An algorithm for the reconstruction of the projected gravitational potential of galaxy clusters from galaxy kinematics

In this work we develop a method to incorporate the information from galaxy kinematics into the reconstruction of the two-dimensional, projected gravitational potential of galaxy clusters. We start by deprojecting the observed line-of-sight velocity dispersions of cluster galaxies with an application of Bayes' theorem, the Richardson-Lucy method, requiring the assumption of a shape for the cluster. Assuming spherical symmetry, after the deprojection we obtain an effective galaxy pressure, i.e. the density-weighted radial velocity dispersions of the cluster galaxies, which is then related to the three-dimensional gravitational potential by using the tested assumption of a polytropic relation between the effective galaxy pressure and the density. The two-dimensional gravitational potential can finally be found by straightforward projection along the line of sight. We test the method with a numerically simulated triaxial galaxy cluster and the galaxies identified therein and perform the reconstruction for three different lines of sight, initially assuming sphericity. Expanding the gravitational potential in the cluster's geometrical ellipticities yields second-order corrections to the spherical reconstruction. By comparing our results with the projected gravitational potential directly obtained from the simulation, we show that the deviation between the projected potential obtained with our reconstruction method and the potential directly extracted from the simulation is $\lesssim10~\%$ within approximately the virial radius ($1.5\,h^{-1}\mathrm{Mpc}$) from the cluster centre in the case of a spherical cluster and remains moderate (below $10\,\%-25\,\%$) within the same radius in the case of an ellipsoidal cluster

Reconstructing the projected gravitational potential of Abell 1689 from X-ray measurements

Context. Galaxy clusters can be used as cosmological probes, but to this end, they need to be thoroughly understood. Combining all cluster observables in a consistent way will help us to understand their global properties and their internal structure. Aims. We provide proof of the concept that the projected gravitational potential of galaxy clusters can directly be reconstructed from X-ray observations. We also show that this joint analysis can be used to locally test the validity of the equilibrium assumptions in galaxy clusters. Methods. We used a newly developed reconstruction method, based on Richardson-Lucy deprojection, that allows reconstructing projected gravitational potentials of galaxy clusters directly from X-ray observations. We applied this algorithm to the well-studied cluster Abell 1689 and compared the gravitational potential reconstructed from X-ray observables to the potential obtained from gravitational lensing measurements. [...] Results. Assuming spherical symmetry and hydrostatic equilibrium, the potentials recovered from gravitational lensing and from X-ray emission agree very well beyond 500 kpc. Owing to the fact that the Richardson-Lucy deprojection algorithm allows deprojecting each line of sight independently, this result may indicate that non-gravitational effects and/or asphericity are strong in the central regions of the clusters. Conclusions. We demonstrate the robustness of the potential reconstruction method based on the Richardson-Lucy deprojection algorithm and show that gravitational lensing and X-ray emission lead to consistent gravitational potentials. Our results illustrate the power of combining galaxy-cluster observables in a single, non-parametric, joint reconstruction of consistent cluster potentials that can be used to locally constrain the physical state of the gas.Comment: 8 pages, 4 figures. Accepted in A&

Joint reconstruction of galaxy clusters from gravitational lensing and thermal gas I. Outline of a non-parametric method

We present a method to estimate the lensing potential from massive galaxy clusters for given observational X-ray data. The concepts developed and applied in this work can easily be combined with other techniques to infer the lensing potential, e.g. weak gravitational lensing or galaxy kinematics, to obtain an overall best fit model for the lensing potential. After elaborating on the physical details and assumptions the method is based on, we explain how the numerical algorithm itself is implemented with a Richardson-Lucy algorithm as a central part. Our reconstruction method is tested on simulated galaxy clusters with a spherically symmetric NFW density profile filled with gas in hydrostatic equilibrium. We describe in detail how these simulated observational data sets are created and how they need to be fed into our algorithm. We test the robustness of the algorithm against small parameter changes and estimate the quality of the reconstructed lensing potentials. As it turns out we achieve a very high degree of accuracy in reconstructing the lensing potential. The statistical errors remain below 2.0% whereas the systematical error does not exceed 1.0%.Comment: 7 pages, 5 figures. To appear in A&

Reconstructing the projected gravitational potential of galaxy clusters from galaxy kinematics

We develop a method for reconstructing the two-dimensional, projected gravitational potential of galaxy clusters from observed line-of-sight velocity dispersions of cluster galaxies. It is the third of an intended series of papers aiming at a unique reconstruction method for cluster potentials combining lensing, X-ray, Sunyaev-Zel'dovich and kinematic data. The observed galaxy velocity dispersions are deprojected using the Richardson-Lucy algorithm. The obtained radial velocity dispersions are then related to the gravitational potential by using the tested assumption of a polytropic relation between the effective galaxy pressure and the density. Once the gravitational potential is obtained in three dimensions, projection along the line-of-sight yields the two-dimensional potential. For simplicity we adopt spherical symmetry and a known profile for the anisotropy parameter of the galaxy velocity dispersions. We test the method with a numerically simulated galaxy cluster and galaxies identified therein. We extract a projected velocity-dispersion profile from the simulated cluster and pass it through our algorithm, showing that the deviation between the true and the reconstructed gravitational potential is less then 10% within approximately 1.2 Mpc/h from the cluster centre.Comment: 8 pages, submitted to A&

Corrigendum to "Cryptosporidium parvum: From foal to veterinary students" [Vet. Parasitol. 219 (2016) 53-56 Doi: 10.1016/j.vetpar.2016.02.001]

The authors would like to make a clarification regarding thestatement “To our knowledge, no zoonotic transmission fromhorses has been reported before”, following the recognition of atleast three previous papers (Choen and Snowden, 1996; Konkleet al., 1997; Okhuysen et al., 1999) in which cases of cryptosporid-iosis in veterinary students after contact with foals had been cited.In particular:Choen and Snowden (1996), in a “continuing education article”about Cryptosporidial diarrhea in foals, reported: “Recently, veteri-nary students exposed to foals with cryptosporidial diarrhea at ourcollege developed parasitologically confirmed intestinal cryptosporid-iosis”.Konkle et al. (1997) described nosocomial transmission of Cryp-tosporidium in a veterinary hospital and stated that the source ofinfection had been a calf that spread Cryptosporidium parvum infec-tion to a pony, an arabian foal (probably the source of infection forthe vet students) and a llama.Okhuysen et al. (1999), in a study dealing with the virulence ofthree distinct C. parvum isolates, reported: “The third isolate, desig-nated TAMU, was collected from a veterinary student who was exposedduring necropsy of an infected foal”.In all the above-mentioned papers, the transmission from foalsto humans was not explicitly defined in the abstract and was notconsidered in the discussion. Furthermore, PubMed search usingthe keywords ‘Cryptosporidium’ and ‘foals’ failed to identify thesepapers The authors thank the reader that pointed out the omission.Other studies applying sub-genotyping, although not describ-ing cases of zoonoses, have indicated that C. parvum causing foaldiarrhea is often indistinguishable from the parasites isolatedfrom local human cryptosporidiosis cases (Grinberg et al., 2008,2009) suggesting that infected foals represent a potential source ofzoonotic cryptosporidiosis.The authors deem necessary to draw the readership’s attentionto these papers in order to remove any possible doubt about thepublic health hazard posed by infected foals

The projected gravitational potential of the galaxy cluster MACS J1206 derived from galaxy kinematics

We reconstruct the radial profile of the projected gravitational potential of the galaxy cluster MACS J1206 from 592 spectroscopic measurements of velocities of cluster members. To accomplish this, we use a method we have developed recently based on the Richardson-Lucy deprojection algorithm and an inversion of the spherically-symmetric Jeans equation. We find that, within the uncertainties, our reconstruction agrees very well with a potential reconstruction from weak and strong gravitational lensing as well as with a potential obtained from X-ray measurements. In addition, our reconstruction is in good agreement with several common analytic profiles of the lensing potential. Varying the anisotropy parameter in the Jeans equation, we find that isotropy parameters, which are either small, β ≲ 0.2, or decrease with radius, yield potential profiles that strongly disagree with that obtained from gravitational lensing. We achieve the best agreement between our potential profile and the profile from gravitational lensing if the anisotropy parameter rises steeply to β ≈ 0.6 within ≈ 0.5 Mpc and stays constant further out

The projected gravitational potential of the galaxy cluster MACS J1206 derived from galaxy kinematics

We reconstruct the radial profile of the projected gravitational potential of the galaxy cluster MACS J1206 from 592 spectroscopic measurements of velocities of cluster members. To accomplish this, we use a method we have developed recently based on the Richardson-Lucy deprojection algorithm and an inversion of the spherically-symmetric Jeans equation. We find that, within the uncertainties, our reconstruction agrees very well with a potential reconstruction from weak and strong gravitational lensing as well as with a potential obtained from X-ray measurements. In addition, our reconstruction is in good agreement with several common analytic profiles of the lensing potential. Varying the anisotropy parameter in the Jeans equation, we find that isotropy parameters, which are either small, β ≲ 0.2, or decrease with radius, yield potential profiles that strongly disagree with that obtained from gravitational lensing. We achieve the best agreement between our potential profile and the profile from gravitational lensing if the anisotropy parameter rises steeply to β ≈ 0.6 within ≈ 0.5 Mpc and stays constant further out