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