Accretion Disk Simulator

Accretion Disk Physics

An accretion disk forms whenever infalling matter carries too much angular momentum to fall directly into the central object. Conservation of angular momentum forces the material into circular orbits; viscosity (or magneto-rotational turbulence) gradually transports angular momentum outward, allowing mass to drift inward and release its gravitational potential energy as heat and radiation.

Accretion is one of the most powerful energy-release mechanisms in the Universe. Around a neutron star or black hole, the accretion efficiency ? = ?E/mc� is:

Temperature Profile

In a steady thin disk (Shakura-Sunyaev), the local effective temperature varies with radius as:

Simulation Method

This simulator integrates N test particles in a gravitational potential using the leapfrog method (second-order symplectic, conserves energy better than Euler). The a-disk viscosity is implemented as a tangential velocity correction proportional to the departure from Keplerian circular speed:

Preset Scenarios

💫 Protoplanetary Disk

A young star (T Tauri phase) surrounded by a disk of gas and dust left over from its formation. Disk mass ~0.01�0.1 M_?; scale height H/r � 0.05�0.1; typical lifetime 3�10 Myr. Planets form via two competing channels: core accretion (dust ? pebbles ? planetesimals ? cores ? planets; dominant at intermediate radii) and disk instability (gravitational fragmentation at large radii where Toomre Q < 1). This preset shows the smooth a-disk spiralling of disk material onto the central star with S ? r?� surface density profile.

🔵 Binary System

Two stars orbit their common barycentre with mass ratio q = M2/M1 (set by slider). Tidal forces from the secondary truncate the disk at roughly 0.3�0.5� the binary separation (tidal truncation radius). The secondary also excites density waves at resonance radii. Adjust the mass ratio slider to see how stronger tidal perturbations modify the disk structure.

🌌 Spiral Galaxy

A galactic disk modelled with a logarithmic (flat rotation curve) potential instead of a Keplerian one. A 2-armed spiral density wave perturbation rotates at pattern speed O_p, exciting the characteristic grand-design spiral structure seen in galaxies like M51 (Whirlpool) and M81. Density waves are not material arms � the gas flows through them, compressing and triggering star formation at the wave crests.

⚫ Black Hole Accretion

A stellar-mass black hole (Schwarzschild) with an ISCO (Innermost Stable Circular Orbit) at r_ISCO = 6 GM/c�. Particles crossing the ISCO are absorbed and respawned in the outer disk. The inner edge glows orange-white at extreme temperatures. High viscosity (set a slider high) drives rapid infall and a more luminous inner disk. This models the accretion state of X-ray binaries such as Cygnus X-1.

🪐 Planetary Gap

A Jupiter-mass planet orbiting at r = 0.38 opens a gap in the disk via Lindblad resonances and launches two-armed Lindblad spiral density waves both inward and outward. The gap width grows with M_planet/M_star and decreasing viscosity. Watch the gap open over ~200 steps and the spiral arms propagate. The orange glow marks the planet.

🌊 Tidal Disruption Event (TDE)

A star cluster approaches a supermassive black hole on a nearly radial (plunging) orbit. Tidal forces from the BH exceed the star's self-gravity (inside the tidal radius r_t = R_? (M_BH/M_?)^(1/3)), ripping it apart. Roughly half the stellar debris is accreted (bound debris, approaching from outside), producing a luminous accretion flare that can briefly outshine the host galaxy. The other half is ejected on hyperbolic orbits.

Key Equations

Keplerian Orbital Period

Viscous Timescale (a-disk)

Tidal Disruption Radius

Gap-Opening Criterion (Crida et al. 2006)

Eddington Accretion Rate

Curriculum Connections

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