---
title: "Molecular line cubes: space, velocity and hidden depth"
description: "Follow a physical velocity field into a saved line cube, then read channels, opacity and a reproducible real ALMA disk."
canonical_url: "https://sandboxphysics.com/stories/molecular-line-cube/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/molecular-line-cube/"
last_modified: "2026-11-05"
---

Molecular line cubes

# Molecular line cubes: space, velocity and hidden depth

Sandbox Physics · 2026-11-04

A bright patch in one channel need not be a separate object. Begin with how velocity selects gas, build the line one physical step at a time and replay the measurement on a real ALMA disk.

1. L1

   ## [Why a velocity channel cannot select one depth](https://sandboxphysics.com/stories/molecular-line-cube/why-velocity-channels-are-not-depth-slices/)

   Gas at different depths can share the same line-of-sight speed. Learn how a spectral channel groups it and what a moving bright patch reveals.

2. L1

   ## [From moving molecules to a line with a width](https://sandboxphysics.com/stories/molecular-line-cube/molecules-gaussian-lines-and-thin-emission/)

   Count emitting molecules, normalize their velocity distribution and integrate a transparent sightline before averaging it into receiver channels.

3. L2

   ## [When gas obscures its own line](https://sandboxphysics.com/stories/molecular-line-cube/opacity-and-the-planck-line-source/)

   Solve emission and absorption on one sightline, retain the Planck source and learn how saturation and a static foreground change line shape.

4. L3

   ## [Reading one cube as maps, spectra and moments](https://sandboxphysics.com/stories/molecular-line-cube/moments-beams-and-a-saved-ppv-cube/)

   Define moments from finite-channel brightness, track beam mixing and cropped flux, and test masks against correlated-noise counterexamples.

5. L3

   ## [Replay real ALMA velocity slices of the TW Hya disk](https://sandboxphysics.com/stories/molecular-line-cube/replay-alma-tw-hya-line-cube/)

   Acquire the fixed small teaching cube, verify native coordinates and beam units, then reproduce spectra, PV cuts, moments and correlated-noise diagnostics.

6. L4

   ## [Density structure or velocity structure? Reading channel analysis](https://sandboxphysics.com/stories/molecular-line-cube/reading-velocity-channel-analysis/)

   Follow the fixed Lazarian–Pogosyan paper from PPV mapping to scale-dependent thin slices, then restore finite-cloud and opacity limits.

## Sources and calculation scope

1. [Mangum & Shirley, How to Calculate Molecular Column Density, arXiv 1501.01703v4 (2017)](https://arxiv.org/abs/1501.01703v4)

   Fixed v4: transfer and brightness equations 13–32, partition section 7, approximations 11–14 and appendices A–C. The printed Gaussian-width power in A4/A5 is checked against the normalized profile; no blanket non-LTE solution is inherited.

2. [Lazarian & Pogosyan, Velocity Modification of HI Power Spectrum, astro-ph/9901241v2 (2000)](https://arxiv.org/abs/astro-ph/9901241v2)

   Fixed 11 January 2000 version. Main PPV mapping/channel-window derivation, figures 1–3 / table 1, finite-cloud appendix E and stated optical-depth/statistical limits. The later generated 2018 draft date is not the scientific version.

3. [Bendo, Avison & Freestone, Measuring the Rotation of TW Hydrae (19 June 2019)](https://www.alma.ac.uk/nas/gbendo/Web/Sci/Teach/experiment_twhyarotation.pdf)

   Complete eight-page official teaching guide and named original image member. The local tutorial uses native header frequencies, beam area and saved processing history; historical distance/inclination are not promoted to current precision.

4. [ALMA Science Verification: TW Hya Band 7 CO(3–2), ADS/JAO.ALMA#2011.0.00001.SV](https://almascience.hq.eso.org/alma-data/science-verification/tw-hya)

   Original 2011-04-22 disk observation and Hanning/effective-resolution provenance. Public SV access/acknowledgment is distinct from precise redistribution terms for separately served teaching derivatives.

5. [Leiden Atomic and Molecular Database, fixed CO data file](https://home.strw.leidenuniv.nl/~moldata/CO.html)

   Exact native table identity is checked in the optional local reader. Its 41 ground-vibrational levels and spectroscopy are separate from the own two-level Lab material; collisional rates are not solved or redistributed here.

6. [Sandbox Physics independent molecular-line science producer and reader package](https://sandboxphysics.com/stories/molecular-line-cube/materials/molecular-line-cube-reader-science-v1.zip)

   Own synthetic input, independent frequency-space/continuous-ray references and retained resolution failures. The native reader obtains exact source files locally; no observed image, native table or app/Node Engine is bundled.