Artwork depicting gravitational waves distorting space, changing the way neutron star pulses arrive at Earth. Credit: David Champion
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Artwork depicting gravitational waves distorting space, changing the way neutron star pulses arrive at Earth. Credit: David Champion

Pulsars, black holes, spacetime, and the search for the center of the solar system

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Jul 3, 2020

“If there’s a shining center of the solar system, you’re on the planet it’s farthest from.”

                        — with apologies to Luke Skywalker


Astronomers have figured out how to find the center of mass of the solar system. And that in turn will help them use überdense stars spinning faster than the blades on a kitchen blender to find gigantic black holes across the Universe that are eating each other.

Right. As you might expect, there’s a bit of a backstory here.

OK, first of all, you might think the location of the center of mass of the solar system is obvious: The center of the Sun. It has 99.8% of all the mass in the solar system, after all!

But that’s not correct. If the planets had no mass, then yeah, the center of the Sun would be the center of mass. But planets do have mass, and that means their gravity pulls on the Sun as well, changing the location of the center of mass, what we call the barycenter.

Two objects of different masses orbit each other; the more massive one makes a little circle and the lower mass one a bigger circle. Credit: NASA/Spaceplace

The location of that point depends on the mass of the planet and how far it is from the Sun. Jupiter dominates here, since it has the most mass of all the planets, but the other planets contribute, too. Worse, they’re all in motion, so the actual barycenter of the solar system is constantly spiraling around as well.

The way to figure out the exact location of the barycenter is to know exactly where the planets are at all times, but that’s extremely difficult to do. Even with spacecraft visiting these other planets there’s only so accurate a measurement we can make on their location, especially over time. And that, it turns out, is not enough for some kinds of scientific measurements.

What kinds? OK, a very slight digression here.

Artwork depicting two black holes orbiting each other. Note the spins don't align. Credit: LIGO/Caltech/MIT/Sonoma State (Aurore Simonnet)

When two supermassive black holes orbit each other they emit what are called gravitational waves, literally ripples in the fabric of spacetime (OK, so this is maybe more than a slight digression). These waves can be detected on Earth as extremely small distortions in distances between two objects — and I mean far smaller than the diameter of a proton, so very small. Still, gravitational wave observatories like LIGO and Virgo have succeeded in measuring them.

They detect the waves created just before and during the merger. But in the years leading up to that moment the black holes are still giving off these waves, but the frequency of the waves is much lower. Detecting those waves is much harder, but scientifically useful. So astronomers came up with a genius idea. Use millisecond pulsars.

Yeah, we’re going to need another digression.

Pulsars are superdense neutron stars, the leftover cores of massive stars that have exploded. They have ridiculously strong magnetic fields, and these can focus twin beams of energy blasting away from the neutron star. As the neutron star spins these beams sweep across space like beams from a lighthouse, and on Earth with radio telescopes we see them as regular blips, or pulses. That’s why they’re called pulsars.

Some pulsars spin incredibly rapidly, hundreds of times per second. We call these millisecond pulsars, and their pulses are fantastically regular, like the Universe’s own ticking clocks.

However, if a gravitational wave passes through the pulsar it distorts the timing of the pulse arrival at Earth, which means that in principle timing the exact arrival of these pulses can be used to measure gravitational waves! The merging black holes are literally warping the shape of our galaxy, subtly changing the distances between pulsars, and that may be detectable. Amazing.

You need a lot of pulsars distributed throughout the sky to do this, and astronomers all over the world observe about a hundred such millisecond pulsars to see if it can be done. This group is called the International Pulsar Timing Array, made up of several different groups looking at different pulsars.

But there’s a problem. As the Earth orbits the solar system’s barycenter (aha! The digressions are over and we’re back on track) it also changes the arrival time of the pulsar blips. Sometimes the Earth is closer to the pulsar, sometimes farther away, and astronomers need to compensate for that or else the timing measurements would be hopelessly off; so much so that it would overwhelm the tiny change due to any gravitational waves. To be able to see gravitational waves well using all these pulsars, the solar system barycenter needs to be known to less than about 100 meters.

Current orbital calculations for the planets aren’t that accurate. Also, the ones currently used don’t typically give the uncertainties in their measurements, which is important in figuring out how far off things might be.

Artwork depicting gravitational waves distorting space, changing the way neutron star pulses arrive at Earth. Credit: David Champion

So, to help, a team of pulsar timing astronomers looked at the equations statistically. They used Bayesian statistics, which I’ve talked about before. It’s a way of using prior knowledge of the situation and including it in the math, learning from the results. By doing this they hoped to get a handle on the uncertainties in the location of the barycenter so that they could then zero in on it.

The math is a tad complex, but in the end… it worked! They were able to nail down the solar system’s barycenter to about 100 meters, and the method can be used to get much better timing on the pulsar pulses. They found the biggest influence on the math was Jupiter, and data from the Juno spacecraft will, over the next few years, hopefully allow them to better calculate its orbit to make the aim of this statistical barycenter method even better.

It may still be some time before the pulsar array can start to detect gravitational waves. Most likely what they’ll find first is the gravitational wave background; the noise from all the combined black hole mergers from all over the Universe at the time (like walking into a crowded bar and hearing the noise from all the people talking at the same time before being able to pick out individual voices). But there’s important science in that as well, and this new barycenter finder will help them get to it.

Knowing how to find the center of mass of the solar system sounds mundane, but once you have it you can unlock incredible science: Using millisecond pulsars to find supermassive black holes eating each other clear across the visible Universe!

In science, nothing is mundane. It all fits together, as it must. It’s describing everything.

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