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When measuring the rotation velocity of a galaxy, most of the times we can only directly measure radial velocity, by looking at the redshift.

I read in a lecture slide that some times it is possible to measure the total velocity (not just radial) if the galaxy is in the local group and presents masers. The teacher didn't give more details, but I'm curious of how can it be done.

What properties of the masers allow for such a measurement and why the same can't be done with stars or gas clouds?

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Masers tend to be extremely bright, compact sources with line emission at cm wavelengths (usually from OH or H$_{2}$O molecules; this is a technique for gas clouds, albeit one that only works in special conditions). This makes them ideal for very long baseline interferometry (VLBI) with radio telescopes, which allows you to get extremely precise and accurate positions. In some cases, if you observe them repeatedly over periods of years, you can detect movement across the line of sight (i.e., proper motion). Since this is line emission, you can also measure the radial velocity from the Doppler shift of the line.

The canonical example is the circumnuclear gas disk in the nearby spiral NGC 4258 (well outside the Local Group), where maser emission spots in the disk have been observed to move with proper motions of $\sim 30$ mas/yr (and radial velocity changes of $\sim 10$ km/s/yr). The combination of this and observations of the disk geometry allows extremely accurate measurements of the central supermassive black hole's mass and the overall distance to the galaxy.

Of course, that isn't the "rotation velocity of the galaxy", it's the rotation of a sub-parsec-scale disk around the supermassive black hole. Large-scale rotation has been measured for the Local Group galaxy M33 (Triangulum) using VLBI observations of maser sources in H II regions over several years by Brunthaler et al. (2005).

It actually is possible to do something like this for individual stars in very nearby galaxies, if you can get accurate enough positions. This has been done with both HST data and (more recently) Gaia data for the Magellanic Clouds, M33, and M31 (e.g., van der Marel et al. 2019); proper motions of stars in the Magellanic Clouds has also been measured using ground-based telescopes (e.g., Niederhofer et al. 2021; it helps that the angular proper motions are large due to the closeness of the galaxies).

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