OBJECT Source name IMSIZE Output image size (cells) OUTNAME Output image name (name) OUTCLASS Output image name (class) OUTSEQ -1.0 9999.0 Output image name (seq. #) OUTDISK 0.0 9.0 Output image disk unit #. APARM 1:Source X1; 2:Source Y1; 3:Major Axis; 4:Minor Axis; 5:Angle; 6,7:Brightness BPARM 1:Source X2; 2:Source Y2; 3:Major Axis; 4:Minor Axis; 5:Angle; 6,7:Brightness CPARM 1:Source X3; 2:Source Y3; 3:Major Axis; 4:Minor Axis; 5:Angle; 6,7:Brightness DPARM 1:Lenx X0; 2:Lens Y0; 3:Angle (Deg) 4:Ring Size 5:Eccentric. 6:Core Radius 8:Lens Model, <2: Blandford >=2: Point Lens 9:Add Source >0 Yes 10:Image<0,Source>0;0=Both

GLENS Task: Model Gravitational LENS Magnification by either a Blandford galaxy or a point mass. The source model is made up of three ellipses which can be placed anywhere within the source plane. GLENS will produce a source plane or image plane map or both images. Glen Langstion, NRL, MPIfR and MIT, NRAO: November 1990 Adverbs: OBJECT.....Object name. IMSIZE.....Desired image size in cells. OUTNAME....Output image name (name). Standard behavior with default = 'SOURCE PLANE' or 'IMAGE PLANE'. OUTCLASS...Output image name (class). Standard defaults. OUTSEQ.....Output image name (seq. #). 0 => highest unique. OUTDISK....Disk drive # of output image. 0 => highest number with sufficient space. APARM......1:Source one x coordinate in Pixels. 2:Source one y coordinate in Pixels 3:Source one Major axis radius in Pixels 4:Source one Minor axis radius in Pixels 5:Source one Orientation angle in degrees. (Clockwise from north) 6:Source one Constant Brightness in arbitray units. 7:Source one Gaussian Brightness BPARM......1:Source two x coordinate in Pixels. 2:Source two y coordinate in Pixels 3:Source two Major axis radius in Pixels 4:Source two Minor axis radius in Pixels 5:Source two Orientation angle in degrees 6:Source two Constant Brightness in arbitray units. 7:Source two Gaussian Brightness CPARM......1:Source 3 x coordinate in Pixels. 2:Source 3 y coordinate in Pixels 3:Source 3 Major axis radius in Pixels 4:Source 3 Minor axis radius in Pixels 5:Source 3 Orientation angle in degrees 6:Source 3 Constant Brightness in arbitray units. 7:Source 3 Gaussian Brightness DPARM......1:X0- Galaxy Center Location in Pixels 2:Y0- Galaxy Center Location in Pixels 3:Theta- Galaxy Mass Major axis orientation (Degrees). (Measured Clockwise from North) 4:Einstein ring radius (pixels) 5:Galaxy projected eccentricty 6:Galaxy core size (pixels) 8:Lens Model, <=1 Blandford Kochaneck Lens, 2=Point Lens 9:Add Source: >0 Implies add source at un-lensed location 10: <0: Produce Image Plane >0: Source Plane 0: Both

GLENS: Task: Model Gravitational LENS Magnification by either a Blandford isothermal galaxy or a point mass. The source model is made up of three ellipses which can be placed anywhere within the source plane. GLENS will produce a source plane or image plane map or both maps. DOCUMENTOR: Glen Langston, MIT, MPIfR, NRL, and NRAO PURPOSE The magnification of by a gravitational lens on background objects (quasars) is modeled by GLENS. Two types of lens models are currently supported, the Blandford lens and a simple point mass lens. First a bit of terminology: GLENS produces two types of images, 1) Source Plane which is a map of the magnification of a background source if it at any position relative to the gravitational lens. 2) Image Plane which is a map of the source after distortion and magnification by the gravitational lens. GLENS allows a three component source model. Each of the three components are ellipses with variable major, minor axies and orientation angles. The surface brightness of each ellipse has two components, a constant part and a gaussian part. Both the Blandford lens and the Point lens have a characteristic size which determines the size of an Einstein Ring produced by perfect alignment of the lens and background object. For the Point lens DPARM(4) is the Einstein ring radius. This value is a function of the mass of the lens,M, and the distances between observer and quasar, D_q, between observer and lens, D_l, and between lens and quasar, D_lq. The ring radius in radians is equal to 1/2 [4 G M D_lq ] DPARM(4) = Theta_R = [----- -------] (pixels or radians). [ 2 ] [ c D_l D_q] The velocity of light is c, G is Newtons constant and the distances are angular distances (when measured from redshifs). The scale of the lensed images are all relative to the angular scale set by the Einstein ring size. The relative positions and sizes of the source components must be calculated by the user converting angular sizes to pixels. For the point lens, the source is always located radially inwards towards the lens relative to the image location. For the isothermal Blandford lens, the angular scale is also set by DPARM(4) which corresponds to the "A" parameter. The exponential parameter alpha is set to 1/2 in this model. Note that the orientation axis is for the galaxy mass, and that the source plane map of the magnification major axis will be orthogonal to the mass distribution major axis. ALGORITHM A difficulty in modeling gravitational lensing is that the mapping from source plane to image plane is ONE-TO-MANY. That is, several points in the image plane correspond to one point in the source plane. This leads to quadradic equations with several roots when starting with a source model and calculating the image plane. GLENS avoids this problem by starting from the image plane and following light backwards to the source plane. Each point in the image plane corresponds to exactly one point in the source plane. The effect of different types of gravitational lenses has been isolated into subroutines. The Point lens and Blandford lens effects are calculated by giving the subroutines the lens model parameters and an input x,y IMAGE location. The subroutines calculate the output x,y SOURCE location and the magnification of the source. Other lens types could be easily added. DEFAULT Running GLENS with all defaults yields a blandford lens with eccentricity = 0.1 and orientation angle = 30 degrees. The Einstein Ring radius is set to a fifth of the X axis size. (It is a fairly pretty default.) REFERENCES Blandford and Kochanek 1987, Ap. J. 321:658. Langston, Conner, Lehar, Burke and Weiler 1990, Nature, 344:43. Turner, Ostriker and Gott 1984, Ap. J. 284:1.