On the gorgeous cosmic stage, the galaxy is brilliant, full of all kinds of strange and mysterious celestial bodies. In addition to those dazzling stars, dreamlike nebulae, and planets and other stars that we can see with the naked eye, there are also some hidden material forms. We are not talking about condensate and dust particles that are difficult to detect with the naked eye, nor about the faint brown dwarfs, but about a well-known spectacle – black holes.

In previous articles, we talked about super-black holes with masses comparable to the entire universe, and at the heart of the quasar TON660, we discovered a giant – a black hole with a mass of up to 0 billion suns. So, are there also the tiniest black holes in this vast cosmic ocean? And how much does it weigh?

How do you measure the quality of black holes in galaxies?

Our exploration of black holes has crossed over from pure theory to practical observation. Not so long ago, we could only talk about black holes on paper, but now we have been able to capture the black hole at the center of the M65 galaxy. The mass of this black hole, up to the mass of 0 billion suns! So, in our own galaxy, what about it?

當我們將世界上最大的射電望遠鏡對準位於銀河系核心的“暗影”塵土飛揚的區域時，所見之景如上圖所示。在人馬座A*，這個狹小而特殊的空間裡，潛藏著一個光亮的射電源。看似平淡無奇，但仔細觀察會發現，周邊的恆星正以極高的速度圍繞此點進行旋轉，根據它們運行的軌跡，我們藉助萬有引力定律不難推算出，這個核心物體的質量達到了400萬個太陽的品質，並且它不發光。這不僅證明了我們銀河系中心存在一個超大品質的黑洞，也揭示了我們如何確定黑洞的品質。

曾經有朋友問起，是否每個星系中心都藏匿著黑洞？實際上，我們目前有充分的理由相信，大多數星系的核心都盤踞著超大品質的黑洞，其中許多的品質都遠超我們銀河系中心的龐然大物。上文中提到的660億倍太陽品質的黑洞，肯定不是宇宙的極限。

據估計，目前已知的最大星系IC 1101中的黑洞尚未得到確認，其品質可能在400億到1000億倍太陽質量之間！

Currently, supermassive black holes are thought to be formed by the fusion of the remains of millions of ancient massive stars.

So, how is an ordinary black hole formed?

When we gaze at a young star cluster, the largest, most massive, and brightest stars are always the most eye-catching. One might instinctively think that these stars, which are huge in size and mass, will live longer because of the abundance of fuel. However, intuition can often mislead us.

像O型和B型的大品質恆星，它們的品質是太陽的幾十倍甚至數百倍。但它們的燃料消耗速度極快，在數百萬年甚至數十萬年的時間內，它們的核心燃料就會耗盡。而我們的太陽，預計可以燃燒120億年左右，這其中的差距顯而易見！在大品質恆星生命的終點，它們往往會以II型超新星的形式爆炸，核心则会塌缩成中子星或黑洞。

Throughout the life of a star, gravity constantly compresses it, trying to destroy it. Nuclear fusion, which occurs in the core of a star, produces radiation pressure that fights gravity and maintains the star's stability. Once fusion in the core stops, gravity gains the upper hand, causing the core to collapse. At this point, the degenerate pressure between the atoms (i.e., the Pauli incompatibility principle) becomes the force that resists gravity.

For sun-like stars, even those that are four times as massive as the Sun, when nuclear fusion ends, their cores shrink to the size of Earth, forming a white dwarf. But they don't shrink any further, and at this point, it's the atoms that hold up the entire star.

However, the pressure of degeneracy between electrons is not unbreakable. A star with a mass more than four times the mass of the Sun, in a supernova explosion, collapses its core to the atomic level, and then "crushes" the atoms, pushing electrons into the nucleus and combining with protons to form a neutron-dominated celestial body, the neutron star.

Neutron stars are comparable in mass to the Sun, but only a few kilometers in diameter. As the mass of the core of the star varies, so does the quality of the neutron star that remains. If the mass of a neutron star exceeds three times that of the Sun, the neutrons are succumbed by gravity and compressed into a black hole with an infinitely small volume and infinite curvature in space.

So, what is the smallest known black hole?

IGR J10-0: This is a black hole in a binary system, and we were able to detect it because the system produced strong stellar winds. Instead of sucking in matter directly, black holes accrete material from companion stars and eject about 0% of the matter into the interstellar medium. It is a low-mass black hole with a mass of about 0 to 0 times that of the Sun.

GRO J2+0: This is also a binary star system, located just 0 light-years from Earth. Some teams believe that it is a neutron star with a mass of about 0.0 times that of the Sun, while others believe that it is nearly four times the mass of the Sun. The jury is still out.

XTE J8-0: Originally officially claimed to have a mass of 0.0 suns, it has since been reassessed to be nearly five times more massive than the sun. It is also a binary star system where the black hole steadily emits X-rays from the accretion disk. Typically, scientists determine the mass of a distant black hole based on the radiation emitted around the black hole in relation to the mass of the black hole.

Whether it's 2.0x, 0.0x, 0.0x, or 0.0x the mass of the sun, the mass is already very small for a black hole. You might think that this is the minimum mass that a black hole can have. But in reality, there are three more possibilities!

In summary, as far as black holes are concerned, there is no smallest but smaller.

Neutron Star - Neutron Star Merger!

兩個中子星的合併過程會創造出宇宙中大多數重元素，如黃金。在宇宙中，中子星的數量遠超黑洞。儘管兩顆中子星的碰撞相對罕見，在每個星系中大約每10000到10萬年發生一次，但考慮到宇宙已有138億年的歷史，擁有近1萬億個星系，中子星的合併在宇宙中是相當普遍的。

很可能，當兩顆中子星相撞時，即使它們的質量沒有超過形成黑洞的門檻，也有可能在超新星爆發后留下一個黑洞。據估計，在我們銀河系中已經發生了大約10萬到100萬次中子星合併。因此，我們有希望在銀河系內部找到一個約2倍太陽品質的黑洞。

In addition, black holes lose mass over time!

Since quantum fluctuations exist in a vacuum, particle-antiparticle fluctuations, whether inside, outside, or in the event horizon of a black hole, occur in a vacuum, and then disappear to keep energy conserved. If one virtual particle waves into a black hole, the other particle will take away the energy and escape as a real particle. Although this process is extremely slow, black holes are slowly evaporated by Hawking radiation.

We learned that this radiation does not come from a stream of particles or antiparticles ejected by a black hole, but from some extremely low-energy, almost constant black-body radiation flux.

On long time scales, such as 69 to the power of 0 or 0 to the power of 0 years, some of the lowest mass black holes will gradually lose mass and eventually evaporate completely.

So if you're looking for a black hole with a smaller mass, it's easy to make that wish come true, because some black holes are already in the process of disappearing. In the past, the existence of miniature black holes (quantum black holes) was envisaged. Next, let's explore it.

Could the universe have had miniature black holes when it was born?

The concept of miniature black holes dates back to the 68s of the 0th century, which was a creative idea, but it turned out that it could not happen. Here's the thing: the universe was originally a hot, dense, uniform, and rapidly expanding state. If the density of a very small region is 0% higher than the average density, then the region will naturally collapse into a black hole. If the universe had many such small regions in the beginning, we might end up with a universe full of miniature black holes.

But by measuring the density fluctuations of the early universe, i.e., the fluctuations of microwave radiation, and how the density fluctuations vary with scale, we find that the largest fluctuations are not 003% above the average, but only 0.0% above the average. As the scale of observation decreases, so the fluctuations become smaller, so it is impossible for a miniature black hole to exist.

That's it for the smallest black holes in the universe, from known black holes to undiscovered black holes, to those that we need to wait!