Can anyone help – I am somewhat confused! I am undertaking an investigation into pulsar dispersion, and thought I would use the data I have for the psrb0139+54 pulsar – which I know you can observe the early harmonics of the pulsar in its spectrum.
Now I had convinced myself that the pulse rate we would observe from the pulsar would exhibit a Doppler shift due to the relative motion between the Earth and the Neutron star; so I undertook a high resolution spectral analysis of 16 seconds of my data from the beginning of my data, and the similar analysis taken from the end of my data with a gap of about 400 seconds between the two data records. What really surprised me was that to within 1/16Hz the harmonics exactly aligned. Not what I was expecting at all.
Thinking that the harmonics weren't what I was looking at, I generated a set of frequency domain Fiducial lines corresponding to the published pulsar period, and sure enough they aligned exactly with my harmonics, so I don't think my Fourier analysis is at fault. The problem must be with my understanding of how the Doppler shift would manifest itself on the pulsar pulses amplitude spectrum, What I was expecting to see was would look like a series of parallel angled lines on a Waterfall diagram – not a series of absolutely vertical lines.
Can anyone put me out of my misery and put me right on what is going on – its probably me having a senior moment.
The dominant acceleration term is from Earth rotation which will exhibit a velocity in the pulsar direction ranging over 0 to a few hundred meters/second. Therefore, depending on the interval between observations, the non-relativistic Doppler shift term (velocity/speed-of-light) at its greatest would approximate 10^2/10^8 which would change only the sixth decimal place of the 0329+54 pulser .715s period. Over the 400 second interval you mentioned, only the ninth decimal place would change. You would not see either of these tiny effects in 1/16Hz Fourier bins. Please do the math yourself to double-check my claims.
I am not sure why you mentioned dispersion in the first paragraph in association with your Doppler shift study. Pulsar 0329+54 won't exhibit significant dispersion over the ~ 8MHz bandwidth of the captured ATA data. An excellent example of dispersion can be seen through Fourier analysis on a giant pulse in the Crab pulsar data.
I would be happy to interact with you by email to further discuss your experiment but won't do so in this forum.
Your input was exactly what I needed. I am really pleased that you told me that I won't see any dispersion from this Pulsar, so that I won't get any shock to find that the phase relationship at the pulsar frequency is linear. I have temporarily stopped working on the Crab as I couldn't extract any evidence of the Pulsar harmonics in its spectral data, and within my limited analysis hadn't seen any giant pulses.
I am really using this experiment to test out my new suite of Fourier tools I have developed in Python to prove that they are working as I think they should.
Thanks for the offer of an EMAIL discussion, I will definately take you up on that offer, I was tempted to send this query directly to you, but felt that I would be imposing on you, after all you have done to give my research such a forward boost.
Thanks once again