A multi-Lorentzian timing study of the atoll sources 4U 0614+09 and 4U 1728-34

We present the results of a multi-Lorentziant to the power spectra of two kilohertz quasi-periodic oscillation (QPO) sources: 4U 0614+ 09 and 4U 1728 34. This work was triggered by recent results of a similar fit to the black hole candidates ( BHCs) GX 339-4 and Cyg X-1 by Nowak in 2000. We find that one to six Lorentzians are needed to fit the power spectra of our two sources. The use of exactly the same fit function reveals that the timing behavior of 4U 0614+ 09 and 4U 1728 34 is almost identical at luminosities that are about a factor of 5 different. As the characteristic frequency of the Lorentzians we use the frequency v(max), at which each component contributes most of its variance per log frequency, as proposed by Belloni, Psaltis, & van der Klis in 2001. When using v(max) instead of the centroid frequency of the Lorentzian, the recently discovered hectohertz Lorentzian is practically constant in frequency. We use our results to test the suggestions by Psaltis, Belloni, & van der Klis in 1999 and Nowak in 2000 that the two Lorentzians describing the high-frequency end of the broadband noise in BHCs in the low state can be identified with the kilohertz QPOs in the neutron star low-mass X-ray binaries. The prediction for the neutron star sources is that if the two kilohertz QPOs are present, then these two high-frequency Lorentzians should be absent from the broadband noise. We find that when the two kilohertz QPOs are clearly present, the low-frequency part of the power spectrum is too complicated to draw immediate conclusions from the nature of the components detected in any one power spectrum. However, the relations we observe between the characteristic frequencies of the kilohertz QPOs and the band-limited noise, when compared to the corresponding relations in BHCs, hint toward the identification of the second highest frequency Lorentzian in the BHCs with the lower kilohertz QPO. They do not confirm the identification of the highest frequency Lorentzian with the upper kilohertz QPO.