5.1 Accretion Disk Theory and Models
2 min read•august 9, 2024
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
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- assumes disk height much smaller than radius
- Thin disks characterized by efficient cooling and low accretion rates
- 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
- () model explains low-luminosity systems
- ADAF occurs when energy release through radiation becomes inefficient
- In ADAF, most energy advected inward with accreting gas
- provides framework for describing accretion disk
- 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 as heat and radiation
- affects disk structure and luminosity
- () drives in accretion disks
- MRI results from coupling between magnetic fields and differentially rotating plasma
Angular Momentum and Viscosity
- 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
- represents theoretical maximum luminosity for spherical accretion
- Occurs when outward radiation pressure balances inward gravitational force
- Eddington luminosity given by
- M represents mass of accreting object, mp proton mass, σT Thomson cross-section
- possible in non-spherical geometries (disks)
Radiative Efficiency and Energy Output
- measures fraction of rest mass energy converted to radiation
- Depends on nature of central object (black hole, neutron star, white dwarf)
- For non-rotating , maximum efficiency ~5.7%
- Rotating black holes can achieve higher efficiencies, up to ~42% for maximally rotating case
- Accretion onto can reach efficiencies of ~10-20%
Key Terms to Review (18)
Accretion: Accretion refers to the process of accumulating mass, particularly in astronomical contexts where matter is drawn together by gravitational forces. This process plays a vital role in the formation and growth of celestial objects, such as stars, planets, and black holes, where material gradually gathers to form a more massive entity over time.
Accretion rate: The accretion rate refers to the speed at which matter accumulates onto a celestial object, such as a star or a black hole, from its surrounding environment. This rate is crucial in understanding how quickly an object can gain mass and energy, influencing its evolution and the dynamics of the surrounding accretion disk. The accretion rate is determined by various factors including gravitational pull, temperature, density of the material in the disk, and the physics governing angular momentum transfer within the disk.
ADAF: ADAF stands for Advection-Dominated Accretion Flow, which is a theoretical model used to describe the behavior of accretion disks around black holes. This model is particularly relevant when discussing the flow of gas in high-energy environments, where the inward flow of material is dominated by advection rather than radiation. In such scenarios, understanding ADAF helps explain the dynamics of accretion onto black holes and how energy is dissipated in these extreme settings.
Advection-Dominated Accretion Flow: Advection-dominated accretion flow (ADAF) refers to a type of accretion flow in astrophysical systems where the energy and mass transport is primarily due to the bulk motion of the accreting material, rather than radiative processes. This flow occurs in environments with low density and high temperature, allowing for a significant amount of energy to be carried away by the infalling matter rather than being emitted as radiation. This concept is critical for understanding how matter behaves around black holes and other compact objects, impacting their observational characteristics.
Angular Momentum: Angular momentum is a physical quantity that represents the rotational inertia and angular velocity of an object or system. It plays a crucial role in understanding how objects move and interact, especially in celestial mechanics, where it helps explain the behavior of stars, galaxies, and accretion disks. The conservation of angular momentum is a fundamental principle, indicating that in a closed system with no external torques, the total angular momentum remains constant over time.
Black holes: Black holes are regions in space where the gravitational pull is so strong that nothing, not even light, can escape from them. They are formed when massive stars exhaust their nuclear fuel and collapse under their own gravity, leading to an extremely dense object with an event horizon that marks the boundary beyond which escape is impossible. Understanding black holes is essential for exploring phenomena such as accretion disks, which are formed from material spiraling into the black hole and play a critical role in the study of high-energy astrophysics.
Eddington Luminosity: Eddington luminosity is the maximum luminosity that a celestial object, such as a star or accreting black hole, can achieve when there is a balance between the outward radiation pressure and the inward gravitational pull. This concept is crucial in understanding how massive stars evolve and the limits on accretion rates in astrophysical systems, particularly in the context of accretion disks.
Gravitational potential energy: Gravitational potential energy is the energy an object possesses due to its position in a gravitational field, often measured relative to a reference point. This energy is crucial in astrophysics, especially in understanding how objects like stars, planets, and accretion disks evolve and interact under the influence of gravity. In the context of accretion disks, the gravitational potential energy plays a key role in the dynamics and stability of the disk as matter spirals inward towards a central mass.
Magnetorotational instability: Magnetorotational instability (MRI) is a type of instability that occurs in differentially rotating astrophysical systems where magnetic fields are present. This phenomenon can lead to the turbulent transport of angular momentum, which is crucial in the dynamics of accretion disks around celestial objects such as black holes and young stars. MRI plays a vital role in the efficiency of accretion processes, affecting how mass and energy are transported within these disks.
MRI: MRI, or Magnetic Resonance Imaging, is a medical imaging technique used to visualize internal structures of the body in detail using strong magnetic fields and radio waves. This non-invasive method has applications in various fields, including astrophysics, where it can help in analyzing the properties of celestial objects by examining their emitted radio waves and magnetic fields.
Neutron stars: Neutron stars are incredibly dense remnants of massive stars that have undergone a supernova explosion, where the core collapses under gravity to the point that protons and electrons combine to form neutrons. These stars are typically about 1.4 times the mass of the Sun but condensed into a sphere with a radius of only about 10 kilometers. The extreme density and strong gravitational forces create fascinating phenomena such as pulsars and accretion disks.
Radiative Efficiency: Radiative efficiency is the measure of how effectively a celestial object converts its gravitational energy into radiation, typically as light or other forms of electromagnetic energy. This concept is particularly important in understanding the processes occurring in accretion disks, where material spirals into massive objects like black holes or neutron stars, converting potential energy into radiation. Higher radiative efficiency means more energy is emitted in the form of radiation, impacting the luminosity and temperature of the accretion disk.
Shakura-Sunyaev α-disk model: The Shakura-Sunyaev α-disk model is a theoretical framework that describes the structure and behavior of accretion disks around compact objects, such as black holes and neutron stars. This model introduces a parameter, alpha (α), representing the turbulent viscosity within the disk, which is crucial for understanding the transfer of angular momentum and energy. By incorporating the effects of radiation and gravity, this model provides insights into how matter accretes onto celestial bodies, contributing to the overall dynamics and emissions observed in astrophysical systems.
Super-eddington accretion: Super-eddington accretion refers to the process where a massive object, such as a black hole or neutron star, accretes matter at a rate that exceeds the Eddington limit. The Eddington limit is the maximum luminosity a body can achieve when there is a balance between the outward radiation pressure and the inward gravitational force. When this limit is surpassed, it has significant implications for the formation and growth of supermassive black holes as well as the behavior and structure of accretion disks around these objects.
Thick Disk Model: The thick disk model is an astrophysical concept that describes a distinct component of the galactic disk characterized by a greater vertical thickness compared to the thin disk. This model accounts for the distribution of stars, gas, and dust within a galaxy, providing insights into the formation and evolution of galaxies by considering factors like stellar populations and kinematics.
Thin Disk Model: The thin disk model is a representation of the structure and dynamics of an accretion disk, characterized by its flat, disc-like shape, where the gravitational force of a central body influences the motion of matter within the disk. This model simplifies the complexities of accretion disks, enabling the analysis of material that spirals inward towards the center, typically around compact objects like black holes or neutron stars. The thin disk model is crucial for understanding various astrophysical phenomena such as star formation and the behavior of active galactic nuclei.
Turbulence: Turbulence refers to the chaotic and irregular flow of fluids, which in astrophysics can be observed in gases and plasma within various astronomical environments. This phenomenon plays a significant role in the dynamics of molecular clouds and star-forming regions, as well as in the structure and evolution of accretion disks around celestial bodies. Turbulence influences the mixing of materials and energy transfer, affecting star formation rates and disk stability.
Viscosity: Viscosity is a measure of a fluid's resistance to flow, representing how thick or sticky the fluid is. In the context of astrophysical processes, viscosity plays a critical role in the dynamics of accretion disks, influencing how matter moves and accumulates around massive celestial objects like black holes or neutron stars. The viscosity of a fluid affects the transport of angular momentum and energy, which are essential for the formation and evolution of accretion disks.