Frequency sensitivity of gravitational wave interferometer with its armlength and with mass of the mergers

To answer your second question lets look at the sensitivity curve for LISA. (There are two reasons to look at LISA instead of LIGO. First, the arm length of LISA was a significant topic of discussion during the recent mission design phase. Consequently, the is plenty of sources discussing the impact of the arm length on the sensitivity. Second, LIGO for the most part observes gravitational waves whose wavelength is much longer than the arm length, whereas LISA will also see sources with wavelengths shorter than the arm length, making the arm length more relevant in the sensitivity curve.)

According to a recent paper by Robson, Cornish, and Liu, a good approximation to the LISA sensitivity curve (lower is higher sensitivity) is given by

$$ S_n(f) = frac{10}{3L^2}left(P_{OMS}(f)+2(1+cos^2(f/f_{*})frac{P_{acc}(f)}{(2pi f)^4}right)left(1+frac{6}{10}left(frac{f}{f_{*}} right)^2 right), $$

where $P_{OMS}$ characterizes the noise introduced by the optical measurement system, $P_{acc}$ is the acceleration noise (i.e. how well the space craft can keep the test masses in freefall), $L$ is the arm length, and $f_{*} = c/(2pi L)$ (the characteristic frequency if light traveling around the detector). We thus see that the sensitivity of LISA depends on the arm length in two ways.

• There is an overall suppression of the noise by a factor $L^2$. That is, making the arms longer, improves sensitivity over the entire frequency range.

• The second is through $f_{*}$, which accounts for a penalty to the sensitivity due to the wave length of the gravitational waves being comparable our smaller than the arm length. At higher, frequencies this penalty pretty much negates any advantage of making the arms longer.

The combined effect of these two effects is that increasing arm length shift the minimum of the sensitivity curve to lower frequencies.

For LIGO, the second effect is less relevant, and the location of the minimum is determined mostly by the competition by other sources of noise that do not depend sensitively to the arm length. (Mostly seismic noise at low frequencies, and shot noise at large frequencies.)