Effects of Scintillation

In practice, the flux density quoted is an estimate for a number of pulsars, as another effect, called scintillation, can greatly enhance signal strength, but then at other times reduce signal strength to very low levels during the time of an observation.  This can be the difference between successful detection and failure.  As an example, the following figure shows the variation in signal strength over an observation period of 85 minutes of the B0329+54 pulsar... 

Scintillation Effects on the B0329+54 Pulsar @ 1.38 GHz to 1.70 GHz 

The frequency range of 1.38 GHz to 1.70 GHz is covered by 128 channels each of bandwidth 2.5 MHz - an individual bandwidth close to that of an RTL_SDR dongle (nominal maximum reliable bandwidth of 2 MHz).  If the above observation was made by such a dongle set to 1.42 GHz, the above figure shows that the pulsar signal would have been almost entirely absent for the whole 85 minutes at that frequency.  If, on the other hand, the dongle was set to receive at 1.495 GHz, then the signal would have been strong for nearly half the observation period.

Additionally, if, by good fortune, an observation was made for, say, only the first 10 minutes @ 1.4 GHz (during the time of the dark blob near the bottom left-hand corner of the figure) then the signal would be strong for the whole 10 minutes.  Conversely, if an observation was made at 1.45 GHz for the same first 10 minute period in time, virtually nothing would have been seen at all.  That is, depending on the current state of scintillation at the observation time and frequency, a signal strength may be observed well above the quoted mean flux density for B0329+54, or possibly no signal is seen at all.  So scintillation can be your friend, but at other times your enemy.

Here below is that same signal strength time/frequency map when 'averaged' over the time and frequency channels...

Signal Strength Averaged Over Time and Frequency Channels 

...which corresponds, presumably, to the level of the quoted flux density of 203 mJy of B0329+54 @ 1400 MHz.  It can be seen in the previous un-averaged graphic ("Scintillation Effects on the B0329+54 Pulsar @ 1.38 GHz to 1.70 GHz") that at times the flux density received is much higher than the average (and also at other times, much lower than the average). By fortuitously picking an observation time during a 'scintillation boost', the received flux density can be significantly higher than the quoted average flux density of 203 mJy.  The B0329+54 pulsar is particularly co-operative in this regard as the 'scintillation boosts' can last for 20 to 30 minutes (see the big black blobs in the un-averaged graphic above).

From this graph of long-term scintillation observations (Figure 7: Long-Term Scintillation Observations of 5 Pulsars at 1540 MHz) it can be seen there is a large variation in flux density around the nominal quoted value of 203 mJy over a period of 18 months...

B0329+54 Long-Term Scintillation at 1540 MHz 

...regularly falling to low values around 100 mJy (sometimes for over a month) and at other to rising to 300 mJy.  Note that there was a period (near MJD 52100) where S1540 rose to just over 500 mJy.  It should remembered that shorter variations (over a few ten's of minutes) will ride on top of this longer term rise - meaning at the time of observation the flux density can be even higher.

The bottom-line to this phenomena is that it may take a number of tries before a good 'scintillation boost' is captured to allow successful detection of B0329+54 @ 21cm wavelengths.

Note that scintillation occurs at faster rates at lower frequencies as this figure of an observation for B0329+54 @ 408 MHz shows...

Scintillation Effects on the B0329+54 Pulsar @ 408 MHz 

At this observation frequency and using a bandwidth of, say, 2 MHz (i.e., 407 MHz to 409 MHz), the peaks and valleys in signal strength over that bandwidth and, say, an observation time of 90 minutes, would average out to be close to the quoted mean flux density - i.e. - no scintillation boost to be had.  It would be expected, excluding other effects, that the results would be fairly similar from observation to observation.

This is likely the reason behind the reports from amateurs that more consistent results for B0329+54, from day to day, are obtained at 400 MHz when compared with 1400 MHz.  However, the effects of long-term scintillation may still cause periods of enhanced or poor results over time scales spanning months.

Note that the use of smaller bandwidths, say, 100 kHz, at 400 MHz would see at least a partial return to the situation where the result would vary depending on frequency chosen and time chosen - as was the case when observing at 1.5 GHz.  In this case it would be expected that results from observation to observation could vary quite significantly.

For other pulsars, say J0835-4510 (Vela), the scintillation peaks and troughs come and go more quickly (in a matter of a few seconds), so over that same 20 to 30 minutes they average out and, therefore, there is no 'scintillation boost' to be had.  The effects of long-term scintillation may also be a factor.