The phase lags of high-frequency quasi-periodic oscillations in four black hole candidates

We measured the phase-lag spectrum of the high-frequency quasi-periodic oscillations (QPO) in the black hole systems (at QPO frequencies) GRS 1915+105 (35 Hz and 67 Hz), GRO J1655-40 (300 Hz and 450 Hz), XTE J1550-564 (180 Hz and 280 Hz) and IGR J17091-3624 (67 Hz). The lag spectra of the 67-Hz QPO in, respectively, GRS 1915+105 and IGR J17091-3624, and the 450-Hz QPO in GRO J1655-40 are hard (hard photons lag the soft ones) and consistent with each other, with the hard lags increasing with energy. On the contrary, the lags of the 35- Hz QPO in GRS 1915+105 are soft, with the lags becoming softer as the energy increases; the lag spectrum of the 35-Hz QPO is inconsistent with that of the 67-Hz QPO. The lags of the 300-Hz QPO in GRO J1655-40, and the 180-Hz and the 280-Hz QPO in XTE J1550-564 are independent of energy, consistent with each other and with being zero or slightly positive (hard lags). For GRO J1655-40, the lag spectrum of the 300-Hz QPO differs significantly from that of the 450-Hz QPOs. The similarity of the lag spectra of the 180-Hz and 280-Hz QPO in XTE J1550-564 suggests that these two are the same QPO seen at a different frequency in different observations. If this is correct, the lags could provide an alternative way to identify the high-frequency QPO features in galactic black hole systems. The lag spectrum of the 67-Hz QPO in GRS 1915+105 (hard lags) is significantly different from that of the 2.7 x 10(-4) Hz QPO in the narrow-line Seyfert 1 galaxy RE J1034+396 (soft lags), which disproves the suggestion that the two QPOs are the same physical phenomenon with their frequencies scaled only by the black hole mass. The lag spectrum of the QPO in RE J1034+396 is similar to that of the 35-Hz QPO in GRS 1915+105, although identifying these two QPOs as being the same physical feature remains problematic. We compare our results with those for the lags of the kilohertz QPOs in neutron-star systems and the broad-band noise component in active galactic nuclei, and discuss possible scenarios for producing the lags in these systems.