Relation between the turnaround radius and virial mass in f ( R ) model

We investigate the relationship between the turnaround radius Rt and the virial mass Mv of cosmic structures in the context of ΛCDM model and in an f(R) model of modified gravity—namely, the Hu-Sawicki model. The turnaround radius is the distance from the center of the cosmic structure to the shell that is detaching from the Hubble flow at a given time, while the virial mass is defined, for this work, as the mass enclosed within the volume where the density is 200 times the background density. We employ a new approach by considering that, on average, gravitationally bound astrophysical systems (e.g., galaxies, groups and clusters of galaxies) follow, in their innermost region, a Navarro-Frenk-White density profile, while beyond the virial radius (Rv) the profile is well approximated by the 2-halo term of the matter correlation function. By combining these two properties together with the information drawn from solving the spherical collapse for the structures, we are able to connect two observables that can be readily measured in cosmic structures: the turnaround radius and the virial mass. In particular, we show that, in ΛCDM, the turnaround mass at z=0 is related to the virial mass of that same structure by Mt≃3.07Mv, while in terms of the radii we have that Rt≃3.7Rv (for virial masses of 1013h−1M⊙). In the f(R) model, on the other hand, we have Mt≃3.43Mv and Rt≃4.1Rv, for |fR0|=10−6 and the same mass scale. Therefore, the difference between ΛCDM and f(R) in terms of these observable relations is of order ∼10−20% even for a relatively mild strength of the modification of gravity (|fR0|=10−6). For the turnaround radius itself we find a difference of ∼9% between the weakly modification in gravity considered in this work (|fR0|=10−6) and ΛCDM for a mass of 1013h−1M⊙. Once observations allow precisions of this order or better in measurements of the turnaround Rt, as well as the virial mass Mv (and/or the virial radius Rv), these quantities will become powerful tests of modified gravity.