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What Does the Milky Way Look Like? Astronomers Use High-School Math to Find Out

We have stunning shots of other galaxies but we don’t exactly know what the Milky Way itself looks like. Large parts of it that lie on the far side from where we are are obscured by thick dust clouds.

A computer-generated image of the Milky Way galaxy. Credit: NRAO

A computer-generated image of the Milky Way galaxy. Credit: NRAO

It is a constant source of amazement how much we know and don’t know about our universe at the same time. For example, we’ve seen some of the most distant stars but we struggle to agree about whether there’s a planet in the outer Solar System. We’ve detected gravitational waves emanating from blackholes that collided billions of years ago but we’re yet to fully understand the supermassive blackhole at the Milky Way’s centre. The Breakthrough Starshot project wants to send swarms of probes to Proxima Centauri within the next decade but we don’t exactly know what the Milky Way looks like (because we’re inside it). Such fascinating contradictions – to understand which we will have to revisit the different kinds of astronomical probes humankind has used across time. But that’s for a different day.

What’s for today is a new study that has a plan to determine what the Milky Way looks like in the next 10 years. The Milky Way is a spiral galaxy 100,000 lightyears across. The Solar System is a speck sitting on one of the spiral arms. Excluding colliding blackholes, most astrophysical phenomena we’ve studied have been events happening within the Milky Way itself. Even the total number of exoplanets we’ve confirmed till date outside the galaxy? Zero. That says a lot about how much we’ve left to explore and learn: significantly more than 99% of all that’s out there. And the far side of the Milky Way is, wondrously enough, part of that 99%. This is because that part of the galaxy is obscured by massive clouds of dust, which block a lot of the radiation from there from reaching us.

However, astronomers from Germany and the US recently announced that they had used the Very Long Baseline Array (VLBA), a set of 10 radio telescopes located across the US, to discern the presence of water molecules in a star-forming region of the Milky Way located a staggering 66,500 lightyears away. “This is the farthest distance measurement ever obtained by trigonometric parallax,” Alberto Sanna, a researcher at the Max Planck Institute for Radio Astronomy, Bonn, and one of the authors of the study, told The Wire. “We almost double the previous record of 36,000 light years!”

But it isn’t as simple as pointing the telescope in the right direction and reading the data. The astronomers were trying to trace the path of the molecules as they moved across the spiral arm they were on. The end goal was to acquire their galactic latitude, longitude and the velocity at which the arm they were on was travelling around the Milky Way’s centre.

So, to achieve all this, they fell back on chapters from high-school math and physics. Specifically, they used simple trigonometry and parallax.

VLBA’s ten telescopes work together as a single large telescope, a technique called long baseline interferometry. The more the distance between the farthest telescopes (i.e. baseline), the more the resolving power of the system as a whole. VLBA has a maximum baseline of 8,611 km – so imagine one giant telescope with a dish diameter running from Lucknow to Lisbon. Because of this size, a signal coming from distance sources in the universe will impinge on each telescope at a different time. So they’re each equipped with an atomic clock to precisely record the time of impingement, as well as to help coordinate between themselves to keep the source in focus.

The difference in times at which the signals are recorded provides some information about where in the universe the source is located. To understand this, imagine a hundred people standing in a large circle, and someone firing a gun into the air from somewhere within that circle. If the firer is standing closer to one part of the circle, the people there will hear the shot at a time earlier than those in the other parts. If all of them hear the shot at the same time, then it could only mean that the firer is standing at the centre. This is sort of like an audio parallax.

The astronomers took this a step further. They used the VLBA to first detect some microwave radiation emitted by water molecules in the far side of the Milky Way. “We first selected regions of strong maser emission in the galaxy from previous surveys, then we targeted them with the VLBA, which allows us to zoom in on the [microwave] sources in great detail,” Sanna said. He added that these sources of radiation “act like lighthouses along the spiral arms of our galaxy, which make them suitable tools to reconstruct the spatial morphology of those spiral arms. Also, because they are so bright they can be observed with the VLBA, at variance with other signals which are emitted by thermal processes.”

Then, to pinpoint the precise location of the molecules itself, they used Earth’s revolution around the Sun to their advantage by invoking the deceptively mundane parallax effect.

Look at an object in front of you – like your desk. If you had both eyes open and looked at the desk, it’s going be in one position. Let’s call this P. If you closed one eye and looked at it, the desk is going to be a little to the right of P. If you closed the other eye and looked at it, the desk is going to be the same distance but to the left of P.

In this example, you were sitting in one place and looking at the desk. But if you were a big telescope sitting on a planet moving around the Sun, things are a little different. When you had only one eye open, that’s the same as the VLBA looking at P – the source of the microwave radiation – from one point in Earth’s orbit. If you had the other eye open, that’s the same as the VLBA looking at P from the diametrically opposite point in Earth’s orbit. The real difference kicks in when factoring the shape of Earth’s orbit itself: approximately a circle.

As Earth, with the VLBA, goes around the Sun, its position in its orbit can be computed using two numbers: distance along the x-axis and distance along the y-axis. Think of the VLBA as a black dot, and its position along the two axes as blue and red dots, and then look at the animation below (ignore the ‘real’ and ‘imaginary’ labels):

Credit: acs.psu.edu

Credit: acs.psu.edu

Notice how the distance of the blue dot from the centre – where the Sun is – varies in the form of a sinusoidal function (right bottom panel). If the dot’s position to the Sun’s right is taken to be positive and to the Sun’s left to be negative, we get a curve that spends half its time above the horizontal and half its time below. This curve traces the path of the sine function in trigonometry.

When you transplant the circular motion of Earth onto a sine curve, the distance of the shift from P will be exactly half of the total height of the curve, from its highest point to the lowest. This is because the highest point of the curve corresponds to one eye being open and the lowest point, to the other eye being open. So in their sine data, the astronomers found that half of the total height of their sine curve to be 0.049 milli-arcsecond. In other units, it is approximately 66,500 lightyears.

The astronomers write in their paper, published in the journal Science on October 13, that the results of their trigonometric parallax method agree with those of a statistical method that used information about the distribution of gas clouds in the galaxy as well as that of a previous study published in August 2016. The latter inferred the distance to the star-forming region by studying its motion in the sky relative to the plane of the Milky Way.

This is a study in observing something across tens of thousands of lightyears using motion. The astronomers wanted to know how a spiral arm of the Milky Way located almost directly behind our Sun, and all the way across the other side of the galaxy, moved. But when they couldn’t make a direct detection, they resorted to using the quirks of motion themselves. They forced the subject of their study to reveal itself in different perspectives, and then used geometry to translate those revelations into location data.

Sanna is now looking forward to future possibilities: “We are conducting a large survey towards hundreds of these star-forming regions in the Milky Way, essentially all those suitable for accurate trigonometric parallax measurements. Under some conditions, e.g. assuming a given galactic rotation curve, we can make a guess on where a star-forming region would lie, if those conditions were correct, and then test it with our direct measurements.”

His and his team’s study is part of a larger project called the BeSSeL Survey, which aims to “study the spiral structure and kinematics of the Milky Way”. And with their record-breaking new measurement now behind them, he predicts that within the next 10 years, “we will be able to answer the question: what does the Milky Way look like?”

Social image credit: esoastronomy/Flickr, CC BY 2.0.