galaxies - Andromeda/Milky Way collision: How, and how accurately, can a galaxy's lateral velocity be measured?

Some sources suggest that the Andromeda Galaxy is likely to collide with our own in approximately 3 to 5 billion years.

We can estimate the distance to the Andromeda Galaxy using various techniques, including measuring the apparent brightness of Cepheid variable stars; its distance is currently estimated to be about 2.5 million light-years.

We can measure its radial velocity (i.e., the rate at which it's either approaching or receding from us) using Doppler shift. One source, the same Wikipedia article I linked to above, indicates that its radial velocity with respect to the Sun is about 300 km/s in our direction; another article says the radial velocity relative to our galaxy is about 120 km/sec, also in our direction. (Presumably the difference is due to the Sun's orbital motion around the core of the Milky Way.)

But that's just the radial component of the velocity. Taking the 120 km/sec figure, it could be moving directly toward the Milky Way (more precisely, its core could be moving directly toward the core of the Milky Way) at 120 km/sec, or it could be moving at a 45° angle at about 170 km/sec, or any of a number of other possibilities.

Without an estimate of the lateral component of the velocity, there's no way to be sure whether the collision will occur or not. I'm reasonably sure we can't measure the lateral velocity directly; 120 km/sec over a century would cause Andromeda to move only about 0.04 light-year (if my calculations are correct).

And yet this Wikipedia article says:

The best indirect estimates of the transverse velocity indicate that it is less than 100 km/s.

with a reference to "Abraham Loeb, Mark J. Reid, Andreas Brunthaler and Heino Falcke The Astrophysical Journal, 633:894–898, 10 November 2005", but the link is invalid.

So how can a galaxy's lateral velocity be measured, or at least estimated? How accurate can such an estimate be with current technology? Can we expect improvements in the near future?

Answer

There's new information on this, just released today (Thu 2012-05-31).

According to this study, based on Hubble data, M31 is on course for a head-on collision with the Milky Way.

Previously, it was unknown whether the far-future encounter will be a miss, glancing blow, or head-on smashup. This depends on M31's tangential motion. Until now, astronomers have not been able to measure M31's sideways motion in the sky, despite attempts dating back more than a century. The Hubble Space Telescope team, led by van der Marel, conducted extraordinarily precise observations of the sideways motion of M31 that remove any doubt that it is destined to collide and merge with the Milky Way.

"This was accomplished by repeatedly observing select regions of the galaxy over a five- to seven-year period," said Jay Anderson of STScI.

The collision will start in about 4 billion years. After an additional 2 billion years, the two galaxies are expected to merge into a single elliptical galaxy.

It is likely the Sun will be flung into a new region of our galaxy, but our Earth and solar system are in no danger of being destroyed.

Phil Plait, the "Bad Astronomer", discusses the findings here, and this article has more information (including that the Triangulum galaxy M33 will likely take part in the festivities, and might even hit the Milky Way before M31 does).

It should be an impressive show, but don't start stocking up on popcorn just yet.

The cool thing about this is that we're now able to measure lateral motion of stars in another galaxy. (The really cool thing about this is, hey, colliding galaxies!)