Allsky search of Nautilus data: data analysis tools

1
All-sky search of Nautilus data data analysis
tools

• Andrzej Królak
• Albert Einstein Institute
• Golm
• and
• Institute of Mathematics
• Warsaw

2
Collaboration

• MOU to search NAUTILUS detector 2001data for
  periodic gravitational-wave signals.
• MOU involves
• 1. ROG collaboration led by Eugenio Coccia
• (contact person Pia Astone).
• AEI continuous GW group led by Maria Alessandra
  Papa.
• A.K. group in Poland.

3
(No Transcript)
4
Parameters of the search

• 1 year of data divided into 2-day sections.
• 2 day sections analyzed coherently using F
  -statistic.
• Bandwidth of 1-2Hz around 1kHz.
• 1 spin down parameter with minimum spin down time
  of 1000 years.
• All-sky search.

5
Upper limit
pD probability of detection C confidence
(say 90) L number data stretches searched
6
Upper limit if no signal detected

• Threshold SNR d 8.2 for 1 false alarm
  probability
• Upper limit for dimensionless GW amplitude for
  the search of 2 day stretch of data when the
  detector was most sensitive (Sh 5 x 10-22
  Hz-1/2)
• hUL 5.7x10-23
• Upper limit for dimensionless GW amplitude for
  the search of 150 of independent 2 day stretches
  of data (Sh 10-21 Hz-1/2)
• hUL 1.8x10-23

7
Maximum Likelihood Detection

• Response of the detector GW signal
• Optimal filtering F-statistic
• False alarm and detection probability
• Grid of templates
• Numerical calculation of the F-statistic
• Tools Fisher Information Matrix
• Correlation function cell concept

8
Response of the detector
9
Neglect amplitude modulation and introduce a
linear parameterization of the phase
Approximation of the response to calculate the
false alarm probability and construct the grid of
templates in the parameter space.
We neglect the component of the vector rD that
is perpendicular to the ecliptic. (rD joins the
center of the Earth and the detector).
10
F-statistic for a periodic signal
11
Number of templates
Spacing
Hypecubic covering
K no. of intrinsic parameters V (hyper)volume
of the parameter space Co- minimum correlation
coefficient G reduced Fisher matrix We choose
Co sufficiently large so that the loss of the
signals is minimized
12
Grid of templates in the parameter space
No. of templates 108
13
Calculation of the F -statistic

• Demodulation

Resampling
FFT
14
(No Transcript)
15
CODE

• Code is being tested
• The aim is to achieve a real time performance,
• i.e. analyze 2 days of data
• (1 Hz bandwidth, 1 spin- down (1000yr), all-sky)
• in 2 days.
• Should be possible with a couple hundred of
• processors.