The Galactic Center IRS 13E cluster is a very intriguing IR object located at \sim 0.13 pc from Sagittarius A ^ { \ast } ( Sgr A ^ { \ast } ) in projection distance .
There are both arguments for and against the hypothesis that a dark mass like an intermediate mass black hole ( IMBH ) exists in the cluster .
Recently we have detected the rotating ionized gas ring around IRS 13E3 , which belongs to the cluster , in the H30 \alpha recombination line using ALMA .
The enclosed mass is derived to be M _ { \mathrm { encl . } } \simeq 2 \times 10 ^ { 4 } M _ { \odot } , which agrees with an IMBH and is barely less than the astrometric upper limit mass of the IMBH around Sgr A ^ { \ast } .
Because the limit mass depends on the true three-deminsional ( 3D ) distance from Sgr A ^ { \ast } , it is very important to determine it observationally .
However , the 3D distance is indefinite because it is hard to determine the line-of-sight ( LOS ) distance by usual methods .
We would attempt to estimate the LOS distance by spectroscopic informations .
The CH _ { 3 } OH molecule is easily destroyed by cosmic ray around Sgr A ^ { \ast } .
However , we detected a highly excited CH _ { 3 } OH emission line in the ionized gas stream associated with IRS 13E3 .
This indicates that IRS 13E3 is located at r \gtrsim 0.4 pc from Sgr A ^ { \ast } .