Dummies on dark matter 1 – the missing galactic masses

Jacinta: So here’s where we try to educate ourselves on dark matter, just for the fun of it.

Canto: But we’re serious. Our blog’s motto is ‘Rise above yourself and grasp the world’, supposedly from the wisdom of Archimedes, and he meant the universe, or would’ve.

Jacinta: Well, smarter guys than us are trying to grasp dark matter, with limited success it seems.

Canto: Yeah but they’ve been smart enough to recognise that there’s this missing matter, when they look at galaxies and find they’re spinner faster than their observed mass suggests they should, because physical laws apparently tell us that the greater the mass, the greater the gravitational effect, which would cause a greater spin towards the black hole sun, I think. But when astrophysicists measure a galaxy’s mass – which must surely be a tricky process, but I think it’s about measuring light spectra – different molecules give off different electromagnetic waves, though how they manage to measure all that is beyond me – anyway when they measure the galaxy’s mass and its spin, the numbers are off by orders of magnitude. I think.

Jacinta: Galaxies contain hundreds of billions of stars, I hear, so they must’ve built some impressive measuring technology. Okay, first research – from Physics LibreTexts:

The mass of [our] Galaxy can be determined by measuring the orbital velocities of stars and interstellar matter.

The article I’m quoting from focuses on our galaxy as a more or less typical example. Our sun is orbiting the galaxy’s centre (a black hole presumably?) at 200 kilometres per second, and it’s calculated that it takes about 225 million years for a full orbit.

Canto: Orbital velocity sounds so much more legitimate than spin, methinks.

Jacinta: So I want to put this explanation of the Milky Way’s proposed mass in my own terms to try to understand it better. Imagine the Sun’s roughly circular orbit around the galaxy, which is shaped somewhere between a sphere and a more or less two-dimensional disc. As Newton worked out, in the case of a sphere like Earth, gravity acts to pull everything towards the centre. Our Sun, which lies in an outer arm of the galaxy, gets whipped around at great speed due to the large mass between it and the galaxy’s centre (some 26,000 light years away). Kepler’s third law comes into play here…

Canto: His third planetary law (from the NASA Science website):

The squares of the orbital periods of the planets are directly proportional to the cubes of the semi-major axes of their orbits. Kepler’s Third Law implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit.

This was presumably simply an observational measurement from Kepler, but Newton and others found that, the further out from the Sun, the faster the planet moved, due to the greater accumulated mass in between. I think.

Jacinta: Uhh no. The period increases rapidly, not the velocity. The word ‘rapidly’ has led you astray. Naughty NASA Science website, it should have said that the period becomes longer, and not just because there’s a greater distance to travel but because the planet itself is revolving more slowly. Don’t forget that’s there’s relatively little, in fact very very very little mass, relatively speaking, added between Jupiter and the Sun than there is between Earth and the Sun. And here’s some figures: Earth is revolving round the Sun at about 107,000 km/h, Jupiter at around 47,051 km/h and Mercury at 170,500 km/h.

Canto: Okay, so galaxies are quite different from solar systems. So in the centuries after Kepler and Newton, astrophysicists used their theories, along with further developments, to measure the Milky Way’s mass, generally maintaining the theory that the vast majority of that mass lay between the Sun and the centre. This was assumed to be reasonable because:

The number of bright stars and the amount of luminous matter (meaning any material from which we can detect electromagnetic radiation) both drop off dramatically at distances of more than about 30,000 light-years from the galactic center.

But this assumption has turned out to be wrong, because we now know that there’s lots more matter well out from the centre, but it happens to be invisible – to us at least, and maybe to our instruments, but then if it’s undetectable how do we know it exists?

Jacinta: Well, Physics LibreTexts gives a good explanation:

We can understand how astronomers detected this invisible matter by remembering that according to Kepler’s third law, objects orbiting at large distances from a massive object will move more slowly than objects that are closer to that central mass. In the case of the solar system, for example, the outer planets move more slowly in their orbits than the planets close to the Sun. There are a few objects, including globular clusters and some nearby small satellite galaxies, that lie well outside the luminous boundary of the Milky Way. If most of the mass of our Galaxy were concentrated within the luminous region, then these very distant objects should travel around their galactic orbits at lower speeds than, for example, the Sun does. It turns out, however, that the few objects seen at large distances from the luminous boundary of the Milky Way Galaxy are not moving more slowly than the Sun.

So I added some italics to help us. If all the mass, or a vast majority, was located at the galaxy’s centre, as our sun with its massive mass is located at the centre of our local system, then this handful of luminous objects that are clearly part of our galaxy but further, sometimes much further, from the centre, should be travelling more slowly than the Sun, but instead they’re travelling faster.

Canto: Which presumably means unaccounted for mass, something to do with e = mc², more mass provides more energy, giving more velocity…

Jacinta: Yeah, something like. But light is a kind of energy, like electromagnetic energy, which presumably dark matter doesn’t have, but it must have energy if it has mass. Or must it?

Canto: Andrew Pontzen, in a Royal Institution lecture, tells us that, according to current calculations there should be five times more dark matter than visible matter, and it’s streaming through the planet, and our bodies, as we write…

Jacinta: Like neutrinos? Are neutrinos a kind of dark matter?

Canto: Ha, well that’s a good thought, maybe. Here’s a quote from an article in Nature India in early 2022:

Physicists have developed a mathematical model that may shed light on the identity of dark matter, the mysterious substance that far outweighs visible matter in the universe. Dark matter is not made of atoms or other known fundamental particles and doesn’t interact with any form of light or electromagnetic radiation, making it difficult to detect. The new model showed that a non-interacting or sterile neutrino is probably a dark matter particle and contributes to the mass of dark matter.

Jacinta: A sterile neutrino?

Canto: Yes, aka an inert neutrino – currently hypothetical, so outside of the Standard Model. The Wikipedia article on this is pretty comprehensive and complex… I’ll quote from the very beginning of the article, and then we can discuss it, hahaha:

Sterile neutrinos (or inert neutrinos) are hypothetical particles (neutral leptons – neutrinos) that interact only via gravity and not via any of the other fundamental interactions of the Standard Model. The term sterile neutrino is used to distinguish them from the known, ordinary active neutrinos in the Standard Model, which carry an isospin charge of ±+1/ 2  and engage in the weak interaction. The term typically refers to neutrinos with right-handed chirality (see right-handed neutrino), which may be inserted into the Standard Model.

Jacinta: Well, just to complicate this apparently dire situation of masses of matter or stuff we know nothing about, there’s also dark energy, which according to another Royal Institution presentation, this time by Peter Fisher in 2022, makes up even more of the unknown stuff in the universe than dark matter, leaving us in the dark about 96% of universal stuff. How can we be so incompetent?

Canto: Well, it’s an increasingly informed incompetence I’m sure. We’ve learned, as you say, that all the particulate matter-energy that we know about makes up only 4% of all there is, so now we (I mean you and I) need to learn how we (the astrophysics community) learned this.

Jacinta: About 73% of the unknown stuff is dark energy, 23% is dark matter. So let’s try to regurgitate Fisher’s talk in our own words, so that we can sound more informed.

Canto: Right so we start with the ‘big bang’ 13.7 billion years ago, followed by ‘inflation’, a very rapid expansion over a relatively short period, resulting in the cosmic background afterglow, after which the universe slows down markedly in its expansion thenceforward, with first stars and then galaxies developing. But then, after about half the life of the universe, it starts to expand slightly more rapidly, apparently due to dark energy.

Jacinta: Yes, according to an illustration I’ve seen before, and which we’ll post here, dark matter dominates in the first half of universe’s history, and dark energy dominates the second half.