SEARCHES FOR MILLISECOND PULSATIONS IN LOW-MASS X-RAY BINARIES

Recent observational and theoretical studies of low-mass X-ray binaries (LMXBs) have given rise to a new class of standard models. In these models, accretion torques have spun the neutron star primary up to millisecond rotation periods. The existence of both millisecond radio pulsars and quasi-periodic X-ray oscillations is interpreted as supporting millisecond spin periods. However, millisecond spin periods remain undetected in low-mass X-ray binaries. Detection of the low pulse fractions expected for binary millisecond X-ray pulsars requires long integration times to enhance signal to noise. One of the significant barriers to detection is the pulse phase modulation which occurs when signals are integrated over a significant portion of a binary orbital cycle. We derive an optimized one-parameter Coherence Recovery Technique (CRT) for recovery of phase coherence. This technique affords a large increase in sensitivity over the method of incoherent summation of Fourier power spectra. In CRT a sequence of quadratic time transformations is applied to the data, followed by a Fourier transform for each trial. One particular transformation results in maximal compensation for the phase modulation and minimization of frequency broadening in the power spectrum. We discuss the range of spin periods expected from LMXB phenomenology, describe necessary constraints on the application of CRT in terms of integration time and orbital parameters, and estimate the residual power unrecovered by the quadratic approximation for realistic cases. An alternative, equivalent CRT approach is described in which a single Fourier transform of the data is followed by the application of a Wiener filter matrix in frequency space. We have applied CRT to high time resolution observations (0.3-5 ms) of several LMXBs obtained with the Ginga and HEAO 1 X-ray satellites. We present upper limits on the pulsed fluxes from Sco X-1, GX 340+0, GX 5-1, GX 9+1, GX 17+2, 4U 1820-30, Cyg X-3, and Cyg X-2. The 95% confidence level upper limit to the pulse fraction for sinusoidal pulses from the two brightest sources observed, Sco X-1 and GX 5-1, is less than 0.7% for frequencies up to 512 Hz, and less than 0.4% for frequencies less than 100 Hz. Our study implies that pulsars in LMXBs must have low pulse fractions (A < 1%), have short pulse periods (P(pul) < 2 ms), or, in those cases where the orbital periods are unknown, be in binary orbits with short orbital periods (P(orb) < 3 hr).