Improved Lemaitre-Tolman model and the mass and turn-around radius in group of galaxies

Abstract We extended the modified Lemaitre-Tolman model (Peirani and de Freitas Pacheco, 2006; Peirani and de Freitas Pacheco, 2008) taking into account the effect of angular momentum and dynamical friction. The inclusion of these quantities in the equation of motion modifies the evolution of a perturbation, initially moving with the Hubble flow. Solving the equation of motions we got the relationships between mass, M , and the turn-around radius, R 0 . Knowing R 0 , the quoted relation allows the determination of the mass of the object studied. The relationships for the case in which also the angular momentum is taken into account gives a mass ≃ 90 % larger than the standard Lemaitre-Tolman model, and two times the value of the standard Lemaitre-Tolman model, in the case also dynamical friction is taken into account. As a second step, we found relationships between the velocity, v , and radius, R , and fitted them to data of the Local Group, M81, NGC 253, IC342, CenA/M83, and to the Virgo clusters obtained by Peirani and de Freitas Pacheco (2006); Peirani and de Freitas Pacheco (2008). This allowed us to find optimized values of the mass and Hubble constant of the objects studied. The fit gives values of the masses smaller with respect to the M − R 0 relationship method, but in any case 30%–40% larger than the v − R relationship obtained from the standard Lemaitre-Tolman model. Differently from mass, the Hubble parameter becomes smaller with respect to the standard Lemaitre-Tolman model, when angular momentum, and dynamical friction are introduced. This is in agreement with Peirani and de Freitas Pacheco (2006); Peirani and de Freitas Pacheco (2008), who improved the standard Lemaitre-Tolman model taking into account the cosmological constant. Finally, we used the mass, M , and R 0 of the studied objects to put constraints to the dark energy equation of state parameter, w . Comparison with previous studies show different constraints on w .