Overlap of task/WU contents

Alas I haven't yet seen the specifics on the Aricebo based search, but I'm pretty sure of the detail for LIGO GW work units. I can talk of that if it helps, as the task is going to possess certain similiarities. [ But beware I last properly read up on this a couple or three years ago. So I may slip on some soap, and of course things change too ... ]

There is certainly attempted overlap in all selected 'volumes' of the problem space - the totality of sky positions and putative signal characteristics/parameters. Viewed as a phase space ( in the classical mechanics sense ) the trick is to select a metric or transform that takes subsets of it, while assessing the coverage for a given probability of detection ( or threshold of non-detection ). These would be ( hyper ) cubes if there were all simple/linear relationships within the problem at hand.

One obvious exception to linearity is the right ascension and declination of sky position, as across the domain equal increments in the arguments don't give equal solid angle or sky area on projection out to the celestial sphere. You can't properly flatten an orange peel to the table without splitting it. For some reason related to the search algorithm applied to each area, you wind up with ellipsoidal shaped probability density 'hills' that overlap. Thus there is not equal probability of detection over the landscape. I think it behaves roughly like the 'circular error probability' quoted with military ordinance accuracy. From memory, some related topological theorem says you can't do this perfectly using a finite number of cuts. So you run a risk of missing signals no matter how granular you get, as absolutely complete coverage is only achieved in the limit of some infinite number of divisions - with 'slow' asymptotic approach. Rapidly diminishing returns. Thus one chooses/accepts some level of possible failure ie. missing a signal, and offset that against computing resources available. You pays your money and you takes your choice ....

The frequency intervals/cuts have 'wings' which overlap with adjacent ones, I think in all about 12 - 15 % of the frequency band is doubled covered in this way.

For frequency derivative ( spin-up or spin down ) the work unit signal templates look at a number of discrete guesses in this parameter - I think about six - with most on the spin down side ( negative frequency derivative ). This is an astrophysical expectation.

Actually the potentially hardest estimates are the signal templates - what GW waveforms should we be expecting? This is a relatively tame issue for E@H, as we only do GW data analysis for the Continuous Wave Group ( that's Bruce Allen's purview ) within LIGO. So you'd expect quasi-monochromatic waves, essentially sinusoidal profiles with a slowly changing intrinsic frequency ( spin-ups and spin-downs ). For the other LIGO groups, not related to E@H, their task is steeper in this respect - transients, rapid inspirals, stochastic background, Kleine-Welle or little wavelets etc.

But now that you've raised this, I'll see if I can ferret about and find something more specific for ABP's .... I too find this aspect quite fascinating. :-) :-)

Cheers, Mike.

( edit ) One other aspect is the amplitude of the signal. This is more related to the quality of data acquisition at the detectors, especially the 'coherence time' for good quality data stretches. The blocks of data are selected for later analysis based upon ongoing detector performance ( locking, simultaneity of collection at multiple sites, "Crab integration time" and inspiral range etc ) and known outages. The S6 run ( the data from which we haven't yet touched upon at E@H ) I believe was fairly messy in this regard compared to prior runs. In any case if you chop the sky up with a finer grid of those ellipsoidal hills mentioned above, you have less chance of missing something in the valleys between them. So there will be some lowest possible points on the probability density terrain and that represents the lowest limit for signal strength that you have probed. Or an upper bound on the weakest signal missed, depending on how you want to phrase it.