Improved Lemaitre-Tolman model and the mass and turn-around radius in group of galaxies. (arXiv:2103.12714v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Popolo_A/0/1/0/all/0/1">Antonino Del Popolo</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Deliyergiyev_M/0/1/0/all/0/1">Maksym Deliyergiyev</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Chan_M/0/1/0/all/0/1">Man Ho Chan</a>
We extended the modified Lemaitre-Tolman model 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 $simeq 90$ % 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 Ref.[New Astronomy 11(4):325, A&A 488(3):845].
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 Ref.[New Astronomy 11(4):325, A&A
488(3):845], 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 $w$.
We extended the modified Lemaitre-Tolman model 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 $simeq 90$ % 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 Ref.[New Astronomy 11(4):325, A&A 488(3):845].
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 Ref.[New Astronomy 11(4):325, A&A
488(3):845], 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 $w$.
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