Notes on exercises to find shear peaks with the MAP statistics (Thomas Erben) ============================================================================= 1. Overall Task: ---------------- I created artificial galaxy fields each containing a gravitational lens in the form of a Singular Isothermal Sphere (SIS) with a velocity dispersion between 600 and 900 km/s. The lens is located at an unknown position in a region of about 64 square arcmin. It is assumed to be in the foreground at a redshift of 0.3 while ALL galaxies you work with are at a redshift of unity, i.e. during your studies you DO NOT need to worry about foreground/background separation but you can use that ALL galaxies are lensed. In a first step you obtain catalogues that list positions and ellipticities of galaxies. You have to implement the Map statistics and to search the mass concentration within your field. The velocity dispersion of the detected mass peak has to be estimated. At a later stage you will have to extract your galaxy catalogues from FITS images which contain the same lens/galaxy configuration as the catalogues. The FITS images resemble deep ground-based observations with a realistic PSF. You will have to go through the KSB formalism to obtain shear estimates and to repeat the application of MAP with your extracted catalogues. The use of this exercise is to develop a feeling for the detection and the analysis of massive (cluster sized) objects with Weak Lensing. Please note that you work under highly idealistic circumstances and the analysis is considerably more involved in reality. An application to real data will be done as a follow-up on this exercise if time permits it. The findings during this exercise are the topic of one of the talks to be held on Friday. 2. The Data ----------- - Everybody finds two catalogues and a FITS file with his/her name, e.g. patricia_ellip.txt and patricia_noellip.txt The 'noellip' version contains the galaxies with an intrinsic ellipticity of zero, i.e. they represent the pure lensing signal. This catalogue should serve you to test your MAP implementation (the detected peak has to be clearly visible here) and to crosscheck obtained results (e.g. the velocity dispersion of the SIS) when you start working on the 'ellip' version where all galaxies have a realistic, intrinsic ellipticity before being lensed. !!!! The Monday exercise ONLY needs these catalogues but NOT the FITS files !!!!! - The FITS file contains a simulated observation of the 'ellip' version of your catalogue. - Technical details on catalogues and simulations: - The catalogues contain four columns: x, y, e1, e2, where x and y are the pixel coordinates of the objects in the FITS file. Each pixel has a physical scale of 0.238 arcsec. e1 and e2 are ellipticities that correspond to DIRECT ESTIMATES OF THE REDUCED SHEAR, i.e. =g_1 and =g_2!!!! The total extent of your catalogues is about eight arcminutes in x and y, i.e. the total area corresponds to 64 square arcmin. - The cosmology used for the simulations is an Einstein de Sitter universe, i.e. Omega_m=1. and Omega_l=0. With zlens=0.3 and zsource=1.0 this leads to D_ds/D_s=0.5384 (you need this number to convert your shear signal to physical quantities such as the velocity dispersion of an SIS lens). 3. Proposed Work Steps: ----------------------- Please consider the following steps as one possibility to proceed for the Monday exercise. I list them to guide those with only little experience. 1. Create a 'stick' plot of your galaxy ellipticities from the catalogues and get a feeling how the STRONG lens looks if you take into account the intrinsic elliticity distribution but NO other errors (in reality you have errors in your measurements, MUCH less objects, a mix of foreground and background galaxies etc.) 2. implement Map and test it with the 'noellip' version of your catalogue. The stick plot from step 1 tells you where the lens is located and this should be the location of your highest peak in the MAP map. Use for the filter function that from eqs. (172) + (173) in Erben (Applications of the weak gravitational lens effect) Implement some mean to estimate the S/N of your shear peak (either use the analytic formula or implement orientation randomisation; how do you obtain sigma_e for the analytic formula?) 3. Run your Map code on the ellip version of your catalogue and interpret your findings with respect to S/N of your detection; dependence of S/N on the filter scale of the MAP aperture; other peaks in the field etc. 4. The number density in your catalogue is about 25 galaxies per square arcmin. The detectability of a lensing signal strongly depends on this number and in real observations you typically will have 8-15 galaxies per square arcmin. Mimic this effect by rejecting half the galaxies of your catalogue and repeat the Map analysis. (Hint: The UNIX command "awk '(NR%2==0) {print $0}' patricia_ellip.txt" prints to the screen a catalogue where every second line of "patricia_ellip.txt" is omitted) 5. Plot the tangential shear around your Map peak and compare it for the 'ellip' and 'noellip' version. The following step would be very useful if you can do it during the Monday session but with the limited time you have I do not expect it! 6. Estimate the velocity dispersion of the SIS with the help of the tangential shear plot from step 5. 4. Input SIS: ------------- The input velocity dispersions and the positions of the SIS lenses in your catalogues and your FITS images are: velocity dispersion (km/s) x (pixels) y (pixels) name 899 1249 1249 Daniela 803 606 507 Fabrice 611 1320 655 Holger 707 963 586 Mike 816 677 744 Patricia 694 892 1349 Patrick