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: Gain measurement equation
Worked solution: The baseline gain product is (1.05 x 0.95) exp[i(8-(-4)) deg]. Therefore |Vobs|=99.75 mJy and arg(Vobs)=12 deg; dividing by both antenna gains recovers Vtrue=100 mJy.
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: Phase decorrelation
Worked solution: For Gaussian phase scatter, coherence=exp(-sigma_phi^2/2). It is 0.9849 at 10 deg and 0.9409 at 20 deg; phase variance, not rms phase linearly, enters the exponential.
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: Correlated uncertainty
Worked solution: Fractional uncertainty=sqrt(0.05^2+0.03^2+0.02^2)=0.06164; sigma_S=7.397 mJy. A shared multiplicative flux-scale term cancels to first order in a source ratio; independent thermal errors 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.
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.