Bound mass of Dehnen models with a centrally peaked star formation efficiency

¹ Energetic Cosmos Laboratory, Nazarbayev University, 53 Kabanbay Batyr ave., 010000 Nur-sultan, Kazakhstan
e-mail: bekdaulet.shukirgaliyev@nu.edu.kz
² Fesenkov Astrophysical Institute, 23 Observatory str., 050020 Almaty, Kazakhstan
e-mail: otebay@aphi.kz
³ Al-Farabi Kazakh National University, 71 Al-Farabi ave., 050040 Almaty, Kazakhstan
⁴ Main Astronomical Observatory, National Academy of Sciences of Ukraine, 27 Akademika Zabolotnoho St., 03143 Kyiv, Ukraine
⁵ Institute of Astronomy, Russian Academy of Sciences (INASAN), 48 Pyatnitskaya str., 119017 Moscow, Russian Federation
⁶ Rudolf Peierls Center for Theoretical Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
⁷ Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, 010009 Nur-Sultan, Kazakhstan
⁸ Center for Theoretical Physics, Eurasian National University, 010008 Nur-Sultan, Kazakhstan
⁹ Physics Department, Nazarbayev University, 53 Kabanbay Batyr ave., 010000 Nur-sultan, Kazakhstan
¹⁰ Helmholtz-Institut für Strahlen- und Kernphysik, Nussallee 14-16, 53115 Bonn, Germany
¹¹ Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
¹² National Astronomical Observatories and Key Laboratory of Computational Astrophysics, Chinese Academy of Sciences, 20A Datun Rd., Chaoyang District, Beijing 100101, PR China
¹³ Astronomisches Rechen-Institut am Zentrum für Astronomie der Universität Heidelberg, Mönchhofstrasse 12-14, 69120 Heidelberg, Germany
¹⁴ Kavli Institute for Astronomy and Astrophysics at Peking University, 5 Yiheyuan Rd., Haidian District, 100871 Beijing, PR China

Received: 12 May 2021
Accepted: 16 July 2021

Abstract

Context. Understanding the formation of bound star clusters with a low star formation efficiency (SFE) is important for improving our knowledge of the star-formation history of galaxies. In N-body models of star-cluster evolution after gas expulsion, the Plummer model with an outer power law density profile has been used in a broad range of studies.

Aims. Here, we study the impact of the density profile slopes on the survivability of the low-SFE star clusters after instantaneous gas expulsion. We compare cases when a stellar cluster exhibits a Plummer profile to those with Dehnen profiles, including cuspy ones of different slopes at the time of formation.

Methods. We determined the corresponding density profile of the residual gas for a given global SFE, assuming that our model clusters formed with a constant efficiency per free-fall time and, hence, with a shallower density profile for the gas than that of the stars. We performed direct N-body simulations of evolution of clusters initially in virial equilibrium within the gas potential following gas removal.

Results. We find that the violent relaxation lasts no longer than 20 Myr, independently of the density profile power law slopes. Dehnen model clusters survive after violent relaxation with significantly lower SFEs when the global SFE measured within the Jacobi radius or within a half-mass radius. Dehnen γ = 0 model clusters show a similar final bound fraction with the Plummer model clusters if the global SFE is measured within ten scale radii. The final bound fraction increases with the γ values for a given global SFE.

Conclusions. We conclude that Dehnen clusters better resist the consequences of the violent relaxation that follows the instantaneous gas expulsion, as compared to the Plummer clusters. Therefore, the shallower the outer density slope of the low-SFE clusters, the better their prospects for survival after gas expulsion. Among the Dehnen clusters, we find that the steeper the inner slope, the higher the bound mass fraction that is retained, following the violent relaxation for a given global SFE.