3.2 Accretion disks

Accretion disks are cosmic structures that form around massive objects due to infalling matter's gravitational pull and angular momentum. These disks play a crucial role in various astrophysical phenomena, from planet formation to powering quasars.

Understanding accretion disks is key to grasping how matter behaves near massive objects. They're found in diverse settings, from young stars to supermassive black holes, and their study reveals insights into the universe's most energetic processes.

Formation of accretion disks

• Accretion disks are flattened structures that form around massive objects, such as black holes, neutron stars, and young stars, due to the gravitational attraction and angular momentum of infalling matter
• The formation and evolution of accretion disks play a crucial role in various astrophysical phenomena, including the growth of supermassive black holes, the formation of planets and stars, and the emission of high-energy radiation

Gravitational collapse

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• Gravitational collapse occurs when a massive object's gravitational force overcomes the internal pressure supporting it, causing the object to contract and increase in density
• As matter falls towards the central object, it accelerates and gains kinetic energy, which is then converted into heat through viscous dissipation and turbulence within the forming accretion disk
• The gravitational potential energy released during the collapse powers the luminosity of the accretion disk and can lead to the formation of powerful jets and outflows

Angular momentum conservation

• Angular momentum conservation is a fundamental principle that governs the formation and dynamics of accretion disks
• As matter falls towards the central object, it typically possesses some initial angular momentum, which must be conserved during the accretion process
• The conservation of angular momentum causes the infalling material to form a disk-like structure around the central object, as the material cannot fall directly onto the object without first shedding its excess angular momentum

Disk vs spherical accretion

• Accretion can occur in two main geometries: disk accretion and spherical accretion
• Disk accretion is the more common scenario, where the infalling matter forms a flattened, rotating disk around the central object due to angular momentum conservation (protoplanetary disks, binary systems)
• Spherical accretion occurs when the infalling matter has little to no angular momentum, allowing it to fall directly onto the central object in a roughly spherical geometry (accretion onto neutron stars, some cases of black hole accretion)

Structure of accretion disks

• The structure of accretion disks is determined by various physical processes, including gravity, viscosity, and radiation transport
• Understanding the structure of accretion disks is essential for interpreting observational data and modeling the behavior of these systems in different astrophysical contexts

Thin disk model

• The thin disk model, also known as the Shakura-Sunyaev disk, is a widely used description of accretion disks in which the disk is assumed to be geometrically thin and optically thick
• In this model, the disk is in hydrostatic equilibrium in the vertical direction, with the gas pressure balancing the gravitational force of the central object
• The thin disk model predicts a characteristic temperature profile, $T(r) \propto r^{-3/4}$, and a spectrum that closely resembles a multi-temperature blackbody

Thick disk model

• The thick disk model, also known as the advection-dominated accretion flow (ADAF), describes accretion disks that are geometrically thick and optically thin
• In this model, the gas pressure is insufficient to maintain hydrostatic equilibrium, and the disk becomes supported by radiation pressure or magnetic fields
• Thick disks are typically associated with low accretion rates and can exhibit different temperature and density profiles compared to thin disks (radiatively inefficient accretion)

Temperature gradients

• Accretion disks exhibit temperature gradients in both the radial and vertical directions
• In the radial direction, the temperature generally decreases with increasing distance from the central object, as the gravitational potential energy release is highest near the center
• In the vertical direction, the disk can have a temperature inversion, with the midplane being cooler than the surface layers due to the effects of radiative cooling and viscous heating

Density profiles

• The density structure of accretion disks is determined by the balance between gravity, gas pressure, and centrifugal forces
• In the radial direction, the density typically decreases with increasing distance from the central object, following a power-law profile (e.g., $\rho(r) \propto r^{-3/2}$ for a thin disk)
• In the vertical direction, the density is highest at the midplane and decreases towards the surface of the disk, often following a Gaussian or exponential profile

Accretion disk dynamics

• The dynamics of accretion disks are governed by a complex interplay of gravitational, viscous, and magnetic forces
• Understanding the transport of angular momentum and the mechanisms driving accretion is crucial for modeling the evolution and observational properties of these systems

Viscosity and angular momentum transport

• Viscosity plays a central role in the transport of angular momentum within accretion disks
• In order for matter to accrete onto the central object, it must lose angular momentum, which is redistributed outwards in the disk through viscous stresses
• The nature of the viscosity in accretion disks is not fully understood, but it is thought to arise from turbulence and magnetic fields (anomalous viscosity)

Magnetorotational instability (MRI)

• The magnetorotational instability (MRI) is a powerful mechanism for generating turbulence and angular momentum transport in accretion disks
• MRI occurs when a weak magnetic field is present in a differentially rotating disk, leading to the amplification of the field and the growth of turbulent motions
• MRI-driven turbulence can provide the effective viscosity needed to explain the observed accretion rates and luminosities of astrophysical accretion disks

Accretion rate and efficiency

• The accretion rate, often denoted as $\dot{M}$, is a key parameter that determines the luminosity and observational appearance of an accretion disk
• The accretion efficiency, $\eta$, relates the luminosity of the disk to the accretion rate through the equation $L = \eta \dot{M} c^2$, where $c$ is the speed of light
• The efficiency depends on the nature of the central object and the accretion flow, ranging from ~0.06 for a Schwarzschild black hole to ~0.42 for a maximally rotating Kerr black hole

Jet formation and collimation

• Accretion disks can launch powerful jets of matter and radiation along the rotation axis of the system
• Jets are thought to be powered by a combination of accretion energy and magnetic fields, which extract rotational energy from the disk or the central object (Blandford-Znajek process)
• The collimation of jets is likely due to the presence of a helical magnetic field structure, which guides and confines the outflowing material on large scales (parsec-scale jets in active galactic nuclei)

Radiation from accretion disks

• Accretion disks emit radiation across a wide range of the electromagnetic spectrum, from radio to gamma-rays
• The radiation from accretion disks carries important information about the physical conditions and processes within these systems

Blackbody radiation

• Blackbody radiation is the thermal emission from an optically thick medium in thermal equilibrium
• Accretion disks often emit a significant fraction of their energy as blackbody radiation, particularly in the optical and ultraviolet bands
• The multi-temperature blackbody spectrum of a thin disk can be described by the Shakura-Sunyaev disk model, with the peak emission corresponding to the temperature at the inner edge of the disk

Compton scattering

• Compton scattering is the interaction between photons and electrons, resulting in the exchange of energy and momentum
• In accretion disks, Compton scattering can modify the spectrum of the emitted radiation, particularly in the X-ray band
• Inverse Compton scattering, where low-energy photons gain energy from hot electrons, is a key mechanism for producing hard X-ray emission in accretion disk coronae and jets

Synchrotron radiation

• Synchrotron radiation is the emission from relativistic electrons spiraling in a magnetic field
• In accretion disks, synchrotron radiation can be generated by electrons accelerated in the disk's magnetic fields or in the jets launched from the system
• Synchrotron emission is often observed in the radio and infrared bands, and it can be used to probe the magnetic field strength and electron energy distribution in these systems

Bremsstrahlung emission

• Bremsstrahlung, or free-free emission, is the radiation produced by the acceleration of electrons in the electric field of ions
• In accretion disks, bremsstrahlung can be a significant source of X-ray emission, particularly in the hot, ionized regions of the disk or corona
• The bremsstrahlung spectrum depends on the temperature and density of the emitting plasma, and it can provide insights into the physical conditions in different parts of the accretion flow

Types of accretion disks

• Accretion disks are found in a variety of astrophysical contexts, each with its own unique properties and observational characteristics
• Understanding the different types of accretion disks is essential for interpreting observations and modeling the evolution of these systems

Protoplanetary disks

• Protoplanetary disks are accretion disks that form around young stars during the star formation process
• These disks are composed of gas and dust, and they serve as the birthplaces of planets and planetary systems
• Protoplanetary disks are typically a few hundred AU in size and have masses ranging from ~0.001 to 0.1 solar masses
• The structure and evolution of protoplanetary disks are influenced by a variety of processes, including viscous accretion, photoevaporation, and planet-disk interactions

Accretion disks around young stars

• Accretion disks around young stars, such as T Tauri stars and Herbig Ae/Be stars, are the remnants of protoplanetary disks that continue to accrete onto the central star
• These disks are often smaller and less massive than protoplanetary disks, with typical sizes of a few tens of AU and masses of ~0.001 solar masses
• Accretion disks around young stars can exhibit a range of observational signatures, including excess infrared emission, spectral line emission (Balmer lines), and variability

Accretion disks in binary systems

• Accretion disks can form in binary star systems, where one star (the donor) transfers matter onto its companion (the accretor) through Roche lobe overflow
• In these systems, the accretion disk forms around the accretor and is fed by the material lost from the donor star
• Examples of binary systems with accretion disks include cataclysmic variables (white dwarf accretors), X-ray binaries (neutron star or black hole accretors), and symbiotic stars (giant star donors)
• The properties of the accretion disk in a binary system depend on factors such as the mass ratio of the stars, the orbital period, and the magnetic field strength of the accretor

Supermassive black hole accretion disks

• Supermassive black holes (SMBHs), with masses ranging from millions to billions of solar masses, are found at the centers of most galaxies
• Accretion disks around SMBHs are some of the most luminous and energetic objects in the Universe, powering the phenomena of active galactic nuclei (AGN) and quasars
• These disks can extend to scales of parsecs or even kiloparsecs, and they are often accompanied by powerful jets and outflows that interact with the surrounding galaxy
• The accretion rate and radiative efficiency of SMBH accretion disks can have significant implications for the growth and evolution of galaxies, as well as the properties of the intergalactic medium

Observational evidence of accretion disks

• Accretion disks are not directly resolvable in most astrophysical systems due to their small angular sizes
• However, there are several observational signatures that provide strong evidence for the presence and properties of accretion disks

Spectral energy distributions (SEDs)

• The spectral energy distribution (SED) of an astrophysical object describes its energy output as a function of wavelength or frequency
• Accretion disks typically exhibit a characteristic SED that combines the contributions from different emission mechanisms, such as blackbody radiation, synchrotron emission, and Compton scattering
• The shape of the SED can provide information about the temperature structure, accretion rate, and radiative efficiency of the disk (multi-wavelength observations)

Doppler broadening of spectral lines

• Spectral lines emitted from accretion disks are often broadened due to the Doppler effect, which arises from the motion of the emitting material
• The rotation of the disk leads to a characteristic double-peaked line profile, with the blue-shifted peak corresponding to the approaching side of the disk and the red-shifted peak corresponding to the receding side
• The width and shape of the broadened spectral lines can be used to infer the velocity structure and inclination of the accretion disk (e.g., broad emission lines in AGN spectra)

Variability and quasi-periodic oscillations (QPOs)

• Accretion disks can exhibit variability on a wide range of timescales, from milliseconds to years
• Rapid variability, such as quasi-periodic oscillations (QPOs), is often associated with the innermost regions of the accretion disk, where the dynamical timescales are shortest
• QPOs are thought to arise from instabilities or resonances in the disk, and their frequencies can be used to probe the mass and spin of the central object (e.g., high-frequency QPOs in X-ray binaries)
• Longer-term variability can be driven by changes in the accretion rate, disk structure, or the interaction between the disk and the central object or jet

Polarization of radiation

• The radiation emitted from accretion disks can be polarized due to various scattering and emission processes
• Synchrotron radiation, for example, is intrinsically polarized, with the polarization direction determined by the orientation of the magnetic field in the disk or jet
• Compton scattering can also produce polarized radiation, with the polarization depending on the geometry and optical depth of the scattering medium
• Observations of the polarization of radiation from accretion disks can provide insights into the magnetic field structure, disk geometry, and the role of scattering in these systems (e.g., polarized radio emission from jets)

Role of accretion disks in astrophysics

• Accretion disks play a central role in many areas of astrophysics, from the formation of stars and planets to the evolution of galaxies and the growth of supermassive black holes
• Understanding the physics of accretion disks is essential for interpreting observations, testing theories, and advancing our knowledge of the Universe

Growth of supermassive black holes

• Accretion disks are the primary means by which supermassive black holes (SMBHs) grow over cosmic time
• The accretion of matter through a disk allows SMBHs to increase their mass by many orders of magnitude, from initial seeds of ~100-1000 solar masses to the observed masses of millions to billions of solar masses
• The growth of SMBHs through accretion has important implications for the evolution of galaxies, as the energy released by the accretion process can have a significant impact on the surrounding gas and star formation (AGN feedback)

Formation of planets and stars

• Protoplanetary disks around young stars are the birthplaces of planets and planetary systems
• The structure and evolution of these disks determine the initial conditions for planet formation, including the distribution of gas and dust, the temperature profile, and the chemical composition
• Accretion through protoplanetary disks also plays a crucial role in the early evolution of stars, as it governs the rate at which stars gain mass and the timescale over which they contract to the main sequence

Feedback on host galaxies

• The energy released by accretion disks around supermassive black holes can have a profound impact on the host galaxy and its evolution
• AGN feedback can take the form of radiative feedback, where the intense radiation from the accretion disk heats and ionizes the surrounding gas, or kinetic feedback, where powerful jets and outflows drive shocks and turbulence into the interstellar medium
• Feedback from AGN accretion disks can regulate star formation, drive galactic winds, and shape the properties of the intergalactic medium, playing a key role in the co-evolution of black holes and galaxies

Accretion disks as probes of strong gravity

• Accretion disks around compact objects, such as black holes and neutron stars, offer unique opportunities to study the effects of strong gravity and test the predictions of general relativity
• The inner regions of these disks, where the gravitational field is strongest, can exhibit phenomena such as gravitational redshift, light bending, and frame-dragging, which are sensitive to the mass and spin of the central object
• Observations of accretion disks in the strong gravity regime, such as the detection of the innermost stable circular orbit (ISCO) or the measurement of black hole spins, can provide stringent tests of general relativity and alternative theories of gravity