Accretion, disks and jets

Inflow can release binding energy

Accretion is the accumulation of material onto an object or into its surrounding inflow. A companion can supply gas through a wind or a stream, as the interacting-binary lesson described. The material can possess substantial angular momentum about the accretor.

Matter moving inward can release gravitational binding energy if the flow dissipates energy. Part can be radiated, carried into the central region as heat or transferred to an outflow. Falling closer does not guarantee that every available joule appears in one observing band.

An accretion disk is a rotating distribution of material around the accretor. Disks can occur around different objects, including white dwarfs, neutron stars and black holes. Not every inflow has the same thickness, temperature structure or radiative behaviour.

The observed system can therefore be bright because its surrounding plasma emits radiation. This does not require light or material to emerge from inside a classical black-hole event horizon. The emitting region and the compact object must be distinguished.

A rotating flow needs a way to redistribute motion

Material on a circular orbit cannot simply move to every smaller circular orbit while retaining its original specific angular momentum. A process that changes the material’s angular momentum is part of the inward-flow problem.

Stress means momentum transfer across parts of the flow. In disk models, stresses can transfer angular momentum outward while some material moves inward. Outflows can also carry angular momentum away. It is redistributed within a complete account rather than disappearing.

Turbulence and magnetic fields in plasma can contribute to those stresses. A single familiar picture of microscopic rubbing does not fully describe every astrophysical disk. A detailed calculation must connect the flow, field and energy transport.

The inner boundary also matters. A material stellar surface, a boundary layer and a black-hole inner flow have different conditions. Replacing all of them with one identical radius and dissipation rule can give a misleading luminosity prediction.

A weak-field power scale is not a horizon calculation

For material initially nearly at rest far from a Newtonian object of mass M, reaching rest at a material radius R releases a gravitational energy scale GM/R per unit mass. Multiplying by a specified supplied rate Ṁ gives the power scale GMṀ/R. This statement assumes a weak gravitational field, GM/(Rc²) ≪1, and the declared initial and final states.

A circular disk, a spinning surface and an outflow can have different energy accounts. The weak-field fall-to-rest scale is not automatically an exact disk luminosity. In particular, inserting a black-hole horizon radius into that Newtonian expression does not derive a relativistic efficiency.

Instead define a radiated accretion luminosity L_acc through L_acc = ηṀ_sup c², with supplied rest-mass rate Ṁ_sup at an explicitly chosen flow boundary. The dimensionless η is the radiative output divided by that supplied rest-mass-energy rate in the adopted model.

This definition does not make Ṁ_sup equal to the black hole’s mass-growth rate. Some material can leave in winds, and energy can be radiated, advected or carried mechanically. The efficiencies and flow rates depend on the specified boundaries and physical state.

The same luminosity can have more than one supplied rate

Choose original inputs Ṁ_sup = 10¹² kg s⁻¹ and exact vacuum c = 299792458 m s⁻¹. Stipulate two separate radiative efficiencies, η = 0.05 and 0.1. They are teaching parameters, not measured spins or universal values.

The corresponding emitted accretion luminosities are approximately 4.493775894 × 10²⁷ W and 8.987551787 × 10²⁷ W. Doubling η at the same supplied rate doubles this model’s radiated output.

Now hold L_acc fixed at 8.987551787 × 10²⁷ W, understood as the rounded display of the η = 0.1 result. The η = 0.1 model requires10¹² kg s⁻¹, while the η = 0.05 model requires2 × 10¹² kg s⁻¹. The same luminosity constrains the product of efficiency and supplied rate, not each separately.

These numbers describe a declared emitted accretion luminosity. A single-band telescope flux, a beamed isotropic-equivalent luminosity or an unknown distance cannot be silently substituted. A real inference needs the observing geometry and energy distribution as well as the flow model.

A jet is neither mandatory nor a unique black-hole signature

Jets are relatively collimated outflows of plasma. Magnetic fields and rotating accretion environments can participate in their launching and energy transfer. The detailed mechanism depends on the system and is not solved by the simple η calculation.

For a black-hole system, the outflow is associated with material and fields outside the horizon. It is not a stream that first escapes from inside the causal boundary. Diagrams that appear to show a jet emerging from a central icon must be read with that physical distinction retained.

Jets are also observed in some neutron-star accreting systems. A jet or high-energy emission alone therefore does not uniquely establish a black hole. Conversely, the absence of a detected jet does not by itself rule one out.

Radiative and mechanical power are different outputs, and their observed signatures depend on viewing angle and propagation. The next lesson brings these examples together as an inference problem: specify which quantity was measured, what the model connects it to and which alternatives remain.

Worked examples

Try the reasoning

1. Does material spiral inward because angular momentum simply disappears?

   Show the answer and reasoning

   No.

   The full account transports angular momentum between flow regions, fields, objects or outflows.

2. Does substituting a horizon radius into GMṀ/R provide a justified relativistic efficiency?

   Show the answer and reasoning

   No.

   The stated Newtonian scale requires a weak field and specific initial/final boundary conditions.

3. Does a detected jet alone prove that the accretor is a black hole?

   Show the answer and reasoning

   No.

   Some neutron-star accretion systems also produce jets, and an identification needs other evidence.

4. Must Ṁ_sup in the defined radiative budget equal the black hole’s mass-growth rate?

   Show the answer and reasoning

   No.

   Radiation, outflows, advection and the chosen boundary affect the material and energy that actually reach the object.

What to carry forward

• Accretion connects material supply, binding-energy release and angular-momentum transport.
• Radiative efficiency is a defined model quantity rather than one universal conversion.
• Disk light and jets arise from an environment whose properties and viewing geometry must be inferred separately from the compact object.