---
title: "Molecular Line Cubes and Velocity Channels Interactive Lab | Sandbox Physics"
description: "Why does the same cloud look different in different velocity channels? Each channel collects gas with a similar speed along the line of sight."
canonical_url: "https://sandboxphysics.com/labs/molecular-line-cube/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/molecular-line-cube/"
last_modified: "2026-11-05"
---

A moving cloud through a spectral line

# Molecular Line Cubes and Velocity Channels

**Why does the same cloud look different in different velocity channels?** Each channel collects gas with a similar speed along the line of sight. Rotation sends different parts of the cloud into different channels. Gas at widely separated depths can share that speed, so a channel image groups motion rather than selecting one physical depth.

Drag a rotating cloud and its axis, then scan its line. Follow the same gas into a channel image, a spectrum and a position–velocity cut.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

This static prescribed ellipsoid uses an exactly two-level teaching transition at 345 GHz, local LTE, an isothermal Planck source and rigid rotation. It is separate from real CO and the fixed ALMA TW Hya disk exercise. Thermal and preset microscopic dispersion, positive finite-channel averaging and a normalized pixel-integrated Gaussian beam produce one 128-by-128-by-96 cube. The fixed physical observer lies on the positive depth axis; display-camera rotation leaves that observer unchanged. Depth in the physical scene is model geometry; the cube’s third coordinate is recession velocity. Cloud-centre and axis changes recompute a full state. Unsupported or failed candidates retain the last accepted state; finite spectral-tail, beam-flux and finite-map-loss limits are checked. Fixed and withheld cases and compound cold/thin/shear/phase endpoints were compared to independent finer references; this finite evidence is not a uniform error theorem over every continuous setting. Temperature and microdispersion change only through tested presets. There is no dynamical collapse, solved turbulence, non-LTE excitation, dust continuum, scattering, interferometric imaging or inferred true cloud mass/depth. Points sample the prescribed physical field. Arrow directions follow local velocity and lengths are schematically scaled; data images below read only the same accepted cube. The relative-brightness display mask is a model-viewing choice, not a calibrated detection rule.

Physics tutorial

## Watch one cloud move between velocity channels

**Background** A spectral line lets a telescope separate light by frequency. Motion shifts that line, so a narrow frequency channel selects gas with a particular speed along the line of sight.

**Why it matters** A cloud may look like two bright patches in one channel and one broad patch in another. Following the gas and the spectrum together explains the change.

Start with the essentials

- **Focus question**: Which part of a rotating cloud contributes to the selected channel?
- **One-sentence intuition**: A channel groups line-of-sight velocities. The physical locations that share that velocity can lie at different depths.

### Core mathematical model

#### Radio velocity convention

$$
v=c(1-\nu/\nu_0)
$$

The reference frequency belongs to the declared transition. Positive velocity means recession; the physical observer stays fixed while the display camera moves.

#### A line through one isothermal ray

$$
\Delta T(v)=[J_{\nu_0}(T)-J_{\nu_0}(T_{\rm bg})](1-e^{-\tau(v)})
$$

The same gas supplies the opacity and the Planck source. Increasing column first brightens the line, then saturates its peak and extends its wings.

#### Integrated line and velocity centroid

$$
W=\sum_i T_i\Delta v_i,\qquad v_{\rm c}=\frac{\sum_i v_iT_i\Delta v_i}{W}
$$

Both sums read the saved finite-channel cube. The centroid is a brightness-weighted velocity, with a declared display mask, rather than the gas speed at one known depth.

### Common difficulties

#### Velocity is not a depth ruler

**Typical misconception** Moving through the channels moves through successive physical layers.

**Better mental model** The same speed can occur at several depths. The three-dimensional gas view shows the prescribed geometry; the separate image combines every point along each sightline.

#### Brightness and molecule number

**Typical misconception** Ten times as many molecules always gives a tenfold peak.

**Better mental model** Opacity reduces how much material deeper in the cloud changes the escaping line. The saturated preset keeps the peak near the source brightness while the wings grow.

### Run the experiment

1. 01

   #### Scan a turning cloud

   Start with A turning cloud and move the velocity-channel control across the line. Compare the bright patch with the gas velocity colours.

   **What to observe:** Receding and approaching gas enter different channels; the position–velocity cut follows the same cube.

2. 02

   #### Change the physical axis

   Drag the purple axis tip, then choose Look along the axis. Orbit the display camera separately.

   **What to observe:** Changing the physical axis changes projected velocities. Moving only the camera changes the physical scene view while the measured cube stays fixed.

3. 03

   #### Move the probe on actual data

   Drag in the channel image to select a sightline. Follow its spectrum and the row used for the position–velocity cut.

   **What to observe:** The spectrum, moments and export use that same accepted generation. The relative-brightness mask is a viewing choice, not a noise significance.

4. 04

   #### Compare thin and saturated lines

   Choose A nearly transparent line, then More molecules, same peak. Compare spectral peak and integrated brightness.

   **What to observe:** The relation between brightness and column changes with opacity; a peak alone does not provide a cloud mass.

Physical conclusion

One physical cloud becomes several useful views when its velocities, line transfer, channels and beam all feed the same saved cube.

## Related experiments and articles

Molecular line cubes and velocity channels · Reading path

### Molecular line cubes and velocity channels

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Why a velocity channel cannot select one depth**](https://sandboxphysics.com/stories/molecular-line-cube/why-velocity-channels-are-not-depth-slices/)
2. [Article **From moving molecules to a line with a width**](https://sandboxphysics.com/stories/molecular-line-cube/molecules-gaussian-lines-and-thin-emission/)
3. [Article **When gas obscures its own line**](https://sandboxphysics.com/stories/molecular-line-cube/opacity-and-the-planck-line-source/)
4. [Article **Reading one cube as maps, spectra and moments**](https://sandboxphysics.com/stories/molecular-line-cube/moments-beams-and-a-saved-ppv-cube/)
5. [Article **Replay real ALMA velocity slices of the TW Hya disk**](https://sandboxphysics.com/stories/molecular-line-cube/replay-alma-tw-hya-line-cube/)
6. [Article **Density structure or velocity structure? Reading channel analysis**](https://sandboxphysics.com/stories/molecular-line-cube/reading-velocity-channel-analysis/)

Waves & optics · Starter path

## From one ray to interference measurement

Start with refraction, find where the ray picture stops working, then use interference to measure tiny distances.

[Start here → **Optical Boundary Explorer** Turn the incident angle and watch reflected and transmitted power trade off. Then switch to the critical-angle scene. Observe · 11 min](https://sandboxphysics.com/labs/optical-boundary-explorer/)

1. [1 Optical Boundary Explorer](https://sandboxphysics.com/labs/optical-boundary-explorer/)
2. [2 Rainbow Caustic Observatory](https://sandboxphysics.com/labs/rainbow-laboratory/)
3. [3 Camera Obscura](https://sandboxphysics.com/labs/camera-obscura/)
4. [4 Coherent Wave Composer](https://sandboxphysics.com/labs/coherent-wave-composer/)
5. [5 Young Double-Slit Bench](https://sandboxphysics.com/labs/young-double-slit-bench/)
6. [6 Michelson Precision Lab](https://sandboxphysics.com/labs/michelson-precision-lab/)

[View the full path →](https://sandboxphysics.com/topics/waves-and-optics/#starter-path)