How do we know how much our galaxy “weighs”?



If you look at the sky on a clear night and at the right time of year, you can distinguish a dense strip of stars that stands out from the rest of the sky. That starry band is the galaxy in which we live, the Milky Way, a grouping of between 100,000 and 400 billion swirling stars in a spiral disk about 100,000 light-years in diameter. Now, we are not able to perceive the true geometry of the Milky Way with the naked eye because our solar system is tucked into this disk of stars, so we see that spiral disk “singing” in the sky.

But, although the true shape and size of that starry strip can be deduced by measuring the position and velocity of the stars around us, how about its mass? How do we know how much “weight” all the matter in our galaxy weighs?

Gravitational problem

Leaving aside the absurd option of placing the galaxy on a gigantic cosmic scale, it could give the impression that the easiest way to estimate the mass of the Milky Way is to count the number of stars in a given region of space, measure its average mass and extrapolate that figure to the rest of its volume. But, in reality, this figure would give us a very wrong figure because only 5% of the mass of a galaxy is made up of ordinary matter, the type of substance from which the things we can see are composed, such as stars or planets . The remaining 95% is dark matter, a type of matter that does not emit or reflect light. Therefore, if we start counting stars to estimate the mass of the Milky Way we will be very short, because we will be ignoring 95% of the mass of the galaxy that we are unable to see.

Luckily, having masses, the presence of dark matter manifests itself through the effects of its gravity. And, as Newton’s laws allow estimating the mass of a celestial body from the velocity and radius of the orbit of any of the bodies that circle around it, astronomers are able to calculate the mass of galaxies based on in the movement of their satellites … Although, in this case, these satellites are not rocky bodies like the Moon, but other smaller galaxies.

With this in mind, the mass of our galaxy has been calculated thanks to Leo I, a small spheroid galaxy that orbits the Milky Way beyond its halo of dark matter, so that all this invisible mass is reflected in the estimate. In this case, after measuring Leo I position changes between 2006 and 2011, a 2012 study concluded that the orbit of this small galaxy requires that the mass of the Milky Way be about 3 trillion times greater than that of the Sun, although the margin of error of this figure exceeded 50%. That same year, another study refined the accounts a little more and estimated that there is a 90% chance that the Milky Way has a mass of between 1 and 2.4 billion solar masses.

But there is another method that gives us a more accurate figure.

Rewinding time

The constant expansion of the universe tends to move galaxies away from each other, but those that are close enough to each other attract enough force to remain in mutual orbit. Taking this into account and simplifying greatly, the so-called “timing argument” assumes that the position of two points that are in orbit today has not changed much in the last 13.8 billion years and uses this data to estimate how intense they have had that be their gravitational interactions to explain their current separation and, therefore, the magnitude of their mass.

In this case, a 2020 study applied this method to 32 stars of the outer halo of the Milky Way that are more than 60 kilometers from the galactic nucleus. The reason why such distant stars were chosen is that they are objects that have completed few turns around the galaxy since they were formed, so their orbits are less likely to have been disturbed during this time. And, based on the analysis of the movement of these 32 stars, it was concluded that the minimum mass of our galaxy is 0.91 billion solar masses, but that the most likely value is around 1.4 billion masses solar, a figure that fits the rest of the estimates and their margins of error.

As you may have noticed, estimating the mass of that starry strip we see in the sky is a much more convoluted task than it may seem because both our eyes and our telescopes detect only a tiny fraction of all the matter it contains. But precisely that is why the laws of physics are so valuable: they allow us to detect phenomena that are beyond the reach of our senses and discover new aspects of the universe that we could never have imagined.

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