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In the Laser Interferometer Space Antenna (LISA) mission proposal document, section 4.2 (page 17) there is a formula for the test mass acceleration noise level: \begin{equation} S_a^{1/2}\leq 3\cdot 10^{-15}\frac{\rm m\cdot s^{-2}}{\sqrt{\rm Hz}}\sqrt{1+\left(\frac{0.4~{\rm mHz}}{f}\right)^2}\sqrt{1+\left(\frac{f}{8~{\rm mHz}}\right)^4}~. \end{equation} My question is -- where do the specific frequencies $0.4$ mHz (first square root) and $8$ mHz (second square root) come from?

I'm trying to figure out how to apply this formula for other gravitational-wave space detectors, e.g. TianQin and DECIGO. But these two numbers will probably be different, but how to find them in each case?

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The answer lies in the scientific goals of the mission. You can find these in the LISA Science Requirements Document.

The so called roll-off is a relaxation of the requirements as the lower frequencies.

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