[Paper Review] Evolution of stellar collision products in open clusters. II. A grid of low-mass collisions

E. Glebbeek, O. R. Pols|ArXiv.org|Jun 4, 2008

Stellar, planetary, and galactic studies42 references22 citations

TL;DR

This paper presents a comprehensive grid of detailed stellar evolution models for low-mass stellar collision products in open clusters, using entropy-sorting and a one-dimensional stellar evolution code to track remnants from contraction through the main sequence and giant branch. It shows that collision products match observed blue straggler locations in M67 and NGC 188, with lifetimes and luminosities differing significantly from normal stars, and provides an analytic recipe for N-body simulations to model these remnants accurately.

ABSTRACT

In a companion paper we studied the detailed evolution of stellar collision products that occurred in an $N$-body simulation of the old open cluster M67 and compared our detailed models to simple prescriptions. In this paper we extend this work by studying the evolution of the collision products in open clusters as a function of mass and age of the progenitor stars. We calculated a grid of head-on collisions covering the section of parameter space relevant for collisions in open clusters. We create detailed models of the merger remnants using an entropy-sorting algorithm and follow their subsequent evolution during the initial contraction phase, through the main sequence and up to the giant branch with our detailed stellar evolution code. We compare the location of our models in a colour-magnitude diagram to the observed blue straggler population of the old open clusters M67 and NGC 188 and find that they cover the observed blue straggler region of both clusters. For M67, collisions need to have taken place recently. Differences between the evolution tracks of the collision products and normal main sequence stars can be understood quantitatively using a simple analytic model. We present an analytic recipe that can be used in an $N$-body code to transform a precomputed evolution track for a normal star into an evolution track for a collision product.

Motivation & Objective

• To systematically model the evolution of low-mass stellar collision products in open clusters, covering relevant parameter space for blue straggler formation.
• To understand how the internal structure and evolution of merger remnants depend on progenitor masses, ages, and entropy profiles.
• To compare detailed collision models with observed blue straggler populations in M67 and NGC 188, particularly in colour-magnitude diagrams.
• To develop a simple analytic prescription that can be used in N-body simulations to transform normal stellar evolution tracks into accurate collision product tracks.
• To quantify differences in main-sequence lifetime, luminosity, and radius between collision products and normal stars, especially in comparison to existing prescriptions.

Proposed method

• A grid of head-on collisions between coeval, low-mass main-sequence stars (total mass ≤ 2.4 M☉) was computed, covering a range of mass ratios and progenitor ages.
• An entropy-sorting algorithm was used to reconstruct the initial structure of the merger remnant from the two progenitor stars, preserving entropy and composition gradients.
• The detailed evolution of each remnant was computed using a fully implicit one-dimensional stellar evolution code, tracking contraction, main-sequence evolution, and ascent of the giant branch.
• The models were compared to observed blue straggler sequences in M67 and NGC 188 using colour-magnitude diagrams to assess consistency.
• An analytic recipe was derived to map normal stellar evolution tracks into collision product tracks, based on the observed dependence of luminosity, radius, and lifetime on progenitor mass and age.
• The role of core sinking (primary vs. secondary) and molecular weight inversions was analyzed using entropy and composition profiles to classify mixing cases (M, P, S).

Experimental results

Research questions

• RQ1 How do the luminosity, radius, and main-sequence lifetime of stellar collision products differ from those of normal main-sequence stars of the same mass?
• RQ2 In what regions of parameter space (mass ratio, progenitor age) do different mixing configurations (core sinking of primary, secondary, or mixed) occur in merger remnants?
• RQ3 To what extent do detailed collision models reproduce the observed blue straggler sequences in M67 and NGC 188 in colour-magnitude diagrams?
• RQ4 Can a simple analytic prescription be derived to accurately represent collision product evolution in N-body simulations, replacing full detailed calculations?
• RQ5 How do entropy and composition gradients in the progenitor stars determine the internal structure and long-term evolution of the merger remnant?

Key findings

• The collision products in the grid cover the observed blue straggler region in both M67 and NGC 188 in colour-magnitude diagrams, confirming their viability as blue straggler progenitors.
• Collision remnants are brighter than normal main-sequence stars of the same mass but less blue than fully mixed models, with main-sequence lifetimes shorter than predicted by the Hurley et al. (2001) BSE prescription.
• Three distinct mixing cases were identified: 'M' (mixed core) for near-equal mass collisions, 'P' (primary core sinking) when the primary is evolved, and 'S' (secondary core sinking) when the secondary is less evolved, especially for mass ratios ≲0.4.
• In the 'S' case, a helium-rich layer forms on top of a hydrogen-rich core, creating a pronounced molecular weight inversion and enabling a hydrogen-burning shell at the core edge.
• The analytic recipe derived allows transformation of normal stellar evolution tracks into collision product tracks by adjusting luminosity, radius, and lifetime based on progenitor mass and age, enabling efficient use in N-body simulations.
• For M67, the models indicate that collisions must have occurred recently, as older remnants would have evolved beyond the observed blue straggler locus.