Ellipsar is a theoretical model in astrophysics proposed in 2022 to describe ring-like explosions originating from massive stars that exhibit a flattened (oblate) geometry due to rapid rotation or binary interactions. The term "ellipsar" is a portmanteau of "ellipse" and "star", reflecting the elliptical iso-density contours of the progenitor star in two-dimensional axisymmetric simulations. The model was introduced by Marcus DuPont, Andrew MacFadyen, and Jonathan Zrake in a paper published in The Astrophysical Journal Letters.^[1]

The model challenges traditional spherical or jet-like explosion paradigms by incorporating asphericity in the progenitor star, potentially explaining certain astronomical transients without requiring a central jet engine.

Astronomical transients such as supernovae and gamma-ray bursts (GRBs) are typically modeled as point-like explosions or collimated jets from spherically symmetric stars. However, observations and theoretical models indicate that many massive stars (>8–10 solar masses) are oblate due to rapid rotation or binary mass transfer, with flattening parameters (ε) up to 0.2.^[1] The ellipsar model explores the hydrodynamic consequences of a point explosion in such aspherical progenitors.

The ellipsar model assumes:

• A massive star progenitor, such as a helium Wolf-Rayet star (~18 M⊙, radius ~0.5 R⊙), evolved using software like MESA.^[1]
• Oblate spheroid geometry with flattening parameter ε = 1 - b/a, where a and b are semi-major and semi-minor axes, optimized at ε ≈ 0.05.
• Point-like explosion at the core with energy E_exp ranging from 10^{51} to 10^{54} erg (fiducial: 5 × 10^{52} erg).
• Cold gas approximation (p/ρ ~ 10^{-6}) in the progenitor and surrounding wind environment with density profile ρ_wind = A r^{-2}, A* = 0.1, v_wind = 10^3 km/s.
• Axisymmetric 2D simulations, ignoring 3D effects, magnetic fields, or detailed rotation.

The stellar density profile is mapped from a 1D spherical model to an oblate form: ρ(r, θ) derived by replacing R_3 in ρ_{1D}(r) with R_ε(θ) = ab / √[(a cos θ)^2 + (b sin θ)^2], where a = R_3 (1 - ε)^{-1/3}, b = R_3 (1 - ε)^{2/3}.

The model employs relativistic hydrodynamics in 2D spherical polar coordinates (r, θ). Key equations include:

The 1D density is approximated as: ${\displaystyle \rho _{1D}(r)\approx \rho _{c}\times \max \left(1-{\frac {r}{R_{3}}},0\right)/\left[1+\left({\frac {r}{R_{1}}}\right)^{k_{1}}/\left(1+\left({\frac {r}{R_{2}}}\right)^{k_{2}}\right)\right]}$ with parameters R_1 = 0.0017 R, R_2 = 0.0125 R, R_3 = 0.65 R, k_1 = 3.25, k_2 = 2.57, ρ_c = 3 × 10^{-7} ρ (ρ = 3M / (4π R^3)).

For oblate mapping: ${\displaystyle R_{\epsilon }(\theta )={\frac {ab}{\sqrt {(a\cos \theta )^{2}+(b\sin \theta )^{2}}}}}$

${\displaystyle p(r)={\frac {3(\gamma -1)E_{\exp }}{4\pi r_{\exp }^{3}}}\times H(r-r_{\exp })}$ for r < r_exp, where H is the Heaviside function, γ = 4/3.

Conservation laws in relativistic form:

• Mass continuity: ${\displaystyle \partial _{\mu }(\rho u^{\mu })=0}$
• Energy-momentum: ${\displaystyle \partial _{\mu }T^{\mu \nu }=0}$, with ${\displaystyle T^{\mu \nu }=\rho hu^{\mu }u^{\nu }+p\eta ^{\mu \nu }}$, ${\displaystyle h=1+\epsilon +p/\rho }$, η^{\mu\nu} Minkowski metric (-+++).
• Equation of state: ${\displaystyle p=(\gamma -1)\rho \epsilon }$

Shock dynamics: Acceleration proportional to density gradient; polar shocks breakout first, forming lobes that collide obliquely at equator, creating high-pressure rings.

${\displaystyle r_{\text{dec}}(\Gamma \beta ,\theta )=M_{\text{iso}}(>\Gamma \beta ,\theta )/(4\pi A)}$, where M_iso is isotropic-equivalent mass.

Simulations use the GPU-accelerated SIMBI code (Python/C++ with CUDA/ROCm), second-order Godunov method with minmod reconstruction (θ=2). Grid: 5609 radial zones (log-spaced), 4096 angular zones; domain r_in = 0.01 R to r_out = 200 R, θ ∈ [0, π].

• Optimal ε = 0.05 produces relativistic ejecta rings (Γβ >10 for high E_exp), confined to Δθ ~6° (~5% sky coverage).
• Energy distribution: E_k,iso(>1) at equator 10× higher than poles; M_iso(>1, θ=90°) ~6 × 10^{27} g (~Earth mass).
• Transients: Explains llGRBs, relativistic SNe, FBOTs; predicts distinct afterglows, high polarization, prolate remnants after ~1 year.
• Cosmic rays: Potential source for 10^{15}–10^{18} eV particles in low-density environments.

• Restricted to 2D axisymmetry; neglects 3D instabilities, turbulence, magnetic fields, radiation losses, or clumpy CSM.
• As of 2025, no direct observational evidence; remains speculative with limited follow-up research.

Given the authors' expertise in high-energy astrophysics, ellipsar has moderate potential for validation through upcoming observatories like Rubin (2025+) or CTA (2027+), potentially within 5–10 years if 3D simulations and matching transients emerge.

• Full article on IOPscience
• Preprint on arXiv
• ResearchGate entry with full text
• Entry on Inspire HEP