Pressure, gravity and direction

Molecular Cloud Collapse and Magnetic Support

Will this gas rebound or gather under gravity? A short density ripple can rebound as pressure pushes gas outward. A longer ripple can grow through self-gravity. A magnetic field changes this response by direction: compression along the field can grow even when cross-field compression is restored.

Watch a gas ripple respond to pressure and gravity. Rotate a field in a separate linear magnetic wave, then probe and save the computed state.

Peak volume density $\rho_{\max}/\rho_0=1.2$

Signed prepared-wave amplitude $D=0.101$

Probe speed · box length per gravity time $v_{p}=0.00188$

Thermal Jeans cells at the peak $N_J=38.9$

Let a density ripple evolve

Wavelength / thermal Jeans length

1.50

J=L/\lambda_{J,0}

Initial peak density contrast

0.200

A

Drag cyan to prepare a new density center; drag amber to sample a cell.

Nonmagnetic gas · a computed representative state is ready.

Units, conservation and operating limits

L_0=\rho_0=t_0=1,\quad t_0=(4\pi G\rho_0)^{-1/2},\quad c_s=(2\pi J)^{-1}

Density is volume density; the third direction is invariant. Mass is per unit depth. Gas uses 64-by-64 cell averages; the separate magnetic branch uses point samples of one strictly linear wave. Velocity arrows are enlarged and compressed for visibility.

The branches use different color-contrast and arrow scales. Compare density and speed using the numerical readouts; equal brightness or arrow length across branches does not imply equal values.

The nonlinear gas window ends at time two. Ten sampled support points and a separate fixed time-two-and-a-half benchmark were compared with an overintegrated independent reference; they are not a uniform error theorem. A candidate below eight thermal Jeans cells is rejected.

The periodic Poisson solve removes mean density. Isothermal closure fixes temperature, without solving heating or radiation. There are no sinks, driven turbulence, stellar feedback or an inferred stellar mass function.

Replay the native input and independent checks

Model assumptions

The nonlinear branch evolves nonmagnetic isothermal Euler–Poisson gas with an invariant third direction, volume density and mass per unit depth. The x/y box is periodic; Poisson responds to density minus its instantaneous mean, so the uniform global-collapse mode is removed. The browser uses a conservative 64-by-64 grid in the sampled Jeans-ratio and amplitude range through time two; sampled convergence comparisons do not establish a uniform error theorem. The fixed time-two-and-a-half reference is a separate benchmark. A candidate below eight local thermal Jeans cells is rejected; that indicator alone does not certify fragmentation. The magnetic branch separately integrates a strictly linear six-variable ideal-MHD–gravity wave on a uniform background and stops before a relative disturbance cap; it is not nonlinear magnetic collapse. Magnetic direction is retained, with no isotropic sound-speed replacement. Density and velocity come from the same saved state. Isothermal closure prescribes temperature, rather than solving thermal balance or radiative losses. There is no driven turbulence, sink conversion, feedback, observed cloud image or stellar mass-function inference. Colors interpolate numerical samples; velocity arrows are enlarged. Dragging the initial-density center prepares a new initial condition.

Read the state, then test its interpretation

Signed wave amplitude through accepted steps

Cyan: computed state. Pale dashed: separate small-wave, start-from-rest limit.

Density across the selected probe row

The amber marker selects an actual cell.

This is a numerical gas section, not a telescope image. The nonlinear gas and strictly linear magnetic wave are separate models. Export saves the accepted arrays, configuration, history, selected probe and units.

Start with the essentials

Focus question: What changes when the same ripple lies along or across a magnetic field?
One-sentence intuition: Pressure opposes compression, gravity favors it, and magnetic forces depend on direction. A linear magnetic wave and a nonlinear gas calculation answer different questions.

Core mathematical model

Continuity

\partial_t\rho+\nabla\cdot(\rho\boldsymbol v)=0

Mass crossing one cell face enters its neighbor. The periodic box has no external mass source.

A small nonmagnetic wave

\omega^2=c_s^2k^2-4\pi G\rho_0

Positive squared frequency gives oscillation. Negative squared frequency permits growth; the initial velocity determines how much growing and decaying motion is present.

Directional magnetic response

\omega^4-[(c_s^2+v_A^2)k^2-\omega_J^2]\omega^2+v_A^2k^2\cos^2\theta(c_s^2k^2-\omega_J^2)=0

The compressive branches retain the angle between wavevector and field. Along-field thermal collapse is not removed by increasing field strength.

Common difficulties

A knot is not a star

Typical misconceptionEach bright numerical patch is a newly formed star.

Better mental modelThis is isothermal gas with no sinks, thermal feedback or stellar mass inference. The calculation stops within a bounded operating window.

Magnetic support has a direction

Typical misconceptionA magnetic field is just a larger sound speed in every direction.

Better mental modelThe separate linear branch evolves magnetic induction and transverse velocity. Rotating the field changes those couplings; it is not a nonlinear MHD cloud.

Run the experiment

01
Watch pressure rebound
Choose Pressure rebound and watch the signed-wave history turn downward.
What to observe: The gas starts at rest. A short thermal wavelength restores the ripple instead of sustaining its growth.
02
Prepare a different center
Choose Gas gathering and drag the cyan center. This restarts from a translated initial density ripple.
What to observe: The full periodic box stays in view. The amber probe samples the current computed cell, independently of the initial center.
03
Turn a real magnetic direction
Choose Linear along-field growth, then drag the field handle toward a right angle.
What to observe: The strictly linear response changes because velocity and magnetic perturbations couple differently. The relative-amplitude stop protects this approximation.
04
Read the same saved state
Pause, move the amber probe, and save the current field. Compare its selected row and wave history.
What to observe: The colors, velocities, probe values and exported arrays all come from the accepted state. The pale small-wave curve is a separate reference.

Molecular Cloud Collapse and Magnetic Support

Read the state, then test its interpretation

Follow a ripple from rest

Core mathematical model

Continuity

A small nonmagnetic wave

Directional magnetic response

Common difficulties

A knot is not a star

Magnetic support has a direction

Run the experiment

Watch pressure rebound

Prepare a different center

Turn a real magnetic direction

Read the same saved state

Related experiments and articles

Molecular clouds, gravity and magnetic direction