Upgrade to Pro — share decks privately, control downloads, hide ads and more …

Accretion flows I

Accretion flows I

This lecture is part of the course "physics of active galactic nuclei" offered to graduate students in astrophysics by Rodrigo Nemmen and Joao Steiner at IAG USP.

https://rodrigonemmen.com/teaching/active-galactic-nuclei/

Rodrigo Nemmen

May 20, 2016
Tweet

More Decks by Rodrigo Nemmen

Other Decks in Science

Transcript

  1. Rodrigo Nemmen
    Accretion Flows
    AGA5727 - Active Galactic Nuclei
    Credit: ESO

    View Slide

  2. A cloud of interstellar gas is rotating slowly around its axis and
    contracting because of the attractive pull of its own gravity. As the
    cloud collapses, it rotates faster.
    The gas in the cloud’s equatorial plane moves inward more slowly
    because its rotation starts to balance the gravity. Gas above and
    below the plane falls inward much faster.
    Gravitational
    contraction
    Rotation
    Faster
    contraction
    Slower
    contraction
    galaxy. In general, galaxies do not
    tic collisions and mergers compli-
    At least some elliptical galaxies, as
    of spiral galaxies, may have arisen
    m in binary star systems when one
    compact, dense white dwarf) grav-
    companion (usually a larger, less
    considerable angular momentum
    otion of the two stars around their
    it typically cannot fall directly in-
    arf. Instead the gas ends up form-
    .
    ch shorter year than Earth—a mere
    nner parts of a disk invariably takes
    bit than does material in the outer
    al periods causes shear: bits of ma-
    stances from the center of the disk
    ox on page 54]. If some form of fric-
    erial, it tries to slow down the more
    s and speed up the more slowly or-
    ar momentum is therefore trans-
    outer regions of the disk. As a con-
    ner regions loses rotational support
    ard. The overall result is a gradual
    he central star or black hole.
    to the innermost orbit of an accre-
    avitational potential energy. Some
    into giving the material the faster
    ls inward; the rest is dissipated into
    y by the friction itself. Thus, the ma-
    very hot, emitting copious amounts
    ay radiation. The energy release can
    dable power sources.
    A cloud of interstellar gas is rotating slowly around its axis and
    contracting because of the attractive pull of its own gravity. As the
    cloud collapses, it rotates faster.
    The gas in the cloud’s equatorial plane moves inward more slowly
    because its rotation starts to balance the gravity. Gas above and
    below the plane falls inward much faster.
    Gravitational
    contraction
    Rotation
    Faster
    contraction
    Slower
    contraction
    of the stars (for example, a compact, dense white dwarf) grav-
    itationally pulls gas off its companion (usually a larger, less
    compact star). This gas has considerable angular momentum
    from the original orbital motion of the two stars around their
    common center of mass, so it typically cannot fall directly in-
    ward toward the white dwarf. Instead the gas ends up form-
    ing a disk around the dwarf.
    Just as Mercury has a much shorter year than Earth—a mere
    88 days—the material in the inner parts of a disk invariably takes
    less time to complete one orbit than does material in the outer
    parts. This gradient in orbital periods causes shear: bits of ma-
    terial at slightly different distances from the center of the disk
    slide past one another [see box on page 54]. If some form of fric-
    tion is present in the disk material, it tries to slow down the more
    rapidly orbiting inner regions and speed up the more slowly or-
    biting outer regions. Angular momentum is therefore trans-
    ported from the inner to the outer regions of the disk. As a con-
    sequence, material in the inner regions loses rotational support
    against gravity and falls inward. The overall result is a gradual
    spiraling of matter toward the central star or black hole.
    As material spirals down to the innermost orbit of an accre-
    tion disk, it must give up gravitational potential energy. Some
    of the potential energy goes into giving the material the faster
    orbital speed it gains as it falls inward; the rest is dissipated into
    heat or other forms of energy by the friction itself. Thus, the ma-
    terial in the disk can become very hot, emitting copious amounts
    of visible, ultraviolet and x-ray radiation. The energy release can
    make accretion disks formidable power sources.
    This phenomenon is what first alerted astronomers to the ex-
    istence of black holes. Black holes themselves cannot emit light,
    but the accretion disks around them can. (This general statement
    ignores the theorized Hawking radiation, an emission that
    would be undetectable for all but the smallest black holes and
    JIAN
    A cloud of interstellar gas is rotating slowly around its axis and
    contracting because of the attractive pull of its own gravity. As the
    cloud collapses, it rotates faster.
    The gas in the cloud’s equatorial plane moves inward more slowly
    because its rotation starts to balance the gravity. Gas above and
    below the plane falls inward much faster.
    Rotation
    Faster
    contraction
    Slower
    contraction
    Blaes, SciAm
    Disks are ubiquitous in
    the universe

    View Slide

  3. M
    L
    r
    Ne
    fully ionized gas
    Eddington limit
    spherical
    accretion

    View Slide

  4. View Slide

  5. View Slide

  6. Equations of hydrodynamics
    D⇢
    Dt
    + ⇢r · v = 0

    Dv
    Dt
    = rp ⇢r + r · T

    D(e/⇢)
    Dt
    = pr · v + T2/µ
    Conservation
    of
    Mass
    Momentum
    Energy
    Rate of change
    “following the fluid”
    D⇢
    Dt

    Dv
    Dt
    = rp

    D(e/⇢)
    Dt
    = pr · v + T2/µ r
    D⇢
    Dt
    + ⇢r · v = 0

    Dv
    Dt
    = rp ⇢r + r · T
    D(e/⇢)
    Dt
    = pr · v + T2/µ r · Frad
    r · q

    View Slide

  7. Equations of hydrodynamics
    D⇢
    Dt
    + ⇢r · v = 0

    Dv
    Dt
    = rp ⇢r + r · T

    D(e/⇢)
    Dt
    = pr · v + T2/µ
    Conservation
    of
    Mass
    Momentum
    Energy
    Rate of change
    “following the fluid”
    D⇢
    Dt

    Dv
    Dt
    = rp

    D(e/⇢)
    Dt
    = pr · v + T2/µ r
    D⇢
    Dt
    + ⇢r · v = 0

    Dv
    Dt
    = rp ⇢r + r · T
    D(e/⇢)
    Dt
    = pr · v + T2/µ r · Frad
    r · q

    View Slide

  8. Equations of hydrodynamics
    D⇢
    Dt
    + ⇢r · v = 0

    Dv
    Dt
    = rp ⇢r + r · T

    D(e/⇢)
    Dt
    = pr · v + T2/µ
    Conservation
    of
    Mass
    Momentum
    Energy
    Rate of change
    “following the fluid”
    D⇢
    Dt

    Dv
    Dt
    = rp

    D(e/⇢)
    Dt
    = pr · v + T2/µ r
    D⇢
    Dt
    + ⇢r · v = 0

    Dv
    Dt
    = rp ⇢r + r · T
    D(e/⇢)
    Dt
    = pr · v + T2/µ r · Frad
    r · q

    View Slide

  9. Equations of hydrodynamics:
    Momentum conservation
    D⇢
    Dt
    + ⇢r · v = 0

    Dv
    Dt
    = rp ⇢r + r · T

    D(e/⇢)
    Dt
    = pr · v + T2/µ
    Rate of change
    “following the fluid”
    Cauchy momentum
    equation

    Dv
    Dt
    = r · + ⇢a
    r · = rp + r · T
    Divergence of
    stress tensor
    viscous forces
    pressure
    forces
    external forces
    viscous forces
    pressure
    forces gravity
    force / volume
    )

    View Slide

  10. Equations of hydrodynamics:
    Momentum conservation
    D⇢
    Dt
    + ⇢r · v = 0

    Dv
    Dt
    = rp ⇢r + r · T

    D(e/⇢)
    Dt
    = pr · v + T2/µ
    Rate of change
    “following the fluid”
    Cauchy momentum
    equation

    Dv
    Dt
    = r · + ⇢a
    r · = rp + r · T
    Divergence of
    stress tensor
    viscous forces
    pressure
    forces
    external forces
    viscous forces
    pressure
    forces gravity
    force / volume
    )

    View Slide

  11. Equations of hydrodynamics:
    Momentum conservation
    D⇢
    Dt
    + ⇢r · v = 0

    Dv
    Dt
    = rp ⇢r + r · T

    D(e/⇢)
    Dt
    = pr · v + T2/µ
    Rate of change
    “following the fluid”
    Cauchy momentum
    equation

    Dv
    Dt
    = r · + ⇢a
    r · = rp + r · T
    Divergence of
    stress tensor
    viscous forces
    pressure
    forces
    external forces
    viscous forces
    pressure
    forces gravity
    force / volume
    )

    View Slide

  12. Equations of hydrodynamics: stress tensor
    http://en.wikipedia.org/wiki/Stress_(mechanics)#/media/File:Components_stress_tensor_cartesian.svg
    orthogonal
    normal stresses
    (pressure)
    orthogonal
    shear stresses

    View Slide

  13. Equations of hydrodynamics: stress tensor
    http://en.wikipedia.org/wiki/Viscosity#/media/File:Laminar_shear.svg
    Bottomline:
    no differential rotation ➠ no shear (no viscosity)

    View Slide

  14. Equations of hydrodynamics:
    Energy conservation
    Rate of change
    “following the fluid”
    D⇢
    Dt
    + ⇢r · v = 0

    Dv
    Dt
    = rp ⇢r + r · T

    D(e/⇢)
    Dt
    = pr · v + T2/µ r · Frad
    r · q
    thermal
    conduction
    viscous
    heating
    radiative
    cooling
    rate of change in
    internal energy

    View Slide

  15. Equations of hydrodynamics
    Plus:
    equation of state
    opacity description
    viscosity
    D⇢
    Dt
    + ⇢r · v = 0

    Dv
    Dt
    = rp ⇢r + r · T

    D(e/⇢)
    Dt
    = pr · v + T2/µ
    Conservation
    of
    Mass
    Momentum
    Energy
    D⇢
    Dt

    Dv
    Dt
    = rp

    D(e/⇢)
    Dt
    = pr · v + T2/µ r
    D⇢
    Dt
    + ⇢r · v = 0

    Dv
    Dt
    = rp ⇢r + r · T
    D(e/⇢)
    Dt
    = pr · v + T2/µ r · Frad
    r · q

    View Slide

  16. Flow Illustrator
    https://www.youtube.com/watch?v=CFXS3MVFmvY

    View Slide

  17. McKinney, Tchekhovskoy & Blandford 13, Science

    View Slide

  18. McKinney & Gammie 04, ApJ

    View Slide

  19. Applying the equations to accretion flows
    Plus:
    equation of state
    opacity description
    viscosity
    D⇢
    Dt
    + ⇢r · v = 0

    Dv
    Dt
    = rp ⇢r + r · T

    D(e/⇢)
    Dt
    = pr · v + T2/µ
    Mass
    Momentum
    Energy
    D⇢
    Dt

    Dv
    Dt
    = rp

    D(e/⇢)
    Dt
    = pr · v + T2/µ r
    D⇢
    Dt
    + ⇢r · v = 0

    Dv
    Dt
    = rp ⇢r + r · T
    (e/⇢)
    Dt
    = pr · v + T2/µ r · Frad
    r · q

    View Slide

  20. vt = (v ) = R⌦
    vp = (vR, vz)
    (vp
    · r)vp =
    rp

    r + ⌦2R + (r · T)p
    Useful way of classifying the complexity of
    accretion flow models
    Poloidal component of momentum equation
    viscosity
    gravity
    rotation
    (is v big?)
    advection
    (is vR big?)
    pressure
    support
    related to
    viscosity

    View Slide

  21. vt = (v ) = R⌦
    vp = (vR, vz)
    (vp
    · r)vp =
    rp

    r + ⌦2R + (r · T)p
    Classifying accretion flow models
    viscosity
    gravity
    rotation
    (is v big?)
    advection
    (is vR big?)
    pressure
    support
    Stars, stellar envelopes &
    atmospheres

    View Slide

  22. vt = (v ) = R⌦
    vp = (vR, vz)
    (vp
    · r)vp =
    rp

    r + ⌦2R + (r · T)p
    Classifying accretion flow models
    viscosity
    gravity
    rotation
    (is v big?)
    advection
    (is vR big?)
    pressure
    support
    Stars, stellar envelopes &
    atmospheres
    no accretion

    View Slide

  23. vt = (v ) = R⌦
    vp = (vR, vz)
    (vp
    · r)vp =
    rp

    r + ⌦2R + (r · T)p
    viscosity
    gravity
    rotation
    (is v big?)
    advection
    (is vR big?)
    pressure
    support
    Classifying accretion flow models
    Spherical accretion:
    Bondi-Hoyle accretion

    View Slide

  24. vt = (v ) = R⌦
    vp = (vR, vz)
    (vp
    · r)vp =
    rp

    r + ⌦2R + (r · T)p
    viscosity
    gravity
    rotation
    (is v big?)
    advection
    (is vR big?)
    pressure
    support
    Classifying accretion flow models
    Thin accretion disks
    (quasi-Keplerian)

    View Slide

  25. vt = (v ) = R⌦
    vp = (vR, vz)
    (vp
    · r)vp =
    rp

    r + ⌦2R + (r · T)p
    viscosity
    gravity
    rotation
    (is v big?)
    advection
    (is vR big?)
    pressure
    support
    Classifying accretion flow models
    Advection-dominated
    accretion flows
    (ADAFs)

    View Slide

  26. Spherical accretion:
    Bondi-Hoyle accretion
    Thin accretion disks
    (quasi-Keplerian)
    Advection-dominated
    accretion flows
    (ADAFs)

    View Slide