Does linear memory effect encode in the gravitational waves? I read from a few papers that the gravitational memory effect has linear and nonlinear parts:
$$\Delta h^{TT}=\Delta h^{TT}_{linear}+\Delta h^{TT}_{nonlinear}$$
 and the nonlinear part is encoded in the GW. 
But the linear part will also cause permanent change in metric at null infinity, so the information of this effect should be also carried by some media, which to me is nothing but GW.
But when people calculate the waveform of memory (like arXiv:1807.00990), they only   consider the nonlinear part, I don't understand why, and I can't find any explanation about this.
So if I misunderstand something about the memory effect here, can someone kindly help me figure it out? or explain how exactly the permanent change happens? 
 A: I think I have understood this just now..
It's simply because we consider the bounded sources, which has vanishing linear memory but nonvanishing nonlinear memory. 
And it's from Favata.2009.
A: @J.-H.'s self answer is correct, but I'll expand it a bit.
Gravitational wave (GW) memory is created by unbound sources.
So two black holes that have a hyperbolic encounter will produce linear GW memory. 
GWs, themselves, follow unbound trajectories out to null infinity.
So GWs will produce non-linear memory.
Non-linear memory because the gravitational field (the GWs) sources the gravitational field (the GW memory).
All GWs produce memory, but the rate of memory accumulation depends on the power of the GWs.  Higher amplitude and shorter timescale GWs will produce more memory faster, making it easier to detect.
The only sources of GWs detected so far has been compact binaries.
For these systems the black holes and/or neutron stars are on bound trajectories, so only non-linear memory is produced.
If you were interested in detecting GWs from a hyperbolic encounter of two black holes, then you would need to consider both the non-linear memory from the the GWs and teh linear memory from the black holes.
