1. Searching for pulsars using the Hough transform Badri Krishnan AEI, Golm (for the pulsar group) LSC meeting, Hanford November 2003 LIGO-G030580-00-Z

2. Outline The Hough transform The frequency-time pattern Hough map statistics Frequentist upper limits Code status Conclusions

3. Need for a hierarchical scheme Want to perform an all sky search for unknown pulsars Parameters 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 10 16 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 { , ,f 0,f i }

4. Set upper-limit Pre-processing Divide the data set in N chunks raw data GEO/LIGO Construct set of short FT (t SFT ) Coherent search ( ,f i ) in a frequency band Template placing Incoherent search Hough transform (  f 0, f i ) Peak selection in t-f plane Candidates selection Candidates selection Hierarchical Hough transform strategy

5. Set upper-limit Pre-processing Divide the data set in N chunks raw data GEO/LIGO Construct set of short FT (t SFT =1800s) Incoherent search Hough transform (  f 0, f i ) 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

6. The Hough Transform  Looks for patterns in frequency-time plane Expected pattern depends on { , ,f 0,f i } f t n   Resolution in sky position ~ 10 -2 rad Spindown resolution ~  f / T coh ~ 1.6 x 10 -10 Hz/s

7. Basic pipeline for a single stage Break up data into N segments and combine them incoherently   Frequency nono n   Candidates For next stage Thresholds chosen by optimizing false dismissal for fixed false alarm rate Used running-median to estimate noise floor Normalized power

8. Noise only case

9. 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 T obs

10. 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 Reduces to binomial distribution when  ’s are same

11. 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: Observed Maximum number count:

12. Setting the upper limit. Frequentist approach. 95 % n*=395   =0.295  h 0 95%

13. 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 h 0 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 parameters    but with fixed value of the amplitude h 0.. 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 h 0 which gives the right confidence level for the observed value of

14. 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