Relaxation timescale of LMP population for different masses using our initial conditions for the number of LMP and the half-mass radius. The relaxation timescale for an Earth mass and a Jupiter mass are from the red line and green line, respectively. The orange line shows the star limit (i.e., the ignition of hydrogen at ≈ 0.08 M_⊙). The red dot shows the timescale considering a mass spectra of LMP in a uniform logarithmic distribution, ranging from Earth mass to Jupiter mass, using the same initial condition of our main models. Finally, the blue line shows results taking into account the initial conditions of the model C05.