What is a hierarchical search?
17 Feb 2007 15:54:11 UTC
Topic 192447
(moderation:
Quote:
January 19, 2006
A couple of days ago Einstein@Home issued the last workunits from our first search of LIGO S5 data. The post-processing of these results will begin in a few weeks when the last result from these workunits is returned. Meanwhile we are gearing up to begin a new type of more sensitive search (called a hierarchical search).
Can project leaders write about this method?
Thank you!
What is a hierarchical search?
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Hi hoarfrost,
I found a pretty good written answer to your question in the following abstract. I'm guessing it's a very busy time for the 'project leaders', who I imagine are working hard on the transition from Initial LIGO to Advanced LIGO (see the Detector Watch threads for more info). That in addition to working on writing up results for S5, and troubleshooting problems with the E@H servers. But your question is a good one, probably on the minds of many who are crunching, so please have a look at the answer I found, as we all look forward to hearing the 'official word' from the scientists... :)
[B1.004] Hierarchical Search Strategy for Detecting Gravitational waves from Inspiraling Compact Binaries with Multiple Interferometers
Shawn Seader (Washington State University), Sukanta Bose (Washinton State University)
Perhaps the most promising gravitational-wave source for detection with Earth-based interferometers is the compact binary system, such as a binary neutron star. For these sources, the inspiral waveform is well-known in the sensitive frequency band of the interferometers. This allows one to match-filter the output of the interferometer with many different templates of the pre-calculated waveforms. While operating, each interferometer takes strain data at a rate of several gigabytes per day. Matched filtering the outputs from multiple detectors, such as in a multi-detector coherent search, becomes very demanding computationally not only due to the enormous amount of data, but also due to the size of the parameter space that is accessible to a network of detectors. Indeed, the non-spinning binary waveform depends on a total of nine parameters, namely, the luminosity distance to the source, the time of arrival, the initial phase, the orbital inclination, the polarization angle, the two sky-position angles, and the two binary masses. Fortunately, it is possible to maximize a network's matched-filter output analytically over the first five parameters. Thus, a GW astronomer need search numerically only over a four-dimensional parameter space for a signal in the data. A "brute force" implementation of such a search is still not practicable. A promising strategy to make the search computationally viable is to perform it in multiple relatively inexpensive steps, i.e., implement it hierarchically. In a two-step hierarchical search, the data is filtered first with a bank of templates that are spaced coarsely on the parameter space. If any of these templates find a signal at or above a pre-set threshold on the signal-to-noise ratio (SNR), then that part of the data is filtered a second time with a more finely spaced bank of templates, centered around the filter that recorded the high SNR in the first, coarse bank. In this work we show how by setting the detection thresholds and the template-spacings for the two steps optimally a multi-detector search becomes computationally feasible, without suffering any loss of detection probability or any increase in the rate of false alarms.
Of course, on the main page
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Of course, on the main page it says were searching for the gravitational waves from individual neutron stars (pulsars). So these would be rotating and either have asymmetries in their shape, or are precessing, or experiencing a 'glitch' (like a starquake). I just ran across this paper (Gravitational Radiation from Rotating White Dwarfs and Neutron Stars) and learned that even rotating white dwarfs are a possible source of gravity waves, and there are quite a few different conditions that will result in a neutron star emitting GWs. So in the hierarchical search we're now crunching, it would be a with a different set of templates than the ones mentioned in the abstract (that pertain to binary systems).
Folks, A hierarchical
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Folks,
A hierarchical search is one in which you do a "first pass" with really coarse resolution in parameter space (sky positions, etc) that you know will degrade your sensitivity. But that's OK because you then do a second pass on anything that looks interesting, even if its statistical significance is pretty low your second fine-resolution search will home in on it if it's there. Because the computational cost is set by the resolution of the search, this lets you afford a much finer search since you're only doing the second (fine) pass on a smaller number of areas which were indicated by the first pass.
Ben