The Case of GRS 1915+105 | Definitions of lag | LAG : a simple derivation | Application
Microquasars - LAG Model / The Case of GRS 1915+105
Muno et al. (2001) studied the hard state (
state in the classifications by Belloni et al., 2000, or radio plateau)
using simultaneous X-ray and radio observations.
In this section we will discuss Fig. 7 and 8 in Muno et al. (2001),
in order to emphasize the observational constraints on the behaviour we are trying to explain here.
The left of their Fig. 8 shows how the temporal properties (QPO frequency on the top and phase lag at the QPO frequency at the bottom) correlate with the different components of the X-ray flux, namely from left to right, the total flux, the thermal/disk flux and the power-law flux. By looking carefully at the plots two populations can be distinguished (the triangle and the cross). This distinction is more apparent in the graph showing the lag.
On the left upper panel of Fig. 8 we see that for a QPO frequency higher than about two hertz, the QPO frequency appears to be correlated with the total flux and the power-law flux (which in fact dominates the total flux). This applies for most of the low-mass X-ray binaries. For a QPO frequency lower than 2Hz, this QPO frequency no longer correlates with any of the X-ray fluxes. In fact all of the frequencies below 2 Hz appear at a similar flux level for both the thermal and power-law flux, i.e. the cluster of triangles is very narrow.
These points are also the ones with a high radio flux (the triangles represent the radio-loud state) as is seen in Fig. 7. These radio-loud points are also the only ones to exhibit a positive phase lag. Concerning this lag, there is also another difference besides the change of sign between the radio-loud and the radio-quiet state : if we look at the left lower panel of Fig. 8, there is no correlation between the lag and any of the X-ray fluxes. However, depending on wherever the source is radio-loud or radio-quiet the clusters of points appear to be perpendicular to each other.
In the radio-loud case, the temporal behavior of the source is modified for quasi constant X-ray fluxes. These modifications are a function of the radio flux. On Fig. 7 is shown the evolution of the temporal properties such as the QPO frequency, the phase lag, the coherence and the ratio of low-frequency power as a function of the radio flux at 15.2 GHz. Once again the radio-loud and radio-quiet points are well separated. The separation occurs at a radio flux of about 60 mJy.
By looking in more detail at the first plot (QPO frequency - radio flux) we see that a QPO frequency less than two hertz is always associated with a radio flux of more than 60 mJy. These same QPOs have a positive phase lag and show much less coherence than the QPOs in the radio quiet state. Moreover, the phase lag which seems totally uncorrelated with the radio flux when it is less than 60 mJy, appears to be correlated with the higher radio fluxes. In the graph of the ratio of low-frequency power as function of the radio flux the possible correlation seems to reverse during the transition between radio-quiet and radio-loud.
Either these QPOs (less than 2Hz, more than 2Hz) arise from a different mechanism (e.g. one related with the jet and the other one not) or there is a threshold in radio flux above which new phenomena appear in addition to the QPO mechanism. This could cause a modification of the temporal behavior of the source, especially relevant to the lag which seems to become proportional to the radio flux. We will focus on this last possibility. The presence of two different unrelated mechanisms, one from the jet and the other from the disk, seems improbable because of the smooth transition in QPO properties as a function of time (see for example Fig. 6 of Muno et al., 2001). However, before exploring the possible origin for the change in temporal properties, we will look at the lag definition and its computation through Fourier transforms.