Joint, parameter-free reconstruction of the mass distribution in galaxy clusters from all available data sets

• Applicant: Professor Dr. Matthias Bartelmann
• Subject Area: Astrophysics and Astronomy
• Term: from 2013 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 241898342

• Final Report Year: 2015

Final Report Abstract

The studies carried out and funded by this project can be summarised as follows: 1. We have completed the algorithm needed to reconstructed the two-dimensional, projected gravitational potential of galaxy clusters from measurements of cluster-galaxy kinematics. This algorithm has newly been developed, based on the central idea that the motion of the galaxies can be described by an effective, possibly anisotropic galaxy pressure related to the density by a polytropic relation. 2. The assumption of spherical symmetry in this algorithm has been relaxed to allow arbitrarily inclined, axially symmetric bodies. Expanding their gravitational potential in terms of its ellipticity, we found that the lowest-order deviation from spherical symmetry is quadratic in the ellipticity. Calibrations of the algorithm including the relaxed symmetry assumptions with numerically simulated clusters have shown that their projected gravitational potential is very faithfully recovered. 3. We have applied our algorithms for cluster-potential reconstruction from X-ray data and cluster-galaxy kinematics for the first time to observed galaxy clusters. In this context, it turned out to be necessary to relax the assumption of spherically-symmetric galaxy pressure by allowing anisotropic galaxy orbits. Allowing the anisotropy parameter to increase rapidly with radius and then to turn over to a constant, we could reproduce the potential profile known from gravitational lensing. Likewise, the application of our algorithm to observed X-ray data has returned a potential profile well in agreement with gravitational lensing. 4. Giving up symmetry assumptions completely, we have developed an integral algorithm for detecting characteristic scales in cluster mass distributions based on the complete information contained in weak gravitational lensing. The algorithm avoids theoretical prejudice and is translation-invariant. We could show that this new algorithm is indeed able to recover typical scales in cluster density profiles in presence of realistic noise. Deviating from our original plan, we have not completed the definition of an optimal χ2 function and the implementation of all available algorithms into the SaWLens code yet. We decided to postpone this because the SaWLens code has undergone substantial revision during the funding period of this project, now allowing reconstructions on fully unstructured grids.

Publications

• Joint reconstruction of galaxy clusters from gravitational lensing and thermal gas. II. Inversion of the thermal Sunyaev-Zel’dovich effect. April 2013, 7 S.
  C. L. Majer, S. Meyer, S. Konrad, E. Sarli, and M. Bartelmann
  
• Reconstructing the projected gravitational potential of galaxy clusters from galaxy kinematics. A&A, 570:A9, October 2014
  E. Sarli, S. Meyer, M. Meneghetti, S. Konrad, C. L. Majer, and M. Bartelmann
  
• An algorithm for the reconstruction of the projected gravitational potential of galaxy clusters from galaxy kinematics. PhD thesis, Heidelberg University, 2015
  E. Sarli-Waizmann
  
• Probing the Matter Distribution on Intermediate and Large Scales with Weak Light Deflections . PhD thesis, Heidelberg University, 2015
  B. Zieser
  
• Reconstructing the projected gravitational potential of Abell 1689 from X-ray measurements. A&A, 574:A122, February 2015
  C. Tchernin, C. L. Majer, S. Meyer, E. Sarli, D. Eckert, and M. Bartelmann
  
• The projected gravitational potential of the galaxy cluster MACS J1206 derived from galaxy kinematics. A&A, 584:A63, December 2015
  D. Stock, S. Meyer, E. Sarli, M. Bartelmann, I. Balestra, C. Grillo, A. Koekemoer, A. Mercurio, M. Nonino, and P. Rosati