Scoring rubric
Each problem is worth 30 points; presentation/reproducibility contributes 10 points across the set. Award credit for correct setup and units before the final number. Identify arithmetic slips separately from conceptual errors. Require correct comparative direction and an honest account of approximation gaps.
Problem 1: Visibility phase
Worked solution: lambda=c/nu; theta=10/206264.806 rad; cycles=-B theta/lambda=-0.679209. Thus phase=-244.5 deg, equivalent to 115.5 deg modulo 360 under V=integral I exp(-2 pi i u l) dl.
Show the governing equation, substitute with consistent units, retain intermediate values, and state which approximation limits the inference. Accept equivalent algebra and convention choices when explicitly stated.
Points: model and derivation 12; units and numerical work 10; uncertainty/limitation 4; interpretation 4.
Problem 2: Resolution versus scale
Worked solution: Using lambda=c/nu, 1.02 lambda/Bmax=0.03942 arcsec, while 0.6 lambda/Bmin=24.73 arcsec. The former is a fine-scale beam estimate; the latter is a broad-structure recovery limit.
Show the governing equation, substitute with consistent units, retain intermediate values, and state which approximation limits the inference. Accept equivalent algebra and convention choices when explicitly stated.
Points: model and derivation 12; units and numerical work 10; uncertainty/limitation 4; interpretation 4.
Problem 3: Inverse problem
Worked solution: The finite uv mask removes low spatial frequencies, so the dirty image loses broad flux. Deconvolution cannot determine unmeasured modes from the data alone; single-dish total power or shorter interferometer baselines add the missing constraints.
Show the governing equation, substitute with consistent units, retain intermediate values, and state which approximation limits the inference. Accept equivalent algebra and convention choices when explicitly stated.
Points: model and derivation 12; units and numerical work 10; uncertainty/limitation 4; interpretation 4.
Common errors
- Converting MHz/GHz or arcseconds/radians incorrectly.
- Confusing per-beam flux with integrated flux or brightness temperature with kinetic temperature.
- Treating flux-scale uncertainty as independent for every source.
- Using a linear Doppler approximation outside its regime or silently changing velocity convention.
- Calling a synthetic record an observation or reporting a completeness correction without its selection assumptions.