[Paper Review] Population synthesis for double white dwarfs. II. Semi-detached systems: AM CVn stars

G. Nelemans, Simon Portegies Zwart+2 more|arXiv (Cornell University)|Jan 9, 2001

Stellar, planetary, and galactic studiesPhysics and Astronomy43 references156 citations

TL;DR

This paper models the formation of AM CVn stars through two channels: mass transfer in double white dwarf binaries and from helium-star donors. It finds that without an accretion disk, mass transfer stability hinges on tidal coupling; explosive helium burning can disrupt systems, yielding a Galactic birth rate of 1.1–6.8×10⁻³ yr⁻¹ and a total population of 1.6–9.4×10⁷ systems, with observable populations constrained by selection effects.

ABSTRACT

We study two models for AM CVn stars: white dwarfs accreting (i) from a helium white dwarf companion and (ii) from a helium-star donor. We show that in the first model possibly no accretion disk forms at the onset of mass transfer. The stability and the rate of mass transfer then depend on the tidal coupling between the accretor and the orbital motion. In the second model the formation of AM CVn stars may be prevented by detonation of the CO white dwarf accretor and the disruption of the system. With the most favourable conditions for the formation of AM CVn stars we find a current Galactic birth rate of 6.8 10^{-3} yr^{-1}. Unfavourable conditions give 1.1 10^{-3} yr^{-1}. The expected total number of the systems in the Galaxy is 9.4 10^{7} and 1.6 10^{7}, respectively. We model very simple selection effects to get some idea about the currently expected observable population and discuss the (quite good) agreement with the observed systems.

Motivation & Objective

• To investigate the formation pathways of AM CVn stars via mass transfer in double white dwarf systems and from helium-star donors.
• To assess the stability of mass transfer in the absence of an accretion disk, which normally provides angular momentum feedback.
• To evaluate the impact of explosive helium burning on the survival of AM CVn systems, particularly for CO white dwarf accretors.
• To estimate the Galactic birth rate and total population of AM CVn stars under different physical assumptions.
• To compare model predictions with observed systems, accounting for basic selection effects.

Proposed method

• Population synthesis simulations track binary evolution from zero-age main sequence to semi-detached phases, incorporating gravitational wave-driven orbital decay.
• The rate of angular momentum loss via gravitational wave radiation is calculated using the standard formula: (dJ/dt)_GWR = -32/5 G³/c⁵ M m (M+m)/a⁴.
• Mass transfer stability is determined by the condition q < 5/6 + ζ(m)/2, where q = m/M and ζ(m) is the logarithmic radius derivative of the donor.
• For systems without accretion disks, stability depends critically on tidal coupling efficiency between the accretor and orbit.
• Explosive helium burning is modeled based on accretion rates and mass accumulation, with detonation occurring at ~0.7 M☉ for CO white dwarfs.
• Two models are constructed: 'efficient' (diskless stability not critical) and 'inefficient' (diskless stability is key), with different thresholds for detonation (0.15 vs. 0.3 M☉).

Experimental results

Research questions

• RQ1 What is the role of accretion disk formation in stabilizing mass transfer in double white dwarf systems destined to become AM CVn stars?
• RQ2 How does the absence of an accretion disk affect the stability and survival of semi-detached double white dwarfs?
• RQ3 To what extent does explosive helium burning in CO white dwarf accretors disrupt potential AM CVn systems?
• RQ4 What are the predicted Galactic birth rates and total populations of AM CVn stars under different assumptions about disk formation and detonation thresholds?
• RQ5 How do simple selection effects influence the expected observable population of AM CVn stars, and how do they compare to observed systems?

Key findings

• In the absence of an accretion disk, mass transfer stability in double white dwarf systems depends critically on tidal coupling between the accretor and the orbit, with inefficient coupling leading to mergers.
• The formation of AM CVn stars from double white dwarfs is severely suppressed if no disk forms, unless tidal coupling is efficient, suggesting magnetically coupled systems may dominate.
• Explosive helium burning can disrupt systems, with detonation occurring when the CO white dwarf accretor reaches ~0.7 M☉, especially in the helium-star donor channel.
• The Galactic birth rate of AM CVn stars ranges from 1.1×10⁻³ yr⁻¹ (unfavourable conditions) to 6.8×10⁻³ yr⁻¹ (favourable conditions), depending on assumptions about disk formation and detonation thresholds.
• The total number of AM CVn systems in the Galaxy is estimated at 1.6×10⁷ (unfavourable) to 9.4×10⁷ (favourable), with observable populations reduced by selection effects.
• Simple selection effects suggest only about 1 in 30 potentially observable systems in the 'inefficient' model originate from double white dwarfs, while both channels contribute roughly equally in the 'efficient' model, consistent with observed period distributions.