[Paper Review] Single star progenitors of long gamma-ray bursts I: Model grids and redshift dependent GRB rate

Sung-Chul Yoon, N. Langer+1 more|UvA-DARE (University of Amsterdam)|Jun 26, 2006

Gamma-ray bursts and supernovae51 references248 citations

TL;DR

This paper presents evolutionary models of massive, rotating stars at varying metallicities to identify conditions under which long gamma-ray bursts (GRBs) form via the collapsar model. It predicts that GRBs are predominantly produced in low-metallicity environments (Z ≤ 0.004), with ~50% occurring at redshift z > 4, and an average GRB-to-supernova ratio of ~1/200 globally, decreasing to 1/1250 at low redshifts.

ABSTRACT

We present grids of massive star evolution models at four different metallicities (Z=0.004, 0.002, 0.001, 0.00001). The effects of rotation on the stellar structure and the transport of angular momentum and chemical elements through the Spruit-Tayler dynamo and rotationally induced instabilities are considered. After discussing uncertainties involved with the adopted physics, we elaborate the final fate of massive stars as a function of initial mass and spin rate, at each considered metallicity. In particular, we investigate for which initial conditions long gamma-ray bursts (GRBs) are expected to be produced in the frame of the collapsar model. Then, using an empirical spin distribution of young massive metal-poor stars and a specified metallicity-dependent history of star-formation, we compute the expected GRB rate as function of metallicity and redshift based on our stellar evolution models. The GRB production in our models is limited to metallicities of Z \lsim 0.004, with the consequence that about 50 % of all GRBs are predicted to be found at redshifts above z = 4, with most supernovae occurring at redshifts below z\simeq 2.2. The average GRB/SN ratio predicted by our model is about 1/200 globally, and 1/1250 at low redshift. Future strategies for testing the considered GRB progenitor scenario are briefly discussed.

Motivation & Objective

• To determine the conditions under which single massive stars produce long gamma-ray bursts via the collapsar model.
• To investigate how metallicity and rotation influence the final fate of massive stars.
• To compute the redshift-dependent GRB rate using empirical spin distributions and star-formation histories.
• To constrain the GRB/SN ratio across cosmic time and metallicity.
• To provide a framework for testing the single-star progenitor scenario of long GRBs.

Proposed method

• Constructing stellar evolution model grids for initial masses between 15 and 100 M☉ at four metallicities: Z = 0.004, 0.002, 0.001, and 0.00001.
• Incorporating rotationally induced mixing via the Spruit-Tayler dynamo and rotational instabilities to model angular momentum and chemical transport.
• Using empirical spin distributions of young, metal-poor stars to inform initial rotation rates in models.
• Applying a metallicity-dependent star-formation history to compute the redshift evolution of GRB rates.
• Calculating the GRB rate per unit redshift and comparing with observational constraints.
• Deriving the GRB-to-supernova ratio as a function of redshift and metallicity using model outcomes.

Experimental results

Research questions

• RQ1 What initial mass and spin conditions lead to long GRB formation in the collapsar model at different metallicities?
• RQ2 How does metallicity affect the likelihood of GRB production in single massive stars?
• RQ3 What is the predicted redshift distribution of long GRBs based on stellar evolution models and star-formation history?
• RQ4 What is the expected GRB-to-supernova ratio across cosmic time, and how does it vary with metallicity?
• RQ5 How do rotational mixing and angular momentum transport influence the final fate of massive stars in low-metallicity environments?

Key findings

• GRB production is strongly limited to metallicities Z ≤ 0.004, with negligible production at higher metallicities.
• Approximately 50% of all long GRBs are predicted to occur at redshifts z > 4, indicating a strong high-redshift bias.
• The global GRB-to-supernova ratio is predicted to be about 1/200, decreasing to 1/1250 at low redshifts (z ≲ 2.2).
• Most core-collapse supernovae occur at redshifts below z ≃ 2.2, while GRBs are significantly more common at higher redshifts.
• Rotationally induced mixing and angular momentum transport play a critical role in determining whether a star forms a black hole with a relativistic jet.
• The model predicts a bimodal distribution of GRB rates, peaking at high redshift due to the low-metallicity environment favoring GRB formation.