Chapter 120 Research Projects on Betelgeuse

Xu Chuan did not expect that the Morning Star Mathematics Prize would be awarded more than two months in advance because of him. At first, he thought it was some observatory’s application or some other good news, but he did not expect it to be this.

Although this is indeed good news from an honorary point of view, it would be the same to him if the Morning Star Mathematics Prize is awarded early to May or if it is awarded in July or August.

It's just that if other people knew about this idea, they would definitely say that he got an advantage and behaved well.

Being able to change the awarding time of the Chinese Fields Medal will be a blessing for a lifetime.

But to him, it really didn't seem to be a big deal.

For him, achievements and intellectual breakthroughs are far more important than gaining glory. Even if he does not win any awards after proving the Weyl-Berry conjecture, he will not mind too much.

It may be pretentious to say this, but that's what he really thinks in his heart.

Sooner or later, or not, he was there.

"You don't seem very excited. Why, do you think the Morning Star Mathematics Award is low?"

In the office, Zhang Zhengping looked at Xu Chuan's condition and asked with a smile.

"That's not true. Winning the Chinese Fields Medal is a worthwhile event for any mathematician. But I'm a little worried. It's suddenly awarded two months in advance. Won't people gossip? ?" Xu Chuan asked curiously.

"Don't worry about this. Just wait and receive the award. No one will gossip."

Chen Zhengping smiled and continued: "Oh, one more thing. The astronomical equipment and observatory you applied for before have been approved and will be used from March 10th to March 30th. Twenty days, during these twenty days you can use various professional equipment in the astronomy department at will."

"Of course, because yours is a scientific research project, you need to pay a certain usage fee, but these can be spent from the scientific research project you applied for."

"Don't worry about money. A total of 2.4 million yuan has been approved for scientific research projects in the name of the follow-up expansion of Xu-Weir Berry's theorem."

Speaking of this, Chen Zhengping sighed: "For a freshman to take charge of a scientific research project worth more than two million yuan, this is probably the first case in the whole of China, and even the whole world, let alone at NTU. "

"The most funded scientific research project I participated in when I was in college was only 80,000 yuan."

"Without the contributions of great scholars like you, teachers, how could we be as prosperous as we are today?" Xu Chuan said with a smile.

"Okay, stop being poor."

Chen Zhengping rolled his eyes at Xu Chuan and continued: "About the scientific research project, this must be your first time here. Tomorrow you go find your senior brother Fan Pengyue. He can help you with the process procedures and documents. Including things like the use of scientific research project funds and reimbursement, you can learn all about it.”

"After all, with your development, it is estimated that there will be no shortage of subsequent scientific research projects, so you still need to be familiar with the processes that you should be familiar with."

Xu Chuan nodded in agreement. Although controlling scientific research funds and projects was very familiar to him, he still didn't really know what the domestic routine was.

On the other side, Chen Zhengping thought for a while and then added: "Oh, by the way, regarding your scientific research project this time, if you need to use some complex and sophisticated astronomical equipment, I suggest you hire someone from the astronomy or astrophysics department. Doctoral student.”

"On the one hand, it is to avoid damaging the equipment, and on the other hand, they have more experience in operating these equipment and can more accurately observe the data you need."

"OK, all right."

Xu Chuan nodded. Even if Chen Zhengping didn't say anything about these things, he would consider them.

He has expertise in the field of science. Although astronomy and physics are also physics, they are not related to his research in his previous life. He really doesn't know how to use those professional astronomical equipment to obtain the data he needs.

After coming out of the instructor's office, the news that his application for the right to use astronomical equipment was approved made Xu Chuan happily look up at the sky.

Although the light pollution in the city is serious, the weather today is good. In addition, it is the time of night, the moon is rising, and the sparse stars are clear and bright on the black curtain.

And in the east, there is a group of bright stars shining.

That is the constellation Orion, which is easily identifiable in the night sky. It consists of seven stars, four of which form a huge quadrilateral, and the three stars in the middle of the quadrilateral are arranged diagonally in a straight line.

Among this group of stars, there is a distinctive star on the upper left shoulder. It emits orange-red light visible to the naked eye, which is completely different from the other stars that emit cool white light.

This star is called Betelgeuse, and it is also the object of his observation this time.

Betelgeuse can be seen year-round in the Northern Hemisphere.

However, winter is the best observation practice, especially in late December when it is easiest to find. It rises from the east at dusk and is located on the shoulder of Orion.

Viewed with the naked eye from Earth, it may be about the size of a fingernail.

But six hundred and forty light years away, it is a star much larger than the sun.

Physically speaking, Betelgeuse's current expansion radius is approximately 8 astronomical units (AU).

If you placed it at the center of the solar system, Betelgeuse would probably extend all the way beyond the orbit of Jupiter.

That is to say, if it is located at the center of the solar system, its surface will exceed the asteroid belt and reach and exceed the orbit of Jupiter, completely sweeping away Mercury, Venus, Earth and Mars, and some people even think it is enough to swallow up the asteroid belt and Jupiter.

The reason for this cognitive bias is that the distance is too far, which makes it impossible to estimate its accurate diameter.

In addition, Betelgeuse itself is also changing its shape periodically. Coupled with the theory of variable star pulsation with luminosity variation, the change of angular diameter with wavelength, and the fact that Betelgeuse has some complex and asymmetric envelopes, etc., its precise diameter cannot be determined.

Xu Chuan is very interested in this star with a huge mass but whose life has reached its old age.

There are many mysteries on it. If some of them can be solved, it will be a historical record.

Now that the astronomical observation equipment has been applied for, it means that it can be studied in another week.

Returning to the dormitory from the tutor's office, Xu Chuan temporarily put aside the research on the "proton radius mystery" and turned his attention to Betelgeuse.

Before this, he had collected a lot of information about Betelgeuse, from basic stellar parameters to photos, to the complex dynamics of Betelgeuse's extended atmosphere and plume gas jets, etc.

He had seen these things once, but he still felt magical.

For example, in 2009, an infrared interferometry study conducted by the Australian Infrared Research Institute showed that Betelgeuse had shrunk by 15% at an increasingly faster rate since 1993, but its apparent magnitude had not significantly dimmed.

In other words, its volume has shrunk by 15%, but its brightness has not changed, neither brighter nor darker.

It's like a 200-pound fat man lost 30 pounds and became 170 pounds, but still looks fat as before.

This is not scientific.

Although scientists later gave some explanations, such as this obvious contraction may be caused by shell activity in the star's extended atmosphere, or a large loss of stellar matter.

But these explanations have their own flaws.

For example, if the volume is reduced by shell activity in the star's extended atmosphere, then the brightness of Betelgeuse should be significantly improved, rather than almost unchanged.

Because if the shell activity in the atmosphere of Betelgeuse is reduced, then with the reduction, the density of the star will become larger and larger, and the materials such as hydrogen and helium in the shell will participate in the nuclear fusion reaction, and the brightness will be significantly improved, rather than almost unchanged.

This is like forging iron. When a piece of red-hot iron becomes smaller in volume under the impact of the forging hammer, the red color on the surface will gradually turn into a fiery white.

Although this description is a bit inappropriate, it is very vivid.

In addition, Betelgeuse is already a massive star in its old age and is about to explode in a supernova, so Xu Chuan is very interested in these changes.

It would be even more exciting if he could see it explode in a supernova in his lifetime.

In the dormitory, Xu Chuan sorted out the information in his hand and took out a stack of white paper.

The black signature pen in his hand hovered over the white manuscript paper, and after a pause, he began to write down the data equations one by one.

".δu/δt＝Δu,t＞０,x∈Ω；u＝０,t≥０,x∈Ω；

".Δ＝∑πj=１δ/δxj"

Δ is the Laplace operator, and δΩ is the boundary of Ω.

To find the standing wave solution of the problem, we use the separation of variables method, let u(t,x)＝ψ(t)·φ(x), substitute this into equation (1) and take into account the boundary conditions, then for λ＞0, we have:

Δφ/φ＝ψｔｔ/ψ＝－λ

It is not so simple to use the Xu-Weyl-Berry theorem to infer the shape and diameter of a star, nor is it enough to directly bring the observed data into the formula for calculation.

The first thing to do is to deform the Xu-Weyl-Berry theorem to a certain extent, so that it can be transformed from isospectral fluctuations to Sobolev space fluctuations, and then through Calculation is performed by presenting an amplitude function of periodic oscillation.

This is a very troublesome task, but fortunately, for a common target, such as an ordinary star or an ordinary black hole, only one deformation and wave conversion is needed.

It is an adaptive formula, which is applicable to stars within a certain range of parameters.

If someone else were to complete this work, it might take a month or two to get the hang of it, but for Xu Chuan, this is nothing more familiar.

He is the founder of the Xu-Weyl-Berry theorem. Except for the two conjecturers Weyl and Berry, no one is more familiar with the Weyl-Berry conjecture than him, and even the two founders may not be as familiar as he is.

Therefore, he can be said to be like a fish in water in the deformation and conversion of the Xu-Weyl-Berry theorem.