What is meant by the velocity of a star?

Question

I recently read somewhere that among other things like size, radius, distance from earth, luminosity, age, etc of a star, velocity was another variable. What is exactly meant by the velocity of a star?

Answer 1

It's pretty natural to think that a star can have velocity - there's no reason a star shouldn't be able to move. The first thing you need to know is "velocity relative to what?" Stars in our galaxy are all in some kind of orbit around the galaxy, so you can talk about velocity in galactic coordinates. Binary stars orbit each other, so you can talk about their velocity in the centre-of-mass frame of the binary. The CMB unambiguously defines another rest frame that you could measure relative to (particularly for extragalactic objects, though it's hard to see individual stars much beyond our galaxy). You could also measure the velocity offset from a systemic velocity, such as in another galaxy, by subtracting the mean motion of all the other stars in the system. And many more options.

Once you've picked a frame, how do you actually go about measuring the velocity? Well, you can only measure velocity in one frame, that of your equipment (getting to velocity in another frame is then just a matter of coordinate transformation). There are 3 components to the velocity - two are "in the plane of the sky", these together are called the "proper motion". A proper motion has a magnitude (how fast) and one angle to specify a direction in the plane of the sky (or any equivalent representation of a 2 component vector). The third is along the line of sight, and is called the "line of sight velocity" (technically this is a scalar and should be called a speed, I guess). The velocity gets split up this way because the components are measured very differently.

Proper motion is by far the more difficult to measure, in practice. In theory all you do is watch the star to see how far it moves in a time interval to get a speed, but this is complicated because (1) you need some reference "stationary" object to measure against and (2) most stars move very slowly, in terms of angle travelled on the sky. For a stationary reference, any object far enough away is in practice stationary. But most things that are far enough away are galaxies, and galaxies are "extended objects" (as opposed to point like stars). This makes defining their exact positions difficult. Quasars are a good choice, they're very far away and point-like, but somewhat rare, so there's not always one available near a star one wants to measure. Usually what's done is to look at many stars that are nearby and look for a set of stars that don't appear to move relative to each other - these will be the most distant stars in the field that are "far enough" that their angular motion is nearly zero. The proper motion can then be measured relative to them. Typical proper motions for reasonably nearby stars are measured in milliarcseconds per year. A milliarcsecond is $\frac{1}{1.296\times10^{9}}$ of a circle. And since the measurement needs to be made over a time interval, one needs to worry about the motion of the Earth around the Sun (parallax), and the motion of the Sun through the galaxy when interpreting the measurements. The Gaia mission, under way, plans to have a precision of about 24 microarcseconds. At this level of precision, the joke is that everything in the sky will move. This is close enough to true, Gaia should be able to get a proper motion for every star it can see (which is meant to be $>10^9$ of them) - it's going to be a pretty revolutionary data set. Just about the only upside with proper motions is that it's easy enough to measure many stars at once - just get good images of the same piece of sky on different dates (ideally years apart).

Line-of-sight velocities are comparatively much easier to obtain. All that's needed is a spectrum of the star showing some absorption line features from the stellar atmosphere. One does need to be a bit careful not to pick a spectral feature due to e.g. absorption by some gas along the line of sight. Once a spectral feature is identified, just measure the wavelength and compare to the rest wavelength of the same feature measured in a lab on Earth using the Doppler shift, and you have a line-of-sight velocity. Precision is limited mostly by the width of the line (the sharper the better) and the apparent brightness of the star (easier to get a high-resolution spectrum of a brighter star). The downside is that it's harder to get large numbers of line of sight velocities since getting spectra means placing slits or optical fibers on the field, which needs to be customised for every exposure. This is becoming somewhat less true with the increasing availability of integral field units.

Answer 2

I would guess that given that the book was designed to teach amateur astronomers that most of the book refers to measurements made with reference to earth. Now, you can measure the component of velocity along the distance line between the star and the earth by using the doppler effect and the adsorption lines for particular elements(measuring the adsorption spectra in a lab and of the star). This is a common measurement in astronomy, and the only common one I can think of involving velocity. Therefore, I think it is almost certain this is the velocity to which it refers.