Pulsar Dispersion, Timing, and Survey Selection ยท instructor use
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.
Worked solution: Delta_t=4.148808 DM(0.4^-2-1.4^-2)=1353 ms. Since delay is linear in DM, sigma_t=delay(0.2/56.8)=4.763 ms.
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.
Worked solution: Using |dt/dnu| Delta-nu, intra-channel smearing is 8.3 microseconds x DM x Delta-nu_MHz/nu_GHz^3=0.7366 ms. It is a substantial fraction of 2 ms and lowers pulse peak S/N.
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.
Worked solution: p_hat=84/100=0.84; sigma_p=sqrt[p(1-p)/N]=0.03666. This binomial error omits sky-dependent sensitivity and injection-model mismatch.
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.