Squinting through their telescopes at the twinkling heavens, few 19th century astronomers would have imagined the cosmic wonders awaiting discovery in the century to come.

Stars so dense, a teaspoon of their matter would weigh as much as a mountain. Objects so compact, literally nothing could escape its gravity. Even galaxies had yet to be revealed in all their sparkling glory.

Theory and technology have opened up the Universe, allowing us to not only see the invisible, but to hear the very footsteps of dark, distant giants. It's hard to believe anything could remain hidden from us out there, yet there are still hypothetical objects that will make your head spin.

Perhaps future astronomers will pin them down.

Black dwarfs

Once they've exhausted their fuel, suns like ours are destined to become Earth-sized spheres of highly compact material, where every cubic centimeter weighs about a tonne. While they continue to glow white hot with leftover heat, we can call these objects white dwarfs.

Since white dwarfs no longer actively squeeze the living daylights out of fusing atoms, they do cool. Eventually. In about a hundred million billion (more or less) years they'll finally be at equilibrium with the background temperature of their environment and completely dark.

Our Universe is barely much older than 13 billion years, so there's no point in looking yet. Give it time, though, and our sky will one day be a graveyard of star corpses we call black dwarfs.

Likelihood of them existing: Near certain (just be patient).

Thorne–Żytkow object

Fortunately, our Sun's retirement is still a few billion years in the future. Before it switches off its engines and becomes a stellar boomer, our nearest star will loosen its grip on its atmosphere and let its waistline go to fatten into a red giant.

It's not entirely clear if the baked remains of future Earth will sit inside the boundary of the bloated star, or if the steady loss of the Sun's mass would cause its orbit to drift sufficiently.

If our planet were to take a hot dip, the constant wash of plasma slapping its surface would be more than enough to put the brakes on its orbit, causing it to spiral inward to its doom in no time.

But what if our planet wasn't a wimpy ball of rock, but something with heft, like another star? Could it hang around at least a little longer, circling the guts of its red giant companion like a cosmic goldfish inside its infernal fishbowl?

That's the idea behind a Thorne–Żytkow object. It's named after physicists Kip Thorne and Anna Żytkow, who in 1977 crunched the sums on the melding of a red supergiant and a neutron star under a particular set of circumstances.

By their calculations, a neutron star could wobble about inside the red giant for as long as a couple of centuries before eventually merging with the core, either forming a heavier neutron star or, if the mass was right, collapsing into a black hole.

Back in 2014, the astronomical community thought they might have found an example of such an object in the star HV 2112. Not all researchers are convinced it's the real deal, leaving the existence of these hypothetical hybrids unconfirmed.

Likelihood of them existing: Pretty likely (the numbers add up - we just need to find one).

Boson stars

According to the Standard Model of physics, particles come in two varieties.

Team fermion represents the building blocks of matter; chunks of reality that don't easily overlap, allowing atoms to congeal and molecules to grow.

Then there's team boson. Its zoo of particles includes those that govern the behaviors of forces which allow fermions to hold together or push apart, giving rise to everything from nuclear decay to the spectrum of light to the entire field of chemistry.

Unlike fermions, bosons have no qualms about occupying the same space. Pile twenty in the one spot, there's always room for twenty more.

Theoretically, there could be a loophole for bosons to resist being so friendly. A hypothetical boson called an axion, for example, could find itself repulsive enough to resist overlapping even when clumping together under its own mass.

Throw enough axions together in a way that balances their positions and you could have a cloud of bosons that wouldn't block light or emit their own. Similar to black holes, we'd only be able to identify these dark boson stars by their gravitational influence on their surroundings.

If they existed, they could help explain dark matter, but that's a big 'if'.

Likelihood of them existing: Low (we still have no compelling evidence axions are a thing).

Darkino fuzzballs

So here we are, at the start of a new decade of the 21st century, and it feels like we're barely any closer to knowing what on Earth this weird phenomenon called dark matter really is.

Is it a slow moving particle? Does it interact with itself in some way? Is it concentrated like a black hole, or does it act like a shadowy fog?

If we make some rather generous assumptions on what it might be - say, a self-gravitating particle with a tiny mass that would make a puny electron look like the Incredible Hulk - we might imagine enough of the stuff just might sink towards a galactic core and form a giant ball.

Thanks to their tiny mass, this ball would be surrounded by a fuzzy halo of dark matter particles taking their time as they sink down. It would stop short of collapsing into a black hole while still collectively weighing as much as a few million Suns.

That's a lot of 'ifs'. Still, it could explain why objects orbiting close to the chaotic center of the Milky Way aren't moving quite as we'd imagine if they were circling a more compact mass.

The gravitational pull from a fuzzball of these so-called darkino fermions could pull just enough on the orbiting masses to account for their orbits.

Likelihood of them existing: Pretty low (we have to work out what dark matter is first).

Antistars

Creating a universe like ours involves an impressive two-for-the-price-of-one deal - for every particle of matter that pops out of the seething ocean of quantum foam, an oppositely charged particle of antimatter also appears.

You need to be quick, though. If those two opposing particles meet again, they'll wink out, leaving nothing but a puff of radiation.

Given all the matter surrounding us, a whole lot of cancelling out clearly didn't take place 13.8 billion years ago. Either a bunch of antimatter never appeared for some reason, or if it did, it was whisked away, locked up, or wiped out before it could cancel out a Universe of stuff.

It's one of those mysteries physicists are hard at work trying to solve.

The funny thing is, if a star made of this missing antimatter happened to be hanging up there in the night sky, it would look just like any other blazing ball of gas. The only hint to its nature would be signature flashes of gamma radiation as its atoms of anti-hydrogen were annihilated by occasional bits of matter that happened to smack into it from time to time.

Earlier this year astronomers published the results of a survey that looked for such tell-tale flashes. After whittling away anything that didn't have an easy explanation, they were left with 14 candidates of antistars.

That doesn't mean there are at least a dozen stars made of antimatter in the Milky Way - these candidates could still end up being known gamma-ray emitters like pulsars or black holes. But if antistars exist, this unique gamma-ray twinkling would be exactly their kind of song.

Likelihood of them existing: Extremely low (might make for a good Star Trek episode, though).