A Model of the Dynamics of Open Clusters: Time-Scales, Core Collapse and Blue Stragglers

Félix Llorente de Andrés; Carmen Morales Durán

doi:doi:10.11648/j.ajaa.20210904.12

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A Model of the Dynamics of Open Clusters: Time-Scales, Core Collapse and Blue Stragglers

Félix Llorente de Andrés, Carmen Morales Durán

Published in American Journal of Astronomy and Astrophysics (Volume 9, Issue 4)

Received: 24 November 2022 Accepted: 12 December 2022 Published: 27 December 2022

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Abstract

This work presents a mathematical model of dynamic of open clusters (OC) from which their time scales are deduced as well as the number of blue stragglers (BS) present in the cluster. The model is based on the expansion of mass through a sphere defined by a radius, and at a time; this variation of mass is translated into a differential equation that it can be integrated for a given radius (r) and a determined time (t). The solution of this equation drives to derive the different time scales what allows us to reach conclusions like: clusters not containing BS stars dilute 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. It is also studied within this work, 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 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, ratio labeled as ƒ, and a factor, named ϖ, which is an indicator of the origin of the BS; ϖ increases as the number of BS increase but it is limited to ~5. This istribution function is expressed as . The validity of this function was carried out by means of matching the number of observed BS stars to the number of predicted ones in the available sample of OCs.

Published in	American Journal of Astronomy and Astrophysics (Volume 9, Issue 4)
DOI	10.11648/j.ajaa.20210904.12
Page(s)	52-66
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Open Clusters and Associations: General, Cluster Kinematics and Dynamics, Blue Stragglers

References

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APA Style

Félix Llorente de Andrés, Carmen Morales Durán. (2022). A Model of the Dynamics of Open Clusters: Time-Scales, Core Collapse and Blue Stragglers. American Journal of Astronomy and Astrophysics, 9(4), 52-66. https://doi.org/10.11648/j.ajaa.20210904.12

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ACS Style

Félix Llorente de Andrés; Carmen Morales Durán. A Model of the Dynamics of Open Clusters: Time-Scales, Core Collapse and Blue Stragglers. Am. J. Astron. Astrophys. 2022, 9(4), 52-66. doi: 10.11648/j.ajaa.20210904.12

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AMA Style

Félix Llorente de Andrés, Carmen Morales Durán. A Model of the Dynamics of Open Clusters: Time-Scales, Core Collapse and Blue Stragglers. Am J Astron Astrophys. 2022;9(4):52-66. doi: 10.11648/j.ajaa.20210904.12

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@article{10.11648/j.ajaa.20210904.12,
  author = {Félix Llorente de Andrés and Carmen Morales Durán},
  title = {A Model of the Dynamics of Open Clusters: Time-Scales, Core Collapse and Blue Stragglers},
  journal = {American Journal of Astronomy and Astrophysics},
  volume = {9},
  number = {4},
  pages = {52-66},
  doi = {10.11648/j.ajaa.20210904.12},
  url = {https://doi.org/10.11648/j.ajaa.20210904.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20210904.12},
  abstract = {This work presents a mathematical model of dynamic of open clusters (OC) from which their time scales are deduced as well as the number of blue stragglers (BS) present in the cluster. The model is based on the expansion of mass through a sphere defined by a radius, and at a time; this variation of mass is translated into a differential equation that it can be integrated for a given radius (r) and a determined time (t). The solution of this equation drives to derive the different time scales what allows us to reach conclusions like: clusters not containing BS stars dilute 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. It is also studied within this work, 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 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, ratio labeled as ƒ, and a factor, named ϖ, which is an indicator of the origin of the BS; ϖ increases as the number of BS increase but it is limited to ~5. This istribution function is expressed as . The validity of this function was carried out by means of matching the number of observed BS stars to the number of predicted ones in the available sample of OCs.},
 year = {2022}
}

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TY  - JOUR
T1  - A Model of the Dynamics of Open Clusters: Time-Scales, Core Collapse and Blue Stragglers
AU  - Félix Llorente de Andrés
AU  - Carmen Morales Durán
Y1  - 2022/12/27
PY  - 2022
N1  - https://doi.org/10.11648/j.ajaa.20210904.12
DO  - 10.11648/j.ajaa.20210904.12
T2  - American Journal of Astronomy and Astrophysics
JF  - American Journal of Astronomy and Astrophysics
JO  - American Journal of Astronomy and Astrophysics
SP  - 52
EP  - 66
PB  - Science Publishing Group
SN  - 2376-4686
UR  - https://doi.org/10.11648/j.ajaa.20210904.12
AB  - This work presents a mathematical model of dynamic of open clusters (OC) from which their time scales are deduced as well as the number of blue stragglers (BS) present in the cluster. The model is based on the expansion of mass through a sphere defined by a radius, and at a time; this variation of mass is translated into a differential equation that it can be integrated for a given radius (r) and a determined time (t). The solution of this equation drives to derive the different time scales what allows us to reach conclusions like: clusters not containing BS stars dilute 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. It is also studied within this work, 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 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, ratio labeled as ƒ, and a factor, named ϖ, which is an indicator of the origin of the BS; ϖ increases as the number of BS increase but it is limited to ~5. This istribution function is expressed as . The validity of this function was carried out by means of matching the number of observed BS stars to the number of predicted ones in the available sample of OCs.
VL  - 9
IS  - 4
ER  -

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Author Information

Félix Llorente de Andrés

Centro de Astrobiología, European Space Astronomy Center (ESAC) Campus, Villanueva de la Ca?ada (Madrid), Spain
Carmen Morales Durán

Ateneo de Almagro, Sección de Ciencia y Tecnología, Almagro (Ciudad Real), Spain

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APA Style

Félix Llorente de Andrés, Carmen Morales Durán. (2022). A Model of the Dynamics of Open Clusters: Time-Scales, Core Collapse and Blue Stragglers. American Journal of Astronomy and Astrophysics, 9(4), 52-66. https://doi.org/10.11648/j.ajaa.20210904.12

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ACS Style

Félix Llorente de Andrés; Carmen Morales Durán. A Model of the Dynamics of Open Clusters: Time-Scales, Core Collapse and Blue Stragglers. Am. J. Astron. Astrophys. 2022, 9(4), 52-66. doi: 10.11648/j.ajaa.20210904.12

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AMA Style

Félix Llorente de Andrés, Carmen Morales Durán. A Model of the Dynamics of Open Clusters: Time-Scales, Core Collapse and Blue Stragglers. Am J Astron Astrophys. 2022;9(4):52-66. doi: 10.11648/j.ajaa.20210904.12

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@article{10.11648/j.ajaa.20210904.12,
  author = {Félix Llorente de Andrés and Carmen Morales Durán},
  title = {A Model of the Dynamics of Open Clusters: Time-Scales, Core Collapse and Blue Stragglers},
  journal = {American Journal of Astronomy and Astrophysics},
  volume = {9},
  number = {4},
  pages = {52-66},
  doi = {10.11648/j.ajaa.20210904.12},
  url = {https://doi.org/10.11648/j.ajaa.20210904.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20210904.12},
  abstract = {This work presents a mathematical model of dynamic of open clusters (OC) from which their time scales are deduced as well as the number of blue stragglers (BS) present in the cluster. The model is based on the expansion of mass through a sphere defined by a radius, and at a time; this variation of mass is translated into a differential equation that it can be integrated for a given radius (r) and a determined time (t). The solution of this equation drives to derive the different time scales what allows us to reach conclusions like: clusters not containing BS stars dilute 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. It is also studied within this work, 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 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, ratio labeled as ƒ, and a factor, named ϖ, which is an indicator of the origin of the BS; ϖ increases as the number of BS increase but it is limited to ~5. This istribution function is expressed as . The validity of this function was carried out by means of matching the number of observed BS stars to the number of predicted ones in the available sample of OCs.},
 year = {2022}
}

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TY  - JOUR
T1  - A Model of the Dynamics of Open Clusters: Time-Scales, Core Collapse and Blue Stragglers
AU  - Félix Llorente de Andrés
AU  - Carmen Morales Durán
Y1  - 2022/12/27
PY  - 2022
N1  - https://doi.org/10.11648/j.ajaa.20210904.12
DO  - 10.11648/j.ajaa.20210904.12
T2  - American Journal of Astronomy and Astrophysics
JF  - American Journal of Astronomy and Astrophysics
JO  - American Journal of Astronomy and Astrophysics
SP  - 52
EP  - 66
PB  - Science Publishing Group
SN  - 2376-4686
UR  - https://doi.org/10.11648/j.ajaa.20210904.12
AB  - This work presents a mathematical model of dynamic of open clusters (OC) from which their time scales are deduced as well as the number of blue stragglers (BS) present in the cluster. The model is based on the expansion of mass through a sphere defined by a radius, and at a time; this variation of mass is translated into a differential equation that it can be integrated for a given radius (r) and a determined time (t). The solution of this equation drives to derive the different time scales what allows us to reach conclusions like: clusters not containing BS stars dilute 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. It is also studied within this work, 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 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, ratio labeled as ƒ, and a factor, named ϖ, which is an indicator of the origin of the BS; ϖ increases as the number of BS increase but it is limited to ~5. This istribution function is expressed as . The validity of this function was carried out by means of matching the number of observed BS stars to the number of predicted ones in the available sample of OCs.
VL  - 9
IS  - 4
ER  -

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