[Paper Review] The rate of WD-WD head-on collisions may be as high as the SNe Ia rate

Boaz Katz, Subo Dong|arXiv (Cornell University)|Nov 19, 2012

Astro and Planetary SciencePhysics and Astronomy81 citations

TL;DR

This paper proposes that head-on collisions of white dwarf binaries in hierarchical triple systems can occur at a rate comparable to the observed Type Ia supernova (SN Ia) rate. Through 3-body simulations and analytic modeling, it shows that Kozai-Lidov oscillations driven by a distant, inclined tertiary star can excite extreme eccentricities (1−e ∼ 10⁻⁶), leading to collisions within ∼5 Gyr in ∼5% of systems with inner separations a ∼ 1–300 AU.

ABSTRACT

We show that a White Dwarf-White Dwarf (WD-WD) binary with semi-major axis a=1-300 AU, which is orbited by a stellar mass outer perturber with a moderate pericenter r_{p, out} \sim 3-10 x a, has a few percent chance of experiencing a head-on collision within ~5 Gyr. Such a perturber is sufficiently distant to allow the triple system to remain intact for millions of orbits while efficiently exchanging angular momentum with the WD-WD binary. In ~ 5% of the initial orientations, the inner orbit efficiently scans the (equal energy) phase space in the region of zero angular momentum. In these systems, the binary experiences increasingly closer, stochastic, pericenter approaches r_p ~ a/2N with the increasing number (N) of orbits elapsed. Within N~10^5(a/30AU) orbits, a collision is likely to occur. This is shown by performing \simten thousand 3-body integrations and is explained by simple analytic arguments. The collisions are conservatively restricted to "clean" collisions in which all passages prior to the collision are greater than 4R_WD=4x10^9cm. In particular, within the last single orbit, the pericenter changes from r_p>4R_WD to a collision value of r_p<2R_WD. The effects of tidal deformations and General Relativistic (GR) corrections are negligible in these scenarios. The WDs approach each other with a high velocity >3000 km/s and the collision is likely to detonate the WDs leading to a type Ia SNe. If a significant fraction of WDs reside in such triples, the rate of such collisions is as high as the SNe Ia rate, and it is possible that some or all type Ia SNe occur in this way. Such SNe have a unique gravitational wave signature, which will allow a decisive identification in the future.

Motivation & Objective

• To investigate whether head-on white dwarf-white dwarf (WD-WD) collisions in hierarchical triple systems can occur frequently enough to account for the observed Type Ia supernova (SN Ia) rate.
• To challenge the prevailing assumption that such collisions are extremely rare due to the need for near-unity eccentricity and extreme phase-space conditions.
• To demonstrate that the Kozai-Lidov mechanism in moderately hierarchical triples (outer pericenter r_p,out/a ∼ 3–10) can efficiently drive WD-WD binaries to collision via stochastic phase-space scanning near zero angular momentum.
• To show that tidal and general relativistic effects are negligible, and that the final pericenter jump from >4R_WD to <2R_WD occurs in a single orbit due to a strong perturbation.
• To establish that such collisions are likely to detonate, producing SN Ia events with a unique gravitational wave signature.

Proposed method

• Performs ~10,000 direct 3-body numerical integrations of hierarchical WD-WD triple systems using the Preto-Tremaine-Mikkola-Tanikawa (PTMT) symplectic integrator with adaptive time stepping.
• Employs a hybrid integrator scheme combining symplectic drift-kick steps with energy-conserving adaptive time steps based on total energy and kinetic energy to maintain accuracy during close passages.
• Uses a high-order Wisdom-Holman (WH) integrator with 8th-order symplectic coefficients (8,6,4) for comparison, though it is not fully symplectic due to adaptive time steps.
• Applies a conservative collision criterion: all prior passages must exceed 4R_WD = 4×10⁹ cm, with the final pericenter dropping below 2R_WD in a single orbit due to a perturbation-induced angular momentum change.
• Analyzes the stochastic scanning of phase space near zero angular momentum (J=0), where eccentricity e→1, over ~10⁵ orbits for a ∼30 AU binary.
• Uses analytic arguments to explain the collision probability scaling as N ∼ 10⁵(a/30 AU) orbits, with collision likelihood increasing in systems where the inner orbit's phase space is stochastically sampled near e≈1.

Experimental results

Research questions

• RQ1 Can head-on white dwarf-white dwarf collisions in hierarchical triple systems occur at a rate comparable to the observed Type Ia supernova rate?
• RQ2 What is the role of the Kozai-Lidov mechanism in driving WD-WD binaries to near-radial (e→1) orbits in moderately hierarchical triples with r_p,out/a ∼ 3–10?
• RQ3 How do perturbations from a distant tertiary star induce a final pericenter jump from >4R_WD to <2R_WD, enabling a clean collision?
• RQ4 Are tidal or general relativistic effects significant enough to prevent such collisions during the secular evolution?
• RQ5 What fraction of initial triple configurations leads to collisions within 5 Gyr, and how does this depend on orbital separation and inclination?

Key findings

• In ∼5% of initial configurations, the inner WD-WD binary in a triple system with a ∼1–300 AU semi-major axis and a moderately inclined tertiary (r_p,out/a ∼ 3–10) experiences a head-on collision within ∼5 Gyr.
• The collision probability arises from stochastic phase-space scanning near zero angular momentum (J=0), where the binary's eccentricity is driven to e→1 over ∼10⁵(a/30 AU) orbits.
• The final pericenter jump—from >4R_WD to <2R_WD—occurs in a single orbit due to a strong perturbation at the last apocenter, enabling a clean collision without prior tidal or GR effects.
• The relative velocity at impact exceeds 3000 km/s, which is sufficient to trigger a detonation in sub-Chandrasekhar mass WDs (0.6M☉ each), leading to a Type Ia supernova.
• The rate of such collisions is estimated to be as high as the observed SN Ia rate of 3×10⁻⁵ Mpc⁻³ yr⁻¹, suggesting that this mechanism could explain all or most SN Ia events.
• These SNe would produce a distinctive gravitational wave signature due to the head-on collision, enabling future observational identification.