figure 1, comparing a 20 year relaxation response to SSN with an 11y low-pass filter, lagged by 10y. The 20y relaxation with an additional 11y low-pass filter is also shown.
The relaxation response has low-pass properties that removes most of the 11y solar ‘cycle’ without further filtering.
Cross-correlation of SSN and SST shows peak correlation at approximately 10 year lag.
It is difficult to propose a physical mechanism that would produce a simple, time-lagged response in the climate system however the exponential relaxation response is a very common phenomenon also referred to as relaxation to equilibrium.
It is a general effect where, the further a system is displaced from its equilibrium state, the quicker its rate of return. As it gets closer to equilibrium the rate of change slows down.
A simple example is a pot of boiling hot water. Initially it cools very quickly, once closer to room temperature is cools much more slowly. The temperature falls roughly exponentially to the ambient temperature.
What is shown above is how such linear system would respond to a variable input related to historical sunspot number records.
triple running mean low-pass filter:
relaxation response ( convolution with exponential ):