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: Inner-Galaxy kinematics
Worked solution: For flat circular rotation, R=R0/[1+v/(Theta0 sin l)]=4.439 kpc. This is a model-based Galactocentric radius, not a unique heliocentric distance; near/far geometry and non-circular motion remain.
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: Completeness-corrected density
Worked solution: Sigma=1200/(20 x 0.84)=71.43 deg^-2; Poisson-only sigma=2.062 deg^-2. Completeness contributes N sigma_C/(A C^2)=2.551 deg^-2, so total first-order sigma=3.28 deg^-2.
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: Comparative survey claim
Worked solution: Survey A is more likely to retain diffuse structure because its beam is less likely to resolve out a 6-arcminute cloud; B separates closer point sources better but has higher point-source rms. Short spacings, surface-brightness sensitivity, primary beam, and calibration matter in addition to rms.
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.