The time-delay spectrum of GX 5-1 in its horizontal branch

Using a cross-spectral technique we investigate time delays between intensity variations of GX 5-1 in 10 X-ray spectral channels. The data were taken during a 1989 Ginga observation during which the source was in its horizontal-branch spectral state. We develope a new method to measure 'time-delay spectra' in fixed Fourier frequency ranges and use it to determine the energy and intensity dependence of time delays in the low-frequency noise (nu less than 2 Hz), the horizontal branch quasi-periodic oscillations (QPO), and the QPO second harmonic. These are the first time-delay spectra of a Z-source in its horizontal branch, and the first detection of time delays in the second harmonic. We consider two mechanisms for the production of the time lags: Comptonization and evolving shots. We perform Monte Carlo simulations of Compton scattering in a homogeneous, isotropic, central corona and show that it qualitatively explain the observed energy and time-delay spectra, but that it cannot explain the differences in the QPO first and second harmomnic time-delay spectra, nor the observed dependence of the QPO fractional rms variability upon energy. We consider implications of our results for millisecond pulsar searches in low-mass X-ray binaries.