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.
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
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
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
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
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 )
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 )
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 )
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
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
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
(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