In Duncan and Lorimer's Handbook of Pulsar Astronomy, the equation for the flux density using a radio telescope is given as (for a top-hat function):

$$S=\frac{\beta\,\mathrm{SNR}\, T_{sys}}{G\sqrt{n_{p}\Delta f\,T}}\sqrt{\frac{W_{eq}}{P-W_{eq}}}$$

Here, $\beta$ is a correction factor, $\mathrm{SNR}$ is the signal-to-noise ratio, $T_{sys}$ is the system temperature, $G$ is the telescope gain, $n_{p}$ is the number of polarizations, $\Delta f$ is the observing bandwidth, $T$ is the integration time, $W$ is the equivalent width of the pulse, and $P$ is the period of the pulse.

How does one go from this to the so-called "modified radiometer equation" that is often used (often for an arbitrarily shaped pulse):

$$S=\frac{\beta\,A\, T_{sys}}{G\,N_{bin}\,\sigma_{off}\sqrt{n_{p}\Delta f\,t_{obs}}}$$,

where $A$ is the area under the pulse, $N_{bin}$ is the total number of phase bins in the profile, $\sigma_{off}$ is the RMS of the noise in the pulsar time series, and $t_{obs}$ is the total integration time of each phase bin.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.