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: Synchrotron scaling
Worked solution: nu_c=4.2e6 B_G gamma^2=4.2e+09 Hz. Holding nu_c fixed while multiplying B by 4 requires gamma_new=gamma/sqrt(4)=5000. The synchrotron kernel is broad, so a spectral peak need not equal nu_c.
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: Dish design
Worked solution: At 1.4 GHz the 25-m dish gives 30.03 arcmin and A_eff=343.6 m^2. Doubling D halves beam FWHM to 15.02 arcmin and multiplies area by four to 1374 m^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: Sensitivity design
Worked solution: From sigma=SEFD/sqrt(n_pol Delta-nu tau), tau=(300/0.001)^2/(2 x 1e6)=4.5e+04 s=12.5 h. Flagging, efficiency losses, and calibration overhead make the real time longer.
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.