depend on the cosmology, the config- uration file starts with the definitions of the energy densitiesΩm,ΩΛand the Hubble constant H0. The image and lens positions are given in pixels and for the conversion to physical units a pixel scale is also required. For the calculation of the deflection angle, surface mass density and the shear, also the region of the sky in which these quantities are wanted needs to be defined. The format of the header is the following:

omega_matter value

omega_lambda value

h0 value

pixelscale value

36 C2. GL-      

The number of lenses can (in principle) be arbitrarily large to accommodate any possible substructure in the lens. For each lens, key profile parameters and a position, ellipticity and position angle can be defined. Any of the above mentioned parameters can also be allowed to have a range of values and the program will then find an op- timal value for that parameter in the range provided. In the following we show the configuration of an NSIE lens.

lens nsie

x y 0/1 (x_min x_max y_min y_max)

redshift

sigma 0/1 (min max)

core_radius 0/1 (min max)

ellipticy 0/1 (min max)

position_angle 0/1 (min max)

The configuration of a lens starts by defining its type. The type can be either nsie, enfw or bbs. Next follows the position of the lens in pixels and a 0 or a 1 indicating if the position is to be optimised. In case the position is to be optimised, then also the range in x and y need to be given. The last positional coordinate is the redshift. The meanings of the next two parameters depends on the lens profile. The first parameter gives the ’strength’ of the lens and the second the ’shape’. For the NSIE profile these are the velocity dispersion and core radius. For the ENFW profile these are r200 and concentrations. For the BBS profile the velocity dispersion and the truncation radius. The last two parameters are the ellipticity and the position angle of the ellipse. All parameters apart from the redshift can be marked as free parameters.

source redshift 0/1 min max weight

image x y image x y image x y

The multiple images used are grouped by their sources. The strength of the lens depends on the distance of the source and so a redshift needs to be estimated for all the sources. Any of the redshifts can optionally be added to the list of free parameters of the model. This can be done in cases where the redshifts of the sources are unknown, or account for the errors in photometric redshifts. The multiple images of a given source are assumed to originate from a singe point in the minimisation. Therefore one should try to select clearly identifiable features in the multiple images. For the source one needs to define its redshift (and possible an allowed range), a weight and

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the image positions. The weight can be used to give different relative importance to the different multiple images. The weight as well as the positions of multiple images are fixed.

The number of free parameters to be optimised is not limited, but the user should make sure that the number of free parameters is reasonable when compared to the constraints from the observed multiple images. Otherwise strong degeneracies between the model parameters can occur. More multiple images and lenses can be included by simply adding an lens or a source entry in the configuration file.

Once this has been done it is time to call GLens and let it do the work. GLens has many command line options but the most important are -s (–save) and -m (–minimise). -s takes no argument but -m needs to know whether the minimisations should be done in the source plane (1) or in the image plane (2). The optimised lens configuration will be saved in the same file (overwriting the old configuration) unless a different name for the output is given with the -o (–output) flag. If -s flag is used then the deflection angle, surface mass density and the shear data will be written to<input f ile>.fits (or to<out put f ile>.fits if<out put f ile>is defined with -o flag).

halkola@cursa:˜/glens>glens -s -m 2 <inputfile>

The fits data cube (where α, κand γare stored) is necessary for the plotting of critical curves and caustics as well as surface mass density contours. The critical curves are areas of very high magnification in the image plane. For a circular source this is also where the einstein ring would be seen. The caustics are the corresponding high magnification areas in the source plane. The data saved in the fits cube can also used to predict images and unlensing the observed multiple images in order to reconstruct the true source shape.