Astronomy · Active galaxies and central black holes

Observations of accretion and surrounding matter

Connect accretion-powered radiation, reprocessing and delayed line response, and calculate how a stipulated radiative efficiency changes the supplied mass-flow inference.

Continue in the approved chapter order. Necessary vocabulary, quantities and assumptions are explained in the lesson.

Back to the chapter

After reading, you can

Distinguish continuum, responding line emission and reprocessed dust radiation.
Use a declared emitted bolometric luminosity and efficiency to infer a conditional supplied rest-mass rate.
Explain why response lags and broad-band spectra require a geometry and time-sampling model.

Follow the emission through surrounding matter

An accreting nucleus contains material with a range of physical conditions. A rotating inflow can produce continuum emission, hot electrons can alter a radiation spectrum, illuminated gas can produce emission lines and dust can absorb and reradiate part of the energy.

A broad-line region is gas associated with broad emission-line components. The velocity distribution, geometry and illumination of that gas affect its measured line profile. A continuum and a broad line therefore provide different information, even when both respond to the same central energy supply.

Dust radiation is reprocessed emission, while intervening gas and dust can also change the direct spectrum. A decomposition into these components is a physical model tested against observations, not a guarantee that one filter isolates one component perfectly.

Multi-band observations and variability help separate alternatives. A single spectral shape need not uniquely determine the inflow rate, geometry or black-hole spin. Inclination, transfer, contamination and the accretion state can change the relation between the emitted radiation and what is received.

Efficiency is a definition with an input rate

Reuse the accretion-energy definition L_acc = ηṀ_sup c². Here L_acc is emitted bolometric accretion luminosity, Ṁ_sup is the supplied rest-mass rate through a declared boundary, c is vacuum light speed and η is radiative efficiency defined relative to that supplied rest-mass-energy rate.

Bolometric means integrated over the full emitted spectrum in the stated budget. An observed band flux must not silently replace L_acc, and a beamed isotropic-equivalent luminosity is not automatically the actual total radiated power.

The supplied rate is also not automatically the black-hole growth rate. Material can leave in outflows and energy can be carried in channels other than the counted radiation. The boundary, energy partition and inflow model determine the connection.

Miller’s accretion and efficiency treatments support this explicit accounting. A weak-field gravitational power scale from an ordinary material radius cannot simply be evaluated at a relativistic horizon to obtain a universal radiative efficiency.

A conditional numerical energy budget

For an original calculation, stipulate emitted bolometric accretion luminosity L_acc = 10³⁸ W. Compare η = 0.05 and η = 0.10 at the same supplied-flow boundary. Neither efficiency is inferred from an image or recommended as universal.

Use c = 299792458 m s⁻¹ and rearrange the definition to Ṁ_sup = L_acc/(ηc²). The numerator has units J s⁻¹, and c² has units J kg⁻¹, so the resulting rate is kg s⁻¹.

For η = 0.05 the supplied rate is approximately 2.225300112 × 10²² kg s⁻¹. For η = 0.10 it is approximately 1.112650056 × 10²² kg s⁻¹. Doubling the assumed radiative efficiency halves the supplied rate required to produce the same stipulated emitted luminosity.

The calculation measures the dependency on an assumption; it does not select the correct efficiency for an actual nucleus. Uncertain attenuation, spectral coverage and directional emission would add uncertainty to any attempted observational luminosity input.

Original conditional accretion budget. Emitted bolometric L_acc = 10³⁸ W and c = 299792458 m s⁻¹ are supplied. Both η values are stipulated at one common supplied-flow boundary. Rates are supplied rest mass, not automatically central black-hole growth.
Assumed η	Ṁ_sup = L_acc/(ηc²), kg s⁻¹
0.05	2.225300112 × 10²²
0.10	1.112650056 × 10²²

A lag is a weighted response, not an imaged wall

Reverberation mapping compares variations in a driving continuum with the delayed response of emission lines. A lag is an inferred time offset or response scale under that analysis. Light-travel time through a geometry can produce such a delay, with different locations contributing different arrival times.

The observed continuum must be a suitable proxy for the radiation driving the gas response. Sampling, observation duration, noise, blended light and changes in the gas can affect the inferred lag. A fitted offset should not be interpreted without the response assumptions.

Peterson and Horne describe how line response can be represented over velocity and delay. Such measurements can constrain both geometry and kinematics, while different models can produce similar unresolved profiles. A response-weighted length c times a suitable rest-frame lag is not necessarily a sharply bounded physical shell.

Combining that response scale with a specified line-width measure can form a virial product, which has mass units. Converting the product into a central mass requires an additional geometry and kinematics factor. The detailed calculation belongs to the next dynamical-evidence lesson in this chapter.

An interpretation should predict more than one feature

A useful component model connects spectra and timing consistently: it should account for which emission varies, which responds later, and which is obscured or diluted. Agreement in only one band may leave several competing explanations.

The same supplied luminosity could arise with different efficiencies and supplied rates, as the table shows. Likewise, similar spectra can hide different geometries, and a line lag can have several contributing regions. Additional observations test these degeneracies rather than eliminating them by assumption.

Report the measured quantity, the adopted correction and the resulting physical inference separately. Keeping a band flux, a bolometric emitted luminosity, an inferred supplied rate and a growth rate distinct makes the conclusion assessable.

The next lesson turns to jets and extended lobes. It will distinguish mechanical transport from radiated power and derive an apparent transverse speed greater than c without requiring any material to travel locally faster than light.

Worked examples

Compare two supplied efficiency assumptions

At fixed emitted luminosity, why is the inferred supplied rate for η = 0.10 half the rate for η = 0.05?

The definition gives Ṁ_sup = L_acc/(ηc²).
The supplied L_acc and c are unchanged between rows.
Doubling η therefore doubles the denominator and halves the inferred rate.

The inverse dependence follows from the declared efficiency definition; it does not establish which efficiency describes a real source.

Check the physical units before interpreting the result

Why does L_acc/(ηc²) have mass-per-time units?

A watt is a joule per second.
The dimensionless η changes no units, and c² is equivalent to joules per kilogram.
Dividing J s⁻¹ by J kg⁻¹ gives kg s⁻¹.

It is dimensionally a mass rate. Dimensional consistency alone does not validate the boundary, efficiency or emission model.

Try the reasoning

May one uncorrected band flux be substituted directly for emitted bolometric L_acc?
Show the answer and reasoning
No.
Distance, full spectral emission, attenuation and directionality must be treated consistently.
Is the specified supplied rest-mass rate automatically the central black-hole growth rate?
Show the answer and reasoning
No.
Outflows and other mass-energy channels affect the connection across the chosen boundary.
Must c times a response-weighted lag be the radius of one sharply bounded imaged shell?
Show the answer and reasoning
No.
The response combines geometry, illumination, transfer and sampling.
Can different line-width conventions be interchanged without changing a reverberation mass model?
Show the answer and reasoning
No.
The virial product and geometry factor must use the specified width definition consistently.

What to carry forward

A nuclear spectrum combines direct and reprocessed components with different physical responses.
An inferred supplied rate depends on the declared radiative efficiency and emitted-power boundary.
Timing adds geometry and kinematic constraints while retaining response-model assumptions.

References

Teaching resources and research supporting this lesson’s explanations and examples.