Molecular line cubes
Molecular line cubes: space, velocity and hidden depth
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.
L1
Why a velocity channel cannot select one depth
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.
L1
From moving molecules to a line with a width
Count emitting molecules, normalize their velocity distribution and integrate a transparent sightline before averaging it into receiver channels.
L2
When gas obscures its own line
Solve emission and absorption on one sightline, retain the Planck source and learn how saturation and a static foreground change line shape.
L3
Reading one cube as maps, spectra and moments
Define moments from finite-channel brightness, track beam mixing and cropped flux, and test masks against correlated-noise counterexamples.
L3
Replay real ALMA velocity slices of the TW Hya disk
Acquire the fixed small teaching cube, verify native coordinates and beam units, then reproduce spectra, PV cuts, moments and correlated-noise diagnostics.
L4
Density structure or velocity structure? Reading 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
- Mangum & Shirley, How to Calculate Molecular Column Density, arXiv 1501.01703v4 (2017)
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.
- Lazarian & Pogosyan, Velocity Modification of HI Power Spectrum, astro-ph/9901241v2 (2000)
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.
- Bendo, Avison & Freestone, Measuring the Rotation of TW Hydrae (19 June 2019)
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.
- ALMA Science Verification: TW Hya Band 7 CO(3–2), ADS/JAO.ALMA#2011.0.00001.SV
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.
- Leiden Atomic and Molecular Database, fixed CO data file
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.
- Sandbox Physics independent molecular-line science producer and reader package
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.