Allsky search of EXPLORER data

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All-sky search of EXPLORER data

• Andrzej Królak
• Albert Einstein Institute
• Golm
• on leave from
• Institute of Mathematics
• Warsaw

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All-sky Search of the EXPLORER Data

• EXPLORER resonant bar detector

The EXPLORER detector is operated by Italian
group ROG led by Eugenio Coccia. The analysis is
performed by a team consisting of Pia Astone,
Kazik Borkowski, Piotr Jaranowski, Andrzej
Królak, Maciej Pietka and is carried out on the
basis of Memorandum of Understanding between the
ROG group and Institute of Mathematics of the
Polish Academy of Sciences.
http//www.astro.uni.torun.pl/kb/AllSky/AllSky.ht
ml
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Collaboration with VIRGO project
Three searches for continuous sources of GW were
performed. Each consisted of analysis of 2 days
of EXPLORER data.
Numerical calculation for two searches were
performed by a network of computers in Bologna
and Rome under an agreement between Rog
Collaboration and the VIRGO project group in Rome
led by Fulvio Ricci.
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• Response of the detector to a continuous GW
  signals.
  

GW
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Linear parameterization
Response of the detector

• For observation time of a few days and a few Hz
  bandwidth linear representation is an adequate
  approximation.

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Maximum likelihood detection
F-statistic
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For a linear phase model F is a homogeneous
random field
False alarm probability

• Characteristic
• correlation
• hyper ellipse

Taylor expansion
Number of cells in the parameter space
Reduced Fisher information matrix
False alarm probability
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Grid of templates in the parameter space

• Expectation value of the statistics when the
  signal is present in the data

Taylor expansion
Signal-to-noise loss
Find a regular grid so that each element of the
grid is inscribed into hyperellipsoid
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Spectral density of EXPLORER data
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Statistical analysis of 13-day set of data taken
by EXPLORER detector in November 1991
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Parameters of search I

• Parameters of the data
• Modified Julian Date of the first sample
  48580.7908507
• Length of observation time 2 days
• Bandwidth of the search 920.9992 -- 921.7598 Hz
  
• Parameters of the search
• Spin down range -9.1762 10-8 -- 9.1762 10-8 Hz
  s-1
• No. of spin downs 2868
• Sky positions All sky, no. of pointings 31915
• No. of filters 183064440
• Sensitivity of the search
• Spectral density (two-sided) 10-21/vHz

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Parameters of search II The same as search I
except that Modified Julian Date of the first
sample 48591.6456387
Parameters of search III The same as search I
except that Modified Julian Date of the first
sample 48582.7853901
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Candidate statistics

• If there is no noise F has ?2distribution with 4
  degrees of freedom.

Search I
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Search II
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Search III
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Results of the searches

• No. of triggers max SNR (astro)
  
• SI 37349 8.19
• SII 21549 8.29
• SIII 42626 8.45

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Trigger verification

• Transformation from parameters (p0,p1,A,B) to
  astrophysical parameters (f, f1, d ,a) .
• Search on a small grid around astrophysical
  parameters.
• Search in a different 2-day stretch of data.
• Search in a 4-day stretch of data containing the
  original 2-day stretch.

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Trigger verification examples
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(No Transcript)
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Additional verification

• 1. Search for signals with parameters of the
  trigger in the whole 13 day long data set
• (Signal-to-noise should theoretically increase by
  250!)
• 2. Search for coincidences among triggers
• for various searches

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Original verification
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Addition verification in all data
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Upper limit
99 confidence upper limit
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Upper limit for the 3 searches