Stochastic gravitational wave background due to gravitational wave
  memory
  Gravitational waves from binary black hole merger leave permanent imprint on
space-time, called gravitational wave memory. Amounts of memory events can form
a ``stochastic gravitational wave memory background'' (SGWMB). Here we find
that SGWMB can be described as a Brownian motion. The power spectral density
(PSD) of SGWMB corresponding to a set of binary black hole coalescence is
proportional to $1/f^2$ where $f$ is the frequency of the background. And the
strength of the SGWMB PSD depends on the event rate of the binary black hole
coalescence. Not like the stochastic non-memory gravitational wave background
of a set of binary black hole coalescence whose PSD has a upper frequency bound
due to the merger frequency, SGWMB can expand to much higher frequency because
of the Brownian motion behavior. Consequently SGWMB dominates the stochastic
gravitational wave background in the relatively higher frequency band. If not
counting SGWMB properly ones may confuse it with the stochastic non-memory
gravitational wave background. Investigating SGWMB properly may let LIGO to
detect the population of supermassive binary black hole systems. Also SGWMB
provides a brand new mean to detect gravitational wave memory and it opens a
new window to explore the gravity theory.
