SCIENCE · INVESTIGATE AND EXPLAIN

Distinguish bound cloud energy from actual star formation

Star formation begins in gas whose gravity can overcome relevant support and whose energy can be redistributed or radiated. Cooling permits contraction without simply maintaining enough thermal pressure to halt it. Rotation, magnetic fields, turbulence, external pressure and feedback can matter; a dense cloud is not guaranteed to become one star.

Learning outcome: Compute total energy and virial residual separately, then compare the density-dependent free-fall reference. Name one missing support or boundary term before describing a real cloud.

Starting recap

Keep geometry, luminosity, support, energy, evolutionary stage and population assumptions distinct.

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Try

For M=2 and R=2, U=−1.2 and K=0.6 in compatible energy units. Total energy is−0.6, while α=1. The cloud is bound in this restricted energy accounting and meets the scalar virial relation, but no evolving collapse has been simulated.

Open the experiment

Predict

Does negative total energy imply zero pressure or immediate collapse?

Your prediction and reason

Experiment

Compute total energy and virial residual separately, then compare the density-dependent free-fall reference. Name one missing support or boundary term before describing a real cloud.

Compare cloud energies without asserting collapse

Worked teaching model · synthetic values · Original uniform isolated sphere G=1, isothermal sound-speed squared 0.2; gravitational U=−3M²/(5R), thermal K=3Mc²/2. No rotation, magnetic support, external pressure or dissipation. Free-fall time is a pressureless comparison, not actual modeled collapse.

Uniform cloud mass: 2 normalized mass Cloud radius: 2 normalized length

Reset keeps your prediction, captures and practice history.

Bound energy, virial balance and actual gravitational collapse are different claims.

Original uniform isolated sphere G=1, isothermal sound-speed squared 0.2; gravitational U=−3M²/(5R), thermal K=3Mc²/2. No rotation, magnetic support, external pressure or dissipation. Free-fall time is a pressureless comparison, not actual modeled collapse.

Original conditional model ledger
Quantity	Value	Unit
Gravitational energy	-1.200000	energy
Thermal kinetic energy	0.6000000	energy
Virial ratio two K over absolute U	1.000000	ratio
Total energy K plus U	-0.6000000	energy
Mean density	0.05968310	mass/length³
Pressureless free-fall comparison time	2.221441	time

Original model records, not measured stars, a self-consistent stellar evolution code or independent observing competence.

Bound energy, virial balance and actual gravitational collapse are different claims.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

1. Define the stellar inference

2. Connect mechanism and assumptions

The original uniform isolated sphere uses G=1 and isothermal sound-speed squared 0.2. Its gravitational energy is U=−3M²/(5R), thermal kinetic energy K=3Mc_s²/2 and virial ratio α=2K/|U|. The total K+U and the virial balance condition 2K+U=0 are different expressions.

At α=1 the restricted virial relation balances, but this is not a proof of dynamical stability. At α=2 total energy is zero; α below two gives negative total energy under the assumed boundary. A negative energy alone does not specify how quickly contraction occurs or whether fragmentation takes place.

The pressureless uniform-sphere free-fall comparison is sqrt(3π/(32Gρ)), withρ=3M/(4πR³). It is a limiting timescale under different support assumptions, not the elapsed time predicted by the thermal model. A forming protostar can radiate gravitational energy before sustained central hydrogen fusion; accretion disks and outflows connect mass and angular-momentum transport.

3. Work the supplied case

4. Predict and investigate

Does negative total energy imply zero pressure or immediate collapse?

Compute total energy and virial residual separately, then compare the density-dependent free-fall reference. Name one missing support or boundary term before describing a real cloud.

Apply the evidence to a changed case

Use M=1 and R=2. Find U, K, total energy and α.

Retain the evidence frame, calculations and assumptions before opening public feedback.

Compare a worked response

U=−0.3, K=0.3, total energy zero and α=2. This marginal energy condition differs from α=1 virial balance and is conditional on the omitted external/support terms.

Source and boundaries

Primary source. Checked 31 October 2026. All numerical records and diagrams here are original supplied models, not measured stellar populations or a full stellar-evolution solver. No direct observing or physical experiment is requested.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Use M=1 and R=2. Find U, K, total energy and α.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Read temperature and luminosity as distinct stellar constraints Next: Integrate stellar support rather than equating force with pressure

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