Estimation of Newtonian noise from the KAGRA cooling system

KAGRA is the first kilometer scale gravitational wave detector to be constructed underground and employ cryogenics to cool down its test masses. While the underground location provides a quiet site with low seismic noise, the cooling infrastructure is known to generate large mechanical vibrations due to cryocooler operation and structural resonances of the cryostat. As cooling system components are relatively heavy and in close proximity to the test masses, oscillation of gravity force induced by their vibration, so-called Newtonian noise, could contaminate the detector sensitivity. In this paper, we use the results from vibration analysis of the KAGRA cryostat to estimate cooling system Newtonian noise in the 1–100 Hz frequency band. Our calculations show that, while this noise does not limit the current detector sensitivity or inspiral range, it will be an issue in the future when KAGRA improves its sensitivity. We conclude that KAGRA may need to implement Wiener filters to subtract this noise in the future.

Figure 1

(a) A simple hollow cuboid cooling system TM configuration is considered to derive the Newtonian noise expression. The TM is located at the origin, and the cuboid is split into N elements each weighing $m_n$ and denoted by the gray squares. (b) Newtonian force on TM due to a single element on the cooling system at position $\overrightarrow{r}(x_n,y_n,z_n)$ is ${\overrightarrow{F}}_{\mathrm{TM}}$. The mass is being displaced (vibrating) by a small amount $\overrightarrow{d}(u,v,w)$, such that $|r|\gg |d|$. The coordinate system considered is shown with purple arrows and the $x$-axis is parallel to the optical axis.

Figure 2

Coordinate system and summary of components considered in the Newtonian noise calculation. Cross section of KAGRA cryostat showing the components (chamber, baffle, breadboard, inner shield, and outer shield) considered for the Newtonian noise calculation. The blue arrows denote the coordinate system. The test mass is considered as a point mass, located at origin as denoted by the purple dot.

Figure 3

(a) Mesh generated and 2D drawing for the breadboard. The cuboid is divided into 33,250 elements each weighing 2.634 g. (b) 3D scatter plot where each dot represents an element n from breadboard mesh while the color is value $S_{n_{\text{breadboard}}}$ of that element in Eq. (11).

Figure 4

(a) Front view of the breadboard, being displaced X $\mathrm{m}/\surd \mathrm{Hz}$. The dotted green circle represent mass that causes gravity fluctuations. (b) A simple point mass representation of Fig. 4 showing relative position of test mass and breadboard point masses m.

Figure 5

(a) Mesh generated for baffle. The cylinder is divided into 29,601 elements each weighing 0.24 g. (b) 3D scatter plot where each dot represents an element n from baffle mesh while the color is value $S_{n_{\text{baffle}}}$ of that element in Eq. (16).

Figure 6

(a) Mesh generated for inner shield with 200,935 elements each weighing 2.4 g. 2D drawing showing top and front view of 8 K shield. (b) 3D scatter plot where each dot represents an element n from inner-shield mesh while the color is value $S_{n_{8\mathrm{K}}}$ of element in Eq. (19).

Figure 7

(a) Mesh generated for outer shield with 262,889 elements each weighing 1.97 g. 2D drawing showing top and front view of 80 K shields. (b) 3D scatter plot where each dot represents an element n from outer-shield mesh while the color is value $S_{n_{80\mathrm{K}}}$ of that element in Eq. (22).

Figure 8

(a) Mesh generated for cryostat with 124,795 elements. Cryostat was split into three parts and the green dots represent the position where vibrations $u_{\mathrm{top}}$, $u_{\text{middle}}$ and $u_{\text{bottom}}$ were measured. (b) 3D scatter plot where each dot represents an element n from cryostat mesh while the color is value $S_{n_{\text{cryostat}}}$ of that element in Eq. (24).

Figure 9

Vibration spectra of various components considered during Newtonian noise estimation.

Figure 10

Comparison of Newtonian noise strain spectral density from each component, the largest contribution comes from breadboard followed by radiation shields, cryostat, and baffle. Note that the force on the test mass due breadboard/radiation shields and cryostat/baffle are in opposite directions.

Figure 11

(a) Comparison of KAGRA design sensitivity and requirement to cooling system Newtonian noise in 1–100 Hz bandwidth. Cooling system NN is below KAGRA design sensitivity but several peaks due cryocooler operation and structural resonances are larger than the requirement. Vibration source of these peaks and contributing component are summarized in Table 2. (b) Comparison of KAGRA inspiral range with and without cooling system Newtonian noise. Note that the $x$-axis represents mass of a component object, assuming equal mass binaries.