Searching for accreting neutron stars C Messenger, V Re and A Vecchio on behalf of LSC-PULG 8th Gravitational Waves Data Analysis Workshop UWM, 17th – 20th December 2003

Outline Astrophysical scenario Data analysis Expected S2 sensitivity General Approach for LIGO S2 data set Expected S2 sensitivity Work in progress and future plans GWDAW8, 17th – 20th December 2003 A Vecchio – Accreting neutron stars

Astrophysical scenario Observational evidence that rotation frequencies in Low Mass X-Ray Binaries (LMXB) are Well below NS breaking frequency Clustered in a narrow (237 Hz – 619 Hz) frequency range (Bildsten, 1998; Chakrabarty et al, 2003) Currently, two are the proposed mechanisms: Magnetic braking (Wang and Zang, 1997), but need for fine tuning of parameters Gravitational waves (Bildsten, 1998) GWDAW8, 17th – 20th December 2003 A Vecchio – Accreting neutron stars

GWs from 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) GWDAW8, 17th – 20th December 2003 A Vecchio – Accreting neutron stars

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