Open clusters: time-scales, core collapse and blue stragglers by Félix Llorente de Andrés et al. on Tuesday 22 November

We developed a mathematical model to derive time scales and the presence of

BS stars. The model is based on the variation of mass through a circle into the

cluster defined by a radius, and at a time; this mass cross is translated into

a differential equation that it can be integrated for a given radius (r) and a

determined time (t). From this equation we can derive the different time scales

that allows us to reach conclusions like: clusters not containing blue

strugglers (BS) stars disappear younger than those clusters containing BS. In

clusters containing BS stars, the volume which takes up half of the cluster

mass is bigger than the one corresponding to clusters without BS stars but the

time to catch it up is shorter. We also studied, by means of this equation, the

core collapse of stars of the cluster and the region where this concentration

is stopped/retained; this region is identified by means of the relation $c/ch$,

being $c=\log(rt/rc)$ and $ch=\log(rc/rh)$. Where rt and rc are the tidal and

the core radius respectively, and rh is the radius where half of the cluster

mass is concentrated. The model also drove us to the conclusion that the number

of the blue straggler stars in a cluster follows a distribution function whose

components are the ratio between relaxation time and the age, labelled as $\it

f$, and a factor, named $\varpi$, which is an indicator of the origin of the

BS; $\varpi$ increases as the number of BS increase but it is limited

to$\sim$5.0. The mentioned distribution function is expressed as $\it NBS$

$\sim$ $\it f^3$($\frac{1}{e^{\frac{f}{\varpi}}-1}$). The validity of this

function was carried out by means of matching the number of observed blue

straggler (BS) stars to the number of predicted ones in the available sample of

OC.

arXiv: http://arxiv.org/abs/http://arxiv.org/abs/2211.10915v1