1. S4 Pulsar Search Results from PowerFlux
Vladimir Dergachev, Keith Riles
(University of Michigan)
LSC Meeting, Hanford August
DCC: G Z

2. Reminder of PowerFlux approach
PowerFlux computes the flux of linearly and circularly polarized CW radiation incident on the Earth from any direction and in-band frequency, with one spin-down parameter allowed, and with explicit correction for antenna pattern and noise weighting (neighboring bins used for noise estimation)
 Allows frequentist upper limit for each sky location separately
 Monte Carlo injections unnecessary for deriving limits (needed only for validation of procedure)
One circular and four linear polarization projections are computed for each set of (RA, dec, f0, df0/dt).
The number of sky points scales quadratically with f0

3. “All-sky” upper limits on linear polarization based on highest of four linear-projection upper limits over “good” sky regions, with conservative correction for polarization mismatch.
 Corresponds to worst-case pulsar orientation ( = π/2)
All-sky upper limits on circular polarization based on highest circular-projection over good sky regions
 Corresponds to best-case pulsar orientation ( = 0)
Limits dominated by least sensitive region of sky or by non-Gaussian detector artifacts (e.g., wandering lines)
But high detection SNR is examined separately, allowing detection sensitivity better than indicated by worst strain limit

4. Where do things stand? March LSC meeting:
Presented preliminary S3 H1 & very preliminary S4 H1/L1 linear-polarization upper limits over the Hz band with no spindown
June LSC meeting:
Presented preliminary S4 H1 and L1 linear- and circular-polarization upper limits for Hz and 50 spindown values: [–5,+5] x 10-8 Hz/s (aggressive “deep spindown search” in relatively clean band for coincident H1-L1 detection  no plausible candidates found)
Today:
Prelim S4 limits (no-spindown) for
H1 ( Hz) H2 ( Hz) L1 ( Hz)
Prelim S4 H1 limits ( Hz) for 11 spindown values [-1,0] x 10-8 Hz/s (partial results from ongoing Hz production run)

5. Where do things stand? Review process:
PowerFlux method & code review began January 13
Review of core code & critical scripts completed July 19
(minor bugs and documentation errors found and fixed – many thanks to Peter Shawhan and other reviewers)
Production analysis:
Launched ongoing 11-spindown production analysis jobs on July 23:
Search range: Hz for H1, H2, L1
(4 jobs / Hz ) x (950 Hz) x (3 IFO’s) = 11 kjobs
Completed so far: ~3 kjobs (H1 up to 800 Hz)
Wall-clock time per job (<1 hour at 50 Hz to 40+ Hours at 800 Hz)
(see figure)

6. LSC meeting approaches (busy cluster)
Time scales with number of sky points: α (frequency)2
(11 spindowns / job)

7. Zero-spindown 95% CL limits – H1 (50-1500 Hz)
Linear amplitude (=0.5*h0worst-pulsar-orient.)
“Good sky bands” (discussed later)
Color coding
Cyan – 60 Hz harmonic
BLUE – Non-Gaussian
Diamond – Wand. Line
Green – Upper Limit
Red point – Candidate (SNR > 7)

8. Why SNR > 7 ?
SNR of highest upper limit over good sky bands (sample)
The crud

9. ? SNR Ceiling for plot Violins Calib / SB’s Injected Pulsars SNR = 10792
754 93
Injected Pulsars
SNR Ceiling for plot
Calib / SB’s
Violins ?

10. Comparing linear to circular polarization limits
Linear amplitude (=0.5*h0worst-pulsar)
Circular amplitude (h0best-pulsar)
Typical: h0worst-pulsar ~ 4 x h0best-pulsar

11. Other IFO’s: H2 & L1 (50-700 Hz) – no spindown H2 L1
Linear amplitude (=0.5*h0worst-pulsar) H2 L1

12. Now for the 11-spindown run: –10-8 Hz/s < df0/dt < 0
Linear amplitude limits
(good sky, all spindowns)

13. Maximum SNR over “good” sky – all spindowns
Most are usual suspects, but many are worse than for zero spindown
WHY?

14. “Bad” means Doppler shift for zero-spindown source is fairly stationary
Sky bands during S4
Empirical: safe to use: |cos(Θband-axis)| < 0.5
DEC
GOOD
BAD
GOOD
BAD
GOOD
Average direction of Sun [= band axis] RA

15. Greatest net frequency stationarity (detector frame) for
But “good” sky can become “bad” for pulsar with spindown  Doppler non-stationarity compensated by opposite spindown
For negative df0/dt (positive spindown), region toward sun can become “bad” for frequency-dependent spindown range
Greatest net frequency stationarity (detector frame) for
df0/dt ~ – (a/c) f0 cos(Θband-axis)
(with a = Earth acceleration)
Numerically,
df0/dt ~ – (2×10-9 Hz/s) [f0 / 100 Hz] × cos(Θband-axis)
 Some part of the sky is bad for
| df0/dt | < (2×10-9 Hz/s) [f0 / 100 Hz]

16. Bad for 0.5 < cos(Θ) < 1.0 (half of good band for df0/dt = 0)
pdf

17. pdf
Restricting to sky bands 0 & 8 gives cleaner map [|cos(θband-axis)| > 0.94]

18. Zooming in to a low-frequency 200-Hz band…
Injected pulsars
Deep-spindown region
Crud

19. Zooming in to a higher-frequency 200-Hz band…
Detchar studies ?
Injected pulsars (both binary)
Calib / SB’s
Violins
(but will check for L1 coincidence!)

20. Conclusions Hope to complete production run soon:
Apply loose coincidence requirements among IFO’s to follow up on candidates – using machinery from deep-spindown search
Attempt at detection (not for upper limits)
But need to decide how to handle good sky vs bad sky in quoting upper limits – may restrict limits to (large) sky regions that are dependent on f0 and df0/dt
Publication plans:
Incorporate single-IFO limits into S4 incoherent search paper
Hope to include corresponding limits from Hough / StackSlide for methods comparisons, in addition to results

21. End Notes for Pulsar Face-to-Face Meeting
Some recent validation studies
H1-L1 coincidence – zero-spindown

22. Some recent S4 validation studies (based on power injections)

23. Some recent S4 validation studies (cont.)
Different from before: |cos(θband-axis)| < 0.3

24. Some recent S4 validation studies (cont.)
Black: df0/dt < 1.E-10 Hz/s
Red: df0/dt < 5.E-10 Hz/s

25. L1-H1 Coincidence check – Zero-spindown
Look for loose coincidence of outliers (blue/red points, red diamonds):
|Δf0| < 10 mHz, |ΔRA| < 0.5 rad, |Δdec| < 0.5 rad
Survivors: Pulsars 2, 8 & 11