Searching for pulsars using the Hough transform Methods
- Slides: 17
Searching for pulsars using the Hough transform: Methods and preliminary results for S 2 A. M. Sintes, Universitat de les Illes Balears, Spain B. Krishnan, M. A. Papa Albert Einstein Institut, Germany LSC Meeting Livingston, March 2004
Outline Ø The Hough transform Ø Pipeline for S 2 Ø Statistics of the Hough maps Ø Preliminary results for S 2: L 1, H 1 Ø Future plans LSC Meeting, March‘ 04, A. M. Sintes B. Krishnan, M. A. Papa
The Radon transform Ø Break up data into N segments Ø Take the Fourier transform of each segment and track the Doppler shift by adding power in the frequency domain (Stack and Slide) Time Frequency LSC Meeting, March‘ 04, A. M. Sintes B. Krishnan, M. A. Papa
The Hough transform Ø Robust pattern detection technique developed at CERN to look for patterns in bubble chamber pictures. Patented by IBM and used to detect patterns in digital images Ø Look for patterns in the time-frequency plane Ø Expected pattern depends on: {a, d, f 0, fn} n f a d t LSC Meeting, March‘ 04, A. M. Sintes B. Krishnan, M. A. Papa
Incoherent Hough search: Pipeline for S 2 Pre-processing raw data GEO/LIGO Divide the data set in N chunks Construct set of short FT (t. SFT<1800 s) Incoherent search Candidates Peak selection in t-f plane selection Hough transform (a, d, f 0, fi) Set upper-limit LSC Meeting, March‘ 04, A. M. Sintes B. Krishnan, M. A. Papa
Peak selection in the t-f plane Ø Input data: Short Fourier Transforms (SFT) of time series Ø For every SFT, select frequency bins i such exceeds some threshold rth time-frequency plane of zeros and ones Ø p(r|h, Sn) follows a 2 distribution with 2 degrees of freedom: Ø The false alarm and detection probabilities for a threshold rth are LSC Meeting, March‘ 04, A. M. Sintes B. Krishnan, M. A. Papa
Hough statistics Ø After performing the HT using N SFTs, the probability that the pixel {a, d, f 0, fi} has a number count n is given by a binomial distribution: Ø The Hough false alarm and false dismissal probabilities for a threshold nth Candidates selection Ø For a given a. H, the solution for nth is Ø Optimal threshold for peak selection : rth ≈1. 6 and a ≈0. 20 LSC Meeting, March‘ 04, A. M. Sintes B. Krishnan, M. A. Papa
Search performed on S 2 data Ø Input data: – S 2_H 1_Funky. Cal 30 Min. SFTs (N=1887) – S 2_L 1_Funky. Cal 30 Min. SFTs (N=690) Ø Search over – frequency band 300– 600 Hz (Δf = 1/1800 Hz = 5. 55× 10 – 4 Hz) – 1 spindown parameter (11 values: Δf 1 = – 1. 09× 10– 10 s– 2) – Areas in the sky (0. 5 rad × 0. 5 rad): • • South pole, (Equatorial coordinates) a=0, d= –p /2 Equator a=0, d= 0 Near south pole a=0, d= – 1. 0 rad Galactic center a=4. 65, d= – 0. 4 – Sky locations: 57 × 57 @ 300 Hz, 113× 113 @600 Hz, Ø Time on Merlin 15 min on 300 nodes (not optimized) LSC Meeting, March‘ 04, A. M. Sintes B. Krishnan, M. A. Papa
Validation code (“Driver”) Ø Signal only case – (f 0=500 Hz) Ø Simulated data – (1440 SFT, 1991 maps, 48× 48 pixels, f 0=300– 301 Hz, a=0. 2231) LSC Meeting, March‘ 04, A. M. Sintes B. Krishnan, M. A. Papa
S 2 Results (Histograms 352 -353 Hz) H 1 L 1 ? LSC Meeting, March‘ 04, A. M. Sintes B. Krishnan, M. A. Papa
S 2 Results (Statistics 352 -353 Hz) H 1 LSC Meeting, March‘ 04, A. M. Sintes B. Krishnan, M. A. Papa
H 1: Maximum number count Δf=0. 1 Hz LSC Meeting, March‘ 04, A. M. Sintes B. Krishnan, M. A. Papa
L 1: Maximum number count Δf=0. 1 Hz LSC Meeting, March‘ 04, A. M. Sintes B. Krishnan, M. A. Papa
Frequentist analysis Ø Band analyzed 352 -353 Hz, patch centered at the galactic center • Close to violin modes for L 1 • No outlyers present in the Hough maps Ø Use ‘makefakedata’ for signal injections on calibrated SFTs – Input SFT → inject one signal → write new SFT in a smaller band Ø Use a different code (single template) – Validating and making extensive consistency checks: • Check distribution for the noise only case • Analyis of many Monte Carlo for debug purpose – Under debug mode each injection analysis takes 20 sec – h 0 value set manualy Ø Need of an optimized code, to search C(h 0) for several values of h 0 at once. LSC Meeting, March‘ 04, A. M. Sintes B. Krishnan, M. A. Papa
Preliminary results for L 1 352 -353 Hz, Galactic center, n*=196 Ø N*=196 h 0=1. 0× 10– 22 N=48200 C=91. 45% h 0=1. 2× 10– 22 N=88000 C=98. 44% h 0=2. 0× 10– 22 N=66000 C=1 h 0 ≈ 1. 1× 10– 22 LSC Meeting, March‘ 04, A. M. Sintes B. Krishnan, M. A. Papa
Preliminary results for H 1 352 -353 Hz, Galactic center, n*=464 h 0=1. 0× 10– 22 N=120000 C=1 h 0=6. 0× 10– 23 N=80000 C=96. 36% h 0=5. 0× 10– 23 N=80000 C=87. 57% h 0=1. 0× 10– 23 N=80418 C=2. 5× 10– 5 h 0 ≈ 6× 10– 23 ? LSC Meeting, March‘ 04, A. M. Sintes B. Krishnan, M. A. Papa
Plans Ø Set upper limits for each 0. 1 or 1 Hz interval Ø Design veto strategies: – Reject frequency bands by comparing results in different sky locations or lines present in the data. – Avoid setting upper limits in frequency bands containing disturbances, or allow bad upper limits. Ø Placement of patches – (0. 5× 0. 5, or of different size) to cover the full sky (or a selected area). Ø Verify consistency of the parameters used – e. g. estimating the noise floor in both analysis and Monte-Carlo injection codes (bias and block size used by the running median code). Ø Developement of a new optimized code to compute C(h 0) for several values of h 0 at once. – It will combine parts of ‘makefakedata’ and the 1 -template search code. – Possibility to obtain upper limit by interpolation LSC Meeting, March‘ 04, A. M. Sintes B. Krishnan, M. A. Papa