Accretion disks are swirling structures of gas and dust that form around massive objects in space. They play a crucial role in various cosmic phenomena, from planet formation to powering the brightest objects in the universe.

Different models describe accretion disks based on their thickness and behavior. These models help scientists understand how matter falls onto celestial bodies, releasing energy and shaping the evolution of cosmic systems.

Accretion Disk Models

Thin and Thick Disk Models

• Thin disk model assumes disk height much smaller than radius
• Thin disks characterized by efficient cooling and low accretion rates
• Thick disk model applies to systems with high accretion rates
• Thick disks feature greater vertical extent and less efficient cooling
• Both models describe different regimes of accretion disk behavior

Advanced Accretion Flow Models

• Advection-dominated accretion flow (ADAF) model explains low-luminosity systems
• ADAF occurs when energy release through radiation becomes inefficient
• In ADAF, most energy advected inward with accreting gas
• Shakura-Sunyaev α-disk model provides framework for describing accretion disk viscosity
• α-disk model parametrizes viscosity using dimensionless parameter α
• α typically ranges from 0.01 to 0.1, determined by observations and simulations

Accretion Disk Physics

Fundamental Accretion Processes

• Accretion involves matter falling onto a central object due to gravity
• Process releases gravitational potential energy as heat and radiation
• Accretion rate affects disk structure and luminosity
• Magnetorotational instability (MRI) drives turbulence in accretion disks
• MRI results from coupling between magnetic fields and differentially rotating plasma

Angular Momentum and Viscosity

• Angular momentum transport crucial for accretion disk evolution
• Outward angular momentum transport allows matter to spiral inward
• Viscosity in accretion disks arises from turbulence and magnetic stresses
• Molecular viscosity insufficient to explain observed accretion rates
• Effective viscosity in disks much higher due to turbulent processes

Accretion Disk Luminosity

Eddington Luminosity and Limits

• Eddington luminosity represents theoretical maximum luminosity for spherical accretion
• Occurs when outward radiation pressure balances inward gravitational force
• Eddington luminosity given by $L_{Edd} = \frac{4\pi G M m_p c}{\sigma_T}$
• M represents mass of accreting object, mp proton mass, σT Thomson cross-section
• Super-Eddington accretion possible in non-spherical geometries (disks)

Radiative Efficiency and Energy Output

• Radiative efficiency measures fraction of rest mass energy converted to radiation
• Depends on nature of central object (black hole, neutron star, white dwarf)
• For non-rotating black holes, maximum efficiency ~5.7%
• Rotating black holes can achieve higher efficiencies, up to ~42% for maximally rotating case
• Accretion onto neutron stars can reach efficiencies of ~10-20%