This is the time constant spectrum of the arrangement measured. The x axis is the (logarithmic) time [sec], the y axis is continuous spectral intensity [K/W/-].
A simplified explanation for time constant spectrum can be the following:
The Zth curves are “bumpy”, contain sections of different slope. This is natural, during heating we can observe how we first heat up the chip, then internal package elements, afterwards the package body, the board etc.
Such a curve can always be interpreted as a sum of exponential components. This exponential composition automatically yields a simple one-dimensional dynamic model, a chain of serial thermal resistance –capacitance pairs.
Figure 3-10: The simplest dynamic thermal model – a parallel thermal resistance and thermal capacitance
In the simplest case the system can be represented by a single thermal resistance expressing heat conductance and a parallel thermal capacitance expressing heat storage (Figure 3‑10).
Applying power on this equivalent network the temperature quickly grows until t=R×C time, then gradually stabilizes at T=P×R value following the 
time function. (In the analogous electric network power is replaced by current, and temperature is replaced by voltage.) At 1W power we get the Z(t) curve.Composing now a Zth curve like the one in we have to sum up such exponential heating curves:
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The addition of temperatures corresponds to the chain model of Figure 3‑11, the same power (“current”) flows along the chain, and the total temperature (“voltage”) is calculated as the sum of the components. At 1W power we get the Z(t) curve again.
Figure 3-11: A popular behavioral dynamic thermal model – a chain of parallel thermal resistance and thermal capacitance stages
We could quantitatively describe the chain model with a large table of Ri and Ci pairs For the visual representation it is practical to give the Ri and t=R×C values instead, because R gives direct information on the magnitude of the given component, and t on the place of the “bump” along the time axis. As large tables are not very easy to use; Ri and ti values are usually plotted in quasi–continuous graphs (time constant spectrum).
Figure 3-12: Tau intensity of the multi-chip module
