Energy leaving a cluster core

AGN Bubbles and Pressure Waves

How does energy from a black hole reach the surrounding gas? A light cavity expands as the surrounding pressure falls. Its enthalpy decreases along the rise, supplying motion and a wake in the gas. Heat appears after that motion dissipates, so the cavity position and the heating profile need not coincide.

Follow two buoyant cavities, turn their axis and compare the dark patches they leave in projection. Then sample a gentle pressure wave as it crosses the cluster gas.

Distance from cluster centre $24.3\,\mathrm{kpc}$

Cavity radius $2.51\,\mathrm{kpc}$

Energy already thermalized $1.76\times10^{49}\,\mathrm{J}$

Deepest projected deficit $5.79\,\%$

One outburst, two rising cavities

Mean on-phase jet power

1.00

P_j/(10^{43}\,\mathrm{erg}\,\mathrm{s}^{-1})

On-duration in a sixty-Myr event

18.0

t_{\rm on}/\mathrm{Myr}

Axis angle from the observer

60.0

i/\mathrm{deg}

Physical time since the outburst began

45.0

t/\mathrm{Myr}

Drag the axis or power grip. Drag the background to turn the display camera.

Calculating the representative outburst snapshot.

Observer, power range and physical assumptions

Power is either off or in the admitted positive interval. The first nonzero slider position switches it on. Axis inclination changes the real geometry; the observer stays fixed when the camera turns.

$P_j=0\quad\mathrm{or}\quad0.25\leq P_j/(10^{43}\,\mathrm{erg}\,\mathrm{s}^{-1})\leq1$

The bubbles receive ninety-five percent of the input. The wave view follows a separate five-percent thermal release at one fixed source setting. The two calculations share the energy input; gas displacement and feedback between them are omitted.

$r_{\rm out}=150\,\mathrm{kpc},\quad k_BT_a=3\,\mathrm{keV}$

Bîrzan and colleagues: cavities, enthalpy and cooling

Model assumptions

The bubble calculation follows two spherical pressure-balanced cavities in a fixed, fully ionized pure-hydrogen atmosphere. They receive ninety-five percent of the prescribed input, expand adiabatically and rise at terminal speed; a specified wake timescale converts released enthalpy into heat. The projection removes thermal emission inside the same two spheres and shows unabsorbed bolometric free-free radiation, with surface lighting for geometry. It is not a Chandra band image or a Perseus fit. The separate spherical Euler calculation includes gravity, free-free cooling and a five-percent central thermal release at one fixed power and duration. Its actual cell means pass spatial and time-step checks; its weak-shock tests fail, so the wave is labelled a compression wave. Bubble power controls do not rescale the gas record. Jet hydrodynamics, cavity displacement in the Euler gas, radio emission, bright rims, mixing, conduction, multiphase condensation and a self-regulating feedback cycle are omitted. The physical observer is fixed when the display camera turns. Every live bubble request checks numerical refinement and the stated weak-inflation and small-cavity limits; a refused request retains the preceding complete state.

Start with the essentials

Focus question: When energy leaves the centre, has it already become heat?
One-sentence intuition: Cavities can carry enthalpy and waves can reversibly compress gas. Dissipation determines how much of that transported energy becomes heat.

Core mathematical model

A cavity stores enthalpy

H=\frac{\gamma_b}{\gamma_b-1}pV=4pV,\qquad\gamma_b=\frac43

Enthalpy includes internal energy and the work needed to make room for the cavity. A relativistic cavity at pressure balance has four times pressure times volume.

A rising bubble releases some of that energy

\frac{H(r)}{H_d}=\left[\frac{p(r)}{p_d}\right]^{1/4},\qquad\dot K_k=\dot W_k-\frac{K_k}{\tau_d},\quad\dot Q_k=\frac{K_k}{\tau_d}

A falling external pressure lets the cavity expand. Released power $\dot W_k$ enters motion in a radial shell. The wake energy $K_k$ gradually dissipates into heat $Q_k$ . Halving the pressure leaves about 84.1 percent of the cavity enthalpy.

Compression and entropy answer different questions

K=\frac{p}{\rho^{5/3}},\qquad \Delta\ln K=\frac56(M-1)^3+O((M-1)^4)

Reversible compression raises pressure and temperature while keeping the entropy index unchanged. A very weak ideal-gas shock produces entropy only at third order in its excess Mach number. In this gentle gas calculation, that excess entropy does not clear the numerical and cooling-control floor.

Common difficulties

A dark patch changes with the view

Typical misconceptionA deeper projected hole means the gas received more heat.

Better mental modelThe viewing angle changes how much ordinary gas lies in front of and behind a cavity. The physical rise and energy release can remain the same.

A temperature rise can be temporary

Typical misconceptionEvery warm pressure ring must be a shock that heated the gas.

Better mental modelGas can warm during compression and cool again as the pulse passes. A shock classification also requires consistent jumps, a speed separated from the sonic limit and detectable excess entropy.

Run the experiment

01
Watch the rising pair
Choose Rising pair and watch the representative late state. Drag the physical-time slider back toward detachment.
What to observe: The same two spheres determine their positions, sizes and projected X-ray deficit. Heat continues to grow after energy has entered the wake.
02
Let the wake hold energy longer
Compare Heat arrives later and Rising pair at the same time.
What to observe: The rise is unchanged. A longer dissipation time retains more energy in motion and leaves less heat behind.
03
Turn the physical axis
Choose Look along the outburst, then return to Rising pair. Drag the background to turn only the display camera.
What to observe: The physical axis changes the projected deficit. The display camera reveals depth without changing that observation.
04
Sample the passing wave
Choose A pressure pulse leaves. Drag the green probe across a warm and a cool band; pause and step through the recorded times.
What to observe: Pressure and velocity are measured relative to matching gas that only cools. The time sequence shows actual complete snapshots at the fixed source setting.
05
See what reaches larger radii
Choose The wave reaches the outskirts, inspect the radial profile and open the shock explanation.
What to observe: A travelling compression remains visible at the final time. The calculation accepts this gentle wave, while the original shock tests remain failed.

AGN Bubbles and Pressure Waves

Follow the energy beyond the black hole

Core mathematical model

A cavity stores enthalpy

A rising bubble releases some of that energy

Compression and entropy answer different questions

Common difficulties

A dark patch changes with the view

A temperature rise can be temporary

Run the experiment

Watch the rising pair

Let the wake hold energy longer

Turn the physical axis

Sample the passing wave

See what reaches larger radii

Related experiments and articles

From cavities to the heating question