For astronomers, looking at the sky can be like watching an unfamiliar sport on TV. We can’t make sense of what we see, but is it because we don’t know the rules, or we can’t see all the players? (Or, worst case, we can’t see the players and we don’t know the rules) For us, the players are the stars, and our best guess for the rules is the laws of motion (and gravity) that Newton wrote down around 350 years ago.*from

The key problem is that when we look at galaxies – the huge collections of stars (including our own Milky Way) that are the largest “building blocks” of the universe – stars within galaxies are moving much too fast for their mutual gravitational fields to be able to hold the galaxies together.

Two solutions are possible. If there are large quantities of dark matter its gravitational field could provide a skeleton that stops the galaxies from coming apart. Alternatively, if gravity works differently at huge distances from the way it behaves in the solar system we might be able to manage without dark matter. Dark matter adds extra players in the game, but modified gravity changes the rules.

Most (actually, almost all) astrophysicists prefer dark matter to modified gravity. Neither is perfect: dark matter does a much better job of explaining the properties of the universe on very large scales but there are many open questions about the dynamics of galaxies themselves. And physicists have no idea what dark matter would be made of, even if we do know that it has to be something fundamentally new – likewise, if gravity works differently on galactic scales than it does at smaller distances, we would need a radical rethink of fundamental physics.

Part of the challenge is that we can’t directly measure the gravitational force exerted on a single star by everything else in the galaxy. Newton’s Second Law, “F=ma” tells us that force is proportional to acceleration. Stars move very quickly (the sun travels at 220 km/s relative to the galaxy as a whole; 300 times faster than a speeding bullet) but accelerate — change their motion — very slowly. In roughly 100 millions years time, the sun will be on the other side of the Milky Way from where it is now, with its direction of motion reversed. But the acceleration needed to make this happen changes the sun’s velocity by less than one centimetre per second per year, roughly the speed at which an ant walks.

Change in velocity (in the line of sight and in proper motion) over ten years, relative to the sun.

However,Hamish Silverwood (Barcelona) and I (Richard Easther, Auckland) recently realised that “next to next” generation stellar spectrographs may actually be able to detect these tiny changes, and thus measure the force exerted on individual stars by all the other mass in the galaxy. This work was posted to the ArXiV; we calculate the likely changed in stellar velocities as a function of their distance from sun, showing that more distant stars undergo a larger change in velocity, they will be more difficult to observe since their greater distance makes them fainter.

The instruments we would use to measure these tiny velocity changes are being developed to find planets around distant stars, and these planets may present the biggest challenge to this sort of measurement.  As a planet moves in its orbit it induces a small change in the speed of the parent star, like an adult and a child on a see-saw; for an earth-like planet moving round a sun-like star, the change is a few centimetres per second per year; the signal we would need to detect will be roughly this size after a decade of observations. A key challenge will thus be disentangling the motion induced by planets, which – ironically – is precisely what motivated the construction of these spectrographs in the first place.

Interestingly, a group based at Michigan and Harvard were simultaneously and independently working on the same idea; their work appeared together with our paper, and they looked in detail at the challenge of removing the planetary component to reveal the the underlying acceleration. The biggest issue will be large slow-moving planets in distant orbits (“cold Neptunes”) which could mimic the slow changes in speed expected from the galactic gravitational field. However, if we observe many stars we would expect that their planets will be randomly aligned, hopefully allowing the underlying signal to be extracted.

If you can directly measure the gravitational forces on stars you can answer a huge range of questions. You can test directly predictions of modified gravity theories, which differ in detail from a model of a galaxy with dark matter and Newtonian physics. Likewise, if dark matter is holding the galaxy together, the distribution of dark matter with the galaxy may be irregular on small scales, and acceleration measurements would directly map the distribution of dark matter.

None of this will happen soon – our calculations assumed a ten year baseline for the changing speeds to become apparent, and next-generation of high-precision instruments that can be attached to a brace of giant telescopes are now under construction. On the other hand, the challenge of explaining the motion of stars within the galaxy is over 100 years old, so even if there would be a long wait before we could put them to use, it is well worth exploring the potential of novel techniques to probe the large scale properties of gravity.

 

* We know that Einstein’s General Theory of Relativity supersedes Newton’s laws in some circumstances (including descriptions of the global behaviour of the expanding universe) but for  the behaviour of stars the two theories make overlapping predicitions.