How does one compute frequency bandwidth based on FWHM

[TheCanadian]

In the following text the authors state:

"The full width at half maximum (FWHM) we measure is about 2 km/s"

and this is in the local standard of rest (LSR), $v_{LSR}$. I have seen basic doppler shift equations to convert from these velocities to frequency (shown below in link). Although if I consider the bandwidth to be 2 km/s and the frequency of 1720 MHz to correspond to ~-45 km/s, then the frequency bandwidth would be on the order of 100 MHz which doesn't seem to be quite right intuitively as masers are typically much narrower. Also, in the paper, they state they observe another OH line at ~30 km/s so I don't believe my above interpretation is correct.

 

[Zeke137]

So, 1720 MHz is the OH transition emission frequency of interest. the $v_{LSR}$ of ~ -45km/s is the observed redshift of that frequency due to the relative motion of the intervening OH cloud, and the 2km/s bandwidth is the FWHM line width, which is rather more than the 0.5 to 0.7 km/s expected thermal line width, and which leads the authors to suggest that "we are most likely seeing a blend of several maser spots along the line of sight."

As you state, another OH line at $v_{LSR}$ ~ -30km/s was also discovered in observations of other PSR's, and also due to OH cloud(s) between those PSR's and earth.

EDIT: So, the 1720 MHz frequency, and the 2 km/s bandwidth, and the $v_{LSR}$ of ~-45 km/s or ~30 km/s are unrelated to each other, apart from their being indicators of relative bulk movement or of masing properties of objects in the line of sight of the observations.