# Which Observation Frequency ?

Note that while the pulsar radiometer equation has a term for the observation bandwidth, there is no term for observation frequency.  Nonetheless, the observation frequency is very important because the signal strength of most pulsars is inversely proportional to frequency - that is, pulsars are generally weaker at higher frequencies.

However, different pulsars 'roll-off' in signal strength at the higher frequencies at different rates - specified by what is called the "Spectral Index" (Spi)...

...where

F1, F2 = observation frequencies

SF1, SF2 = flux densities at F1 and F2

Large negative values indicate a fast roll-off in signal strength at higher frequencies.   Smaller negative values indicate a flatter roll-off, where signal strengths are largely maintained at higher frequencies.

For example - the pulsar B0531+21 (J0534+2200) has a flux density of 550 mJy @ 400 MHz, but 'drops like a rock' @ 1400 MHz with only 14 mJy (nearly 16 dB drop) - giving an Spi = -2.9.

In contrast, B1641-45 (J1644-4559) has a flux density of 375 mJY @ 400 MHz and largely maintains that at 1400 MHz @ 310 (less than a 1 dB drop) - giving an Spi = -0.15.

Why go to higher frequencies if the signal strengths are lower ?   The usual reasons are...

Bottom line - choosing the operating frequency is a result of finding the best compromise considering the spectral index of the target pulsar and the local environment.   Generally speaking, the more 'urbanised' the location of the observatory, the more likely that higher frequencies will yield a better chance of success.

Note that for many pulsars there a 'turn-over' point in the usual increase of flux density with decreasing observation frequency.

That is, for those pulsars, there is a frequency where the flux density is a maximum and falls away at both higher and lower frequencies.  For the first pulsar detected (PSR 1919+21) this peak is around 70 MHz - making it a good candidate for the Cambridge antenna array operating at 81.5 MHz.  For B0329+54 the peak is about 390 MHz - making 408 MHz the prime spot to detect this pulsar if signal strength was the only determining factor, i.e., no local RFI.

The Vela Pulsar (B0833-45) is the strongest pulsar given as 5000 mJy @ 400 MHz and 1100 mJy @ 1400 MHz - but it has a 'turn-over' @ 600 MHz (according to published literature), so 400 MHz is not actually the strongest flux density frequency.   Using the quoted Spi of -2.4, it is estimated that the peak @ 600 MHz is close to 7000 mJy, falling away to 5000 mJy @ 400 MHz - about 1.5 dB lower.  This might not seem to be much, but it would require half the observation time at 600 MHz to get the same S/N as at 400 MHz (all else being equal).