searching for pulsars using the hough transform badri krishnan aei, golm (for the pulsar group) lsc...
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Searching for pulsars using the Hough transform
Badri Krishnan AEI, Golm
(for the pulsar group)
LSC meeting, Hanford November 2003
LIGO-G030580-00-Z
Outline
• The Hough transform
• The frequency-time pattern
• Hough map statistics
• Frequentist upper limits
• Code status
• Conclusions
Need for a hierarchical scheme
• Want to perform an all sky search for unknown pulsarsParameters involved :
• If we want to search for one spin-down parameter over an observation time of say 6 months and frequency band of a few 100 Hz using the optimal search - would need a 1016
Flops computer
• Idea of a hierarchical search: perform a first sub-optimal search to reduce parameter space volume and use optimal method only for small number of candidates in parameter space
{,,f0,fi}
Set upper-limit
Pre-processing
Divide the data set in N chunks
raw data GEO/LIGO
Construct set of short FT (tSFT)
Coherent search (,fi)
in a frequency band
Template placing
Incoherent search
Hough transform(f0, fi)
Peak selection in t-f plane
Candidates
selection
Candidates
selection
Hierarchical Hough transform strategy
Set upper-limit
Pre-processing
Divide the data set in N chunksraw data
GEO/LIGO
Construct set of short FT (tSFT=1800s)
Incoherent search
Hough transform(f0, fi)
Peak selection in t-f plane
Candidates
selection
Incoherent Hough search:Pipeline for S2
Want to perform an all sky search over a frequency range of ~ few 100 Hz including one spin down
parameter
The Hough Transform
Looks for patterns in frequency-time plane
Expected pattern depends on
nc
t vt f t f t fˆ
) () ( ) ( ) (0 0
{,,f0,fi}
f
t
n
Resolution in sky position ~ 10-2radSpindown resolution ~ f / Tcoh
~ 1.6 x 10-10 Hz/s
Basic pipeline for a single stage
Break up data into N segments and combinethem incoherently
Frequency
no
n
0nn
CandidatesFor next stage
Thresholds chosen by optimizing false dismissal for fixed false alarm
rate
Used running-median to estimate noise floor
Normalized power
Noise only case
Sensitivity of the Hough search
For coherent directed search with false alarm of 1% , false dismissal rate of 10% :
For incoherent Hough search with 1% false alarm and 10% false dismissal rate for large N and looking at a single pixel on the celestial sphere:
Sub-optimal nature of Hough search leads to loss in sensitivity by a factor of
Currently code is being used with ~ 1900 SFTs each 1800s long In future will also be run with input from F statistic code which allows a
smaller value of N and larger Tobs
obs
GWn
T
fSh 4.110
obs
GWn
coh
GWn
T
fSN
T
fS
Nh 4/1
4/10 0.100.10
4/1N
Statistics of the number counts
Distribution of power: with 2 d.o.f. with non centrality parameter
Detection probability :
This statistic changes between SFTs because of non-stationarities in the noise and also due to amplitude modulation of signal. Thus detection probability changes with time. Thus to set upper limits we have to perform Monte Carlo simulations
To obtain a number count value n, we must have selected n SFTs and rejected (N-n) . The probability for this happening is
N
iNiiii
m
nnnNnnhNnp
10 )1)...(1(...
)!(!
1),,,|(
121
)(
|)(~
| 2
gwncoh
gw
fST
fh
o
dp
)|(
Reduces to binomial distribution when ’s are same
Example: Run Hough code in 1Hz frequency band (263.5-264.5Hz), sky patch 0.5 rad on a side centered on the South pole with 1887 SFTs each 1800sec long:
443nObserved Maximum number count:
Setting the upper limit.
Frequentist approach.
95 %
N
nn
%
n|hp*
95
00.95
n*=395 =0.295
h095%
The Monte-Carlo simulation
Aim is to set an upper limit for every 1Hz band Run the Hough driver over the 1Hz band for a large sky-patch and obtain
the Hough maps, the distribution of the number counts, and files with the detector velocity at the timestamps of the SFTs.
To obtain upper limits we must obtain the number count distribution with a signal injected and find the value of the amplitude h0 for which the number
count is at least with 95% probability. Generate signals with random values of sky position within the chosen sky-
patch, frequency within the 1Hz band, and pulsar parametersbut
with fixed value of the amplitude h0.. Inject these signals into SFTs and
find the Hough number count at the correct point in parameter space.
Repeat for a range of amplitudes and find the value of h0 which gives the
right confidence level for the observed value of
n
n
To-do list
Driver code ready: Stand alone code accepts SFTs as input and produces Hough maps for a reasonably large sky patch and includes spindown parameters.
Code for Monte Carlo signal injection is also ready and preliminary results are available.
Current status of code
Perform Monte-Carlo runs over a large frequency range and large sky-patch for a range of signal amplitudes and find the upper limit : by march lsc
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