To finish his very enjoyable visit, van Haasteren (Leiden) gave the astro group meeting seminar in the morning, with lots of banter and feedback from the crowd. He focused on stochastic signals, but got the most crowd reaction about single-source signals. On the stochastic side, Dubovsky (NYU) pointed out that there are even models in which the stochastic background might have a characteristic frequency.
At lunch and afterwords, van Haasteren and I discussed possible projects. The one we liked most is to try to improve the timing itself by going hierarchical on the pulse shapes. Commenter Steve T on my post of a few days ago was pessimistic, but in fact even a bad model of the variability among pulse shapes and pulse-to-pulse correlations in shape could have a big impact on the precision of pulsar timing. Big theme of my research: You do much better if you model the noise, but then marginalize out those noise-related parameters.
Now off to a weekend of proposal re-writing.
I'm only really pessimistic about a general solution -- I think that you could make real progress if you pick a particular pulsar (and perhaps frequency) and model that. Since the power of existing timing arrays for gravitational background work is dominated by a relative handful of the best pulsars, it isn't unreasonable to treat each as a particular source.
ReplyDelete(I was working on just this type of analysis when I found what we later showed were power-law giant pulses from B1937+21 -- As I recall, the specific thing I was trying to do when I stumbled on these was to test for orthogonal polarization mode switching, in part to better model the data to improve timing -- and the varying strong circular polarization helped the giant pulses jump out of my analysis.)
You will find that playing with modern pulsar data opens some really interesting challenges. Most single pulse work on slow pulsars is smoothed over timescales so that B\tau is much greater than 1, and gaussian noise approximations start to be reasonable. But working with pre-detection data or with unsmoothed detected data this is far from true, and for strong sources (or strong microbursts) the source is not necessarily an insignificant contributor to the receiver temperature (which is one of the things that makes a sophisticated noise model _interesting_). And thinking about the way that the chirp filter used to dedisperse the data correlates the receiver noise in samples taken at different times makes my head hurt. You get to choose: work in a world where the ISM has correlated your signal in complex ways, or in a world where your anti-ISM processing has correlated your noise!
An example that comes to mind of your more general strategy (which is very much aligned with my approach to these sorts of problems): one of the important contributors to variable pulse shape in many stars is scattering in the ISM that effectively convolves the observed profile with an exponential scattering window. So we can improve the timing results by adding an exponential component and marginalizing over the unknown width at each epoch.
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