ASTR 472 · Lecture 13

Lecture 13: Galactic H I: Rotation, Geometry, and Mapping

Radio Astronomy

A 21-cm velocity cube turns a line-of-sight Doppler field into a model-dependent map of Galactic gas and kinematics.

Objectives and route

  1. Use the flat-rotation inner-Galaxy relation to infer Galactocentric radius from longitude and radial velocity.
  2. Distinguish measured LSR velocity from inferred distance and radius.
  3. Explain near-far ambiguity and non-circular motions.

Route: identify what the receiver measures, derive the physical/instrument relation, calculate a scale, then test its assumptions against a diagnostic.

Terms for This Lecture

Local standard of rest

Definition: A conventional velocity frame that removes an adopted Solar motion before Galactic interpretation.

Why it matters here: It is needed to answer At fixed longitude, how does a positive non-circular velocity perturbation propagate into inferred R in this model? Give the derivative sign. and to interpret The 21-cm line is observable through much of the Galactic disk, including dusty sightlines.

Relationships: Use it with Rotation curve and Tangent point; the lecture model is \(R=\frac{R_0}{1+v_{\rm LSR}/(\Theta_0\sin l)}\).

Boundary or common confusion: The flat, axisymmetric rotation curve is an idealization; streaming velocities of order tens of km/s can shift inferred radii and distances substantially.

Observation before interpretation

A 21-cm velocity cube turns a line-of-sight Doppler field into a model-dependent map of Galactic gas and kinematics.

Keep four layers distinct in your notebook: raw correlation or spectrum, calibrated product, model parameter, and physical claim.

Physical model

Set Theta(R)=Theta0 and solve v_LSR=Theta0(R0/R-1)sin(l) for R=R0/[1+v_LSR/(Theta0 sin(l))]. This gives Galactocentric radius for a chosen longitude under circular rotation. Heliocentric distance requires a second geometric step and has a near/far ambiguity inside the solar circle.

\(R=\frac{R_0}{1+v_{\rm LSR}/(\Theta_0\sin l)}\)

Define each quantity and convention before substitution. A relation is useful only inside its stated regime.

Worked calculation

Inputs: R0=8.2 kpc, Theta0=236 km/s, l=30 deg, v_LSR=100 km/s.

R_GC = 4.439 kpc

The flat, axisymmetric rotation curve is an idealization; streaming velocities of order tens of km/s can shift inferred radii and distances substantially.

Independent audit: carry SI units through the derivation, then check the limiting direction and scale.

Read the geometry or data relation

Galactic longitude lvLSRtangent velocity
The 21-cm line is observable through much of the Galactic disk, including dusty sightlines.

Identify what is directly encoded in the figure and which inference requires an instrument model or physical assumption.

Where the inference can fail

The flat, axisymmetric rotation curve is an idealization; streaming velocities of order tens of km/s can shift inferred radii and distances substantially.

Reasoning prompt

At fixed longitude, how does a positive non-circular velocity perturbation propagate into inferred R in this model? Give the derivative sign.

Write the predicted scaling first; then identify which measurement would falsify it.

Connection to the observing workflow

This lecture feeds into the paired lab: Survey Completeness and Galactic H I Mapping. Preserve the raw-to-calibrated-to-inferred chain and carry the same units and assumptions into the analysis.

For a real observation, archive the project identifier, correlator setup, antenna configuration, calibration version, flags, beam, and data-release citation.

Synthesis

Galactic H I: Rotation, Geometry, and Mapping is one stage in a measurement chain: celestial signal → antenna and receiver → sampled data → calibration → image/spectrum → uncertainty-aware inference.

Next: connect this result to Radio Surveys: Catalogs, Confusion, and Reproducible Analysis.

References and scope

OpenStax Astronomy 2e §20.2 introduces interstellar gas and 21-cm observations; HI4PI (2016) provides an all-sky spectral data product for modern mapping.

Primary/authoritative material and provenance levels are recorded in ../reference-log.md. Numeric examples are reproducibly calculated by ../src/generate_astr472_package.py; figure geometry is original and lecture-specific.