rest wavelength
Definition: The laboratory or source-frame wavelength assigned to a spectral transition before Doppler shifting.
Why it matters here: It is the reference \(\lambda_0\) against which an observed displacement is converted to velocity or redshift.
Relationships: The measured shift is \(\Delta\lambda=\lambda_{obs}-\lambda_0\), entering \(v/c\approx\Delta\lambda/\lambda_0\) at low speed.
Boundary / common confusion: Air and vacuum wavelength conventions differ slightly, so the convention must match the calibration.
observed wavelength
Definition: The calibrated wavelength at which a spectral feature appears in the recorded observer-frame spectrum.
Why it matters here: It is the direct spectral measurement paired with a rest wavelength to infer motion.
Relationships: Its uncertainty combines centroiding, wavelength-solution residuals, line shape, and instrumental drift.
Boundary / common confusion: A measured feature is not automatically the intended transition; identification and blending must be checked.
redshift
Definition: A positive fractional wavelength increase \(z=(\lambda_{obs}-\lambda_0)/\lambda_0\).
Why it matters here: It quantifies the consistent displacement of multiple lines toward longer wavelengths.
Relationships: For small speeds \(v\approx cz\); at high speeds or cosmological distances the physical interpretation requires relativistic or cosmological models.
Boundary / common confusion: Redshift is an observed ratio, not always a simple peculiar velocity.
blueshift
Definition: A negative wavelength shift in which a feature is observed at shorter wavelength than its rest value.
Why it matters here: It is the sign expected for approaching radial motion in the low-speed Doppler interpretation.
Relationships: With the lecture convention, \(\Delta\lambda<0\) gives \(v<0\).
Boundary / common confusion: Calibration offsets can shift every line blueward, so sign alone does not establish physical approach.
radial velocity
Definition: The component of an object’s velocity along the observer’s line of sight.
Why it matters here: It is inferred from calibrated line shifts and is the physical quantity tested by the three-line agreement.
Relationships: At \(v\ll c\), \(v/c\approx\Delta\lambda/\lambda_0\); multiple lines should yield a common value.
Boundary / common confusion: It excludes transverse motion and may include systemic, orbital, rotational, and observer-motion contributions.
line blend
Definition: A spectral feature formed by two or more unresolved transitions whose profiles overlap.
Why it matters here: A blend can shift the apparent centroid and imitate a radial-velocity change.
Relationships: Whether components blend depends on their separation relative to the line-spread function and resolving power.
Boundary / common confusion: Treating a blended centroid as a single isolated line yields a model-dependent, potentially biased velocity.
systemic velocity
Definition: The center-of-mass line-of-sight velocity of a source system relative to a stated reference frame.
Why it matters here: It provides the common baseline around which orbital or internal line velocities vary.
Relationships: Repeated multi-line measurements can separate a stable systemic component from time-dependent motion.
Boundary / common confusion: The value depends on the adopted reference frame and is not necessarily the velocity of every emitting component.