What spectral feature was used to confirm that S0-2 is "single and available"? What is Brγ? The Phys.org article Astronomers discover S0-2 star is single and ready for big Einstein test describes the results of a careful analysis of radial velocity measurements of the star S0-2, which orbits the supermassive black hole at the center of our (Milky Way) galaxy with a period of only 16 years. The paper itself (Devin S. Chu et al, 2018) is available for open access at ArXiv, and also ApJ.

The only mention of the word wavelength is in Section 2.2:


  The radial velocity of S0-2 is measured from both data sets by fitting a Gaussian to the Brγ absorption line.


What exactly is a Brγ ("Br" + gamma) absorption line?



below: "The orbit of S0-2 (light blue) located near the Milky Way's supermassive black hole will be used to test Einstein's Theory of General Relativity and generate potentially new gravitational models. Credit: W. M. Keck Observatory (Click for full size)
Brγ is a line in the emission spectrum of Hydrogen, or single-electron (and therefore) hydrogen-like Rydberg atoms in general. In particular, it is the emission due to an electron moving from the 7th to the 4th energy level.

Br is short for Brackett, after Frederik Brackett, and gamma because 


$\alpha: \ \ 5 \rightarrow 4,$ 
$\beta:  \ \ 6 \rightarrow 4,$ 
$\gamma: \ \ 7 \rightarrow 4,$ 


...and so on.

Brγ has a wavelength of 2166nm, as you would get from the Rydberg formula, which is well in the infra-red part of the spectrum. It is probably chosen as it has low absorption by the dust towards the centre of the galaxy.

Screenshot from here.