The Case of GRS 1915+105 | Definitions of lag | LAG : a simple derivation | Application
Microquasars - LAG Model / Definition of lag and coherence
We will briefly go over the definition of the lag as presented by Vaughan & Nowak (1997).
Suppose that .gif){kind=small}
and .gif){kind=small}
represent the X-ray flux
in two energy bands (soft and hard) at time 
. We note .gif){kind=small}
and as their Fourier transforms at the frequency 
:
The time lag between the hard and soft X-ray is then defined as :
(1)
Modification of one of the two phases (lowering the phase of the soft band or increasing the phase of the hard band) could induce the lag to change sign. More generally, any change in the phase of one of the bands, caused by internal or external phenomena, could lead to a sign change in the lag.
The coherence is a measure of how much of a signal f can be predicted knowing a signal h. In our case it means how much of the high energy flux can be predicted knowing the low energy flux. If the two signals are related then the coherence is high; the maximum equals one, which correspond to the case where there is a linear transformation to go from one to the other.