Sco-X1search : S2 results C Messenger, V Re and A Vecchio on behalf of LSC-PULG LIGO Scientific Collaboration Meeting UMich, 4th – 5th June 2005

Outline Astrophysical scenario Data Analysis Pipeline S2 results Data-set selection Parameter space &Template bank F-statistic Search Coincidence test Injections Upperlimits Work in progress and future plans UMich LSC Meeting, 4th – 5th June 2005

Accreting neutron stars Conjecture for LMXBs: GWs are the limiting physics that prevents NSs from being spun-up to the braking frequency Two models: Density fluctuations – “mountain” on neutron star (Bildsten, 1998; Ushomirsky, Cutler, Bildsten, 2000; Cutler, 2002) fgw = 2 frot R-modes (Andersson et al, 1999; Wagoner, 2002) fgw = 4/3 frot (from Cutler and Thorne 2000) UMich LSC Meeting, 4th – 5th June 2005

Data analysis pipeline Data-set selection Template bank generation F-statistic Search Coincidence test Chi-squared test Injections & Upperlimits UMich LSC Meeting, 4th – 5th June 2005

S2 results : Data-set selection LLO LHO Tstart 7324 Tend # SFT 192 Tspan 18535 20302 Tobs Data-set selected based on sensitivity factor Factor in the noise floor across the search band & sky position sensitivity Limited to 6 hour maximum observation span (Tcomp a Tspan5) UMich LSC Meeting, 4th – 5th June 2005

S2 results : Parameter Space & Template bank 2+1 dimensional parameter space 2 orbital parameters (Projected Semi-Major axis & Periapse passage) + Intrinsic GW emission frequency Orbital period NOT a search parameter for coherent observation times < 1 week Spin down NOT a search parameter for coherent observation times < 1 month Projected Semi-Major Axis {1.44 +/- 0.18} (sec) at 1 sigma Time of periapsis {731163327 +/- 299} (GPS sec) at 1 sigma Frequency range split into 2 bands {474 +/- 10 & 614 +/- 10} Hz METRIC used to place filters in orbital parameter space (frequency projected out) & frequency space (independent of orbital parameters) UMich LSC Meeting, 4th – 5th June 2005

S2 results : F-statistic search The F-Statistic in the presence of Gaussian noise should be Chi2_4 distributed We have “good” and “bad” bands. The “bad” bands deviate significantly from the expected distribution in the tails resulting in statistically unlikely large values. Usually due to large “spikes” not removed by the running median. UMich LSC Meeting, 4th – 5th June 2005

S2 results : Coincidence test The method involves finding orbital templates that could be common closest filters to a possible signal. Have to search a finite range of frequencies around possible event frequency. UMich LSC Meeting, 4th – 5th June 2005

S2 results : Candidate Events The parameter space contains features after coincidence appearing as planes of events at constant frequency. Event densities in orbital parameter space appear isotropic UMich LSC Meeting, 4th – 5th June 2005

S2 results : Injections & ULs Upperlimits are ~4x1022 in both bands. Coincidence analysis helps us in the case where one detector is “clean” and one detector is “not clean”. UL’s around the 60 Hz power line harmonic at 480 Hz are dominated by very large loudest events inconsistent with the statistics. UMich LSC Meeting, 4th – 5th June 2005

Work in Progress & future plans Improvements in h0 sensitivity are obtainable with better data-set selection (taking into account injection distributions) – Note that the upper limits are correct (fingers crossed) for the data set we used. This coherent pipeline is clearly not the way to search for GW’s from Sco-X1 (but we knew that). An incoherent approach (Virginia Re, Greg Mendell) is the way forward. This approach is currently suitable for other LMXB’s (Domonic Kasprzyk) with smaller orbital parameter and frequency uncertainties (giving far longer observation times) Maybe need to use a different noise floor estimate at power line harmonic(s) ? Extend the frequency band to fill the gap UMich LSC Meeting, 4th – 5th June 2005

Data analysis Source position: known Orbital motion Circular orbit to a very good approximation Search with discrete mesh over 3 orbital parameters (period, projected orbit semi-major axis, initial phase) Phase Doppler shift much more severe than for isolated sources Signal confined to a single bin for Tobs < 150 sec (Sco X-1) .Df ~ 0.2 Hz (Sco X-1) P: binary period q = m2/mNS GWDAW8, 17th – 20th December 2003 A Vecchio – Accreting neutron stars

Data analysis (con’t) Intrinsic change in GW frequency (“spin down”) System is in equilibrium – GW emission balances accretion torque: frequency makes a “random walk” as the accretion rate (Mdot) changes in time We can not model this frequency evolution using low-order polinomial in time However, the signal is confined to a single frequency by for Tobs < 2 weeks Rotation frequency, and therefore GW frequency, not very well known: Df ~ 1 – 40 Hz t: time scale over which torque doubles or turns off GWDAW8, 17th – 20th December 2003 A Vecchio – Accreting neutron stars

Computationally bound search Computational load comes from two poorly constrained set of parameters: Emission frequency: search over a fairly large bandwidth (tens of Hz) Orbital parameters (Sco X-1: N_filt ~ 106 for 1 day of coherent integration) Long integration times Search strategy: Hierarchical: simplest approach is to use a “stack-slide” search (Brady and T Creighton, 1999) Coherent integration over Tc Concatenate incoherently M chunks of length Tc (total observation time = M Tc) Stack-slide search code development is well underway GWDAW8, 17th – 20th December 2003 A Vecchio – Accreting neutron stars

Approach for S2 analysis Target Sco X-1 (the brightest source) The analysis can be extended in a straightforward way (in principle) to the other LMXBs Only coherent analysis (the core of the entire search strategy) over: Relevant band for emission at twice the rotation frequency (but if enough processing power is available we’ll explore band for 4/3 rotation frequency) The longest possible observation time for available computational resources (Tsunami: 200 CPUs) T(coherent) < 1/2 day Frequency domain analysis (different flavour of analysis carried out for S1) GWDAW8, 17th – 20th December 2003 A Vecchio – Accreting neutron stars

Scorpius X-1 Neutron star in a binary system accreting from a low-mass (0.42 M_sun) companion Distance: 2.8 (+/- 0.2) kpc Orbital parameters Period: 0.787313(1) day = 18.9 hrs Projected semi-major axis: 1.990 sec < a < 2.213 sec “Initial” orbital phase: Da = 0.1 rad Circular orbit (e < 10-3) Rotation frequency from twin kHz QPOs (van der Klis et al, 1997; van der Klis, 2000) 232 – 242 Hz 302 – 312 Hz GWDAW8, 17th – 20th December 2003 A Vecchio – Accreting neutron stars

S2 preliminary analysis One-stage coherent FD analysis (F statistic) Tobs = 3 hrs (set by Tanalysis = 1 week on 100 CPUs) Same data segment for L1, H1 and H2 Search carried out over: Wide frequency band “lower band”: 464 – 484 Hz “upper band”: 604 – 624 Hz Discrete mesh over 2D parameter space (10% mismatch) Period known to high accuracy (not a search parameter for Tobs < 1 month) Mesh on a and a: 39,487 filters (upper-band) Frequentist upper-limits on ten 4 Hz wide bands covering the relevant frequency range GWDAW8, 17th – 20th December 2003 A Vecchio – Accreting neutron stars

Expected sensitivity for S2 We will set an upper-limit on Sco X-1 using the most sensitive S2 data stretch ~ 6 hrs long from L1, H1 and H2 (in coincidence) The analysis – search and Monte Carlo’s – will take ~6 weeks on 200 CPUs (Tsunami, B’ham cluster) The expected “angle-averaged” upper-limit at 95% confidence will depend on the frequency band h0(95%) ~ a few x 10-22 (on “clean” band) h0(95%) ~ 10-21 (on “noisy” band(s), which we know are there) We are implementing Itoh’s veto to reject spurious events GWDAW8, 17th – 20th December 2003 A Vecchio – Accreting neutron stars

Conclusions Coherent search analysis pipeline is in place S2 analysis is in progress However, any further sensitivity improvement rely on Lower detector noise (expected) Hierarchical search approach (well underway) Future plans Full stack-slide analysis code ready for S3 analysis Place upper-limits on other accreting neutron stars Place upper-limits on emission at 4/3 frot GWDAW8, 17th – 20th December 2003 A Vecchio – Accreting neutron stars