Improving lensing cluster mass estimate with flexion

Abstract

Gravitational lensing has long been considered as a valuable tool to determine the total mass of galaxy clusters. The shear profile as inferred from the statistics of ellipticity of background galaxies allows to probe the cluster intermediate and outer regions thus determining the virial mass estimate. However, the mass sheet degeneracy and the need for a large number of background galaxies motivate the search for alternative tracers which can break the degeneracy among model parameters and hence improve the accuracy of the mass estimate. Lensing flexion, i.e. the third derivative of the lensing potential, has been suggested as a good answer to the above quest since it probes the details of the mass profile. We investigate here whether this is indeed the case considering jointly using weak lensing, magnification and flexion. We use a Fisher matrix analysis to forecast the relative improvement in the mass accuracy for different assumptions on the shear and flexion signal -to -noise (S/N) ratio also varying the cluster mass, redshift, and ellipticity. It turns out that the error on the cluster mass may be reduced up to a factor ∼ 2 for reasonable values of the flexion S/N ratio. As a general result, we get that the improvement in mass accuracy is larger for more flattened haloes, but it extracting general trends is a difficult because of the many parameters at play. We nevertheless find that flexion is as efficient as magnification to increase the accuracy in both mass and concentration determination.

Analysis of the Yukawa gravitational potential inf(R)gravity. II. Relativistic periastron advance

“…The parameter λ naturally arises from the theory, and acts as a screening mechanism. It makes the Yukawa correction be negligible at small scales while relevant at galactic, extragalactic and cosmological scales providing a possible way to explain galaxy rotation curves, cluster of galaxies and the accelerated expansion of the Universe without requiring Dark Matter and/or Dark Energy [27,28,82,[84][85][86][87].…”

Dark matter in galaxies

“…From the theoretical point of view, the main problem of these models is the use of additional hidden parameters which are absent in the classical theory. The MoND uses the parameter a 0 , Horava-Lifshitz theory [22] uses four parameters for function Φ N N (r; m) ; the similar situation occurs in the conformal gravity theory [23] and in other theories exploiting diverse gravitational potentials. However, only observations of galaxies and their systems can play a decisive role in testing different approaches, which in some cases revealed serious discrepancies of data with MoND predictions.…”

“…baryonic) mass of galaxies on the radial velocity corresponding to the rotation curve plateau (the so-called Tully-Fisher baryonic relation), which indeed is close to M bar ∝ V 4 . Other forms of the gravitational potential different from the classical expression have also been proposed [22]: Φ(r) = −Gm/r + Φ N N (r; m) or Φ(r) = −Gm/(r(1 + δ(r))) .…”

A nonextensive approach for understanding the van der Waals’ equation

“…The modification coefficients a and b are generally thought to originate from the interactions between particles in the gas and the temperature T is a constant everywhere. If the intermolecular interactions can be expressed by Lennard-Jones potential, 12 6 0 0 0 ( ) 2 r r r r r…”

“…In recent years, a new statistical theory about the complex systems, called as nonextensive statistics, has been developed very well on the basis of the nonextensive entropy proposed by Tsallis in 1988 [4]. Nonextensive statistics can help us to understand the complex systems being in nonequilibrium states and having inter-particle interactions, and it has also obtained a lot of valuable applications in a variety of different science and technology fields, such as astrophysical and space plasmas [5][6][7][8][9][10], self-gravitating systems [11][12][13][14], chemical physics [15][16][17][18] and many other scientific researches [19][20][21]. Martinez et al discussed a generalization of the van der Waals' equation in nonextensive statistics [22].…”