SPAMMS Framework

Spectroscopic PAtch Model
for Massive Stars (SPAMMS)

3D spectral synthesis for distorted stars and interacting binaries

Massive stars are rarely well described by spherical symmetry. Rapid rotation and binary interactions induce significant geometric distortion, producing surface gradients in effective temperature and gravity that directly impact their emergent spectra. These asymmetries cannot be captured by traditional one-dimensional models. SPAMMS addresses this limitation by modelling the star as a collection of surface elements in 3D, each characterized by its own local physical conditions.


Core Methodology

SPAMMS merges surface geometry from PHOEBE II with advanced LTE and non-LTE atmosphere codes like FASTWIND, TLUSTY, and Kurucz. The process is divided into four stages:

SPAMMS Workflow
  • Mesh Generation: Creating a 3D triangulated surface reflecting rotational or Roche distortion.
  • Local Physics: Setting to each patch its physical conditions (Teff-logg) using the Roche model and gravity darkening laws (von Zeipel, Espinosa-Lara).
  • Spectral Synthesis: Assigning specific intensities from the stellar grid for each triangle.
  • Integration: The visible surface is then integrated to yield the total synthetic line profile, including contributions from both the photosphere and stellar wind if relevant. Relevant parameters like path visibility and projection in the sky, Doppler shifts, and limb darkening are all self-consistently accounted for in the integration process.

Key Applications

Rapid Rotators

3D surface modeling of gravity darkening and rotational broadening using the Roche model for single stars.

Binary Systems

Self-consistent modeling of binaries and tidal distortions using the Roche geometry, with time-dependent implementation.


Examples of SPAMMS capabilities

VFTS352 Binary

Model of VFTS 352: The evolution of Helium lines across an orbital cycle in an overcontact system.

Rapid Rotator

A star at 90% critical rotation: Latitudinal temperature gradient and inclination effects.



1) The animation on the left shows SPAMMS in action for the overcontact binary VFTS 352. The top panel displays the local temperature distribution, while the bottom panel shows the evolving HeI and HeII lines across orbital phases. This system, with surface temperature variations exceeding 10.000 K, cannot be accurately analyzed with spherical models. SPAMMS models both components and their interaction self-consistently, including the contact bridge region that is usually neglected.

2) One of the core innovations of SPAMMS is its intrinsic modeling of rotational broadening, built directly into its patch-based geometry. Unlike conventional techniques that apply a post-processing rotational convolution to 1D spectra, SPAMMS computes the true line-of-sight velocity field across the stellar surface by assigning Doppler-shifted synthetic line profiles to each individual mesh triangle. This allows the model to naturally reproduce asymmetric, inclination-dependent line shapes — without relying on arbitrary projected velocity parameters.
The animation on the left demonstrates SPAMMS's ability to model a star rotating at 90% of its critical speed. The top panel reveals the latitudinal temperature gradient caused by gravity darkening—hotter poles and cooler equator—while the bottom panel shows how the spectral line profile evolves with inclination. When viewed pole-on, the hotter polar regions dominate the projected surface, enhancing HeII lines and weakening HeI due to increased ionization. This can lead to a systematic overestimation of temperature if not modeled in 3D. When viewed equator-on, the cooler, rapidly rotating equatorial zones contribute broader but shallower HeII lines.