Unbiased All-Sky Search (Michigan) [as of August 17, 2003] [ D. Chin, V. Dergachev, K. Riles ]

1. Unbiased All-Sky Search (Michigan)[as of August 17, 2003][ D. Chin, V. Dergachev, K. Riles ] Analysis Strategy: (Quick review) • Measure power in selected bins of averaged periodograms • Bins defined by source parameters (f, RA, d) • Estimate noise level & statistics from neighboring bins • Set “raw” upper limit on quasi-sinusoidal signal on top of empirically determined noise • Scale upper limit by antenna pattern correction, Doppler modulation correction, orientation correction • Refine corrected upper limits further with results from explicit signal simulation

2. Overview of Data Pipeline for Unbiased All-Sky CW Search Raw Data Simulated Data Create 30-min SFT’s Creation of Power Statistic • Loop over frequency and sky: • Determine search range and control sample range • Determine upper limit on detected power • Apply efficiency corrections (Doppler, AM, orientation • Determine limit on h0 and store Determine efficiency corrections

3. Creation of Power Statistic and finding upper limits Simulated Data Raw Data LHO LDAS 1-minute, 30-min calibrated SFTs(Xavier) 1800-second raw data 2048(?)-second calibrated SFT’s (Greg) (Vladimir) 1800-second calibrated SFT’s (cross check) Medusa system (cross check) • Power Statistic Creation: (Vladimir) • Simplest: Average calibrated powers bin-by-bin • Allow summation of raw and simulated SFT’s • Apply epoch vetoes (high noise, bad calibration, artifacts) Michigan computers Upper Limits Finder (Dave et al)

4. Upper Limits Finder (schematic) • Loop over values of f0 (SSB frame), RA, sin(δ) in steps of • ¼ (17 mHz, 0.5 mHz): • Determine the freq bin(s) of search and the large control range (nearly neighboring) • Compare total power in bin(s) and compare with histogram to find upper limit (~2σ) on detected power in h • Apply efficiency corrections (Doppler modulation, antenna pattern, worst orientation) to find 95% C.L. upper limit on h flux at earth • Store upper limit fDetected Measure Counts Upper limit Power (h2)

5. SFT Generation Problem: Need 30-minute SFT’s but calibration drifts non-negligible at times. Want a method to use 1-minute calibration α coefficients with minimal new artifacts. • Present baseline calibration procedure (“stitched”) • Create 1-minute SFT’s (high-passed & Tukey-windowed • Apply 1-minute calibration info, window again in Fourier domain • Compute inverse transforms, window again, and stitch to make 30-minute interval • Compute SFT from 30-minute interval • Machinery is in place with flexible control of parameters: • Tukey window ramp intervals • High-pass and low-pass filtering • Strong-line suppression (mean-padding in Fourier domain) • Trouble: Periodic windowing introduces 1/60 Hz residual “comb” • Optimum tradeoff not yet clear – Xavier working on alternative approaches (averaging; Dirichlet kernel) – Coordinating closely – Stay tuned

6. Flow chart for generating 30-minute calibrated SFT’s using the stitching method (Vladimir)

7. Validation of SFT’s Verified code works correctly for constant, unfiltered calibration (comparing stitched SFT to 1800-sec SFT) Varying filter and Tukey window parameters in time and freq domain, including up to extreme of Hann window. Trying to find reasonable tradeoff between data retention and small artifacts from 1/minute modulation (sharp windowing leads to 1/60 Hz residual “comb” structure) Hann window defines asymptote for smooth window behavior, but large data loss Tukey window with sharp ramp ( rectangular window) defines asymptote for high data retention, but 1/60 Hz artifacts

8. Validation of SFT’s • Established that Tukey window with sharp ramp preserves calibration line magnitude and phase well • But bigger worry is leakage of large lines into spectral troughs • Can see appreciable (~1-10%) variation in trough noise, even with aggressive filtering of low-frequency, high-frequency, line noise • Ultimate figure of merit: • How well we can reconstruct hardware-injected pulsar signals (hardware injection automatically accounts for calib variation) • Work underway • Also coordinating closely with Xavier on his Dirichlet-kernel and averaging methods

9. Detailed running history of SFT and power statistic development with validation tests can be found on Vladimir’s home page: • http://tenaya.physics.lsa.umich.edu/~volodya/

10. Sample Power Statistic (derived from 701 SFT’s) L1 200-400 Hz 60 Hz harmonics & violin modes prominent, but other artifacts present too • Expect exponential distribution for power in each SFT bin. • Kolmogorov-Smirnov statistic using median to define reference curve (but expect ~0.02 for 701 points!)

11. Status of programs ProgramAuthorStatus SFT maker VladimirComplete – Under validation(SFT’s generated for H1, H2, L1) Power statistic maker VladimirBaseline complete – evolving(Statistic generated for L1) Antenna pattern code DaveComplete - LALified Freq modulation code KeithCrude baseline complete Search engine KeithIn progress